Thursday, May 12, 2016

Aristotle, Searle, and computation in Nova et Vetera (UPDATED)


My article “From Aristotle to John Searle and Back Again: Formal Causes, Teleology, and Computation in Nature” appears in the Spring 2016 issue (Vol. 14, No. 2) of Nova et Vetera.  There is also a response to the article by Fr. Simon Gaine.  These papers were presented at the symposium on the theme What Has Athens to Do with Jerusalem? that was held at the Dominican School of Philosophy and Theology in Berkeley in July of 2014, and the issue contains all the other plenary session presentations (by Fr. Michael Dodds, Alfred Freddoso, John O’Callaghan, Fr. Michał Paluch, John Searle, Fr. Robert Sokolowski, and Linda Zagzebski), along with the responses to those presentations.

There is a lot of new material in my paper, and in particular a much more detailed analysis of the notion of computation than I’ve given elsewhere, and fairly extensive interaction with the literature on Searle’s argument for the observer-relativity of computation.  Here are the opening paragraphs of the paper, which will give the interested reader an idea of what’s in it:

Talk of information, algorithms, software, and other computational notions is commonplace in the work of contemporary philosophers, cognitive scientists, biologists, and physicists. These notions are regarded as essential to the description and explanation of physical, biological, and psychological phenomena. Yet, a powerful objection has been raised by John Searle, who argues that computational features are observer-relative, rather than intrinsic to natural processes. If Searle is right, then computation is not a natural kind, but rather a kind of human artifact, and is therefore unavailable for purposes of scientific explanation.

In this paper, I argue that Searle’s objection has not been, and cannot be, successfully rebutted by his naturalist critics. I also argue, however, that computational descriptions do indeed track what Daniel Dennett calls “real patterns” in nature. The way to resolve this aporia is to see that the computational notions are essentially a recapitulation of the Aristotelian-Scholastic notions of formal and final causality, purportedly banished from modern science by the “mechanical philosophy” of Galileo, Descartes, Boyle, and Newton. Given this “mechanical” conception of nature, Searle’s critique of computationalism is unanswerable. If there is truth in computational approaches, then this can be made sense of, and Searle’s objection rebutted, but only if we return to a broadly Aristotelian-Scholastic philosophy of nature.

The plan of the paper is as follows. The next section (“From Scholasticism to Mechanism”) provides a brief account of the relevant Aristotelian notions and of their purported supersession in the early modern period. The third section (“The Computational Paradigm”) surveys the role computational notions play in contemporary philosophy, cognitive science, and natural science. The following section (“Searle’s Critique”) offers an exposition and qualified defense of Searle’s objection to treating computation as an intrinsic feature of the physical world—an objection that, it should be noted at the outset, is independent of and more fundamental than his famous “Chinese Room” argument. In the fifth section (“Aristotle’s Revenge”), I argue that the computational paradigm at issue essentially recapitulates certain key Aristotelian-Scholastic notions commonly assumed to have been long ago refuted and that a return to an Aristotelian philosophy of nature is the only way for the computationalist to rebut Searle’s critique. Finally, in “Theological Implications,” I explore ways in which computationalism, understood in Aristotelian terms, provides conceptual common ground between natural science, philosophy, and theology…

UPDATE 5/20: Readers who use Project MUSE can get online access to my article and the rest of the articles from the current issue of Nova et Vetera

82 comments:

Anonymous said...

Speaking of nature, how are those books you are writing coming along?

Greg said...

Regarding O'Callaghan: His book is finally being re-released by the University of Notre Dame Press.

Anonymous said...

This looks like an awesome paper! Who says Aristotle is irrelevant to contemporary issues? So exciting.

Moonfall said...

Looks interesting. Any possibility the entire article will end up online?

Thursday said...

OT

I know that an artifact, like a knife, has its final cause imposed from the outside. It is purpose of the human mind that makes it the kind of thing it is.

But I am wondering whether a category like "hunting animal," which would include things like dogs and horses but not salmanders and gophers, would be considered an artifact as well, even though human beings have not have formed the dogs and horses into dogs and horses the way they may have shaped the metal of the knife blade.

As opposed to a category like "hunting animal," IIRC, a category like "mammal" would be a substance, with the final cause of its mammalness coming from within rather than being imposed from without.

----

It may not seem like it, but I'm trying to think through how all this works in relation to the categories of man and woman. There is a sense in which the modernist/postmodernist attack on essentialism is based on the idea that we can impose our own purposes on things; we can create them, in a sense. If I've got that right, there really are some things, such as artifacts, where that is true, at least to an extent (you can't make a knife out of jello). But that doesn't mean there are not other things that exist as themselves and do not require us to impose our purposes on them for them to exist.

In any event, it does seem that modern people seem to treat everything in the world as an artifact. This tendency may well be amplified by the fact that we live in an increasingly technological world where almost everything we interact with, except for other human beings, is an artifact of one kind or another.

-----

Anyway, I'm wondering what to call it if a person imposes a category on the world which is valid for his purposes, but does not correspond to a natural kind.

Justin Green said...

A "hunting animal" such as a pit bull or blood hound has final causes or tendencies that happen to benefit humans with respect to certain endeavors such as hunting or tracking.

It seems that something like a watch is more of an artifact than the use of the natural tendencies of a hunting dog. In hunting dogs, we take advatage of the already existent tendencies of those animals to a greater degree, whereas iron or brass or other metals have their natural tendencies much further removed from the purpose of keeping time.

To the extent we use a hunting dogs natural instincts and properties of being good at following scents and trails, it would not be an artifact. It just so happens that the natural tendencies of those animals also benefits certain human endeavors.

Thursday said...

It seems that something like a watch is more of an artifact than the use of the natural tendencies of a hunting dog. In hunting dogs, we take advatage of the already existent tendencies of those animals to a greater degree, whereas iron or brass or other metals have their natural tendencies much further removed from the purpose of keeping time.

But what about a fortuitously shaped stone that is used as a knife. It is our purpose that is making the thing a knife, even though we haven't actively done anything to shape the thing.

-----

Also, if its not an artifact, what do Scholastics call the kind of category that "hunting animals" is?

Brandon said...

By the nature of the term, and to avoid confusion, I think 'artifact' should be confined to things actually made by productive reason (which culminates in art). Hunting dogs and horses are living instruments of practical reason (which culminates in prudence). The knife example is actually handy here, since it is both artifact and instrument -- artifact in its being made, instrument in its being used.

Chris Lansdown said...

Is talking about software and computation in philosophy really more than a just-so story whose primary use is to give bad ideas the armor of a picturesque mental image? I ask this as a professional programmer who has never seen a software / computational philosophical argument myself.

Thursday said...

Brandon:

So, if you had a found object, a stone with just the right shape to be used as a knife, would that knife simply be an instrument? Or if you don't believe the knife thing, perhaps a found piece of wood that, without any modification, makes a nice club?

Am I correct that the final cause of both an instrument and an artifact is imposed from the outside.

What about things that are social conventions, like borders, or political offices such as President of the United States? How are those kinds of things classified in Thomism?

Are there any specific books or other resources you could point me to on these kinds of issues?

Brandon said...

(1) On the stone and the piece of wood -- in their use, yes, they would be instruments. If I've found them and do not use them as such, they are just natural substances with properties that could be useful for an instrument.

(2) On the final cause: the final cause of instrument may be either imposed from the outside or not. Your organs (like your hands, the 'instrument of instruments') are instruments that do not have their final cause imposed from the outside. (Although like any other physical thing they could have additional final causes imposed from the outside, e.g., if I grab your hand and hit somebody with it.) Their final causes are, as it were, imposed from the inside.

