Monday, December 29, 2014

Causality, pantheism, and deism


Agere sequitur esse (“action follows being” or “activity follows existence”) is a basic principle of Scholastic metaphysics.  The idea is that the way a thing acts or behaves reflects what it is.  But suppose that a thing doesn’t truly act or behave at all.  Would it not follow, given the principle in question, that it does not truly exist?  That would be too quick.  After all, a thing might be capable of acting even if it is not in fact doing so.  (For example, you are capable of leaving this page and reading some other website instead, even if you do not in fact do so.)  That would seem enough to ensure existence.  A thing could hardly be said to have a capacity if it didn’t exist.  But suppose something lacks even the capacity for acting or behaving.  Would it not follow in that case that it does not truly exist?

To affirm that conclusion without qualification would be to endorse what Jaegwon Kim calls Alexander’s Dictum: To be real is to have causal powers.  (The dictum is named for Samuel Alexander, who gives expression to the idea in volume 2 of Space, Time, and Deity.  Kim has discussed it in many places, e.g. here.) 

Even if one thinks this too strong -- say, on the grounds that Platonic Forms might exist but be causally inert -- one might still endorse a more restricted version of Alexander’s Dictum.  One might hold, for example, that for material objects to be real, they must have causal powers.  Trenton Merricks endorses something like this restricted version of Alexander’s principle in arguing for an eliminativist position vis-à-vis inanimate macrophysical objects (Objects and Persons, p. 81).  He argues that for a macrophysical object such as a baseball or a stone to be real, it must have causal powers.  And yet (so he claims) it is only the microphysical parts of such purported objects -- their atoms, say (though “atoms” is for Merricks just a placeholder for whatever the appropriate micro-level objects turn out to be) -- that are really doing all the causal work.  Baseballs, stones, and the like do not as such really cause anything.  Hence baseballs, stones, and the like do not really exist.  It is only atoms arranged baseballwise, atoms arranged stonewise, etc. that exist.  (Merricks does not draw the same eliminativist conclusion about living things.  At least conscious living things do in his view have causal powers over and above those of their microphysical parts, and maybe other living things do too.)

I certainly don’t agree with Merricks’ eliminativist conclusion.  (See Scholastic Metaphysics, chapter 3, especially pp. 177-84.  As longtime readers might have already noticed, it is, from an Aristotelian point of view, telling that even Merricks thinks that at least the divide between the non-sentient and the sentient, and perhaps between the inorganic and the organic, mark breaks in nature where explanations exclusively in terms of microphysics give out.)  But in my view, the problem with his position is not his commitment to a variation on Alexander’s Dictum -- a variation I think is essentially correct.

The thesis that for a material object to be real, it must have causal powers is the key to understanding how occasionalism tends toward pantheism.  Occasionalism is the view that God is not merely the First Cause -- “first” in the sense of being the source of the causal power of other, secondary causes -- but the only cause.   Common sense supposes that it is the sun that melts a popsicle when you leave it on the table outside; in fact, according to occasionalism, it is God who melts popsicles, ice cubes, and the like, on the occasion when they are left in the sun.  You blame fungus for the dry rot that destroyed the wall in your garage; in fact, according to occasionalism, it is God who causes dry rot, on the occasion when fungus is present.  And so forth.  Neither the sun, nor fungus, nor anything other than God really has any causal power, on this view.  It is only God who is ever really doing anything.  Thus, the activity that we attribute to material objects must really be attributed to God. 

But if this is true, and if it is also true that for a material object to be real, it must have causal powers, then material objects aren’t even real.  Only God is real.  So, if occasionalism is true, then there is a sense in which, when you think you are observing the sun melting a popsicle, or a baseball shattering a window, or what have you, what you are really observing is just God in action, and nothing more than that.  Compare Merricks’ view that what we call a baseball shattering a window is “really” nothing more than just atoms arranged baseballwise causing the scattering of atoms that had been arranged windowwise.  Just as, on Merricks’ view, baseballs and windows dissolve into arrangements of atoms, so too on occasionalism the world essentially dissolves into God, which leaves us with a kind of pantheism.  You might say that, given occasionalism, “the sun,” “fungus,” “stone,” “baseballs,” etc. are really just nine billion names of God (with apologies to Arthur C. Clarke).

Just to be clear, Merricks does not even discuss occasionalism and pantheism, much less defend them.  But the parallel between his argument for eliminativism about inanimate macrophysical objects and occasionalism is instructive.  Consider now another aspect of Merricks’ position, and a parallel with another view about God’s relation to the world.  Merricks argues that if (say) a baseball played any causal role in the shattering of a window over and above the role played by its atoms, then the shattering would be “overdetermined,” insofar as the atoms alone are sufficient to bring about this effect.  But we should assume that no such overdetermination exists unless we have special reason to affirm it.  The baseball would be a fifth wheel, an unnecessary part of the causal story.  So we should eliminate it from the story.  Only the atoms are real.

Once again, I certainly don’t agree with Merricks’ eliminativist conclusion.  But the problem has to do with his assumption that the microphysical level is metaphysically privileged (an assumption I criticize in Scholastic Metaphysics).  We need not take issue with Merricks’ rejection of overdetermination.  (Note that the issue of “overdetermination” has nothing to do with causal determinism.  The idea is just that if a cause A suffices all by itself to explain an effect E, the assumption that there was some further cause B involved would make E overdetermined in the sense of having more causes than are necessary to account for it.  Whether the relationship between A and E is one of deterministic causation, specifically, is not at issue.)

Now, consider deism, which in its strongest version holds that God brought the world into existence but need not conserve it in being.  Any view which allows that the world could at least in principle exist apart from God’s continuous conserving action essentially makes of him something like the baseball in Merricks’ metaphysics.  In Merricks’ view, the atoms that make up the purported baseball are really doing all the causal work, and the baseball is a fifth wheel that would needlessly overdetermine the atoms’ effects.  Similarly, if the natural world is, metaphysically, such that it could in principle carry on apart from God’s sustaining causal activity, then God is a fifth wheel.  His sustaining the world in being would be an instance of overdetermination.  Hence, just as the baseball should in Merricks’ view be eliminated from the causal story, so too is God bound to drop out of the causal story given the view that the world might in principle carry on from moment to moment without him.  Just as occasionalism tends toward pantheism, deism tends toward atheism.  If God does everything, then everything is God; if God does nothing, then nothing is God. (Once again, Merricks himself doesn’t address any of these theological issues.  I’m just using his views for purposes of comparison.)

So, the theist is well advised to steer a middle course between occasionalism and deism, and that is of course exactly what concurrentism -- defended by Aquinas and other Scholastics -- aims to do.  According to concurrentism, natural objects have real, built-in causal power, but it cannot be exercised even for an instant unless God “concurs” with such exercise as a cooperating cause.  Some analogies: Given its sharpness, a scalpel has a power to cut that a blunt piece of wood does not; still, unless the surgeon cooperates in its activity by pushing it against the patient’s flesh, it will not in fact cut.  Given its red tint, a piece of glass has a power to cause the wall across from it to appear red; but unless light cooperates by shining through it, the glass will not in fact do so.  Similarly, created or secondary causes cannot exercise their powers unless God as First Cause cooperates.  Because these powers are “built into” natural objects (as the sharpness is built into the scalpel or the tint built into the glass) occasionalism is avoided.  Because the powers cannot operate without divine concurrence, deism is avoided.

Not all models of God’s relationship to the world adequately convey this middle ground concurrentist position.  For example, comparing God’s relationship to the world to the soul’s relationship to the body would have obviously pantheistic (or at least panentheistic) implications.  As I have argued many times, thinking of the world as a kind of machine and God as a machinist is also a very bad model.  Of course, the world is in some ways like a machine.  For example, machines can be very complex, and the world is very complex.  And God is in some ways comparable to a machinist.  For example, machinists are intelligent and God is intelligent.  But that does not suffice to make the machine/machinist analogy a good one, all things considered.  After all, God is also in some ways comparable to a soul, and the world is in some ways comparable to a body.  For example, like a soul, God is spirit rather than matter; like a body, the world is an integrated system.  But the soul/body analogy is still a very bad analogy for the relationship between God and the world (at least from a classical theist point of view), and the machine/machinist analogy is also a very bad one.

As I have argued elsewhere (for example, in my Nova et Vetera article “Between Aristotle and William Paley: Aquinas’s Fifth Way”), the machine/machinist analogy has both occasionalist and deist implications.  The deist implications are easy to see.  Machines chug along automatically, and can continue to do so even if the machinist dies.  Hence if the world is like a machine, it is not metaphysically necessary that there be a machinist.  Naturally, “design arguments” for the existence of the machinist are at best merely probabilistic inferences.  And naturally, one can, like Laplace, make the case that the machinist hypothesis is unnecessary.  Whether it is or not, though, such a machinist would not be the God of classical theism, since for the classical theist the world could not even in principle exist for an instant apart from God’s conserving activity.

To see the occasionalist implications requires introducing a further concept.  For many Scholastic theorists of causal powers, and for many non-Scholastics too, the notion of a causal power goes hand in hand with the notion of immanent finality.  That is to say, a causal power is inherently “directed toward” some particular outcome or range of outcomes as to a final cause.  To appeal to some of my stock examples, the phosphorus in the head of a match is inherently “directed toward” generating flame and heat, an acorn is inherently “directed toward” becoming an oak, and so on.  If this were not the case, the fact that efficient causes exhibit the regularity they do -- the fact that their effects are typically of a specific sort rather than random -- would not be intelligible.  In short, efficient causality presupposes final causality.   Hence if a material thing had no inherent finality or “directedness” toward an end, it would have no inherent or “built-in” causal power either.  (Once again, see Scholastic Metaphysics, especially pp. 92-105, for the full story.) 

Now the “mechanical world picture” of the early moderns was more than anything else a rejection of Aristotelian immanent or “built-in” finality or teleology.  There is, on this picture, no directedness or finality inherent in the material world.  Any final causality or teleology we might attribute to it is really only in the mind of some observer (whether human or divine), extrinsic to the material world itself.  Unsurprisingly, the early moderns also tended toward what Brian Ellis has called a “passivist” view of nature -- that is to say, a view of natural objects as passive or devoid of any intrinsic causal power.  On this view, natural objects behave in the way they do not because of any intrinsic tendencies but because God has simply stipulated that they will so behave, where his stipulations are enshrined in “laws of nature.”  The view of the world as a kind of artifact -- as, for example, a watch, with God as watchmaker -- is suggested by, and reinforces, this non-teleological and passivist conception of nature.  Just as the time-telling function of a watch is entirely extrinsic to the bits of metal that make up a watch, so too is all teleology or finality entirely extrinsic to the natural order.

This picture of things is implicitly occasionalist.  If the finality or directedness is really all in God and in no sense in the world, then (given the thesis that causal power presupposes immanent finality) causal power is really all in God and in no sense in the world.  And thus the view is also implicitly pantheist.  For if a material thing has no causal power, then (given the variation on Alexander’s Dictum we’ve been considering), it isn’t real.  In short: No immanent finality, no causal powers; no causal powers, no material objects; so, no immanent finality, no material objects.  To abandon an Aristotelian philosophy of nature is thus implicitly to abandon nature.  What we take to be nature is really just God in action.  (Homework exercise: Relate this absorption of the world into God to the tendency in modern theology to absorb nature into grace.) 

And so, unsurprisingly, while some of the moderns went in a deist or even atheist direction, others went in a radically anti-materialist and even pantheist direction.  Hence the occasionalism and near-pantheism of Malebranche, the outright pantheism of Spinoza, the idealism of Leibniz and Berkeley, and the absolute idealism of post-Kantian philosophy. 

Of course, the machine analogy is often used by people who have no deist, occasionalist, or pantheist intent -- for example, by Paley and other defenders of the “design argument,” and by contemporary “Intelligent Design” theorists.  And the analogy has an obvious popular appeal, since the “God as watchmaker” model is much easier for the man on the street to understand than the Scholastic’s appeal to act and potency, essentially ordered causal series, and so forth.  But metaphysically the analogy is superficial.  Indeed, it is a theological mess.  Its implications are not more widely seen because those who make use of it typically do not think them through, being satisfied if the analogy serves the apologetic needs of the moment.  (As I have pointed out many times, it is the metaphysical and theological problems inherent in this analogy, rather than anything to do with evolution per se, that underlie Thomistic misgivings about ID theory.)

To reason from the world to God is to reason from natural substances to their cause.  If the reasoning is to work, one had better have a sound metaphysics of causality and a sound metaphysics of substance.  The machine analogy, and other views which explicitly or implicitly deny inherent causal power to natural substances, reinforce a bad metaphysics of causality and of substance.

218 comments:

1 – 200 of 218   Newer›   Newest»
John West said...

On concurrentism, do ideas in God's mind exist, or do humans subsist?

Thursday said...

Politically, this is why both materialists and New Agers end up as liberals.

Thursday said...

Despite the fact that on the surface they are seemingly far, far apart.

Greg said...

He argues that for a macrophysical object such as a baseball or a stone to be real, it must have causal powers. And yet (so he claims) it is only the microphysical parts of such purported objects -- their atoms, say (though “atoms” is for Merricks just a placeholder for whatever the appropriate micro-level objects turn out to be) -- that are really doing all the causal work.

I wonder if one could object to this view on this basis: It should be an open question whether material objects are continuously divisible or whether, at some level, there are fundamental 'particles' (or something analogous). At any stage of scientific develop, to be sure, we won't know, and the constitutional regress (this mid-sized object is composed of these molecules, which are composed of these atoms, which are composed of theses subatomic particles, which...) is not vicious. But then: 1) If at every level, the entities are divisible (and therefore don't really exist since their constituents are what are actually causally efficacious), then it is not the case that anything is causally efficacious! But that's not true. 2) This of course could be resisted by positing a bottom level, but that appears to be too substantive a conclusion to be decided on this basis. The question could also be asked: Given that we have no idea how many 'levels' remain unobservable (perhaps physically unobservable to us), why should we expect it to be the case that only micro-level objects are causally efficacious, when according to that principle the objects that are causally efficacious are likely not observable to us at all?

Greg said...

why should we expect it to be the case that only micro-level objects are causally efficacious, when according to that principle the objects that are causally efficacious are likely not observable to us at all?

What I want to get across here is that, if it is true that what is causally efficacious is what is at the lowest level, then it is likely that we don't even know what is causally efficacious--but if that is the case, on what basis do we believe that what is causally efficacious is at the lowest level anyway?

Anonymous said...

Wouldn't it be correct to say, following Aristotle, that the first thing the intellect knows is being. So if the intellect knows something, any nature or substance outside the mind, it knows that that nature or substance exists. No qualifiers here, just the bald fact of existence. To have a nature, simple or composite, is to exist.
This is self-evident, the sine qua non upon which all knowledge must be built - I think Aquinas would agree.

Linus2nd

John West said...

Greg,

So basically, the argument is that it's equally likely there are fundamental particles as that particles are infinitely divisible. Based on the history of science, there is in principle no way for us to know there are fundamental particles using science. So, there is no way to know, from scientific inquiry, whether there is reason to treat non-atomos objects like homeless people and kick them out of our ontologies.

Scott said...

@Greg:

A possible reply to your possible objection: The constitutional infinite regress may not be vicious in and of itself. However, together with Alexander's principle, such a regress would imply that nothing was causally efficacious, and we know that's false. Therefore, the regress can't be infinite; there must be a bottom-most level, and it is not "an open question whether material objects are continuously divisible."

Scott said...

(In other words, according to this reply, what you've actually shown is that a constitutional infinite regress is inconsistent with Alexander's principle, and that anyone who accepts the second should reject the first.)

John West said...

Assuming I have your argument right (if I have it wrong, sorry for jumping the gun).

I think the Quinean would accept the second premise from scientific history, but argue that your second premise could also be used to dismiss all science. But since our current best scientific theories are our best source of knowledge about the physical world, we ought to accept as real the posits of our current best scientific theories.

So, I think the Quinean would accept the centerpiece of your argument, argue as above, and admit that if the science does change, she will just have to change her philosophical theories (but that despite this, science is our best source of knowledge about the physical world, so we ought to accept it anyway).

So then the question would be, “Does our current best scientific theory say there are fundamental particles, or not?”



(I think the above can be taken as is without much of the holist and canonical language baggage, so I leave those complications out of it)

Greg said...

@ John West

So basically, the argument is that it's equally likely there are fundamental particles as that particles are infinitely divisible.

The qualification I would make is: I wouldn't say it is equally likely. I don't think we could even attempt to ascribe a probability. But: There either are or there are not, and both results are consistent with science.

Granting that only those material things that are causally efficacious are real, it should not be the case that we can rule out that matter is continuously divisible (given its consistency with science in principle and the fact that the composition regress is not vicious) on the basis of causal reductionism. This is especially true given that, if whatever is causally efficacious is presently unobservable to us (which is certainly epistemically possible), then we don't even observe genuine causation in the natural world. So whence the judgment that causation in fact occurs at the micro-level rather than the macro-level? The argument undermines itself.

Scott said...

"[I]f it is true that what is causally efficacious is what is at the lowest level, then it is likely that we don't even know what is causally efficacious."

My hypothetical respondent would say that we don't have to. We just have to know that something is causally efficacious, and you've already acknowledged that we know that much.

Greg said...

@ Scott

Yes, I was sort of thinking of that but you have stated it more clearly.

I don't think the argument is quite decisive for that reason. However, two points:

1) The A-T position, on which causality can occur on a given level in spite of divisibility, might be consistent both with the infinite constitutional regress and with the existence of a bottom level; perhaps one could argue that it should be preferred for that reason. (Perhaps a bottom level is inconsistent with the doctrine of materia prima? I am not sure; on the face of it it seems like it might be but there may be other nuances and I know it is a difficult topic.)

2) I give a slightly different argument in my last response to John West. The constitutional regress need not be infinite; if the bottom level is not presently observable, then it would follow that we don't genuinely observe causation. But in that case how do we know that (despite appearances) causation really appears at the micro-level? It would be by analogy with the reduction of higher-level causation to atomic-level causation, but the argument implies the possibility that there isn't really causation at the atomic level.

John West said...

Consider the discovery of Germanium. In 1871 there had be no known causal contact (therefore observation) with this element, and causal contact didn't come until Wincker isolated the metal in 1887. However, because of the “gap” in Mendeleeff's periodic table corresponding to the position of germanium, much was known of its chemical behaviour.

Greg said...

Hmm I'm not satisfied. I'll continue thinking about it. (I have thought about a similar argument for a while but Merricks' principle seems to yield a good way to format it.)

Scott said...

@Greg:

"So whence the judgment that causation in fact occurs at the micro-level rather than the macro-level? The argument undermines itself."

Well, speaking on my own behalf and not just that of a hypothetical respondent, I'd say you're pointing out that this judgment requires independent justification, not that an argument that relies on it is self-undermining. But the question itself is a very good one: what is the basis of that judgment?

Greg said...

This is especially true given that, if whatever is causally efficacious is presently unobservable to us (which is certainly epistemically possible), then we don't even observe genuine causation in the natural world. So whence the judgment that causation in fact occurs at the micro-level rather than the macro-level? The argument undermines itself.

Someone could object that what Merricks' argument really would imply is that, if the bottom level is sub-observation, then nature's genuine causes are not observable. From that, the objection would go, it doesn't follow that we don't observe causation in nature, for we observe the effects but not the causes (as is typical).

However, to give preference to the micro-level, there still has to be some sense in which we can regard the micro-level as more of a genuine cause than the macro-level (even though neither of them contain genuine causes). And we expect that to continue to at the sub-atomic, sub-sub-atomic, etc. levels. I find that odd.

Scott said...

@Greg:

"Perhaps a bottom level is inconsistent with the doctrine of materia prima? I am not sure[.]"

Nor am I, but I don't think there's any inconsistency there. I would say (provisionally) that we could never be epistemologically certain that we had actually reached a bottommost level because of course all we ever see is form: we're never going to reach a level at which we say, "Aha! Prime matter at last!" and so there will always be an epistemological possibility that there are further levels of form that we haven't yet discovered. But our not being able to know we've reached a bottommost level doesn't seem to be inconsistent with there being one.

Greg said...

@ Scott

Right. And, even supposing that there is materia prima, it might still be nomologically impossible to get 'past' a certain 'bottom' level (i.e. the entities are not simple, but they are composed of entities that are constituted such that, to speak crudely, as soon as they were to 'come apart' they would latch back together).

John West said...

Scott,

But couldn't the same line of reasoning be used about our experience of change?

John West said...

(I mean, I can always concoct an elaborate four-dimensionalism to account for the appearance)

Jeremy Taylor said...

Greg,

Couldn't you also use the traditional distinction between what is indefinite and what is infinite? Material things may be divisible indefinitely, as regards our knowledge of them (most especially illustrated in the fact the distance between two points can be divided again and again indefinitely), but not infinitely because what is material is determined (it occupies one particular location and time and not another, it has one set of qualities and not another, and so on) and to be determined is to be limited (and therefore not infinite or without limits).

Greg said...

@ Jeremy

I think you could say that 'indefinite' is what I am looking for. But what I mean by 'infinite' here is just that the series of reductions of levels (sub-atomic, sub-sub-atomic, sub-sub-sub-atomic, ...) might be infinite; the entities of any given level are composite.

There might be some difficulties here with a somewhat naive view of what constitutes a 'level'. Also I am being imprecise, since what is on a level with composite entities would not in fact be entities if Merricks is right, because if they're composite then their causation can be reduced to that of their constituents, so they are 'real' and aren't entities at all. But insofar as these are difficulties for my argument, they are difficulties for the formulation of Merricks' position.

Greg said...

so they are 'real' and aren't entities at all. But insofar as these are difficulties for my argument, they are difficulties for the formulation of Merricks' position.

Oops: so they aren't 'real'.

Also, I say they are difficulties, but I haven't read Merricks and I assume he has something to say about how one can talk about the higher-level objects to which we naively refer, even if they are not real because causally inefficacious.

John West said...

Precis of Merricks's Objects and Persons.

Jeremy Taylor said...

Greg,

But, surely, corporeal reality cannot be divided infinitely because (to speak clumsily) only what is infinite can be so divided? And corporeal things are, and cannot be, infinite. This means there must be some bottom level to corporeal reality, even if (as I believe is correct) it is beyond human discovery.

Daniel said...

@Linus2nd,

Wouldn't it be correct to say, following Aristotle, that the first thing the intellect knows is being.

I think we should be careful how this is read - one may equally take the phrase 'being' in question to refer not to 'existence' but to identity, to a being, that the intellect is always 'about an X', a statement which is the principle of Intentionality and perfectly true.

Scott said...

@John West:

"But couldn't the same line of reasoning be used about our experience of change?

(I mean, I can always concoct an elaborate four-dimensionalism to account for the appearance)"

I'm not sure which line of reasoning you're referring to here, but I don't think four-dimensionalism can account for change or our experience of it.

Mind you, I don't see any problem in principle with a four-dimensionalist description of "change" as long as we remember that it's not the whole story. Taking to be the whole story rather than a mathematical/structural description leaves out the very thing it was supposed to be describing, namely (our experience of) change itself.

John West said...

Scott,

I was referring to your comment at 9:11 PM on the 29th, which your reply answers nicely.

L said...

Are the likes of William Lane Craig commited to this modern version of the world that makes it independent of God?

This could be a good oportunity for an apology for thomism in face of theist personalists.

I think they would say that the argument from contingency would be good enough to avoid this critique.

John West said...

Greg,

Also, I say they are difficulties, but I haven't read Merricks and I assume he has something to say about how one can talk about the higher-level objects to which we naively refer, even if they are not real because causally inefficacious.

To steal an example from Michael Burke, can one simply see a baseball anymore than one can simply see, during a baseball game, that there is a conjunctive object consisting of a baseball, a bat, a batter, and a pitcher?

Relevantly, Burke also writes that, “Unlike Peter van Inwagen (Material Beings), with whose ontology Merricks's has much in common, Merricks does not temper his eliminativist ontology with folk-friendly semantics [...] he does not seek to construe ordinary talk of baseballs in such a way that (much of) it comes out true.”

Irish Thomist said...

An interesting way of looking at it I must say. I still think Concurrentism needs updating with slight modifications - and it helps shed new light on Why there is Evil or POE to do so. It won't be something I get to write on for a long time. I would put the emphasis differently I suppose...

Greg said...

@ Jeremy

But, surely, corporeal reality cannot be divided infinitely because (to speak clumsily) only what is infinite can be so divided? And corporeal things are, and cannot be, infinite. This means there must be some bottom level to corporeal reality, even if (as I believe is correct) it is beyond human discovery.

But in what sense would a corporeal object have to be "infinite" in order to be divided infinitely? It would not have to be infinite in extension, nor would it need to have any actually infinite power. (I suppose you could say that it could potentially be divided into infinitely many constituents, but you could never do that.)

Greg said...

@ John West

Well then--I guess Merricks is not aiming at that.

Though, in response to Burke's first question, I think the answer is yes, we do 'simply see' a baseball 'more than' we 'simply see' that conjunctive object (though I can't tell if 'simply' has some technical sense here, and 'more than' seems inappropriate).

I assume that Burke wants to say that in referring to conjunctive objects we could refer to the naive macro-objects just as well. But that doesn't seem to be the case, at least where 'seeing' is concerned. Suppose that the baseball just is the collection of fundamental particles arranged baseball-wise (where that is, I suppose, cashed out in some way that eliminates the need for the baseball). Then "I see the baseball" and "I see the collection of fundamental particles arranged baseball-wise" are not even necessarily both true, since "I see..." is an intensional context.

Jeremy Taylor said...

Greg,

But to divide something, there must be fresh constituent entities that you end up with. But if corporeal reality is not infinite, there must be a limit to these fresh entities that can be discovered by dividing it. Only what is infinite, surely, can be divided infinitely to discover new levels or entities.

Kiel said...

I wonder if an atheist has ever formulated a worthless problem of evil objection on concurrentism, namely, that an all loving God at every moment is the source of the causal power that enables things to cause and experience suffering and pain.

Irish Thomist said...

@Kiel

That is very likely. I would not say it is a worthless question to be honest.

Greg said...

@ Jeremy

But to divide something, there must be fresh constituent entities that you end up with. But if corporeal reality is not infinite, there must be a limit to these fresh entities that can be discovered by dividing it. Only what is infinite, surely, can be divided infinitely to discover new levels or entities.

Well, the interval [0,1] is 'infinitely divisible' in the sense I am talking about. I can divide it at any point between 0 and 1 and obtain two intervals. Then I could divide those into two intervals by choosing a point between their endpoints. There is no limit to the number of times I may divide the remaining intervals. But [0,1] is not 'infinite'. (It contains uncountably many points, I suppose, but in the analogy we are developing, we could stipulate that only the intervals are correlates of matter, rather than the points, which are just 'markers' of length/extension/measurement or something. So then a bit of matter might be infinitely divisible without there being any actual infinity.)

TheOFloinn said...

The interval [0,1] is infinite but bounded.

grodrigues said...

@Greg:

Putting I_n = [1/2^n, 1/2^(n + 1)] you get a division of the unit interval in a countably infinite collection of closed, non-degenerate intervals overlapping only at the end points. Does this count as the "Only what is infinite, surely, can be divided infinitely to discover new levels or entities" that Jeremy asked?

grodrigues said...

I should probably note that in the previous post I am not claiming that the union of all I_n is the unit interval -- it is easily seen that 1 is not in the union (and it is the only element of the unit interval that is not).

note(s):
- one *can* partition the unit interval in a countably infinite family of pairwise disjoint non-degenerate intervals, but they cannot be all closed (or all open).

Jeremy Taylor said...

Greg,

Hm. I'm not a mathematician and my knowledge of maths is somewhat lacking, but isn't the interval you refer analogous to dividing the distance of point again and again and so on? In this case, would it not be best to say it is indefinite and not infinite? Is there truly no limit?

How can there be no limit, in fact, as we are still talking about determinate entities, which are by definition limited?

I would argue that there is, in fact, only one thing (to speak clumsily) that is infinite, God. If something has separate existence, if it is determined and conditioned, then it has bounds or limits and cannot be infinite.

Jeremy Taylor said...

- that should be dividing the distance between two points.

By the way, I once came across a proof of God on this very score, or at least a proof of infinite reality (as usual, more work has to be done to show this reality has the divine attributes). Existence, or possibility if you will, must be limitless, because what could limit it could only be something that exists, some possibility or other, and this would be part of existence. Nothingness cannot limit existence, because it is pure negation, or impossibility.

John West said...

Could it be that (as Greg suggested possible earlier) there's a failure of analogy between the unit interval and the separation of entities or levels?

John West said...

physical entities^

Daniel said...

@Jeremy,

Out of interest you remember the source for that proof? It sounds rather like Hegel's adaption of the Ontological Argument to the effect that the Infinite cannot suffer limitation or it would not be the true Infinite. I think Nicholas of Cusa had a similar, more Pythagorean argument along the same lines too.

For one thing conflating Nothingness and Impossibility would seem to risk a Category Mistake. For another things can 'not exist' contingently and of necessity - the impossible 'accrues' for want of a better word to aspects of the possible (the predicate 'squareness' excluding 'circularity'); on a fair reading the argument might be trying to capture this with the clause about the only thing that only something possible could act as a limitation. What does it mean to say a Possibility exists though? That truths of Essence e.g. 'squareness' excluding 'circularity' hold? We cannot treat Possibility and Actuality as the same; we need some principle to move from one to the other even, I suspect, if we claim as Spinoza did that all that is Possible is Actual.

On second thoughts it now looks like a variation on Parmenides’ famous dictum from On Being

Jeremy Taylor said...


I think it was a work of Lord Northbourne's. He no doubt got it from elsewhere, though not, I would guess, from Hegel. The argument no doubt is of Platonic (in the broad sense) origins.

He does not use the term possibility in the sense of Aristotelian potency. Rather, he refers to the infinite itself as all-possibility, equating all that is possible and all that exists in some sense or other. I think this is particularly open to question. For something to be possible it must in some sense have existence (taking existence to mean all reality and not, as is sometimes the case, just creation). By impossibility he refers to what in no sense has possibility of being - like a married bachelor. In this sense, I certainly do not think it is correct to say it is a category mistake to equate impossibility and nothingness. Anyway, though, this terminology is not, it seems to me, important for the argument itself. One could make a similar argument without talking of possibility and wasn't central to the point (and I brought up the argument itself only an interesting aside).

Jeremy Taylor said...

- that should have been this is not particularly open to question.

Daniel said...

He no doubt got it from elsewhere, though not, I would guess, from Hegel. The argument no doubt is of Platonic (in the broad sense) origins.

It sounds a bit like Proclus' definition of the One as the union of the Infinite and the Determining Limit. If he got it from a Platonic source it’s more than likely to be the source of Hegel's argument too (since he drew a lot from Christian and Pre-Christian Neoplatonism).