(3) On social conventions: a nice question. I imagine there's more than one way they can be considered (sometimes we just mean common actions), and I don't know that there is a standard position, but I think the way of doing so that's probably most useful for this context is this: insofar as we think of them as distinct from particular actions, they are artifacts of liberal art rather than (like the knife or club) of manual art. The point of the phrase 'liberal art' is to deal with the fact that some of the making-skills we have are geared to making things that serve no (immediate) purpose than the ends of reason themselves -- mathematical devices (the models of astronomy, the diagrams and proofs of geometry, the proportions and ratios of music, the calculations and calculating methods of arithmetic) and linguistic devices (the sentences of grammar, the discourses of rhetoric, the syllogisms of logic). I'm fairly sure that the best way to situate social conventions in the kind of context you have in mind, using only terms recognizably Thomistic, would be to see them as artifacts of rhetoric. (But I'm only piecing that together from things Aquinas says; it could be that there are nuances I am overlooking, and I don't know of anyone who has discussed it.)

Exactly how artifacts in this sense relate to artifacts like knives and clubs is a trickier question, and I'm not sure it's ever been discussed.

(4) Unfortunately, I'm not sure I know either any good books specifically on any of these concepts (artifact, instrument, liberal art) from a Thomistic perspective. Instrument is actually quite important due to the fact that Aquinas thinks of both divine providence and sacraments in terms of instrumental causation, but Aquinas is not really interested in the intellectual habit of art as such, and so the other two only come up in the context of other things, rather than as given any rigorous examination on their own.

I'm not sure at all why instrumental causation tends not to be discussed as such, given its importance, but you can certainly find articles dealing with it in various specific contexts. Sean Collins recommends de Koninck's Introduction to the Study of the Soul, but I only know bits and pieces of that work, so I couldn't say how useful it would be for your purposes in particular. (On the other hand, he does talk, if I recall, about the body as instrument, so that might indeed be useful for you.)

In short, the issues raise are things for which you can find relevant things in Thomism, but usually only dealt with in passing.

seanrobsville said...

@Chris Landown
All computational activities, software programs and programmable systems etc are reducible without remainder to a human artifact - the Turing Machine. The Turing Machine needn't be implemented as a physical mechanism, it's more of a mathematical construct or thought-experiment. But as the Turing Machine is a purely syntactical device, it makes you wonder where semantics comes from.

DNW said...

"If Searle is right, then computation is not a natural kind, but rather a kind of human artifact, and is therefore unavailable for purposes of scientific explanation."

That is the interesting question, isn't it. What does it mean to assert, and what is implied, when to the contrary computation is granted as a natural kind, or as an objective mind independent feature of reality.

I'm sure there has been a great deal in the way of the construction of firebreaks in anticipation of that problem.

Johannes said...

The subject of the implicit computational complexity of the operation of physical systems is connected to the issue of whether the explanation of quantum events by (ontic) random causation is acceptable for the purposes of the Principle of Sufficient Reason (PSR), because if the PSR requires deterministic natural causation for all physical events not directly caused by the free action of rational or intellectual beings, then one must hold that the correct interpretation of QM, i.e. the one which describes the operation of quantum systems as it really is, is Bohmian Mechanics (BM). (FWIW, I recently presented my view on this issue in the Classical Theism forum.)

A known issue with BM is the enormous additional computational work required for simulating the operation of a quantum system according to it in comparison with simulating its operation according to the Copenhaguen Interpretation (CI), as noted by quantum computing scholar Scott Aaronson:

"My conclusion is that, if you believe in the reality of Bohmian trajectories, you believe that Nature does even more computational work than a quantum computer could efficiently simulate—but then it hides the fruits of its labor where no one can ever observe it." [1]

This is so because, in BM, the evolution of a system is described by its "wave function", which evolves in Hilbert space according to Schrödinger's equation, plus a "guiding equation" whose arguments are the wave function and the coordinates of all the elements of the system. In other words, the coordinates (such as position and velocity) of each element of the system at each time are determined by a guiding equation which contains the coordinates of all the elements of the system plus the wave function of the system, which itself evolves in Hilbert space according to Schrödinger equation.

Therefore, if BM describes the way quantum systems really operate, then the mode of divine concurrence in the operation of quantum systems seems to be quite different from the mode of divine concurrence in the operation of systems described by General Relativity (GR), as the first case seems to involve a kind of direct divine guidance of events which is not present in the second. Because, if the elements of a system were blindfolded monkeys, in GR they would be just rolling down a slope while in BM they would be coordinately dancing a ballet. (To note, this speculative hypothesis of direct divine guidance, or conduction, of the elements of a quantum system is not occasionalism, because when a particle X bumps into a particle Y, X is a real cause of the changes in Y.)

Of course, we might just go Aristotelian and say that the tendency of quantum systems to evolve according to their wavefunction and guiding equation is just embedded, imprinted, or infused in matter. And I used the last equivocal term on purpose, because it highlights the danger present in this position: panpsychism, which is not just a purely speculative observation, as David Bohm himself flirted with panpsyquism (or fell into it, depending on how his statements are interpreted) [2].


References

[1] http://www.pbs.org/wgbh/nova/blogs/physics/2015/06/can-quantum-computing-reveal-the-true-meaning-of-quantum-mechanics/

[2] Bohm, D. 1986. “A New Theory of the Relationship of Mind and Matter.” Journal of the American Society of Psychical Research, 80(2), p. 131.

“It is implied that, in some sense, a rudimentary consciousness is present even at the level of particle physics”

http://www.iep.utm.edu/panpsych/

Thursday said...

Brandon:

It is an important topic, because it really is true that we, as humans, can create certain things by imposing our purposes on the world. We can give things their final cause. They exist in relation to our purposes. The problem is that this leads many people to assume that all categories are human made, and therefore we can make them as we will. I don't think that is true, but it is important to understand why.

I have been thinking of this article in particular:
http://slatestarcodex.com/2014/11/21/the-categories-were-made-for-man-not-man-for-the-categories/

Thursday said...

Anyway, my thoughts here are tangentially related to Searle, as he famously asserts the objective existence of things like money, which are at bottom social conventions.

Vincent Torley said...

Ed's paper on Aristotle, Searle and computation sounds interesting. Personally, I like Searle's "Chinese room" argument, but I've always been leery of his claim that computation, or syntax, is "observer-relative," and not an intrinsic feature of reality. If (per impossible) a calculator were to somehow assemble spontaneously in a lifeless cosmos and if something happened to press its buttons and made it calculate that 2+4=6, I would still call that a computation. Some replies to Searle's "computation argument" are briefly discussed here:

http://plato.stanford.edu/entries/chinese-room/

I'll be very interested to see how Ed resolves the arguments put forward by both sides.

I might add that "information" is not the same thing as computation, and that the word "information" has a multitude of senses. It seems absurd to deny that a DNA molecule contains information, as well as a digital code. There are important differences between a DNA molecule and the molecules in the paint on the wall (to use one of Searle's examples).

Re the distinction between things whose final cause imposed from the outside and things whose final cause is intrinsic to its nature, what about things which are made up of parts that have no natural tendency to come together spontaneously, but that have a natural tendency to stay together and function in a way that supports the stability of the whole, once they have been brought together by an agent? Couldn't they now be said to have a final cause which is intrinsic to their nature?

Jack said...

Quantum physicists say that certain subatomic particles seem to spontaneously come into existence. This seems to undermine our notion of cause and effect, but I'm wondering if this can't be used to support an Aristotelian metaphysics. If subatomic particles seem to come in and out of existence, does this not suggest that there is something "beneath" matter, organising it? Could it be that the substantial form of the substance is what causes these material particles to come into existence whenever it is needed?

Erich said...

@Johannes – very interesting stuff. I always come late to these exchanges – apologies.

May I ask a clarifying question, especially with regard to the post you linked to? It is this: under a truly non-deterministic interpretation of QM (i.e. setting aside the Bohm interpretation), why could the even Thomist most deeply invested in PSR not accept that one observation is made over another precisely because God is investing the universe with possibility from the outset – that the expression of possibility itself in creation explains the character of the quantum event? If strict determinism does not apply to the rational intellect, why must it apply everywhere else? In other words, if QM strongly suggests an interpretation of randomness, then PSR could be argued to demand an explanation of the randomness, not of which event actually occurred.