He does not use the term possibility in the sense of Aristotelian potency.

Neither did I. I was careful to use the term Possibility as the correlate of Actuality here not Potentiality.

equating all that is possible and all that exists in some sense or other. I think this is not particularly open to question. For something to be possible it must in some sense have existence

Forgive me for saying so but I fail to see the sense of this. Possibility is a Necessary condition for existence but save in the case of necessary beings it is not a Sufficient condition.

One could make a similar argument without talking of possibility and wasn't central to the point

I would be interested to see someone attempt to take it further but I think if they were to do so it would still require some further clarification of modality. Of course one would have to cash it out with far more terminological clarity.

Chris said...

Daniel,

Jeremy was, I think, referring to this essay by lord Northbourne- "With God All Things Are Possible"

Jeremy Taylor said...

Daniel,


Forgive me for saying so but I fail to see the sense of this. Possibility is a Necessary condition for existence but save in the case of necessary beings it is not a Sufficient condition.

To argue this, wouldn't you have to be saying that something could be possible and yet not exist at all, in any sense?


I would be interested to see someone attempt to take it further but I think if they were to do so it would still require some further clarification of modality. Of course one would have to cash it out with far more terminological clarity.

As I said, I don't see why the use of the framework Northbourne uses is absolutely necessary. One could simply say that what exists can only be limited by what exists, and therefore existence must be infinite.

Jeremy Taylor said...

- that is to say, what exists must be illimitable.

Scott said...

@Chris:

Thank you. And here it is.

Jeremy Taylor said...

Chris,

I own the Essential Lord Nortbourne, and digging it out I find that is indeed the essay. According to the footnote, Northbourne appears to have derived his argument from Guenon. Northbourne, though he made some insightful presentation of religious and philosophical ideas (his essay on the Beauty of Flowers is particularly moving), was not reaslly a philosopher or metaphysician. Where Guenon derived it from I don't know. It is likely to have roots in Platonic or Vedantin thoughts, or some offshoot. Whether it was expressly formulated by any of these schools or only by Guenon, I don't know.

Jeremy Taylor said...

I see Scott found a link before I did. Interestingly, that site appears to have Northbourne's essay on Flowers (called on the Beauty of Flowers in my anthology). I won't post it because it is very much offtopic. But I found it quite moving.

Anonymous said...

J. Taylor,

"Existence, or possibility if you will, must be limitless, because what could limit it [...]."

First, existence is not possibility. Second, why do you keep bringing in Perrenialist nonsense? like the absurd idea that '(All-)Possiblity' is the principle of things/creation. This the problem with these mystic mongering perreniliasts - they haven't had a proper philosophical training, even in the Platonic tradition some people claim they espouse.

Here's my advice to you for ridding yourself of this particular false belief: go read the Metaphysics, Book Theta, where Aristotle demonstrates the priority of actuality in every significant respect to potency and hence possibility. and read it carefully too, lest you're tempted to nonsensically retort something along the lines of "well All-Possiblity paradoxically is pure actuality", etc, etc.

Daniel said...

I'm just going to assume this is trolling and that nothing can gained from replying to it. As for the statement that All Possibility a certain famous dictum about God's Essence and Existence comes to mind...

For more subtle accounts of Actuality and Possibility and how they stand to Potency I recommend a dose of Scotus.

@Jeremy,

To argue this, wouldn't you have to be saying that something could be possible and yet not exist at all, in any sense?

Yes, I would make that claim in as much as, say, there being no instances of the concrete Substance 'Dodo' is equivalent to saying Dodos do not exist at all. This does not mean though that metaphysical 'entities', though this word is of course used in a somewhat lose analogues sense, pertaining to the identity 'Dodo' like Divine Exemplars or Platonic Forms do not in some sense have being.

Glenn said...

Well, no, the Anonymous above is not trolling. Not at all.

Jeremy Taylor said...

I don't know if Glenn is joking or not, or whether anonymous's comment counts as actual trolling. But it is certainly a pretty pointless comment. It manages to equivocate over possibility, which is clearly being used differently from Aristotelian potency here (and I said as much), and to not make an actual argument, all the while castigating the philosophical acumen of others (one wonders what philosophical training means here, and whether Aristotle could have had it).

But I just mentioned this particular argument as an aside, and was much more interested in the discussion with Greg.

Daniel,

Northbourne is not saying that what is possible exists in the sense of created existence. He is not saying that because a dodo is a possibility it must have existence, at this time, as an actual corporeal being. I think that a Dodo does exist precisely as some sort of Divive Exemplar. That is existence (depending on how one uses the term).

Jeremy Taylor said...

And, indeed, a Dodo would surely exist as more than just a Divine Exemplar. It exists within our minds as well, so far as we are thinking about and discussing it at least.

Glenn said...

Jeremy,

No, I wasn't joking. But in asserting that Anonymous isn't trolling, I certainly didn't mean to imply that I'm in agreement with those characterizations which may be taken as being of a disparaging nature.

o [O]ur choice is always concerned with our actions. Now whatever is done by us, is possible to us. Therefore we must needs say that choice is only of possible things.

o [A]n end cannot be possible, unless the means be possible. Now no one is moved to the impossible. Consequently no one would tend to the end, save for the fact that the means appear to be possible.

o [C]hoice is an act of the will, fixed on something to be done by the chooser. And therefore it is by no means of anything but what is possible.

Anonymous is more comfortable with the Actuality underlying whatever may be seen as 'possible'. This is not to his discredit.

Anyway, I know from past discussions that the Anonymous above is neither troll nor troller. (Far from it.) I meant only to insert a comment to that effect, and not at all to intrude upon or disrupt your discussion with Daniel.

John West said...

Jeremy Taylor,

Well, I'm no enemy of "perennial" philosophy:

[T]o divide something, there must be fresh constituent entities that you end up with. But if corporeal reality is not infinite, there must be a limit to these fresh entities that can be discovered by dividing it. Only what is infinite, surely, can be divided infinitely to discover new levels or entities.

But in the case of your second sentence here, it seems to me that, whether finite, corporeal entities are infinitely divisible is the very matter being argued about. Could you expand on this proposition for me? Thank you.

Greg said...

@ TheOFloinn and grodrigues

You both identify a sense in which [0,1] is infinite.

I suppose this is my response: I am attempting to draw an analogy between the interval and some composite object.

So suppose that there is some such composite object. On a Thomist view, its proper parts exist virtually, so there is just one object. I could divide it and get two objects. I could divide each of those and get four objects. (I could also chop up the intervals as did grodrigues.) But it seems to me that, at least given Thomism, where the whole is ontologically prior to the constituents, I might be able to continue dividing ad infinitum. At any given point, I have finitely many objects (which can then be further subdivided). At no point will I have made the countably many divisions requisite for the collection of intervals given by grodrigues. (So my claim that there's a sense in which [0,1] is not infinite apparently depends on stipulating a rule as to how it can be divided that is related to the case of a composite object.)

On Merricks's view, the parts do not exist merely virtually. The 'object' itself in fact does not exist and is reduced to whatever constituents are capable of standing in causal relations. That view would seem to entail that the object is not infinitely divisible in the sense I've specified, since regardless of how I partition the interval (suppose I am just refining it by adding one point at a time), each of the remaining intervals can be further subdivided, from which it will follow that none of the 'remaining intervals' (i.e. the proper parts of the original object) stands in causal relations (because their constituents do). But if that is the case for any partition, then there would be no constituents capable of standing in causal relations, so there would be nothing there at all. So there would have to be some bottom level. (That would be another sense in which Alexander's Dictum, reductionism, and infinite divisibility are inconsistent.)

Though at this point I am worried that I am glossing over significant metaphysical questions, and I am not confident that the mathematical analogy holds.

Jeremy Taylor said...

Glenn,

Well, I think that Lord Northbourne, if he derived the terminology from Guenon, does not have in mind so much action as abstract metaphysics. I don't recall Guenon making this argument for God's existence and infinity (though he may have), but he certainly uses the terminology of all-possibility and uses it as a principle of the most abstract metaphysics.

I have just reread Dr. Feser's book on philosophy of mind and Guenon means by possibility something to similar to what Dr. Feser meant when he refers to metaphysical possibility in that work - everything that is not logically contradictory. However, Guenon, one. takes all possibilities to have reality, to exist, in order that can be thought of and in any sense be possible. Two, he differentiates firmly between the circumstances in which possibilities are real, or exist. He in no sense argues that possibilities must all exist as corporeal entities. Father Christmas is a possibility and therefore real, but this does not mean he exists as a corporeal being. In fact, Guenon claims that some (a limitless amount, in fact) possibilities are of the essence that they cannot exist corporeally and can only exist within the Divine Essence.

Really, all he is saying is that God encompasses all that is or ever could be, conversant to the mode and circumstances in which it exists. What is impossible, in this schema, is nothingness, that which can in no sense have reality. What is logically contradictory, like a married bachelor, is included as an impossibility.

The argument for God, would be along the lines that, then, what is possible must be illimitable, or infintie, because all that could limit a possibility would be another possibility (impossibility here being equated to nothingness) and woul itself be contained within all-possibility. Personally, I think you could well make the argument by simply refering to the real or what exists, without bringing up the terminology of possibility.

Anonymous said...

IMV, the distinction between being and acting does not exist at the microphysical level. God's sustaining a quark, a photon, or any boson or fermion in being is at the same time and inseparably God's concurring with that particle's acting.

Of course, in quantum mechanics a particle's behavior is probabilistic, so we could take the issue to level of the realized outcome, with 3 possibilities:

Full steering: God chooses all and every quantum outcome, in such a way that they seem probabilistic and random.

Deism: God just sustains the particles into being and acting (which as I said are not really distinct) and does not intervene in the selection of outcomes.

Strategic steering: middle way. God chooses those outcomes that are important for his design.

Jeremy Taylor said...

John West,

Well, I'm not a Perennialist per se, though I hold a not dissimilar universalist, yet traditionalist, views on religion. I'm more influenced by Henry Corbin and the Temenos Academy and Rene Schwaller De Lubicz amongst twentieth century figures. I just find some of the Perennialists interesting contemporary thinkers in the Platonic tradition. Contrary to what anonymous claimed, however, though obviously not trained or even interested in modern analytical philosophy, Guenon, Coomarswamy, Schuon, and Nasr (and perhaps Evola, if he counts as a Perennialist), at least, are clearly very knowledgeable, to one degree or another, about Platonic, Aristotelian, and many others kinds of thought and philosophy, including even modern philosophy from the Seventeenth to the the Nineteenth century.

Anyway, I suppose my point was analogous to the argument about God's infinity. It is the reverse, in a sense: there is only one infinite, that which is entirely without limits in any respect. Anything that is finite is surely limited; being one distinct or determined thing and not another, this is by definition a limit. It cannot be infinite in one respect and not in another, allthough we may not be able to discover its limits within corporeal reality.

John West said...

Jeremy Taylor,

You recommended Lubicz. I look forward to reading Lubicz. He is on my list.

Anyway, I suppose my point was analogous to the argument about God's infinity. It is the reverse, in a sense: there is only one infinite, that which is entirely without limits in any respect. Anything that is finite is surely limited; being one distinct or determined thing and not another, this is by definition a limit. It cannot be infinite in one respect and not in another, although we may not be able to discover its limits within corporeal reality.

I guess I'm going to have to read Northborne's essay again with fresh eyes.

You write, "There is only one infinite, that which is without limits in any respect." So defined, clearly a finite thing cannot be infinitely divisible only (I'll call this endlessly divisible to avoid equivocating on infinite). This fact follows effortlessly from your definition of infinite.

But, Greg's argument can readily concede some-quantity-of-physical-matter has many limits. In fact, for the sake of argument, the physical matter can be limited in every possible way but its divisibility. On your definition of infinite, it would then still be finite but fulfill the criteria Greg needs. What is the argument against making this move?

Also, you write that only God is infinite. Since your argument discusses division of composites into constituent entities and God is absolutely simple, could God also be endlessly divisible in the manner being discussed, or given my previous paragraph is nonsense is "endless divisibility" just impossible?

Jeremy Taylor said...

John West,

Are you asking why an entity might not be infinite in one (or more) of its attributes and fininte in others? This is not possible because the infinite and finite are incommensurable, there is no common measure between them. It would be analogous to positing a triangle with two finite sides and an infinite side.

I'm not sure it would make sense to talk about God as divisible in this way. The process of divisibility implies finite material.

I do think one complication that someone advancing the argument for God I brought up would have to deal with is, in fact, how to explain potency in the Aristotelian sense, or contingency. Presumably, for example, it is metaphysically possible for corporeal Dodos to exist now. What limits this possibility? Perhaps this is what Daniel was getting at?

Daniel said...

Many thanks to Chris, Scott and Jeremy for the background info and links, I’ll print out the essay and have a look over it at the weekend. Whatever way one might interpret it the argument certainly strikes as interesting – rather like some of the modal arguments Spinoza and Leibniz came up with.

@Jeremy,

Well Potency generally assumes that there is some prior material being that can take on the substantial form in question - this is one of the reasons Scotus thought it better to talk of Possibility primarily in terms of the ways God could create ex nihilo if He so chose (for instance one might have a universe in which there were only a very few existing substances, none of which had the potential to take on a whole array of more complex substantial forms yet those non-existent substances would still be possible). So I was talking about Broadly Logical/Metaphysical Possibility.

I think that a Dodo does exist precisely as some sort of Divive Exemplar. That is existence (depending on how one uses the term).

I think if one calls the possible real we must add an additional term to refer to what is normal meant by real i.e. actual. I would agree about Divine Exemplars (though one cannot assume them if one is aiming to prove the existence of the Absolute with this argument).

When I say about existence what I mean is this: a dodo is a concrete substance and the universal Dodo is not so, ergo in order for the proposition 'Dodos exist' to hold there must be one instance of that concrete substance. Alternatively put: all dodos share 'dodoness' but 'dodoness' itself is not a dodo (one of the reasons Third Man type objections don't work).

It exists within our minds as well, so far as we are thinking about and discussing it at least.

I know it sounds as if I'm being purposely contrary but this is dangerous territory too. To think about an object is to be about an object even if there exists no such object to tally with it not to have a surrogate immanent object in the mind. The worst mistake of modern philosophy was to confuse our concepts, 'concept' being a way of talking about our 'being about' rather than a real component object, with the essences/identities of which they are about.

Glenn said,

Anonymous is more comfortable with the Actuality underlying whatever may be seen as 'possible'. This is not to his discredit.

I would imagine many of the posters here have a similar view though still manage to maintain a level of civil discourse. Also it is not clear from the wording that this is not precisely what Jeremy’s argument does claims i.e. that of its very nature there is an Actual ground of all Possibility.

Daniel said...

On an aside if the argument under discussion is from Guénon then it most likely comes either from Multiple States of Being or The Symbolism of the Cross*, his most significant treatise on 'pure' metaphysics.

*I have a spare copy of The Symbolism of the Cross - free to anyone in the UK (or nearby as long as the p&p is reasonable).

John West said...

Jeremy Taylor,

Are you asking why an entity might not be infinite in one (or more) of its attributes and fininte in others? This is not possible because the infinite and finite are incommensurable, there is no common measure between them. It would be analogous to positing a triangle with two finite sides and an infinite side.

I was. Thank you. As counterexample, consider a line on the Cartesian plane. Its length is infinite both ways, but its width visibly limited.

Anon at 5:51 PM said...

I've just realized that the distinction between being and acting does not exist at the level of living beings either. God's sustaining Fido in being as a living dog is at the same time and inseparably God's concurring with Fido's vital processes.

It does not matter the particular way in which the aggregation of those vital processes appears to an outside observer. Fido's sleeping, walking, or eating at a certin point in time are just particular ways of carrying on his living.

And regarding God's intervention in the instantiation of those particular ways of living, it seems that there are the same three possibilities as in the case of subatomic particles: full steering, deism, and strategic steering.

I personally am seriously in need of God's intervention to steer my neural processes into sleep some nights.

Glenn said...

Daniel,

> Glenn said,

>> Anonymous is more comfortable with the Actuality underlying whatever may be seen as 'possible'. This is not to his discredit.

> I would imagine many of the posters here have a similar view though still manage to maintain a level of civil discourse. Also it is not clear from the wording that this is not precisely what Jeremy’s argument does claims i.e. that of its very nature there is an Actual ground of all Possibility.

Sure. But pardon my asking, what's so civil about dismissing someone as a troll simply because something of his discourse is uncivil? Especially when that discourse is not uncivil in its entirely, i.e., when sans the uncivility something important is being said? Why throw the baby out with the bathwater?

Glenn said...

In general...

The quotations in the four mini-sections below occur consecutively in a single paragraph in James Lindsay's 1922 The Philosophy of Possiblity:

1. "The possible, in the logical sense, is what is free from contradiction; but all possibility is possibility of something, however indeterminate."

2. "The philosophy of possibility cannot evade the question of the origin of possibilities."

3. "Can we trace possibility simply to the human mind? Do possibilities not exist before the human mind comes into being? Will the possibilities not exist after the human mind has ceased to exist? Can we even ascribe the possibilities to the universe? If the universe were done away, would possibilities not remain in undiminished form? For, are the possible universes not infinite? And, is not possibility necessary and eternal? These are among the questions that may be asked."

4. "The philosophy of possibility can hardly be satisfied to accept possibilities as accounting for themselves."

It is 2. and 4. which strike me as being salient. (I don't mean to suggest that 2. and 4. ought to be salient for anyone else, only to say that they are for me.) And of 2. and 4., it is 4. which is the most salient, for it prompts in me a recollection of St. Thomas' third way of proving the existence of God.

Daniel said...

Glenn,

Well trolling is making disruptive or inflammatory posts with the intention of causing a fight isn't it? The reason I say that poster was a troll is because what he said, though derived from a valid and important philosophical dispute, wasn't particularly well informed (since both Guenon and Nasr, the leading contemporary representative of Perennialism/Traditionalism, both read and taught philosophy in an academic setting) and presented its primary aim as a personal criticism of Jeremy and others. In other words he didn't seem particularly interested in actually having a discussion about Actualism v Possibilism.

I don't necessarily challenge the Actualist thesis, in fact I would endorse it for similar reasons as you give there though perhaps not the same way as that poster might (in fact my earliest sort of proto-philosophical reflections in my teens were similar to those in point 3).

There's a book about Aristotle and Actualism I want to bring up in the next 'Links of interest' combox.

Glenn said...

Daniel,

There's a book about Aristotle and Actualism I want to bring up in the next 'Links of interest' combox.

I look forward to seeing what it might be.

Scott said...

"I look forward to seeing what it might be."

As indeed do I also moreover too, in addition besides.

John West said...

Scott,

As indeed do I also moreover too, in addition besides.

Rebelling against the starting of sentences with "But"?

Scott said...

@John West:

"Rebelling against the starting of sentences with 'But'?"

But however, in contrast, not really. ;-)

Glenn said...

Scott,

>> "I look forward to seeing what it might be."

> As indeed do I also moreover too, in addition besides.

Heh.

It would have been simpler to say, "I look forward to the link." But as interesting as I find links to be, I find books to be more interesting.

Wll, then, perhaps it would have been simpler and better to say, "I look forward to the book." But that a book addresses a subject I'm interested does not mean the book itself is interesting or actually worth reading.

And my crystal ball is out of commission just now, so until I know which book will be linked to, and more about it beyond what subject it deals with...

- - - - -

(And, in addendum, permit me to say... oh, never mind.)

Glenn said...

("...interested in...")

Anonymous said...

I think I can help to sort all of this out. Here is precise breakdown of how it all hangs together:

Sincerely - Murph

http://youtu.be/HkmfVsWunJ0

Anonymous said...

Oops. Here's the link:

http://youtu.be/yvFDrBJP6OM

Irish Thomist said...

There were a lot of comments so I skipped my way through a few of them.

What interested me was some talk somewhere in there about (it seems) divisibility and infinity?

Sure God can divide space up 'infinitely' (because even if it is physically impossible it is not so to him) but I argue we cannot (and I mean in relation to the universe not just the ability of humans). Things are not infinitely divisible according to their natures. When we start to think about what space actually is and how things are proportional relative to their final ends we bump up against problems in the thought experiment. For what does it mean to say something numerically can be infinitely divided (even if only into distances) if in reality 'no thing' can be? Interesting angles to look at it from. Anyway just throwing it out there.

Tangent over.

Carry on.



Irish Thomist said...

Anonymous said...

IMV, the distinction between being and acting does not exist at the microphysical level. God's sustaining a quark, a photon, or any boson or fermion in being is at the same time and inseparably God's concurring with that particle's acting.

Of course, in quantum mechanics a particle's behavior is probabilistic, so we could take the issue to level of the realized outcome, with 3 possibilities:

Full steering: God chooses all and every quantum outcome, in such a way that they seem probabilistic and random.

Deism: God just sustains the particles into being and acting (which as I said are not really distinct) and does not intervene in the selection of outcomes.

Strategic steering: middle way. God chooses those outcomes that are important for his design.


What if God sustains the causal nature and end directedness of the thing instead but concurs with events in a dynamic way i.e. not A so then B but rather... anyway I'm giving away too much of my thesis. Sorry for being an unintentional tease.

Jeremy Taylor said...

Daniel,

I suppose it depends how you are using the term existing. I know Guenon himself sometimes refers to creation alone as existence, and God as beyond being and existence. But you seem to be making use of an Aristotelian framework that privileges concrete or corporeal entities. I don't think Guenon would agree. He specifically makes the claim that Divine Exemplars are more real than anything created. Or perhaps I'm just misreading you.

When it comes to the existence of what we can think or understand, this is, though, a classic Platonic position. I recall Giovanni Reale writing that the Platonist concludes that there must be a realm of mathematical objects between the realm of Form (or lesser Forms) and the corporeal realm, precisely because he knows of mathematical objects. The difference between the Platonist and many moderns is perhaps that the Platonist always sees concepts as derived from an objective level of being, and not the other way around.

Anyway, as for the objection I bought up - that this argument might seem to imply all possibility must exist (and therefore destroy contingency) - I think, on reflection, someone making it could presumably appeal to Aristotle's doctrine of potency and actuality.

John West,

But is that length on a line on a Cartesian plane infinite? Or is it indefinite? Surely, the infinite is entirely incommensurate with the finite, and therefore it wouldn't make much sense to bring them into relations like this.

John West said...

Jeremy Taylor,

But is that length on a line on a Cartesian plane infinite? Or is it indefinite?

At least in Euclidean geometry, any line segment can be extended forever - that is, without limit - in both directions, forming a line.

Surely, the infinite is entirely incommensurate with the finite, and therefore it wouldn't make much sense to bring them into relations like this.

This is the proposition to which I'm trying to produce a counterexample.

Jeremy Taylor said...

But what does forever mean in this instance? Doesn't this presume that a line can be infinite? It is one thing to say it can go for ever, just as one may talk about infinite anything, but I struggle to see how one could understand something that has definite form and determination - limits - in one respect and not another. Strictly speaking, there is a complete discontinuity between what is finite and what is infinite, even if the former is of indefinite extension. I don't see, then, how it would make bridged in an object like a line. This would suggest that, though the line may be informally said to go on forever in either direction, it doesn't do that.

Jeremy Taylor said...

To put it another way, the length of the line is one thing and width of the line is another. This is, surely, a limit, suggesting that the length of the line is limited. Or, that space as a condition of corporeal being is not infinite, no matter how indefinite it may seem to us.

John West said...

Jeremy Taylor,

To put it another way, the length of the line is one thing and width of the line is another. This is, surely, a limit, suggesting that the length of the line is limited. Or, that space as a condition of corporeal being is not infinite, no matter how indefinite it may seem to us.

To clarify, you're saying even if the line could potentially expand to infinite length in terms of just the line itself, it would eventually - to write crudely - bang up against something due to the limits of its existing in finite space in a finite physical realm?

Jeremy Taylor said...

I'm saying it couldn't be of an infinite length, that to qualify infinity in such a way is to limit it. When someone talks about a line extending forever, they are talking loosely. All it can mean is it extends indefinitely, beyond direct human apprehension.

Daniel said...

@Jeremy,

We had a discussion about the meaning of terms like 'Being' and 'Beyond-Being' a while ago remember? It was on one of the PSR threads I think _ I should really go and dig it out though I confess I don't have the stomach for wading through hundreds of Santi posts this morning

I use Being in a logical sense primarily to refer to Identity, to all entities actual, possible and impossible qua identities (Being in a quintessentially 'essentialist' way which would have made Heidegger and Gilson pull their hair out). Historically Platonism operates with a three tire system with the world of particulars as the world of Becoming, the world of Forms as the world of Being and the One/Form of the Good as Beyond-Being. On those lines it does make sense to speak of God as Beyond-Being.

But you seem to be making use of an Aristotelian framework that privileges concrete or corporeal entities

Not at all. I certainly don't deny that the exemplar is more ontologically fundamental than particular existing dodos, and, being an aspect of the Godhead exists of necessity, only that strictly speaking the exemplar is not a dodo (for instance we can make lots of propositions about one which does not hold for the other), and there is a Categorical difference between the two. ‘Dodoness’ is the common nature which determines all dodos to have the features that they do (did) though it itself doesn’t possess this features (in a way it is these features). As Coplestone said when critiquing Aristotle’s arguments against the theory of Forms: Just because the Form of Man includes the property of corporeality it does not follow that the Form of Man itself is corporeal. Similar points could be made with immaterial particulars like angels of course.

When it comes to the existence of what we can think or understand, this is, though, a classic Platonic position. I recall Giovanni Reale writing that the Platonist concludes that there must be a realm of mathematical objects between the realm of Form (or lesser Forms) and the corporeal realm, precisely because he knows of mathematical objects. The difference between the Platonist and many moderns is perhaps that the Platonist always sees concepts as derived from an objective level of being, and not the other way around.

Yes, but that doesn't go against what I said about concepts, in fact that's sort of the point I was trying to make. It's similar to the arguments Frege and Husserl used against Psychologism to show that Universals, Numbers et cetera were mind-transcendent and not subjective-intramental constructs as the Empiricists wanted to claim.

Jeremy Taylor said...

Daniel,

Though interesting, I'm now somewhat confused about what much of what you are saying has to do with Lord Northbourne's argument?

I think there is a sense in which the Platonist would deny, in one sense, the distinction between corporeal entities and forms (although, paradoxically, he would affirm it), to the degree that he would say the form carries with it all the possibilities inherent in it. Though, on the other hand, he would also affirm the forms transcendence at the same time. The Platonist is ultimately a non-dualist, and this is true, in relative sense, of the forms as archetypes and what participates in them.

But, still, I'm not sure Northbourne's argument rises and falls with any of this.

Jeremy Taylor said...

That is, it is clear you are using the term impossibility in a different way to Northbourne (and Guenon), so I don't see he is wrong to suggest impossibilities cannot exist according to his definition of possibility and impossibility.

John West said...

Jeremy Taylor,

Thank you for your reply. To be clear, I understand the distinction between infinite and indefinite.

Or, that space as a condition of corporeal being is not infinite, no matter how indefinite it may seem to us.

I don't need the line to be a physical entity to use it as an example against the claim only entities infinite in every way can be infinite in any way.

But what does forever mean in this instance?

In this instance, I'm saying the line can be infinitely long, but has limited width. You had written the finite and infinite are completely incommensurable. Does not my line example show a way they are, in fact, commensurable?

Also, as Greg points out, all that's needed is the potentiality for an entity to be infinite in some respect but not others.

Doesn't this presume that a line can be infinite?

I'm not begging the question. I'm appealing to one of the axioms of Euclidean geometry, the definition of a line, that “any line segment can be extended forever in both directions, forming a line.”

It is one thing to say it can go for ever, just as one may talk about infinite anything, but I struggle to see how one could understand something that has definite form and determination - limits - in one respect and not another.

Infinite sets, intervals, lines, are all infinite in some respects but not others. Unless you posit fictionalism about mathematical entities, I don't understand the complication.

Strictly speaking, there is a complete discontinuity between what is finite and what is infinite, even if the former is of indefinite extension. I don't see, then, how it would make bridged in an object like a line.

Does this not appeal to the principle you're supposed to be defending in order to defend it?

To put it another way, the length of the line is one thing and width of the line is another. This is, surely, a limit, suggesting that the length of the line is limited. Or, that space as a condition of corporeal being is not infinite, no matter how indefinite it may seem to us.

Well, my point relies on the length and width being two different properties of the line. The line's width is limited. I'm saying that, in Euclidean geometry, the length can at the same time be infinite. Your claim is that only entities infinite in every way can infinite in any way. On Euclidean geometry, this is not so.

I'm saying it couldn't be of an infinite length, that to qualify infinity in such a way is to limit it. When someone talks about a line extending forever, they are talking loosely. All it can mean is it extends indefinitely, beyond direct human apprehension.

If it's only infinite in length, it's not infinite in all respects. But I see no incompatibility between a line having limited width but infinite length. In Euclidean geometry, it's in the definition of line.

Also, when others write of unit intervals being “infinite but bounded”, doesn't that also cause problems for your definition of infinite?

John West said...

Daniel,

We had a discussion about the meaning of terms like 'Being' and 'Beyond-Being' a while ago remember? It was on one of the PSR threads I think _ I should really go and dig it out though I confess I don't have the stomach for wading through hundreds of Santi posts this morning.

It's on page three of Nudge nudge, wink wink. If you CTRL+F the search bar, punch in "Jeremy Taylor", and scroll to the 21st instance, you should be right about at the start.

Daniel said...

@Jeremy,

The main aim of that post was in answer to some of the points you brought up in the context of discussing possibility. Also I wanted to make clear I my concerns weren't linked to specifically Aristotelian commitments.

so I don't see he is wrong to suggest impossibilities cannot exist according to his definition of possibility and impossibility.

I never claimed he was! What I did say was that it makes no sense to say possibilities exist/or have being, to use Guenon's extended term, unless assume something like Exemplars from the beginning. I think the argument is getting at something important but we must first be careful to tease it out all the modal niceties unequivocal language.

@John West,

Many thanks ;)

Glenn said...

Jeremy and Johm,

FWIW, St. Thomas notes in his discussion of the infinity of God that both God and things other than God can be infinite, although only God is absolutely infinite, while those things other than God which are infinite are only relatively infinite. He also mentions wood as an example of something which can be both finite and infinite, though not in the same respect: "[W]ood is finite according to its own form, but still it is relatively infinite, inasmuch as it is in potentiality to an infinite number of shapes." ST 1.7.2

Jeremy Taylor said...

John West,

The point is that, although one may posit that lines are infinite, this doesn't mean that this phrase makes sense in the final analysis.