It's in such a related space, if I understand correctly, that arguments for panpsychism subsist (if mind is an aspect of sentient beings, why exclude it a priori from other kinds of being), as well as the connections proposed by some between the "freedom" of QM and the matter of free will. I don't (currently) subscribe to either of these positions, incidentally; I'm just trying to map out the territory.


pck said...

VT:
If (per impossible) a calculator were to somehow assemble spontaneously in a lifeless cosmos and if something happened to press its buttons and made it calculate that 2+4=6, I would still call that a computation.

A computation is a matter of specific, and thus intentional, symbolic manipulation according to some set of rules R (syntax). For a computation to take place, it is not enough for some part of the world to go through certain changes, even if these changes are in accord with R. Thus your claim amounts to the exact same thing as the Chinese Room actually being able to speak Chinese.

A calculation is a computation that has a defined meaning according to a goal, purpose, or interpretation (semantics). For example, I might calculate the intersection of two sets. This is more than a computation, as I interpret the formal steps I execute on paper to be about sets and set operations. No mechanical calculator has ever calculated anything. Only humans using mechanical calculators have.

Logically, syntax presupposes semantics, and semantics presupposes practice. In a lifeless cosmos -- one without practice -- there are neither semantics nor syntax. Thus there are no calculations or computations. The missing ingredients are intentionality and use.

It is a common error of modern thought to invert the hierarchy of syntax, semantics, and practice. To think that syntax comes first is as misguided as it is to assume that rules can mechanically generate meaning and ultimately even reality. The concept of a rule is not even intelligible without the concepts of intentionality and use. However, since syntax is far more easily analysed and formalised than meaning or practice, late moderns, especially after the arrival of the computer, have tended to gravitate towards the notion of the preeminence of syntax.

Erich said...

@pck & @VT

I basically agree with pck's recent post. But there is still a sense in which we can meaningfully characterize physical or mental systems as computational, even if only metaphorically, in a way that distinguishes them from other systems characterized in different ways. So while I agree that VT's "machine" in a lifeless cosmos does not actually compute, it would still be correct – and enlightening as to the character of the object – to describe it as an object with the potential to perform certain kinds of computation.

A less hypothetical example: in generative theories of the grammars of human languages, the grammar of a language L is described in terms of computational system, such that (I'm drastically simplifying here) for a given language L, the grammatical sentences/phrases/structures of L can be "computed," while ungrammatical arrangements of words cannot. This is not even a claim about whether or not the brain "chugs out" language in real time by way of "computation" (though many cognitive scientists go on to assume that it does): it's merely a way of characterizing what grammars are, in a way that distinguishes them from systems described by, say, differential equations, and that captures (what appear to be) their essential properties.

So it seems there is some productive "residue" left to the concept of "computation" which we can apply to non-intentional objects, even if as we properly assert that no actual computation takes place without intentionality. Would you agree?

pck said...

Erich:
So it seems there is some productive "residue" left to the concept of "computation" which we can apply to non-intentional objects, even if as we properly assert that no actual computation takes place without intentionality. Would you agree?

Yes, that "residue" is syntax. (Which is integral to the concept of computation and not accidental. The point is not to downplay the importance of syntax, but to give it its proper place in the hierarchy mentioned.)

pck said...

I would not call the residue "productive" though, since syntax in and of itself does not produce anything. Mathematics is done by mathematicians, not by its axioms. As you say, we apply the "residue" to non-intentional objects.

Timocrates said...

@ Jack,

Could it be that the substantial form of the substance is what causes these material particles to come into existence whenever it is needed?

That can't be as the substantial form of any material form does not exist and is therefore non-causal without its material basis.

@ Vincent,

Couldn't they now be said to have a final cause which is intrinsic to their nature?

Temporally, final causes for material forms typically precede the full actuality of the form. Vaguely speaking, the final cause of, say, a human being is just being an adult human being. Hence everything that happens to a child from conception through childhood through adolescence is explained by the inherent goal of becoming a man or adult human being.

Let's remember the principle of finality: every agent acts for an end. This is related to the principles of causality and sufficient reason. Remember also that in certain formulations the principle of identity can sound like a tautology but we know it is not. Finality is similarly basic and necessary. A monkey is a monkey because it is a monkey sounds like a tautology and indeed may be the incorrect answer to a question (which is a proof, actually, that there must be more than one kind of cause). It is the wrong answer if what is being sought is the efficient, material or final cause of the monkey. The answer isn't exactly wrong if the formal cause is being sought after; i.e., the question of what is it. Remember that form and actuality are on the same side of the column, so to speak. In a very real sense, the formal cause is ultimately more correct and answer to the why of a thing than its material cause, as the material cause is only potentially that thing. Wood is only potentially a wooden table.

Very often formal and final causes can seem almost identical, which is perhaps part of the reason why final causes might seem superfluous or redundant. But the end or goal is a starting point of explanation for a thing's coming to be and is causal before the form is. A house isn't a house until it is built, at which point it is no longer under construction; it is therefore incorrect to imagine that the as yet non-existent house could possibly be causal during the construction process. But the desire or need for a house is a causal factor in the house's coming to be.

Spontaneous existence of certain material things, then, can't be explained causally by reference to the substantial form. But if something sufficiently powerful to bring about just desires the substantial form for its own sake, then there is no problem.

Erich said...

@pck –

Thanks - yes, that makes perfect sense.

Of course, syntax does not "produce" anything; I meant "productive" only in the sense that it helps us get a handle on the essence of things. But for that very reason its "proper place" in the hierarchy is still a special place, it seems, one that semantics and intentionality adhere to, can be "applied to" (to use your words), with a curious naturalness...

Tony said...

I want to thank Vincent for his link to the stanford discussion on the Chinese Room. I used to be intimidated by professional philosophers, but it is completely obvious now that many of them are, not to put too fine a point on it, exceedingly clever, and DUMB. (The "exceedingly" is meant exactly: their cleverness exceeds useful and helpful bounds. Better that they were less clever, and had more common sense.)

pck said...

Erich:
Of course, syntax does not "produce" anything; I meant "productive" only in the sense that it helps us get a handle on the essence of things.

I would agree, except for the use of "essence". A dog essentially has four legs, but the number 4 does not belong to its essence. (Rather, it is an essential part of how we talk about dogs.)

But for that very reason its "proper place" in the hierarchy is still a special place, it seems, one that semantics and intentionality adhere to, can be "applied to" (to use your words), with a curious naturalness...

My point (and yours too, I believe) was that semantics and practice do not follow a syntax in the sense that they are generated by it. They adhere to a syntax because we sculpt syntax in order to accommodate the regularities we observe in nature. But this process cannot begin with syntax, it ends in it. Thus its place is at the bottom of the hierarchy, not at the top. Once the process of formal modelling is completed, we must resist the temptation to put the cart before the horse and declare the model to be what drives reality, or that its internal correlations are reflections of correlations in the world.

We therefore must resist Wigner's question about the "unreasonable effectiveness of mathematics". It's not unreasonable at all, because we specifically tailor the glove in a way to make it fit. If the axioms/syntax of set theory allowed for a proof that 1+1 equals 3, we would not think that we had been wrong about elementary arithmetic all along. Rather, we would change the axioms in such a way that 1+1=2 could be proved.

The effectiveness of math, including the fact that almost all humans agree on its results, is due to arithmetic abstracting from very elementary human abilities, such as being able to draw distinctions (between this and that), to learn to handle quantities, order, and so on. Elementary features of our common human nature give rise to similar ways of formalization. But we thereby do not discover human nature, we express it.

(Also, there is a lot of math which is not "effective" at all, a point which Wigner never addressed.)

pck said...

They adhere to a syntax because we sculpt syntax in order to accommodate the regularities we observe in nature.

I should add that this is true only of the syntax used in theories, not of the syntax of language in general.

pck said...

But we thereby do not discover human nature, we express it.

As for the question of nature in general (Wigner did not talk about human nature specifically), we discover nature by being in the world and exercising our abilities (=> practice), not by looking at syntax and reading the essence of the world off of it.

Johannes said...