I don't think I'm assuming what needs to proven. Rather, I'm examining (albeit clumsily) what is inherent in the conception of the infinite itself. The infinite is entirely without limits. This means it is inherently incommensurate with what is finite, which is limited. If a line had infinite length, it would be infinitely greater than any finite line, of any length. In fact, it would be infinitely greater than two finite lines of the different lengths. Besides, the infinite lacks all limits, which means all determination, such as the distinction between length and width. As length is limited by width (for a start), it cannot be infinite.

Daniel,

That is certainly a worthy ambition.

I would still say, though, that possibilities are real in some sense, and one doesn't have to assume exemplars to make this point. Father Christmas is real in some sense precisely because we can think of him, talk of him, draw him and so on (unlike a married bachelor, he doesn't turn out to be a contradiction on closer inspection). The question is the level and mode of reality he possesses. You are certainly correct that one bear in mind the exact kind of variety such entities have. Such a point may point towards exemplars, but I don't think it assumes them beforehand. Someone, like the materialist, who was opposed to the existence of forms and exemplars would have to explain, if they wished to, how Father Christmas can be completely unreal and yet be thought of, described, drawn, and so on.

Guenon himself at one points makes a relevant aside on hallucinations. He points out those who say what we seen in hallucinations is not real are wrong. What we see is real; those misled by hallucinations are seeing what is real, but they are misled about the sort of reality these visions have.

Glenn,

I don't know, but it seems to me that St. Thomas might mean by the relative infinite, the indefinite?

Glenn said...

Jeremy,

Glenn,

I don't know, but it seems to me that St. Thomas might mean by the relative infinite, the indefinite?


That's an interesting question.

Of the process of one thing moving another, that mover being moved by something else, and that something else itself being moved, etc., St. Thomas does say in one place that it cannot go on to infinity [1], and in another place that it cannot go on indefinitely [2].

In light of that, I would agree that there is at least one case in which 'relatively infinite' and 'indefinite' may be taken as being synonymous [3].

[1] "[W]hatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity because then there would be no first mover[.]" ST 1.2.3

[2] "As everything which is in motion must be moved by something else, a process which cannot be prolonged indefinitely, we must allow that not every mover is moved." ST 1.75.1.1

[3] I don't know of a case where 'relatively infinite' and 'indefinite' ought not be taken as being synonymous, and I don't know for a fact that there are any such cases, so my phrasing above is just a hedge against the possibility that such a case does exist.

John West said...

Jeremy Taylor,

The point is that, although one may posit that lines are infinite, this doesn't mean that this phrase makes sense in the final analysis.

I don't think I'm assuming what needs to proven. Rather, I'm examining (albeit clumsily) what is inherent in the conception of the infinite itself. The infinite is entirely without limits. This means it is inherently incommensurate with what is finite, which is limited. If a line had infinite length, it would be infinitely greater than any finite line, of any length. In fact, it would be infinitely greater than two finite lines of the different lengths. Besides, the infinite lacks all limits, which means all determination, such as the distinction between length and width. As length is limited by width (for a start), it cannot be infinite.


This is just a reiteration of everything to which I have already replied. Thank you for the conversation.

Jeremy Taylor said...

Yes, John, but I think that your response was precisely just to repeat what I myself had tried to address. You bring up infinite lines, in various mathematical frameworks, but do not really show how these must equate to reality, any more than talk of married bachelors equates to any reality (though the situation is a little different). Maybe I'm just ignorant of mathematics and would realise my error if I knew more about maths, but when you say things like "in Euclidean geometry, the length can at the same time be infinite", how is this demonstrated within the Euclidean system in such a way that it would refute my critique of such phrases? How is it shown that talk of infinite length is not just loose talk for what is in reality indefinite. I see no answer to this query in your posts, though I may have missed it.

In that case, I think my clumsy points about the incommensurate nature of the infinite have some validity. Indeed, even if we leave aside the question of entities posited to have both finite and infinite attributes, I still think what I brought up was meaningful as concerns the problems with so mixing the infinite and finite.

John West said...

Jeremy Taylor,

I apologize in advance for any lack of delicacy this morning—out of coffee.

In that case, I think my clumsy points about the incommensurate nature of the infinite have some validity. Indeed, even if we leave aside the question of entities posited to have both finite and infinite attributes, I still think what I brought up was meaningful as concerns the problems with so mixing the infinite and finite.

I never said it was meaningless (and probably would've ignored it if I thought so).

Yes, John, but I think that your response was precisely just to repeat what I myself had tried to address. You bring up infinite lines, in various mathematical frameworks, but do not really show how these must equate to reality, any more than talk of married bachelors equates to any reality (though the situation is a little different). Maybe I'm just ignorant of mathematics and would realise my error if I knew more about maths, but when you say things like "in Euclidean geometry, the length can at the same time be infinite", how is this demonstrated within the Euclidean system in such a way that it would refute my critique of such phrases?

If you're a mathematical realist, what you need to show is how such examples don't equate to reality, without simply appealing to the proposition about “infinite” you're defending (which would be circular), especially given the plenitudinous view of existence you express to Daniel.

This fictionalistic talk of “within the Euclidean system,” isn't open to the mathematical realist.

John West said...

(Or, as another example, perhaps my last sentence should quote: "in various mathematical frameworks")

Glenn said...

Jeremy,

Lord Nourthbourne wrote (in the article earlier linked to by Scott), "[O]nce one has abandoned the idea that possibility is limited by the conditions of our terrestrial experience, there is no conceivable reason to assign any limit to it whatsoever."

If that is the case, then surely it must also be the case that, "Once one has abandoned the idea that a line is limited by its breadth, there is no conceivable reason to assign any limit to it whatsoever."

IOW, surely there is nothing unusual about talk of infinite lines (even though an infinite line may be limited through the assignment of a fixed breadth).

Yes? Maybe? No?

Glenn said...

s/b "...nothing unusual or inaccurate about talk of infinite lines..."

o "There is nothing to hinder a thing from being infinite in one way and finite in another, as when in quantities we imagine a surface infinite in length and finite in breadth. ST 3.10.3.2

o Hence, if there were an infinite number of men, they would have a relative infinity, i.e. in multitude; but, as regards the essence, they would be finite, since the essence of all would be limited to one specific nature. But what is simply infinite in its essence is God, as was said in the FP, Q[7], A[2]." ibid

o "[T]he species of even numbers are infinite, and likewise the species of odd numbers are infinite; yet there are more even and odd numbers than even. And thus it must be said that nothing is greater than the simply and in every way infinite [i.e., God]; but than the infinite which is limited in some respect, nothing is greater in that order; yet we may suppose something greater outside that order. In this way, therefore, there are infinite things in the potentiality of the creature, and yet there are more in the power of God than in the potentiality of the creature." ST 3.10.3.3

Jeremy Taylor said...

John West,

It is probably just my ignorance of mathematics, but I don't understand what you mean when you suggest a mathematical realist must except the existence of infinite lines. Surely, a mathematical certainly believes that mathematical objects exist, but I don't see why he must accept that the positing of infinite, instead of indefinite, lines is correct. So, you will really have to explain this to me.

And I don't think my argument has been circular, because it has relied on a (albeit clumsy) investigation of what is inherent in the notion of infinity. Indeed, what you seem to be saying is that I must prove their is no such thing as infinite lines without making use of the concept of infinity.

Glenn,

Lord Northbourne's point is about all-possibility. Guenon, from whom he took his basic framework in the essay, was always stressing that there is only one thing infinite, God and no qualified infinities, like mathematical infinity. He did this for the reasons I have point out: the fact that determination or form or conditioning of any kind is a limit and only what is entirely undetermined and unconditioned can be infinite.

As for the quotes for St. Thomas, does he mean infinite or indefinite. I know, to the Platonist-Pythagorean, Number comes from the One (within being) and the Dyad. The One is form and the Dyad is matter. The Dyad is sometimes referred to as the many, as it makes possible the separate existence of the possibilities inherent in the One (within being). The Dyad is indefinite, however, and not infinite. Only God, the One beyond being, is infinite.

John West said...

Jeremy Taylor,

It is probably just my ignorance of mathematics, but I don't understand what you mean when you suggest a mathematical realist must except the existence of infinite lines. Surely, a mathematical certainly believes that mathematical objects exist, but I don't see why he must accept that the positing of infinite, instead of indefinite, lines is correct. So, you will really have to explain this to me.

On what grounds do you accept the existence of some entities of mathematics, but not others infinite in some respect but not other respects? If you say on the grounds that only entities infinite in every way can be infinite in any way, then you are appealing to the proposition which I'm providing examples against to defend that proposition.

And I don't think my argument has been circular, because it has relied on a (albeit clumsy) investigation of what is inherent in the notion of infinity. Indeed, what you seem to be saying is that I must prove their is no such thing as infinite lines without making use of the concept of infinity.

I appeal to the fair-mindedness of other readers. Is this a fair description of what I've been saying?

Jeremy Taylor said...

Guenon's work on Infinitesimal Calculus (a work I have not read before) is available online.:

http://www.mediafire.com/download/wk441od7e13dt9y/0900588128+-+Rene+Guenon+-+The+Metaphysical+Principles+of+the+Infinitesimal+Calculus-o.pdf

The first chapter covers the Infinite and Indefinite, the Second Chapter is called The Contradiction of Infinite Number.

Number, space, and time, to which some people wish to apply the notion of this so-called infinite, are determined conditions, and as such can only be finite; they are but certain possibilities, or certain sets of possibilities, beside and outside of which there exist others, and this obviously implies their limitation. In this instance still more can be said: to conceive of the Infinite quantitatively is not only to limit it, but in addition it
is to conceive of it as subject to increase and decrease, which is no less absurd; with similar considerations one quickly finds oneself envisaging not only several in finites that coexist without confounding or excluding one another, but also infinites that are larger or smaller than others; and finally, the infinite having become so relative under these conditions that it no longer suffices, the 'transfinite'
is invented, that is, the domain of quantities greater than the infinite. Here, indeed, it is properly a matter of 'invention', for such conceptions correspond to no reality. So many words, so many absurdities, even regarding simple, elementary logic, yet this does not prevent one from finding among those responsible some who even claim to be 'specialists' in logic, so great is the intellectual confusion of our times!


He does bring up the Scholastics, Glenn:

It is true that the Scholastics admitted what they called the infinitum secundum quid [the infinite in a certain respect], and that they carefully distinguished it from the infinitum absolutum [the absolute
infinite], which alone is the metaphysical Infinite; but we can see here only an imperfection in their terminology, for although this distinction allowed them to escape the contradiction of a plurality of infinites understood in the proper sense, the double use of the word infinitum nonetheless certainly risked causing multiple confusions,
and besides, one of the two meanings was then altogether
improper, for to say that something is infinite only in a certain respect-and this is the exact significance of the expression infinitum secundum quid-is to say that in reality it is not infinite at all.

Jeremy Taylor said...

John West,

If you say on the grounds that only entities infinite in every way can be infinite in any way, then you are appealing to the proposition which I'm providing examples against to defend that proposition.

I don't understand this. I'm not just asserting the proposition. I was offering, however limited and flawed, a support for it. Therefore, I see nothing wrong with suggesting that it implies your example is incorrect.

As I said, I lack detailed mathematical knowledge. I have not read Euclid. So, maybe I'm missing something here. But you will have to explain it in more detail for me to understand what.


I appeal to the fair-mindedness of other readers. Is this a fair description of what I've been saying?

Then, in what sense is my point circular?

Jeremy Taylor said...

That is, I'm not really understanding why we should not view the invocation of infinite lines as just a convention, loose term for indefinite lines. Maybe it is just my mathematical ignorance, and Euclid or whoever proved or demonstrated there were infinite lines. But that is what would challenge or refute my point, not the fact that lines are just sometimes spoken of as infinite. Perhaps it is obvious to someone who has studied mathematics at more than a secondary school level, and I'm missing something you think obvious. But I have studied maths in this way, so you will have to explain what I'm missing, if I am missing something.

Jeremy Taylor said...

- I haven't studied maths in that way, I mean (though I plan to study when I get around to it).

Scott said...

@Jeremy Taylor and John West:

If I'm following the discussion correctly, the two of you seem to be using the word infinite in two different senses. Jeremy is using it to mean something like not in any way limited (so that anything with a nature is "finite," including a line of what mathematicians would call infinite length), whereas John is using it in its mathematical sense of unbounded. In Jeremy's sense, God alone is "infinite," but in John's sense, a Euclidean line is of infinite extension in one dimension and finite in all others.

John's sense of the word is mathematically unexceptionable (and no, it doesn't just mean "indefinite"), but it's not the same as the more strictly Platonic sense. In that sense, as Jeremy says, a line if "finite" because it has a limited nature. I'm not clear, though, why that means it can't be mathematically infinite in extent.

John West said...

Which I noted on January 1st, 2015 when I wrote:

You write, "There is only one infinite, that which is without limits in any respect." So defined, clearly a finite thing cannot be infinitely divisible only (I'll call this endlessly divisible to avoid equivocating on infinite). This fact follows effortlessly from your definition of infinite.

But, Greg's argument can readily concede some-quantity-of-physical-matter has many limits. In fact, for the sake of argument, the physical matter can be limited in every possible way but its divisibility. On your definition of infinite, it would then still be finite but fulfill the criteria Greg needs.

Scott said...

Indeed you did.

John West said...

Glenn and Jeremy Taylor,

 "[T]he species of even numbers are infinite, and likewise the species of odd numbers are infinite; yet there are more even and odd numbers than even. And thus it must be said that nothing is greater than the simply and in every way infinite [i.e., God]; but than the infinite which is limited in some respect, nothing is greater in that order; yet we may suppose something greater outside that order. In this way, therefore, there are infinite things in the potentiality of the creature, and yet there are more in the power of God than in the potentiality of the creature." ST 3.10.3.3

In a similar vein concerning species and infinitum secundum quid, consider Euclid's proof for primes. Suppose there are a finite number of primes, p_{1}, p_{2}, ..., p_{n} (where 1, 2, etc. are subscripted to p). Multiply them together and add 1:

(p_{1})(p_{2})(p_{3})... (p_{n})+1

The integer we just constructed leaves a remainder of 1 when divided by any of the primes p_{1}, p_{2}, ..., p_{n}. This means it has no prime divisor between 1 and itself and is therefore prime. This prime is larger than the largest prime, which is impossible, so there could not be a finite number of primes. Therefore, there are an infinite number of primes. Therefore, the species of prime numbers must be infinite-in-this-respect.

Glenn said...

Jeremy,

Thanks for the link. I've read some of the PDF linked to, and I see that I have stepped in it -- from a Guenonian perspective, that is.

Guenon seems to have held that 'infinite' applies to God only, since only God is truly Infinite, and that it is illogical or improper to speak of infinity with respect to anything but God.

My question is this: was he consistent?

That is, did he also hold that, e.g., 'good' applies to God only, since only God is truly Good, and that it is illogical or improper to speak of good with respect to anything but God?

To take the question one step further, was he hyper-consistent, i.e., did he hold a similiar view of anything and everything which might be said or predicated of God?

If not, why not?

Jeremy Taylor said...

Hm. Maybe, but there still does seem a problem to me of talking of a Euclidean line as of infinite extension in one direction and not in all others. How can the infinite and finite enter into a relationship in this way? And surely the line, and space itself, is sequential, if you will, just as time is sequential. But what is sequential is not infinite.

Guenon also, from that link, appears to mean that, as well, there cannot be a line of infinite extension. Not only does he specifically (from my skimming) see to use the term indefinite for such lines, but says:

Here are some examples of ~he contradictions introduced by those who would allow the existence of infinite magnitudes, when they apply this
notion to geometric magnitudes: if a straight line is considered to be infinite~ its infinitude must be less, and even infinitely less, than the infinitude constituted by a surface such as a plane, in which
both that line and an infinite number of others are also contained, and the infinitude of the plane will in turn be infinitely less than that of three-dimensional space. The very possibility of the coexistence of all of these would-be infinities, some of which are supposed to be infinite to the same degree, others to different degrees, suffices to prove that none of them can be truly infinite, even apart from any consideration of a more properly metaphysical order;


He may be wrong, but this is the sort of issues I'm clumsily referring to.

Scott said...

@Jeremy Taylor:

"He may be wrong…"

He may indeed. I've only just downloaded the file, but so far his understanding of mathematical infinities is frankly not very impressive. The passage you've just quoted, for example, is simply wrong: the points in a plane don't constitute a "higher" infinity than the points on a line.

Jeremy Taylor said...

Glenn,

Yes, I do think Guenon thought God was the only thing absolute good, or beautiful and so on. He held a non-dualist viewpoint. I'm not really fit to explain it in depth, however.

John West,

That is a good example. But doesn't it rely on the prime numbers being sequential. That is, rising sequentially: 1, 2, 3, 5,... But is what is infinite sequential in this way? Traditionally, one of the distinctions between the perpetual and the eternal is that in perpetual time there was still duration, still past, present, and future, whereas for the eternal all time is ever present. Wouldn't this have to be the case for the infinite?

Jeremy Taylor said...

Scott,

Isn't his point that a surface is made up of an infinite number of infinite lines, according to those who accept infinite lines?

John West said...

Jeremy Taylor,

That is a good example. But doesn't it rely on the prime numbers being sequential. That is, rising sequentially: 1, 2, 3, 5,... But is what is infinite sequential in this way? Traditionally, one of the distinctions between the perpetual and the eternal is that in perpetual time there was still duration, still past, present, and future, whereas for the eternal all time is ever present. Wouldn't this have to be the case for the infinite?

As written, an infinite number of primes are present. No one has to count the species.

Scott said...

@Jeremy Taylor:

"Isn't his point that a surface is made up of an infinite number of infinite lines, according to those who accept infinite lines?"

Very likely that's the sort of thing he has in mind, yes. But mathematically, it's false that a Euclidean plane contains a "higher" infinity of points than a Euclidean line; the points on a line can be put into one-to-one correspondence to the points in a plane (and higher-dimensional spaces).

Jeremy Taylor said...

John West,

But, nevertheless, even if no one could count it, isn't a sequence implied?

Scott,

I didn't quote it for brevity, but before the passage I did quote, Guenon says this:

THE LOGICAL DIFFICULTIES, and even contradictions which
mathematicians run up against when they consider 'infinitely great' or 'infinitely small' quantities that differ with respect to one another, and even belong to different orders altogether, arise solely
from the fact that they regard as infinite that which is simply indefinite. It is true that in general they do not seem very concerned with these difficulties, but they exist nonetheless, and are no less serious for all that, as they cause the science of mathematics to appear as if full of illogicalities, or, if one prefer, of 'para-logicalities', and such a science loses all real value and significance in the eyes of those who do not allow themselves to be deluded by words.


I think he is saying that these contradictions, or alleged contradictions, are not his discoveries. He seems to be saying that others are perplexed by questions like this, and that the reason they have got themselves tangled up is because or the wrong use of the term infinity.

John West said...

(Also, no it doesn't rely on them being sequential. I did that for ease of reading. I could have rearranged the product of the primes into any order for the proof.)

Scott said...

@Jeremy Taylor:

"I think he is saying that these contradictions, or alleged contradictions, are not his discoveries. He seems to be saying that others are perplexed by questions like this, and that the reason they have got themselves tangled up is because or the wrong use of the term infinity."

Very well, let's grant that others are perplexed by those questions too. It doesn't matter who "discovered" them; that doesn't alter the facts that (a) those questions have mathematical answers (in terms of the mathematical meaning of "infinity," not merely "indefiniteness") and that (b) he doesn't address them (unless he does so later in the text).

Jeremy Taylor said...

John,

I mean, I mean prime numbers, being numbers, are sequential.

Scott said...

@Jeremy Taylor:

"I mean, I mean prime numbers, being numbers, are sequential."

Sure they are, in the sense that they're ordered. That doesn't in and of itself mean they're "sequential" in time, nor does it mean that the existence of the sequence has to wait upon our apprehension of it.

Jeremy Taylor said...

Scott,

My meagre mathematical knowledge prevents me from defending Guenon further. My point is that (1) given the fact Guenon undoubtedly had a good knowledge of higher mathematics and its history (at least until 1914), and (2) he seems to think that others (and from those he quotes previously it seems likely to be important mathematicians) are similarly perplexed, he is unlikely to have made an obvious blunder. There may well be a problem of mistranslation (Guenon wrote in French) or misunderstanding somewhere.

Scott said...

@Jeremy Taylor:

"My point is that (1) given the fact Guenon undoubtedly had a good knowledge of higher mathematics and its history (at least until 1914), and (2) he seems to think that others (and from those he quotes previously it seems likely to be important mathematicians) are similarly perplexed, he is unlikely to have made an obvious blunder."

Likelihood doesn't enter into it; the passage you quoted unambiguously contains such a blunder. At the very least Guenon does not (in that passage, anyway) consider the standard mathematical understanding of infinity, state that the points on the line and in the plane are commonly understood to be of the same order of infinity, and explain why he thinks that's wrong. (Perhaps he does so later, though the fact that Georg Cantor is mentioned just once in the entire book suggests that he doesn't.)

Scott said...

And one more thing:

"(at least until 1914}"

I'm afraid that won't do. He was writing in 1946.

John West said...

If you like, just to be absolutely thorough, I can check the original French to see if the same blunders are made. But as Scott writes, it's a straightforward blunder.

Jeremy Taylor said...

Scott,

But are not numbers sequential, in that they represent a sequential order of (discontinuous) magnitudes of quantity ? If one was to say that quantity or length were infinite, wouldn't a sequential nature conflict with that?

Apparently, Guenon studied mathematics at a tertiary level in the first decade of the twentieth century.

It is probably my ignorance talking, but I'm not sure Guenon is saying what you are suggesting. I think he is saying there is a contradiction between on the one hand saying just, as you are suggesting, that a line has infinite points and is not infinitely less, though, than a plane made of infinite such lines and the very fake it is so constituted. I think he is alluding to a logical problem here: that something has been important. It is hard to tell. Guenon tended to try to pack many meanings into a very concise mode of expression.

Jeremy Taylor said...

-fact, not fake.

- that something important has been missed.

Jeremy Taylor said...

That is, to be clear, what I took him to be saying is not that those saying a line has infinite points and a plane infinite lines were suggesting the plane was infinitely more than the line, but that conceptually this would seem to be implied. Hence there is a contradiction. It seems from the context that others had noticed these conceptual problems (though they may have somewhat marginalised them) and this had led them to propose various paralogical schemes to get around them.

Scott said...

@Jeremy Taylor:

"But are not numbers sequential, in that they represent a sequential order of (discontinuous) magnitudes of quantity ? If one was to say that quantity or length were infinite, wouldn't a sequential nature conflict with that?"

I've already acknowledged that (of course) numbers are "sequential"in the sense of "ordered." Why does that "conflict" with there being infinitely many of them?

"I'm not sure Guenon is saying what you are suggesting."

I'm not "suggesting" that he's saying anything in particular. My objection is not to what he says but to what he doesn't say. To wit…

"I think he is saying there is a contradiction between on the one hand saying just…that a line has infinite[ly many] points and is not infinitely less, though, than a plane made of infinite such lines and the very [fact] it is so constituted."

…in order to back that up, he needs to deal with what, in 1946, was the standard mathematical understanding of that alleged contradiction, which appears to resolve it with no problem. He doesn't do so.

Cantor was as surprised as anyone to discover that the points on a line could be placed into one-to-one correspondence with the points in a plane (or indeed in any n-dimensional space). But mathematically, the result doesn't involve a "contradiction," and anyone trying to show otherwise in 1946[!] (Cantor died in 1918) was not entitled to content himself with "try[ing] to pack many meanings into a very concise mode of expression."

Scott said...

Incidentally, doesn't Augustine make a remark somewhere about jumping into the very pit of iniquity and saying that God knows not all numbers? Why would a Platonist have an issue with there being infinitely many natural numbers in the mind of God?

John West said...

Scott,

Incidentally, doesn't Augustine make a remark somewhere about jumping into the very pit of iniquity and saying that God knows not all numbers? Why would a Platonist have an issue with there being infinitely many natural numbers in the mind of God?

I thought Platonists hold operational numbers exist in a middle realm, at a fairly far degree of separation from God, not only in God's mind.

Jeremy Taylor said...

Scott,

I am not convinced that was Guenon's meaning. I don't know that he is arguing that the points of a line cannot be brought into a one to one relationship with those of a plane. He seems to be referring to an issue which quite notoriously led others to set up paralogics to account for it.

Jeremy Taylor said...

Anyway, I think I will bow out of the conversation now. My mathematical ignorance prevents me from putting my case properly. It wad a very interesting conversation. It has reinforced my awareness I must increase my knowledge of maths. Was going to try and learn more maths six months ago, but chose Latin instead. So much to read and learn and so little time.

Glenn said...

I've poked around some, and have found Guenon's Fundamental Distinction Between the "self" and the "ego", in which he writes that there is something called, "the Personality, which alone is the true being, because It alone represents its permanent and unconditioned state, and because there is nothing else which can be considered as absolutely real."

Given the bee in Guenon's bonnet re 'infinity' employed in reference to something other than God, one would expect that he might then go on about the illogicality and impropriety of speaking of 'being' with respect to something other than 'the Personality'. IOW, one would expect him to have a second bee in his bonnet, one reserved for talk of, say, human beings.

But, no, he simply then says, "All the rest is, no doubt, real also, but only in a relative way[.]" **

Well, if 'being' not pertaining to 'the Personality' can exist and is real, even if only in a relative way, then why does Geunon insist that 'infinity' not pertaining to God cannot exist and isn't real, not even in a relative way?

- - - - -

** Perhaps Guenon elsewhere does go on about the illogicality and impropriety of speaking of 'being' with respect to something other than 'the Personality' (aka 'true being'), the confusion breed by such talk, and how it's just as bad (or nearly so) as speaking of 'infinity' with respect to something other than God. Perhaps. But notwithstanding the fact that all the reading I've done of anything written by Guenon has occurred entirely in the past 14 hours or so, I'll give odds of 10,000-1 that he does not.

Glenn said...

("...14 hours or so..." Based on the times of my prior two comments, the actual span of time is much smaller than that.)

Jeremy Taylor said...

I think for the indefinite is the infinite.

In that work he seems to be giving an exposition of the Vedantin. He certainly had no problem with the use of being for other than God. Indeed, like many Platonists he saw God as beyond being.

Jeremy Taylor said...

Sorry, meant I think the indefinite is the relative infinite for Guenon.

Jeremy Taylor said...

I also believe Guenon was especially concerned with the infinite because it ( and the absolute) bear a peculiar place in his presentation of Vedantin metaphysics ( which he takes to be ultimately compatible with Platonism and Sufi metaphysics). I lack the expertise in either Vedanta or Guenon's thought to give a proper exposition of them.

John West said...

Jeremy Taylor,

Anyway, I think I will bow out of the conversation now. My mathematical ignorance prevents me from putting my case properly. It wad a very interesting conversation. It has reinforced my awareness I must increase my knowledge of maths. Was going to try and learn more maths six months ago, but chose Latin instead. So much to read and learn and so little time.

Thank you for the conversation. The university will insist you focus on calculus first. May I suggest you not be afraid to study number theory and geometry as well. Most countries' elementary schools completely ignore proper education in number theory and geometry, even though these branches provide knowledge important to most of mathematics. They will also help you rebuild any atrophied numeracy.

Glenn said...

Jeremy,

1. In that work he seems to be giving an exposition of the Vedantin.

I too had noticed that at the top of the first page of Guenon's _Fundamental Distinction Between the "self" and the "ego"_ is a parenthetical comment indicating that it is a chapter from his _Man and His Becoming according to the Vedanta_, and that the first sentence begins with, "IN order thoroughly to understand the teaching of the Vedânta as it pertains to the human being, it is essential to..."

2. He certainly had no problem with the use of being for other than God.

Right. So why did he have a problem with the use of infinity for other than God? IOW, why did he see the use of 'infinity' for other than God as illegal and verboten (so to speak), but did not see the use of 'being' for other than God as likewise illegal and verboten? Perhaps the answer to this question is in the last statement of your response:

3. Indeed, like many Platonists he saw God as beyond being.

It is unclear to me, however, just what this is supposed to mean.

Does it mean that Guenon saw God beyond all being which isn't 'true being', i.e., beyond all being which is merely relative being? Or does it mean that Guenon saw God beyond all being including 'true being'?

If the former, then you're basically saying with different words what had already been quoted from him, and the question in 2. stands. If the latter, then it would seem to follow that Guenon held that God cannot be considered as absolutely real. **

- - - - -

** And this for the reason that, according to Guenon, "the Personality...alone is true being', and nothing else, i.e., nothing other than that "true being", can be considered as absolutely real.

(If God is beyond all being including 'true being', then God is beyond 'true being'. But, according to Guenon, nothing other than 'true being' can be considered as absolutely real, so God is beyond what can be considered as absolutely real. And if God is beyond what can be considered as absolutely real, then, and again according to Guenon, God cannot be considered as absolutely real.)

Anonymous said...

Wow. This is an excellent blog. Readers should go and read Dr. Richard Conn Henry's review of Quantum Enigma.

http://henry.pha.jhu.edu/quantum.enigma.html

As he points out (having himself converted from atheism to theism about 10 years ago), physicists (of which he is one) have been writhing in denial about quantum mechanics, trying desperately to hang on to materialism/reductionism/realism for the last 100 years.

Chris said...

I don't wish to ruffle any feathers with any more "mystic mongering", but a quick remark. .......
As I understand it, Guenon equated "Being" and "Beyond-Being" with Saguna and Nirguna Brahman in Advaita Vedantist terminology- which (from Guenon's pov) corresponds with Eckhart's Gottheit and Gott.

Jeremy Taylor said...

Glenn,

I did not open the link. The title itself indicates the subject matter. Guenon did have a bee in his bonnet, you might say, about the Self vs ego, based on Vedanta.

Anyway, obviously the Platonic use of the term beyond being for God is not meant to render God unreal, far from it. I would suggest reading the antique Platonists if you are interested in their terminology. The distinction certainly does not originate with Guenon. In fact Guenon eschewed originality.

As I said, Guenon thought there was only one infinite for reasons like those I clumsily made the arguments for, which are distinct from questions of being quite clearly. Also, as I said, the infinite held a special place in his thought. I am not the one to explain his philosophy.

John West said...

Glenn,

I don't know about Guenon, but I've seen Beyond-Being used to mean not-created.

Jeremy Taylor said...

Glenn,

Also, I have a couple questions about St. Thomas.

He writes:

http://www.newadvent.org/summa/1044.htm

"Therefore all beings apart from God are not their own being, but are beings by participation."

Does this mean that for Aquinas we not human beings? That they are God's being? Did he object to the term human beings?

Also, he writes:

Further, the final cause is the first of causes.

Isn't this a contradiction. How can it be the final cause if it is the first of all causes? Does he mean relatively final?

Scott said...

@Jeremy Taylor:

"Does this mean that for Aquinas we not human beings? That they are God's being? Did he object to the term human beings?"