@Erich

What you suggest in the first paragraph, that God may have created the universe so that randomness is an inherent feature of the behaviour of matter/energy, and not just an epistemic feature of human limitations, is fine with some Thomists, e.g. Prof. Alexander Pruss, but not with others, mainly out of their view of how divine concurrence works. BTW, I do not know Prof. Feser's position regarding this issue.

Now, if randomness if ontic, there is no room for panpsychism. The argument for pansypchism arises only in the Bohm interpretation, and even in that case is not really strong. Because the reasonable view of Bohmian mechanics is systemic Aristotelianism: it is the system as a whole which behaves according to the guiding equation and the wave function, and therefore it does not make sense to ask "how does one particle know where all the other particles are?". In that respect, to the problem of the mechanistic conception of nature that Prof. Feser has already pointed out in a number of works, we could add another problem: the isolationist conception of nature, the focus on isolated particles and not on the system as a whole. Conversely, we could say that the correct conception of nature is not just Aristotelianism, but systemic Aristotelianism ("systemic" not in the sense of the system of Aristotelian doctrines but in the sense of the system of matter-energy). This systemic approach, as I said in the forum, is apparent in the title of Bohm's posthumous book: "The Undivided Universe: An Ontological Interpretation of Quantum Theory" (Bohm & Hiley 1993).

Now, while this may be the correct approach in phylosophy of science, it is not so in practical science, due to our inherent observational and computational limitations. Therefore, even if (a hypothetical developed version of) Bohmian mechanics describes the operation of the universe as it really is, it makes sense for practical purposes to use the Copenhaguen or Relational interpretations of QM.

Erich said...

@Johannes – thank you for your references – just what I was looking for.

I'm afraid I don't follow your connection between panpsychism and the Bohm interpretation; it was not a connection I made or ever thought to make. Would you be willing to say more?

Panpsychism in the most general sense cares little for the particulars of any physical theory: the "essential assertion," as it were, is that all physical descriptions are in some way inherently associated with mind, and any real "thing" in one's ontology in some sense has mind, however exotica and unrecognizable it may be to us.

On the surface, then, since "randomness," or better, non-determinedness, would seem to point to a degree of freedom fundamental to nature, and since we must surely assert a similar degree of freedom in the mind of the rational animal, we have in "randomness" particularly friendly grounds for panpsychism. So it seems to me, but you strongly suggest otherwise. I'm very curious about this!

Erich said...

@pck – thanks for your comments. I think we agree on what were discussing. But your further comments puzzle me greatly!

I'm not convinced at all that the number 4 does not belong to the dog's essence. The dog is a kind of creature possessed of locomotion of a specific biophysical kind, and the four-ness of its limbs is surely an essential aspect of that biophysics, not simply to "how we talk about biophysics" – even allowing for very different theories of quadruped locomotion that might not mention the number 4. It is not for nothing that we call animals like dogs "quadrupeds" and humans (and chickens) bipeds.

Similarly, the convexity of the lens of the eye – another mathematical notion – is surely essential to the lens.

I may be missing something in your point.

Similarly, I don't see your point regarding Wigner; your example is not conclusive. If we had an axiomatization of set theory that proved 1+1=3, that would be neither here no there; the question would be whether the axiomatization was consistent or not, and how numbers themselves were interpreted (since ordinals and cardinals will need to be defined set-theoretically in the first place). There's nothing tailor-made going on here.

Similarly, we can axiomatize geometry to prove that the sum of the angles of any triangle must be 180 degrees, since this is a useful geometry to have; we can axiomatize otherwise to describe non-euclidian spaces in which the equation does not hold, and these too often prove to be useful (though they might not have); we can also axiomatize in ways that are not consistent all, and are thus worthless.

And your claim that the effectiveness of math is "due to arithmetic abstracting from very elementary human abilities, such as being able to draw distinctions (between this and that), to learn to handle quantities, order, and so on" is especially troublesome. Not only does this not "explain" the effectiveness of math, but you go on to say

Elementary features of our common human nature give rise to similar ways of formalization. But we thereby do not discover human nature, we express it.

How do you know enough about human nature to be able to say we do not discover it but express it? That we express it is not controversial; it is impossible for us not to. But you speak of "elementary features of human nature:" how do you know what they are, so that you can make any claims about, say, "formalization," if we are never capable of discovering them? If all of our statements about human nature are not really about what we have discovered about it (however accurately) but are nothing more than expressions of it, then they are utterly meaningless, and consistent only with the idea that there is no human nature – a rather foucauldian take on things, perhaps…

So perhaps we don't agree after all. When you say,

semantics and practice do not follow a syntax in the sense that they are generated by it. They adhere to a syntax because we sculpt syntax in order to accommodate the regularities we observe in nature. But this process cannot begin with syntax, it ends in it

you seem to be saying that syntax is mere a post-hoc description, sculpted arbitrarily in a way that says nothing about the essence of semantics, only of our ways of talking about observed regularities. That seems to me to be complete nihilism.

Johannes said...

@Erich

It's true that non-deterministic behaviour in matter is analogous to free will in human souls, as noted by Prof. Alexander Pruss in p. 168 of his book "The Principle of Sufficient Reason: A Reassessment".

http://books.google.com/books?id=8qAxk1rXIjQC

However, that analogy does not suggest that there may be mind in matter, because the non-deterministic events in question are quite basic: an unstable atomic nucleus breaks up now or in 10 seconds; an electron shows up here or there, etc.

In contrast, in Bohmian mechanics the deterministic behaviour of matter is highly coordinated, as the evolution of a system is described by the guiding equation, which contains the wave function and the coordinates of all the elements in the system, where the wave function evolves according to the Schrödinger equation in Hilbert space! It is this highly coordinated behaviour which prompted Bohm to flirt with panpsychism.

Try to see the difference between this behaviour and that described by General Relativity (GR). In GR, each particle moves according to the curvature of space at its location, and that's all. There's nothing fancy about balls rolling down a slope which may give a hint of panpsychism. Of course, the curvature of space depends on the positions and masses of all particles. But you cannot take space out of the picture and say that "a particle moves according to the positions and masses of all other particles" and wonder how the particle knows all the other particles' positions and masses.

In contrast, in Bohmian mechanics there is no physical entity that plays a mediating role similar to that of space in GR, because the wave function evolves in Hilbert space! So you can:

- go Platonic and say that the Hilbert space where the wave function evolves is real and is perceived by the minds of the particles, which then compute the guiding equation. There you are: platonism and panpsychism together, to the delight of Marsilio Ficino.

- or posit that God computes the wave function and the guiding equation and directly guides the evolution of the system.

- or go Aristotelian and say that QM-compliant systems of matter have a natural tendency to evolve according to a guiding equation which contains the wave function, so that both are just mathematical expressions of that natural tendency.

Erich said...

@Joahannes,

Thanks for your excellent reply. I'm going to familiarize myself with the Bohmian approach as well as I am able; I never got past college-level QM, and that was years ago, but we shall see.

In the meantime, I wonder whether there is still something to discuss.

The analogy between non-deterministic QM on the particle level and free will in human souls is exactly that: an analogy. The differences between an electron and, say, my aunt Katie are more than huge, but if we allow ourselves to simplify across this difference, we can call it a matter of coordination – as you point out.

Given that, I return to my previous point: if everything is deterministic at a fundamental level, it is difficult to see how determinism could fail to subsist in a coordinated system dependent on that fundament. Contrastingly, if the fundament is non-deterministic – even if perfectly random and uncoordinated – we can imagine in principle that more complex systems gain what we call the "freedom" of the soul through the coordination of their interacting elements.

So, run this in reverse: If "mind," to be what we can plausibly recognize as mind, will have a definite element of unpredictability and some degree of coordination, then a fundament that has even sheer randomness at their core would appear to allow mind to subsist quite generally, at whatever level of coordination we might come across. Very little coordination in an unstable nucleus about to discharge an alpha particle, perhaps – so, very little of what we call "mind" – but it becomes plausible that this is only a matter of degree, and that's all the panpsychist needs.

(Or, perhaps, this is not truly panpsychism, since coordination too is required, something not to be found everywhere – but how to define that?!)