Surely he just means that we don't have our being of ourselves but owe our being to another. That doesn't mean we're not beings, only that we're not self-existent.

"Isn't this a contradiction. How can it be the final cause if it is the first of all causes? Does he mean relatively final?"

All that matters is that he doesn't mean temporally final. As Aquinas himself says in reply to the objection you're quoting (which should not be taken to represent Thomas's own opinion anyway), God "is one in reality. But this does not prevent us from mentally considering many things in Him, some of which come into our mind before others."

But I don't think I'm telling you anything you don't know here. I must confess to harboring a suspicion that you're joking, or somehow trying to suggest that Guenon is no worse than Aquinas in some supposedly relevant respect.

Jeremy Taylor said...

Yes, I was certainly attempting to parody Glenn's somewhat, to me at least, strange approach in his last few posts, though I suspect he too was trying some kind of subtle humour.

Scott said...

@Jeremy Taylor:

Fair enough; Glenn is certainly both subtle and humorous, often at the same time. But I think you've left his genuine question unanswered: why did Guénon have a problem with the use of the term "infinity" for anything other than God when he didn't have any similar objection to the use of "being"?

Jeremy Taylor said...

Well, Guenon certainly agreed with those who situated the One beyond being. He makes this quite clear. Infinity, and the related ideas of all-possibility and possibility, hold a peculiar place in his thought - the infinite and the absolute being the two highest hypostases of the One for him. In expositions of Hindu doctrine, the role of possibility and its infinitude is central. This is presumably why he was so interested in the matter. His thought is essentially Shankarian and Platonic non-dualism (which he takes to be fundamentally the same), and this is how he frames the relationship of created beings to God, as well as qualities like goodness. But, as I said, I'm not competent to explain his position any more than that.

Jeremy Taylor said...

Or, to put it another way, Guenon does see all creation and its qualities as relative. I know his disciple Schuon would often use the term the relative to refer to what is outside the divine essence. This is classic Shankarian and Platonic non-dualism, though you will have to look to someone else for a proper explanation or defence of it. The indefinite - the dyad - is the relative absolute, the reflection of God's infinity. The reason he most objected to the use of the term infinity for the indefinite has to do with the role the infinite, and infinite or all possibility, had in his exposition of Vedanta and what he felt were errors caused by misunderstanding the true infinite. Other qualities didn't have the same kind of conceptual role for him.

Jeremy Taylor said...

- sorry, meant the indefinite is relative infinite.

Glenn said...

Jeremy,

My questions were genuine. I'll try again, using a different approach (with less diplomacy and less tact).

In the article you linked to, Guenon writes that, "[T]here can obviously be only one Infinite, for two supposedly distinct infinites would limit and therefore inevitably exclude one another; consequently, every time the term 'infinite' is used in any sense other than that which we have just mentioned, we can be assured a priori that this use is necessarily improper, for it amounts in short either to ignoring the metaphysical Infinite altogether, or to supposing another Infinite alongside it."

In the chapter I linked to, Guenon writes that, "[T]he Personality, which alone is the true being, because It alone represents its permanent and unconditioned state, and because there is nothing else which can be considered as absolutely real. All the rest is, no doubt, real also, but only in a relative way[.]"

In the first quotation, Guenon seems like anything but a normal person. To wit, he confidently states that, in the event someone uses 'infinite' (note the lower case 'i') in any sense other than the sense to be understood by the similar looking yet completely different term 'Infinite' (note the uppercase 'I'), we can be assured that the one using it is either ignoring that which is indicated by some other term that he is not using, or supposing that there is not one but two of a something to which he has not referred.

In the second quotation, Guenon seems like a normal person.

I just wonder why Guenon seems to go haywire when it comes to 'infinite' and 'Infinite', but doesn't go haywire when it comes to the one 'true being' and 'being'.

I didn't come across the second quotation until after I had initially asked whether Guenon was consistent, i.e., until after I had asked whether he "also h[e]ld that, e.g., 'good' applies to God only, since only God is truly Good, and that it is illogical or improper to speak of good with respect to anything but God?"

Given the seemingly unfounded, if not peculiar, confidence Guenon exhibited with regard to his ability to know -- from the mere the fact that a certain term is employed -- the intent, point and purpose of that term's employment, the question just begged to be asked.

The discovery of second quotation, and its juxtaposition with the first, just makes the oddity of the first quotation stand out in sharper relief.

Glenn said...

Jeremy,

Glenn,

I did not open the link. The title itself indicates the subject matter.


I was unaware that discussion of the Self and the Ego necessarily involved the Vedanta, so had assumed you did open the link.

My mistake.

Glenn said...

Jeremy,

Also, I have a couple questions about St. Thomas.

He writes:

http://www.newadvent.org/summa/1044.htm

"Therefore all beings apart from God are not their own being, but are beings by participation."

Does this mean that for Aquinas we not human beings? That they are God's being? Did he object to the term human beings?


Aquinas didn't object to the term human beings. And neither did Guenon. But Aquinas also did not object to the use of 'infinite' when not referring to the Infinite that pertains to God, whereas Guenon did. Thus the questions having to do with a difference centered on what Guenon had said, rather than on what Aquinas had said.

Also, he writes:

Further, the final cause is the first of causes.

Isn't this a contradiction. How can it be the final cause if it is the first of all causes? Does he mean relatively final?


He meant, to put it most generally and quite simply, that the end is at the beginning.

(Sounds odd, doesn't it? Yet there is nothing odd-sounding about "means to an end" -- even though the actual employment of some means to and end cannot occur unless the end itself exists prior to the employment of the means. The apparent confusion is easily cleared up by thinking of, e.g., 'aim', 'goal' and 'purpose' as synonyms for 'end'.)

Glenn said...

(s/b "...some means to an end...")

Jeremy Taylor said...

Glenn,

I may be misreading because of the problems of combox discussions, but throughout this discussion your tone has seemed unnecessarily hostile. I have done my best to answer you several times now.

The word infinite means unlimited. It is that which is without limits. Guenon held particular ideas about infinity and related ideas of limits, possibility, and so on. He thought the relativity of creation meant that God's infinity was reflected as the indefinite. He felt that misuse of the concept of infinity took away from significant metaphysics ideas linked to infinity, limits, and so on. Guenon did hold a Shankarian and Platonic non-dualism which saw the being, goodness, and so on, of creation as relative. But all these qualities do represent different aspects of the One. It is these differences, how Guenon saw the infinite, and the role it played in his thought which led him to make the claims you quote. You may disagree with his views, but I hardly see how, in context, what he said is some galling absurdity.

As I said, though, I am not competent to explain his views more than this.


Jeremy Taylor said...

I have Guenon's The Multiple States of the Being , perhaps it most important metaphysical work (as usual it is rooted in Vedanta). The first chapter is called Infinity and Possibility. The first three sentences of the chapter read:

To understand properly the doctrine of the multiplicity of the being, it is necessary to return, before considering anything else, to the most primordial of all ideas, namely to that of metaphysical infinity envisaged in its relationship with universal possibility. The infinite, according to the etymology of the term, is that which is without limits. If we to keep to the proper sense of this word we must reserve it for the designation only of that which has absolutely no limits whatsoever, excluding things which are free only from certain limiting conditions while remaining subject to other limitations inherent in their own natures.

He then goes on to make extensive use of the concepts of infinite, limits, and possibility, setting up the entire work.

Given the role of the infinite and limitless within his metaphysics, and the fact he felt the truly limitless was only something that could be to God, one can see why he disliked misuse of the term infinite. He may be wrong in both his metaphysics and his feelings on the consequences of the use or misuse of the term, but I don't think his concerns are simply absurd.

Glenn said...

Jeremy,

I may be misreading because of the problems of combox discussions, but throughout this discussion your tone has seemed unnecessarily hostile. I have done my best to answer you several times now.

I just wonder why there's one term and one term only which Guenon would not allow can be used of God in one way and of other than God in another way.

You say you have given responses (to my various ways of asking the same basic question), and, yes, you have given responses. But none of your responses looks like a straight answer to a simple question.

If I remember correctly, you have previously mentioned or alluded to Swedenborg. I have looked him up. Swedenborg wrote, "That is called indefinite which cannot be defined and limited by number; nevertheless what is indefinite is finite relative to what is infinite, and so finite there is no ratio between the two." He also used the term 'infinite' in ways that Guenon later would have insisted are inappropriate. For example, Swedenborg stated that the number of things a person does not know are infinite in comparison with the number of things which he does know; he also claimed that the aspects of wisdom are infinite in number, and that each individual aspect of wisdom is itself capable of infinite expansion.

St. Thomas, well before Swedenborg, and to the apparent distate of Guenon much later, did use terms which may be predicted of God for other than God. In doing so, however, St. Thomas was quite clear that the sense of such terms was equivocal.

If Guenon's metaphysics is such that an equivocal use of the term 'infinite' is illegal in his 'system', then fine. But that its usage for something other than God is illegal in Guenon's 'system' does not make it illegal in other 'systems'.

Jeremy Taylor said...

Well, I have tried to give the best answer I could, given my lack of expertise. It is no doubt that lack of knowledge and inexact expression on my part on the problem.

Guenon had great knowledge and admiration of St. Thomas and the Schoolmen. But he put the notion of the unlimited , especially as involves unlimited possibility, at the centre of his thought. He believed that understanding the limitless and possibility was a foundation for understanding metaphysics properly. I have discovered that the proof of God from Lord Northbourne I quoted does originate in Guenon's work (well it might go back to another source, I don't know). And it is based on notions of possibility and the limitless. He also believed that creation was such that it could only be indefinite (and he made philosophical use of the quality of the indefinite), whereas the relationship between created being and God, or God's goodness and created goodness, is more complex. This last point is important. He was well aware, no doubt, that all such properties in creation are relative. But the fact the infinite becomes the indefinite is a unique pattern compared to the other qualities. Combined with the use he made of both the infinite and indefinite, this explains his concern.

One could call him wrong on either fact or his concern with word usage, but I don't think he was absurd on the latter or inconsistent. I am sure there are many examples in the history of philosophy where philosophers have been keen to have a key term used only in a specific way.

This is as straight an answer as I can give.

Jeremy Taylor said...

Although I alluded to it earlier, I was perhaps not clear enough about the distinction between the infinite/indefinite and other divine qualities. For Guenon, as mentioned, the relative infinite is the indefinite, the Dyad. The indefinite is the outcome of the reflection of God's infinity into creation.Although it is not perhaps strictly accurate, Guenon position on God's qualities and ours is not dissimilar to Aquinas' notion of analogical predication. Now, the distinction between the infinite and the indefinite is quite clear and easy for man to understand. Even the average Gnu could hardly fail to see the distinction between the infinite and the indefinite. For the human mind, however, we have a harder time wrapping our minds around the distinction between God's being, etc., and ours - the sense in which there is a distinction and yet we share the qualities is complex. The Gnu would no doubt dismiss analogical predication as meaningless words. And we must remember, as the distinction between the infinite and the indefinite is quite clear, if you don't believe there can be anything infinite but God, as Guenon did, then the use of the term relative infinite must seem obscure and misleading. For someone like Guenon, the sense in which there is no infinite outside God, only the indefinite, is clear enough, but the way in which God is true reality and yet we share, in a relative and analogical sense, his reality is far more intricate and complex. So the infinite, from this point of view, is not just quality alongside, goodness, being, beauty, and so on. Add to this the role the infinite and indefinite play in Guenon's thought (and he does not make similar use of being or goodness), then one can see, if not agree with, the reasons he was most concerned about its misuse.

John West said...

All this banter about indefinite/infinites raises an interesting question. How do Thomists generally feel about philosophy making rulings on scientists or mathematicians' practices?

John West said...

Jeremy Taylor,

As far as our conversation earlier, I think the metaphysic in question was Trenton Merricks's, so I really wasn't concerned with Guenon. He does seem interesting though. Contemporary continental philosophy is very different.

Glenn said...

Jeremy,

But he put the notion of the unlimited, especially as involves unlimited possibility, at the centre of his thought.

Just as one might see the use of 'infinite' for other than God as a kind of denial of God, or as a supposition of a second God, so too might another see 'unlimited possibility' as a kind of denial of the priority of actuality, and, by extrapolation, as a kind of denial of God, or as a replacement for God.

This is as straight an answer as I can give.

One can ask of another no more than that he give his best. So, thank you.

Daniel said...

For Glenn and Jeremy (and John because of the mathematical Platonists).

Dermot Moran has uploaded the text of a volume, Phenomenology 2010,to his Academia profile. It features an interesting essay on Georg Cantor's distinction between the 'Transfinite' and the 'Absolutely Infinite' and its origins in the Platonic tradition. Perhaps it will have some bearing on this conversation:

https://www.academia.edu/10053608/Phenomenology_2010._Volume_4._Traditions_Transitions_and_Challenges

Glenn said...

Thanks, Daniel. I've downloaded and saved it; will get to it later this afternoon or evening.

John West said...

Daniel,

https://www.academia.edu/10053608/Phenomenology_2010._Volume_4._Traditions_Transitions_and_Challenges

Very interesting. Thank you.

Those who haven't already read it may also be interested in this link from Step2.

Glenn said...

Yes, it had happened before.

But this time I did not overlook the fact that the entrance to the trail leading to the overlook that would entrance me is not wide enough to accommodate the Infiniti. It was on the moped, then, that I moped as I exited the commune on my way to commune with nature.

Whilst deep into thinking how I could not brook that that it is odd for one word to have multiple meanings, or even that it is wrong for different words to have the same spelling yet different meanings, a bear leapt over a brook and onto the trail from the right.

Yikes.

To its presence did I object, and I made this clear by hurling at it the only sizeable object near at hand, the helmet on my head.

It was with a mighty swipe of its paw that the bear did bat the helmet away. He was, apparently, unamused. Uh-oh. (Boy, was I glad I spoke with my father last night, and told him much I appreciated him.)

But unamused as the bear may have been, my message of unwelcome must have dawned, for it then turned and fled back into the woods, like a bat into a cave just before, heh-heh, sunrise.

Startled by the close encounter, and having retrieved my helmet and placed it back on my head, I then sought to recap in my mind what had led to the state of depression I no longer was in. Aha. Well, the solution is simple, and should suffice to close the matter.

Rather than replace all instances of a certain usage of 'infinite' with 'indefinite', the thing to do is place 'infinite' on a list of homographs. That would definitely work, and should take infinitely less time to accomplish.

John West said...

Glenn writes:

Rather than replace all instances of a certain usage of 'infinite' with 'indefinite', the thing to do is place 'infinite' on a list of homographs. That would definitely work, and should take infinitely less time to accomplish.

Replacing all instances of certain usages of “infinite” with “indefinite” would also never fly with others. In fact, I suspect most mathematicians would instead join David Lewis in expressing general concern about philosophers as un-accommodating to other fields as Guenon in earlier quotes:

I am moved to laughter at the thought of how presumptuous it would be to reject mathematics for philosophical reasons. How would you like the job of telling the mathematicians that they must change their ways, and abjure countless errors, now that philosophy has discovered that there are no [mathematical infinites]? Can you tell them, with a straight face, to follow philosophical argument wherever it may lead? If they challenge your credentials, will you boast of philosophy's other great discoveries: that motion is impossible, that a Being than which no greater can be conceived cannot be conceived not to exist, that it is unthinkable that anything exists outside the mind, that time is unreal, that no theory has ever been made at all probable by evidence (but on the other hand that an ideal theory cannot possibly be false), that it is a wide-open scientific question whether anyone has ever believed anything, and so on, and on, ad nauseam? (David Lewis, Parts of Classes)

I disagree with Lewis's implication about Anselm's argument, and think philosophy is of vast importance. But I just don’t see why Guenon is so stuck on this one point.