Erich said...

@Johannes –

I seem to be on a misspelling spree, even with proper names I know well. Apologies!

Erich said...

@Johannes – or are you suggesting the quantum events themselves must be coordinated, "from within" as it were, rather than from above? If so then perhaps I see what you're saying above – but what would make that necessary?

Johannes said...

@Erich

There are several planes involved in your last comment, I mean the long one.

First, let me state clearly my position on panpsychism: it's BS. I mentioned it because it is the specific kind of BS that comes up when you posit that Bohmian Mechanics describes the behaviour of matter/energy as it really is. Therefore, if a Thomist adopts BM because its realism and determinism "soothes his ontological pains", he must be aware of the specific kind of BS which he must be able to refute.

Second, your speculation "that more complex systems gain what we call the "freedom" of the soul through the coordination of their interacting elements" is just emergent (or emergentist) materialism:

https://en.wikipedia.org/wiki/Emergent_materialism

Specifically, it looks like a kind of weak emergentism as held e.g. by Mario Bunge:

http://www.iep.utm.edu/emergenc/#SSSH2ai2

Now, while emergent materialism is clearly an accurate description of the "psyche" (or whatever you may call it) of a chimpanzee, pace David Bentley Hart, for a theist it is definitely not an accurate description of the human soul, which for a theist is spiritual and directly created and infused by God in each human body.

Moving on to your following paragraph, we have two scenarios depending on whether we posit that BM describes the behaviour of matter/energy as it really is:

QM interpretat. -- Behaviour at - Behaviour of complex systems
ontically true: -- micro level -- at macroscopic level

Bohmian Mechanics - Determinism - Epistemic indeterminism for human observers;
- real determinism for observers with unlimited
- observational and computational capabilities.

Copenhaguen or
Relational Interp - Indeterminism - Real indeterminism.

Let me state this clearly: in both scenarios the Copenhaguen/Relational Interpretation is operationally true, in the sense that it always makes the right predictions of the probability of observations.

Then, if you hold BM as ontically true, then you hold that events in the chimpanzee's brain are fully deterministic, so that a non-divine observer (i.e. an entity which does not directly see the future) could accurately predict the chimp's behaviour if he had unlimited observational and computational capabilites.

Now, since the human soul is inherently free in his decisions, a theist holding BM as ontically true must necessary hold that there is an ongoing violation of a physical law, specifically of BM, in the human brain, at least while the person is awake and thus taking free decisions.

I am quite aware of this issue because I discussed it a couple of months ago with a Thomist of the strict observance, who stated that there is no real violation of a physical law in this case, because physical laws apply only when there is no direct operation of spiritual substances on matter. Since the spiritual human soul operates directly on the human brain, the resulting evolution of physico-chemical events in the brain against the deterministic predictions of BM is not really a violation of a physical law, because the law does not apply in this case.

I will not link to the discussion because it was in Spanish.

Johannes said...

I forgot that the comment editor collapses leading spaces. In my intended formatting,

"- real determinism for observers with unlimited"
"- observational and computational capabilities."

should have been below, and aligned with:

"Epistemic indeterminism for human observers;"

i.e. under the heading "Behaviour of complex systems at macroscopic level".

Erich said...

@Johannes

Many thanks for your generous and detailed replies.

I too think panpsychism is BS; let that be clear. I am interested in how the thought of it comes about, in what "space" it becomes articulable, given some set of assumptions or experiences.

You suggest that the distinction between the animal psyche and the human soul is decisive here. But that is not clear to me. If the fundament bears within it a degree of freedom that does not admit of prediction, then every complexity built out of that fundament will have the potential to bear the same; this is really not any different than saying that if electric charge is a property of fundamental particles, we should not be surprised to find it in macroscopic objects.

What exactly does the human soul have, that everything else does not have, with respect to indeterminacy? And whatever it is, does it entail that, say, non-human animals are not sentient, have no mind? I would think not: sentience is surely.

So how far back are we allowed to go before "mind" must be removed? Protoplasm? Single-cells? Whirlpools and eddies? I don't see any limit here; the psychic would appear pervasive. Each form "organizes" the "jostles" of indeterminacy.

Your point concerning BM goes on to rely on the presumption that the human soul is possessed of a freedom of decision unavailable to the chimpanzee. I see now the logic of your position, for which many thanks. But do you actually think this qualitative distinction is real, and not just a matter of degree? If you do, and this difference is crucial to what we mean by imago dei, then aren't you breaking every relation, be it ontological or epistemological, between human freedom and the nature of creation?

That might rub a Catholic the wrong way. As Cardinal Ratzinger said in his Introduction to Christianity: "[A]t the summit stands a freedom that thinks and, by thinking, creates freedoms, thus making freedom the structural form of all being." Freedom is there from the start, from the first day, in everything.

Johannes said...

@Erich

"You suggest that the distinction between the animal psyche and the human soul is decisive here. But that is not clear to me."

I not only suggest, but state most definitely. It is not a matter of discussion for a theist and even less for a Catholic, as it has been defined by the Ecumenical Councils of Vienne and Lateran V.

"What exactly does the human soul have, that everything else does not have, with respect to indeterminacy?"

Regarding its substance, it's spiritual. Regarding its operational capabilities, abstract thinking and libertarian free will.

"And whatever it is, does it entail that, say, non-human animals are not sentient, have no mind? I would think not: sentience is surely."

Of course they are sentient, but whether they can be said to really have "mind" depends on the definition of "mind", which is outside the scope of this discussion. Being clear that this issue remains pending, I will refer to a chimp's "mind" below.

Now, when talking about determinism, we have to distinguish between physical and mental determinism. Physical determinism at the micro level may or may not be ontically true, depending on whether BM is true at the ontic level or not.

If physical determinism (BM) is ontically true at the micro level, then full determinism is ontically true for the chimpanzee's "mind", even though from our viewpoint the case is epistemic indeterminism.

If physical indeterminism (Copenhaguen/Relational) is ontically true at the micro level, then a certain degree of indeterminism is ontically true for the chimpanzee's "mind". How much a degree depends on how much the neural network compensates the randomness of individual quantum events at a synapsis.

"Your point concerning BM goes on to rely on the presumption that the human soul is possessed of a freedom of decision unavailable to the chimpanzee."

Exactly.

"But do you actually think this qualitative distinction is real, and not just a matter of degree?"

I most definitely "think this qualitative distinction is real, and not just a matter of degree".

"If you do, and this difference is crucial to what we mean by imago dei,"

It is.

"then aren't you breaking every relation, be it ontological or epistemological, between human freedom and the nature of creation?"

I assume that by "the nature of creation" you mean "the nature of purely material creatures", because human beings are part of creation. Having said that, I am certainly stating that human beings are at a qualitatively higher level than purely material beings.

(continues below...)

Johannes said...

(... continues from above)

"As Cardinal Ratzinger said in his Introduction to Christianity: "[A]t the summit stands a freedom that thinks and, by thinking, creates freedoms, thus making freedom the structural form of all being." Freedom is there from the start, from the first day, in everything."

Several points on this last paragraph:

1. "Introduction to Christianity" is a 1968 book of then-still-young Professor Joseph Ratzinger, not of Cardinal Ratzinger. In particular, its treatment of Christology has severe notes of heterodoxy, revealing a Theilardian influence.

2. In the passage you quote, Prof. Ratzinger is clearly assuming that the Copenhaguen/Relational Interpretation of QM is true at the ontic level.

3. If the assumption 2 is correct, then matter has "freedom" at the micro level. However, that is a blind kind of freedom, which cannot be compared to the freedom of intellectual creatures, which consists of freely choosing the good they understand with their intellect.

4. This higher-level freedom of human beings resides in the spiritual soul, and can be excercised irrespectively of whether the behaviour of matter has intrinsic randomness at the micro level or not. The difference is that, if the behaviour of matter is deterministic at the micro level, human free will requires frequent violations of physical laws in the human brain, at least while the person is awake and thus taking free decisions. While this is certainly not an elegant scenario, it is not metaphysically unacceptable.