John West said...

edit: ... on this one point. It's pointlessly alienating. He can say the same thing without insisting on crippling other fields.^

Scott said...

@John West:

"He can say the same thing without insisting on crippling other fields."

Indeed. And it would have been nice if, in saying what he wanted to say, he had evinced the slightest willingness to engage with what Cantor and other like-minded mathematicians actually had to say about the transfinite or relatively infinite (as opposed to the Absolute Infinite, a subject on which Cantor would probably have agreed with him).

Scott said...

Guénon also, for example, says that there's a problem in regarding the "infinite number" of integers as being the same as the "infinite number" of even integers: this allegedly contradicts the dictum that the whole is greater than the part. But that's nonsense; the even integers are a proper subest of the integers, and so the whole is greater than the part. Guénon merely assumes that the only way the whole can be greater is to be greater in number.

Jeremy Taylor said...

John West,

Leaving aside whether Guenon is right about the existence of anything but the indefinite outside God, surely there is a quite a clear distinction between the infinite and indefinite? I suppose people can use what terminology they like, but I'm not sure what is wrong with critiquing terminology used if one thinks it is confused and leads to greater confusion.

Would not Thomists and many others do just that if scientists or whoever started using terminology they thought led to confusion, especially confusion surrounding spiritual, metaphysical, or philosophical issues? This is clearly what Guenon thought - even without the distinction between the indefinite and the infinite - given the metaphysical infinite holds a peculiar place in his metaphysics. Glenn brings up the possible problems a Thomist might have with the Guenon's use of the terminology of possibility. But in that instance possibility and potency are at least distinct words and can be differentiated in meaning more easily.

I think you are right to a degree, but doesn't it come down to the way in which philosophy claims a final appellate jurisdiction?

Scott,

In your last post, I'm not sure I follow you, as a mathematical layman. In what way could infinite number of integers be greater than the infinite number of even integers accept in number?

Also, I was reading the Wikipedia entry on Actual Infinity:

http://en.wikipedia.org/wiki/Actual_infinity


I have a couple of question. Is this the same issue as that Guenon is discussing?Also, that article quotes Henri Poincare:

There is no actual infinity, that the Cantorians have forgotten and have been trapped by contradictions.

Would he be referring to the same issues that Guenon was? Where can one read more on these issues?

Jeremy Taylor said...

- except.

Of course, on the other hand, one can say that potentially misleading or not, as long as people realise how the term is being used, who cares what term it is. I suppose it depends upon your concerns about the use and misuse of language. Some people take precision in language very seriously. Personally, I think the language aspect is not the most central part of this discussion. I can see why Guenon was concerned, and don't think that his reasons are absurd or inconsistent, but I can also see why it might not matter as much as he might have thought. There may be something ironic though in caring so much why Guenon cared so much about the use of the term. The actual concepts involved seem exponentially more interesting and important to me.

Daniel said...

Guenon was, like others before and after him, unwise to try to stretch mathematical language to present analogises between mathematics and metaphysics. Do we need to get so heated about it though? After all it alone forms no objection to the metaphysical point he was trying to illustrate with that analogy.

Claire Ortiz Hill is supposed to be translating Cantor’s later metaphysical correspondence and documents pertaining to his connection with the Rosicrucians. I’ve probably mentioned it before but there’s interesting stuff available on her website about Frege, Husserl and Cantor

http://rancho.pancho.pagesperso-orange.fr/Writings.htm

@Scott,

Yes, he ought to have engaged more with Cantor and contemporary mathematical theories of the infinite. He was like the Neo-Scholastics in as much as he tended to routinely ignore contemporary happenings in philosophy and focus on critiquing Mill, Spencer and co.

@Jeremy,

Cantor was in a sense on the same side as Guenon in that he stressed the usage of the term 'Transfinite' to refer to higher than normal finite numbers as opposed to Absolutely Infinite which he, in later life at least, preferred to keep as a metaphysical concept pertaining to God alone. He undertook a series of polemics against Neo-Scholastic writers who claimed his concept of the 'Infinite' i.e. Transfinite lead to Pantheism, a charge he adamantly denied.

@John West,

Perhaps I’m misremembering but did you post on one of the recent blog entries asking about people’s opinions on the relationship between philosophy and other disciplines?

John West said...
This comment has been removed by the author.
John West said...

Jeremy Taylor,

I suppose people can use what terminology they like, but I'm not sure what is wrong with critiquing terminology used if one thinks it is confused and leads to greater confusion.

But who is confused? No mathematician of which I know is in the slightest perplexed by different usages of “infinite”, and certainly the Scholastics avoided committing fallacies of equivocation over infinite.

Would not Thomists and many others do just that if scientists or whoever started using terminology they thought led to confusion, especially confusion surrounding spiritual, metaphysical, or philosophical issues?

As I wrote, who is confused? Guenon seems to summon ghost mathematicians to rail against their confusion over infinites. Worse, as Scott writes, Guenon fails to interact with mathematicians contemporary to him. In any case, even if there were confused mathematicians, no one seems confused now.

Also, at least in the quotes you share, Guenon doesn't suggest that his usage of infinite be kept to philosophy. He forcefully insists others, such as mathematicians, ought to follow his usage.

I think you are right to a degree, but doesn't it come down to the way in which philosophy claims a final appellate jurisdiction? 

In this case, I don't think it does. This is the reason I pointed out that, “[Guenon] can say the same thing without insisting on crippling other fields.” If we hope for a complete picture of reality, philosophy must to some degree be contiguous with other areas of knowledge. I think it dangerous to let the overdepartmentalization of the academy become the overdepartmentalization of knowledge.

[You wrote to Scott:] Where can one read more on these issues?

You may be interested in Solomon Feferman's Infinity in Mathematics: Is Cantor Necessary? and Infinity in Mathematics: Is Cantor Necessary? (Conclusion), in which he answers: “No.” David Hilbert also fussed about infinites in essays and in his famous hotel. He was, however, a formalist and had other, more materialistic, anti-realist commitments. Formalism has collapsed.

John West said...

Daniel,

Perhaps I’m misremembering but did you post on one of the recent blog entries asking about people’s opinions on the relationship between philosophy and other disciplines?

You remember correctly. In this thread I wrote: "All this banter about indefinite/infinites raises an interesting question. How do Thomists generally feel about philosophy making rulings on scientists or mathematicians' practices?"

Though, I'm also interested in people's opinions more generally. As I'm sure you're aware, it's an issue of great interest among many recent philosophers.

Scott said...

@Jeremy Taylor:

"In what way could infinite number of integers be greater than the infinite number of even integers [except] in number?"

As I said, by the latter being a proper subset of the former. The one set contains the other and more besides.

I see John West has already recommended some further reading, so I'll just add this book, which came up recently in another thread.

Jeremy Taylor said...

John West,

By confusion I meant, firstly, that Guenon thought that the doctrine of all-possibility and infinity was very important for metaphysics and spirituality and seemed to think that misuse of the term infinite, as he saw it, was leading people away from this understanding. Guenon could at least argue that Westerners, except for the Platonists, have missed what he took to be important metaphysical truths. But, anyway, I think there is little point fussing ourselves about the issues with Guenon's alleged fussing over terminology.

Secondly, the confusion is over the infinite versus the indefinite. Of course, Guenon may be wrong about this, but if he were right those claiming things like infinite numbers existed would be confused.

I'm not quite convinced Guenon made the blunder he was accused of. I'm a complete layman, but what I quoted from him doesn't seem to say the exact same thing as said blunder. It may have the same meaning and this has just escaped my ignorant eyes.

Again, maybe this is my ignorance talking, but at this level, aren't mathematics and philosophy highly related? In what sense would a work like Proclus' Commentary on Euclid be acceptable if you are correct? Or philosophy of mathematics in general? Isn't a greater and more comprehensive conceptual understanding of mathematics (and any other discipline) important? Guenon himself had undertaken tertiary studies in both. Indeed, I think overdepartmentalisation is a strange accusation to level at a Perennialist, indeed the arch-Perennialist (with Schuon). Guenon held a peculiar notion of philosophy (actually he differentiated between philosophy and metaphysics, and subordinated the former to the latter), one quite distinct from modern academic ideas on philosophy and, although he would no doubt think there was room for distinctions in disciplines, he would not support overspecialisation of knowledge.

To me this is not really about jurisdiction or terminology but the truth of the claims about the indefinite and infinite, though I have little to say on that subject given my lack of mathematical knowledge.

Scott said...

@Jeremy Taylor:

"Of course, on the other hand, one can say that potentially misleading or not, as long as people realise how the term is being used, who cares what term it is."

That's true, but in this instance it doesn't resolve the problem. When mathematicians say that the unit interval [0, 1] contains an uncountable infinity of real numbers, that's what they mean; they don't mean that it contains an "indefinite" number. And an uncountable infinity is actually greater than a countable infinity (like the positive integers).

Whether such infinities can be physically realized is another question, and I would tend to agree with Aristotle and Aquinas that they can't. But as mathematical objects they're quite unexceptionable.

John West said...

Jeremy Taylor,

Again, maybe this is my ignorance talking, but at this level, aren't mathematics and philosophy highly related? In what sense would a work like Proclus' Commentary on Euclid be acceptable if you are correct? Or philosophy of mathematics in general? Isn't a greater and more comprehensive conceptual understanding of mathematics (and any other discipline) important? 

These questions aren't in line with what I thought I said at all.

Glenn said...

Jeremy,

To me this is not really about jurisdiction or terminology but the truth of the claims about the indefinite and infinite.

How can it be both: a) not about terminology; and, b) about claims involving (things signified by) terms?

Given Guenon's insistence that one term be replaced by another, and for the reason that, so he held, the original term necessarily breeds confusion, whereas the replacement term clears up that confusion (without breeding any of its own), it seems unlikely that it isn't about terminology.

But let's suppose it really isn't about terminology. In this case there seems to be no good reason for anyone to defend, either directly or indirectly, Guenon's claim that one is assured a priori that anyone using 'infinite' rather than 'indefinite' for something other than God is either denying God or supposing the existence of a second God.

Daniel said...

@John West,

A quick response to that question (a full one would probably take a while).

I have always seen philosophy as a science of science, a kind of ‘metaknowledge’ that encompasses and unifies all other fields of knowledge within itself. There's no way 'outside of' philosophy, particularly philosophy as ontology, since taken as a whole it’s just the science of reality. This is why calls for a ‘metaphysics-neutral’ logic are a waste of time.

Whilst it's easy to sympathise with the emotional responses some of specialised referred therein might give Lewis' statement on its own seems like an invitation to pure dogmatism (we'll understand Dogmatism to mean asserting that something is true without giving any reason why that should be the case even if that very something has just been called into question - of course this is the point Kant makes against those members of the Scottish School of Common Sense who objected to Hume's problem of Causation on the ground it was absurd). For instance if an Evolutionary Biologist or an Astrophysicist should divest Positivism of its 'pro-science' clothing and grasp that phenomenalistic solipsism mean that neither evolutionary development nor cosmic change occurred when they, the sole subject, were not perceiving it, and then claim that position utter madness and should be rejected, that response alone would constitute no proper objection.

Of course the knowledge experts in other fields possess may well give them a positive philosophical advantage: to stick with the Hume example if one was to claim along with the Treatise that Pure Mathematics is impossible due to epistemic reasons the theoretical mathematician may well reply with something to the effect that our ability to reason with abstract mathematical concepts such as Sets shows that Pure Mathematics is possible, ergo there must be a problem with the background epistemology that prompted the critic to make that denial: in this case though they have really left mathematical praxis behind and stepped into the arena as a philosopher in their own right.

Jeremy Taylor said...

Glenn,

What I mean is we can distinguish between the claim that there are no things like infinite numbers, rather than indefinite numbers from the claim that the term infinite used for other than God leads to confusion (in fact, Guenon could, without it being absurd or inconsistent, though not necessarily a good argument, make his claim about misuse of the term infinite, even if he didn't make the claim about no infinite numbers, because of the supreme importance he placed on the philosophy of all-possibility). Obviously, this latter claim is terminological, but the former one is conceptual.

I think, if Guenon is right about the fact that no infinite numbers and the like can exist, the use of the term infinite is a little improper, but I don't see such usage as that important. I just don't Guenon's objection to it as necessarily absurd or inconsistent, just not in the end necessary. I also don't think it is an especially important issue for us to keep discussing though. The issue of whether infinite numbers and the like can exist seems an exponentially more interesting topic (though my mathematical ignorance means I have little to say on it).

John West said...

Jeremy,

Of course, Guenon may be wrong about this, but if he were right [...]

I'm not quite convinced Guenon made the blunder he was accused of [...]

To me this is not really about jurisdiction or terminology but the truth of the claims about the indefinite and infinite, though I have little to say on that subject given my lack of mathematical knowledge.

Given your antecedents and qualifiers, I think lack of mathematical—definitely not total—knowledge is where we're getting hung up.

Many of your claims rely on the truth of your antecedents. People have argued and given examples against the truth of those antecedents. You respond that you're unable to reply to them due to lack of mathematical knowledge. I don't know what else to say. You seem to be choosing to tough it out for now on the basis of respect for Guenon, but I don't see how I can further add to the conversation.

Jeremy Taylor said...

John West,

I have retreated from defending much of Guenon's mathematical views. I was just defending Guenon from what I saw as a somewhat over-the-top attack on his claims about terminology. I don't think that particular defence requires more mathematical knowledge than I claim.

John West said...

Right. Okay. Thanks for clarifying.

Scott said...

@Jeremy Taylor:

"I think, if Guenon is right about the fact that no infinite numbers and the like can exist, the use of the term infinite is a little improper, but I don't see such usage as that important."

Well, that's a pretty big if, isn't it? Not only that, but it's precisely the if that you've repeatedly said you're not competent to judge.

At any rate the term "infinite" is not "improper" for what mathematicians mean when they use it; the term "indefinite" simply doesn't capture what they intend to say. A Euclidean line is infinite in length, not "indefinite." If Guénon thinks they're wrong to mean what they mean, then he really needs to engage their thought rather than just brush it off breezily with an inept comment or two.

Jeremy Taylor said...

Scott,

My point was not to judge whether Guenon was correct or not on that condition.

Jeremy Taylor said...

Well, I did think he had a point at the beginning of the discussion. But in the latter discussion I was just defending him against claims of inconsistency and absurdity as regards his terminological views based on his own perspective, though not necessarily agreeing with him. But, anyway, I'm not sure there is much more to be said on that score. It is not an especially interesting discussion anyway.

Scott said...

And I'm emphasizing that his views are not merely "terminological" even if he's right about transfinite numbers—and still less so if he's wrong. Indeed, whether he's right about transfinite numbers is itself a pretty substantive issue.

Glenn said...

Obviously, this latter claim is terminological, but the former one is conceptual.

It has been said that Guenon's "thought is essentially Shankarian" (though not exclusively so). One work for which Shankara is well-known is the Crest-Jewel of Discrimination. And we find in this work, or at least in a variety of English translations of it, that 'infinite' is used for something other than God (Atman, Eternal Self, Supreme Brahman, One without a Second, etc., etc., ad infinitum), and that, indeed, the term 'infinite' is attributed to things of our world. For example, Atman is compared to our infinite sky, the Eternal Self is said to be outside the infinite universe of the manifested world in which we live, the shining moon of our world is said to give infinite delight, and so on.

Jeremy Taylor said...

I agree his views are not just terminological.

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