Thus, human intellect-enlightened freedom neither is a property which emerges out of matter's blind freedom at the micro level, nor does it require such freedom, which, once more, is ontically the case iff the Copenhaguen/Relational interpretation is true at the ontic level.

Erich said...

@ Johannes -

I hope you find this exchange as interesting as I do! If not I won't feel offended if you need to move on to other things.

I said: "You suggest that the distinction between the animal psyche and the human soul is decisive here. But that is not clear to me."

And you replied "I not only suggest, but state most definitely. It is not a matter of discussion for a theist and even less for a Catholic, as it has been defined by the Ecumenical Councils of Vienne and Lateran V."

Well, I don't recall that the Ecumenical Councils or any other church pronouncement has had anything to about the matter of panpsychism! I did not say there was no distinction. I said that it was not clear that the distinction was decisive concerning where it is that mind is manifest in creation.

Yes, we are possessed of abstract thinking and libertarian free will. The question at hand is to what extent mind, or things bearing characteristics we are willing to call "mind" – especially both sentience (which, oddly, has not yet really been discussed by either of us, I now notice) and a thing's capacity to organize itself around a degree of freedom it may call its own – exists in the rest of the world of creation.

What does abstract thinking have to do with sentience? Neither Aristotle nor Aquinas denied animal life sentience. I can't imagine anyone who's ever had a pet dog or cat would say the creature was not sentient. Could this be "sentience without mind?" That seems an odd way of using the words. Perhaps only humans have "mind" but all sorts of things have "sentience…" We don't want to play with semantics that way.

So I can't agree that whether or not other creatures have "mind" or not is outside the scope of the discussion. It is the very heart of the discussion. Panpsychism understands "mind" to permeate the ontology of creation. So we need to be clear what we mean. My original point was that if mind properly requires a dimension of non-determinism, as we understand mind to have it in human existence, then a QM theory that sustains non-determinism at the most basic level of nature would allow, at least as far as non-determinism is essential to mind (if it is), a space for mind on all sorts of ontological levels. There may be other reasons to rule out "mind" at other levels, in other beings, and therewith to rule out panpsychism: but non-determinism per se won't be one of them.

So we do need to have some operative notion of mind if we really want to discuss the viability of panpsychism.

(cont'd)

Erich said...

@Johannes (cont'd)

Following on (as you echo the exchange), I say

"and this difference is crucial to what we mean by imago dei,"

And you say "It is."

So I reply, "then aren't you breaking every relation, be it ontological or epistemological, between human freedom and the nature of creation?"

And you say, "I assume that by the nature of creation' you mean 'the nature of purely material creatures', because human beings are part of creation. Having said that, I am certainly stating that human beings are at a qualitatively higher level than purely material beings."

So your answer to my question is affirmative: the "qualitatively higher level" of the human lies in his not being purely material, and furthermore, this does indeed break every relation, ontological and epistemological, between human freedom and our material aspect. Is that right? (I will express concern with that interpretation below.)

Finally, concerning Ratzinger:

1. You observations are duly noted, but I see nothing heterodox in the passage I quoted.

2. Correct me if I'm wrong, but I doubt that Prof. Ratzinger knew much if anything at all about the different interpretations of QM.

3. Whether or not your assumption in 2 is correct, I don't think it matters. Of course any freedom at the micro level will be "blind." The question is whether that freedom can be organized at successively higher levels of organization, and whether the capacity to do so is related to human freedom, and to imaginable intermediate levels of freedom in other simpler beings. If it can, then the panpsychist has grounds for saying, "See? Even 'freedom' of the will as we understand it has primitive reflexes elsewhere in being." If it cannot, than human freedom is entirely disjoint from non-determinacy at the micro-level. That smashes the dreams of the panpsychist who wants to see non-determinism of some kind everywhere he sees mind, to be sure. But it also disconnects the freedom of the human soul from its best conceivable analog in the material world: the non-determinacy of fundamental physical laws...

4. … which is what you suggest in 4, in fact. Whether the behavior of matter is deterministic or not, you are saying, human freedom has nothing to do with it; neither is dependent on the other – under either relevant interpretation of QM. I agree it's not an elegant scenario either way. But that's a big problem, I think. Our freedom has, then, no relation to the rest of creation, no real relation to our materiality. That is deeply dissatisfying, at least, even if metaphysically viable: if that freedom is essential and unique to us, why, then, were we made material creatures at all? How can we relate to the rest of material creation as free creatures? Why the Incarnation – Truth embodied – rather than a few choice spiritual words dictated by an Archangel or charismatic prophet? Why should we look forward to the resurrection of the dead?


Johannes said...

@Erich

"What does abstract thinking have to do with sentience?"

Obviously they are different capabilities, the first being higher than the second and revealing that the soul having it is of spiritual nature.

"Neither Aristotle nor Aquinas denied animal life sentience."

Neither did I. In fact, I can't see where this issue is coming from.

"So I can't agree that whether or not other creatures have "mind" or not is outside the scope of the discussion. It is the very heart of the discussion. Panpsychism understands "mind" to permeate the ontology of creation. So we need to be clear what we mean."

Of course we need to be clear what we mean by "mind", specifically whether it is restricted to abstract thinking or whether it includes the capabilities of a chimp, a dolphin, etc. But there are two powerful independent reasons why that clarification is outside the scope of this discussion:

1. The issue of whether self-aware animals, i.e. those able to pass the mirror test, or all mammals, or even all vertebrates, or even all (vertebrates + molluscs + arthropods) have "mind", has nothing to do with panpsychism.

2. I just don't want to get into that matter.

"this does indeed break every relation, ontological and epistemological, between human freedom and our material aspect. Is that right?"

Yes. Free will is something that humans have in common with angels, not with chimps.

"1. You observations are duly noted, but I see nothing heterodox in the passage I quoted."

Neither do I.

"2. Correct me if I'm wrong, but I doubt that Prof. Ratzinger knew much if anything at all about the different interpretations of QM."

On the contrary, I am almost certain he was familiar with the concepts of QM according to the Copenhaguen Interpretation. On the other hand, I am also almost certain he had not even heard of Bohmian Mechanics, which even today is just a curiosity for most physicists.

(continued below...)

Johannes said...

(...continuing from above)

"The question is whether that freedom can be organized at successively higher levels of organization, and whether the capacity to do so is related to human freedom,"

It is not.

"then human freedom is entirely disjoint from non-determinacy at the micro-level."

It is. The only role of non-determinism at the micro level is to make the physical implementation of human freedom, i.e. the interface between the spiritual soul and the physico-chemical processes in the brain, much smarter in both senses or the word, i.e. revealing of wisdom (of the Designer) and elegant.

"But it also disconnects the freedom of the human soul from its best conceivable analog in the material world: the non-determinacy of fundamental physical laws..."

Which is a lousy analog, because human freedom presupposes human intellect, which has no analogy at the physical micro level.

"Our freedom has, then, no relation to the rest of creation, no real relation to our materiality."

Exactly. As I said, our free will is precisely due to our soul being spiritual. We have it in common with angels, not with chimps.

"That is deeply dissatisfying, at least, even if metaphysically viable:"

It is deeply satisfying to me, but of course, satisfaction is in the eyes of the customer.

"if that freedom is essential and unique to us, why, then, were we made material creatures at all?"

Because otherwise we would be angels.

"How can we relate to the rest of material creation as free creatures?"

It exists just for our good. Which of course includes the good of future human generations, so let's take care not to screw things up.

"Why the Incarnation – Truth embodied – rather than a few choice spiritual words dictated by an Archangel or charismatic prophet?"

For two reasons, depending on whether there was human sin to be atoned or not.

If there had been no human sin to be atoned for, it would have still been fit that the Logos would assume a human nature and not an angelic nature, because angels can see humans but humans cannot see angels.

With human sin to be atoned for, it was necessary that the Logos assumed a human nature given the divine design that He would satisfy for our disobedience.

"Why should we look forward to the resurrection of the dead?"

Because the human soul has not been created to be apart from a body. We are not "angels trapped in flesh".

pck said...

Erich:
the four-ness of its limbs is surely an essential aspect of that biophysics, not simply to "how we talk about biophysics"

So according to you, "four-ness" is a property of the dog's legs? Do any three of them then have the property of "three-ness"? And is this three-ness somehow inferior to the four-ness of them all?

This kind of reification is very common and leads into all sorts of confusions. We speak of mathematical "objects", and forget that we are not dealing with objects at all, but with rules of transformation (e.g. in arithmetic).

It is not for nothing that we call animals like dogs "quadrupeds" and humans (and chickens) bipeds.

It's definitely not for nothing. Language is what differentiates us most from any other species on the planet. Note your own use of "call" here.

If we had an axiomatization of set theory that proved 1+1=3, that would be neither here no there;

Which is why we would reject the axiomatization.

the question would be whether the axiomatization was consistent or not

We would reject it even if its consistency could be proved.

and how numbers themselves were interpreted (since ordinals and cardinals will need to be defined set-theoretically in the first place). There's nothing tailor-made going on here.

Except it is, because we have a pre-formal notion of arithmetic which is not up for debate. Thus, numbers defined as by set theory are not an interpretation of our pre-theoretic notions. Rather, set theory *must* deliver what our pre-formal notions say.

But you speak of "elementary features of human nature:" how do you know what they are

By looking at common elementary schemes of explanation in our language(s). If you doubt that the ability to draw distinctions is an elementary feature of human nature, I can't help you. The evidence for that is contained in almost anything we do and say.

you seem to be saying that syntax is mere a post-hoc description, sculpted arbitrarily in a way that says nothing about the essence of semantics, only of our ways of talking about observed regularities. That seems to me to be complete nihilism.

Obviously, syntax and semantics cannot be separated completely, so syntax is not "post-hoc". Rather, it is "cum-hoc". It is created in practice, together with the semantics. (Practice still being logically prior to semantics and syntax.) That syntax is arbitrary is neither hard to see nor does it pose any problems. I suppose you have noticed that there is more than one language being spoken on the planet. Also, note that I added that the remarks in my earlier post are only true of theories, not of all language.

The inference to nihilism is a bit ridiculous, and particularly puzzling coming from someone with naturalistic tendencies.

Erich said...


@Johannes -

Thanks again for your comments. I hope you understand that my replies are exploratory exercises!

The whole first part of your reply shows that we have quite different ideas of what panpsychism is. As I understand it, panpsychism affirms the existence of "mind" not only in human beings but throughout the universe in objects of potentially any kind, "mind" being a fundamental feature of the universe. If by "mind" we mean exactly the features of human mind, then it is obviously false, since even our closest living animal relatives do not share in our capacities for abstract thinking, as far as we know, and neither does anything else.

So as you say, it is quite important to be clear about what we mean by "mind" if we're going to talk about panpsychism, about which you and I have been making claims vis-a-vis fundamental physics. If sentience is involved, then what sort of things are sentient has everything to do with panpsychism. Similarly if the ability to behave non-deterministically is necessarily involved in mind.

Can you tell me what you mean by panpsychism in the first place? I fear I am missing a significant kernel of what you're suggesting.

The same goes for "free will." I agree we share it with the angels, but is there nothing of it in the apes? What do you mean by it?

* * *

I didn't make myself clear about Prof. R's knowledge of different interpretations. I meant only that I doubt he was particularly advised on the matter of there being different interpretations, and as you say, it is certainly the Copenhagen interpretation, which is the most "popularized," so to speak, that he'd be following.

Your first "It is not" is ambiguous. Do you mean "That is not the question," or, if freedom can be successively organized at higher levels of organization, then "the capacity to do so is not related to human freedom"?

(cont'd)

Erich said...

@Johannes (cont'd)

I said: "then human freedom is entirely disjoint from non-determinacy at the micro-level."

And you replied, "It is. The only role of non-determinism at the micro level is to make the physical implementation of human freedom, i.e. the interface between the spiritual soul and the physico-chemical processes in the brain, much smarter in both senses or the word, i.e. revealing of wisdom (of the Designer) and elegant."

This too is a bit unclear to me, but one way of reading it asserts what I'm suggesting: that the spiritual soul, incarnate as it is in the physico-chemical processes of the brain, is not incidentally related to indeterminacy at the micro-level, but deeply related to it by an elegance of design.

The analogy is not lousy. Of course, "human freedom presupposes human intellect," as you say. Likewise, freedom at the micro-level presupposes lack of intellect: hence it is random. But freedom is fascinatingly and surprisingly there at both extremes. I find it hard to imagine there is no relation there.

Then I say, "if that freedom is essential and unique to us, why, then, were we made material creatures at all?"

And you reply: "Because otherwise we would be angels."

Well, yes, but we are not angels, we are specifically material beings, and that is so essential that for Thomas, we are not at home without our bodies, even as our souls pass beyond our physical dissolution. As you say, "the human soul has not been created to be apart from a body. We are not 'angels trapped in flesh'." If the flesh does not trap us, then materiality itself must has as much room for our human freedom as it has for our size and shape. Our materiality expresses us – and conversely. Isn't QM, then, almost a vindication of the well-suitedness of materiality to the freedom of the human spirit?

Doesn't it show us that freedom is indeed a principle of Being, in the created world as in all Being (pace Ratzinger) – right on down to the "dry" mathematical equations – allowing us to understand human being as its apotheosis?

Erich said...

@pck –

Many thanks for your replies, both thoughtful and thought-provoking.

You ask: "So according to you, 'four-ness' is a property of the dog's legs? Do any three of them then have the property of 'three-ness'?"

Well, no, of course. I was talking about the locomotion of the dog, a very complex coordination of physical parts (including legs, muscles, nerves, brain), its need for balance, for forces exerted against the ground, and so on – the coordination of all these to provide the animal with its particular power of locomotion. There is "fourness" in that, not in the arbitrary collection of limbs.

I don't know what would be gained by looking at just three-out-of-four legs of a dog, other than some arbitrary desire to count to three!

"And is this three-ness somehow inferior to the four-ness of them all?"

Yes, since "three legs" is just an arbitrary collection of limbs, and doesn't provide any insight into the way the animal moves of its nature.

* * *

As for our discussion of set theory, you are right to the extent that we seek to axiomatize a system that can provide us with the natural numbers, and our concepts of arithmetic operations – which we are interested in "pre-theoretically." But we can axiomatize all sorts of systems, depending on what we're interested in doing. Category theory has a quite different agenda, for example. We indeed might be interested in other axiomatizations that deliberately violate our pre-theoretic intuitions, to see where they lead.

Not only that, but a particular axiomatization that seemed to accommodate our pre-theoretical notions might lead us to all sorts of violations of of those notions – and the history of set-theory has surely proven that it does. It was a goal at one point to guarantee the simultaneous consistency of arithmetic and of the completeness of all true statements of arithmetic, but that turned out to be provable impossible. No "re-axiomatization" (that doesn't emasculate the system entirely of its expressive power) is possible.

(cont'd)

Erich said...



@pck (cont'd)

Another example: the existence of measure that could not be captured as ratios of intgers was also "not up for debate" in the ancient world, and the proof of the irrationality of the diagonal of a unit square was quite troubling. There was no re-axiomatization" to be had.

But now we accept such quantities without trouble. There is, in fact, no such thing as the purely "pre-theoretical" in these domains. There may be a sort of pre-theoretic "universal grammar" of possible intuitions, but – whatever that may be – until actual experience with counting, with math, with geometry, comes along, there is no "pre-theory."

To that extent I think you're absolutely right to invoke the notion of practice.

* * *

I hardly doubt that "the ability to draw distinctions is an elementary feature of human nature." Is this a human ability not shared by other natures? If it is not shared, then, you allude to something distinct about human nature. Is that distinction real, or simply a reflex of our ability to draw distinctions?

As a linguist, one of my chief concerns has been the diversity of languages spoken on the planet, and how their diversity converges with their invariance to tell us something about human nature. As far as that goes, the syntax of human languages is hardly arbitrary – yet that does not pose any problems either, not for this discussion. Of course we are talking about formal theory.

I apologize if my comment about "nihilism" came off as an accusation! It's just that it seems to me that to see all of our formal endeavors as expressions only of our minds, our axiomatizations as "nothing but" designs that suit our pre-theoretical prejudices, then we preclude the possibility of discovery; our "life world" of practice and experience then becomes strangely self-enclosed. Does that make sense?

Erich said...

@pck –

One more question, if you'll indulge me: what gives you the impression that I have "naturalistic tendencies?" It genuinely concerns me that I might have made such an impression.

Johannes said...

@Erich

I'm leaving the conversation, answering just a specific question.

> Your first "It is not" is ambiguous. Do you mean "That is not the question," or, if freedom can be successively organized at higher levels of organization, then "the capacity to do so is not related to human freedom"?

I meant the second option.

Erich said...

@Johannes –

thank you for the conversation.

pck said...

Erich:
I was talking about the locomotion of the dog, a very complex coordination of physical parts [...] There is "fourness" in that, not in the arbitrary collection of limbs.

Ok, but how exactly is the number four a property or part of the dog's locomotion? Saying "the dog has four legs" is not to predicate "fourness" of it or its movements. (Neither is "swiftness".)

Even in cases where numbers are predicated of the body of an animal, they reference techniques of measurement and do not indicate a presence of number(s). "He is 6 feet and 2 inches tall" does not mean that his body contains 6 instances of a foot and 2 instances of an inch. My height depends on the shape of my body, but my body does not cause its height. In other words, my body does not stand in any relation to my height. (The same is true of my body and my soul. My soul is not my body's soul, even though it depends on my body. You discussed this earlier with Johannes.)

But we can axiomatize all sorts of systems, depending on what we're interested in doing. [...] We indeed might be interested in other axiomatizations that deliberately violate our pre-theoretic intuitions, to see where they lead.

I agree, but the latter cannot happen for natural numbers and their arithmetic. If such a violation (1+1=3) occurred in a formalism F, we would no longer call F's domain "the natural numbers". At best, we can have equivalent ("isomorphic") formal systems of natural numbers. What makes two systems F and F' isomorphic is that we can put them to the same use. This is usually expressed in a homomorphic (= structure-preserving) 1-to-1 mapping between F and F'. But it is not existence of the mapping that makes F and F' isomorphic. The mapping only expresses the isomorphism formally.

Now this way of putting things -- "F and F' are isomorphic and a certain expression formally captures this relationship" -- very easily leads to the (misguided) idea that the "real" isomorphism is "out there" in the world and our formalism is a logical picture of it. But what is out there is not some intangible object which relates F to F'. Rather, what is out there are transformatory practices. The number 4 is not a part of the dog, its legs or its locomotion. It is part (*) of our practice of counting, and ascribed to dogs, not discovered in or of them. (Although I can discover that *this* dog does in fact have the usual number of legs we expect a dog to have.)

(*) "Part" is not to be understood in the sense in which a door is a part of a house. It means that the term "four" is used in certain acts we call "counting".

Category theory has a quite different agenda, for example.

All of mathematics, including a model of the natural numbers, can be constructed from the axioms of category theory. You're right that CAT was invented for different reasons. But none of this pertains to our question whether we invent or discover the natural numbers.

pck said...

Not only that, but a particular axiomatization that seemed to accommodate our pre-theoretical notions might lead us to all sorts of violations of of those notions – and the history of set-theory has surely proven that it does.

It hasn't with respect to natural numbers and their arithmetic. The stranger bits of set theory all derive from the attempt to formalize the concept of infinity; the concept of a "completed" or "actual" infinity, to be more precise. But we don't need a concept of actual infinity to do finite arithmetic. Tarski showed that we don't even need a concept of infinity in order to formalize the concept of finiteness. (A set M is Tarski-finite iff every subset of the powerset of M has a minimal element with respect to inclusion. It's possible to derive a (provable, non-axiomatic) principle of induction from this definition.)

Regarding concepts of (actual) infinity, it is true that pre-theoretical notions may fail us, and that is mostly because we try to extend notions that work for finite sets to infinite sets without checking whether the extensions in question retain sense. Which is tough to do since we do not have the hands-on experience with infinity that we have with finite concepts. In math, once you go (actual) infinite, the existence quantifier is robbed of its connection to human experience. In short, you lose your semantic anchor(s) and begin dealing in purely formal extensions and analogies. (This notably happens in the construction of irrational numbers.)

It was a goal at one point to guarantee the simultaneous consistency of arithmetic and of the completeness of all true statements of arithmetic, but that turned out to be provable impossible.

Well, the consistency of arithmetic is in fact provable if you accept a certain (very intuitive) principle of induction -- see "Gentzen's consistency proof". Completeness in Gentzen's system is not an issue either. Contrary to a wide-spread belief, one cannot use Gödel to put a lid on this topic once and for all.

To this day there is no agreement among mathematicians and logicians about the meaning of many of the results of proof theory. Which, for the reasons given above, is not a surprise. But all of this is somewhat beside the point with regard to simple statements such as 1+1=2. As long as we stay finite, there are no consistency (or completeness) problems.

pck said...

the existence of measure that could not be captured as ratios of integers was also "not up for debate" in the ancient world, and the proof of the irrationality of the diagonal of a unit square was quite troubling. There was no re-axiomatization" to be had.
But now we accept such quantities without trouble.


"Acceptance" in mathematics is often simply a matter of ignoring problems. In calculus, topology, and algebra I accept the Axiom of Choice, since without it many theorems become rather awkward and ugly. But some of the consequences of AC are so counterintuitive (e.g. the Banach-Tarski paradox) that they immediately call into question the ability of the real numbers to "describe reality". However, without AC, it is impossible to prove a number of very intuitive and useful theorems.

Some modern mathematicians do not accept irrational numbers, the chief reason being that nobody has managed to give a proper formal extension of arithmetic to them. It's no problem to topologically "complete" the rationals, but it's another thing to define the operations of addition and multiplication on this new set. You'll find no textbook which gives an explicit constructions of those. They silently switch to axiomatics for that. This is the unresolved dirty secret of the irrationals.

There is, in fact, no such thing as the purely "pre-theoretical" in these domains.
There may be a sort of pre-theoretic "universal grammar" of possible intuitions, but – whatever that may be – until actual experience with counting, with math, with geometry, comes along, there is no "pre-theory."
To that extent I think you're absolutely right to invoke the notion of practice.


I'm very skeptical about universal grammar, but otherwise that was my point exactly. And where there is no pre-theory to a formalism F, there can be no semantics which connect F to the semantics of ordinary everyday language. For example, there is nothing in the rules of chess that suggests what chess can or should mean to us. The rules of chess are arbitrary impositions on the chessboard and pieces. (But once they are fixed, we have nonetheless generated sense and thus meaning, e.g. of the expression "check-mate". It's just that the meaning of chess does not automatically connect to other areas of meaning in our lives.)

Syntax does not have a unique form, and there is lots of syntax the semantics of which is a matter of decision, not of discovery.

So in situations which do have a "pre-theory", can we read the "essential features of reality" off of syntax in those? No. It is like trying to read the taste of a cake off of its recipe.

pck said...

The meaning of 1+1=2 is established together with learning the syntax of it. The meaning is immanent in practices in which we speak of a transformation of "1 and 1" into "2" or vice versa. We do not learn what "1" means independently of what "2" means and then *discover* that 1+1 actually equals 2. All arithmetical concepts, numbers, addition, equality are learned simultaneously. Our understanding of arithmetic is in this sense holistic. It is anchored in reality because we apply it, not because reality contains numbers, addition and equality, or things corresponding to them.

Because we learn how to add in practice, within the stream of life, we cannot deepen, only widen, our understanding of it (the practice, not the formalism) by focusing on its formalized rules and relations. The formal consequences of those rules are what they are. Since they bear no relation to reality (just like the cake recipe bears no relation to the cake's taste), we cannot hope to learn anything about the world by looking at a formalization of addition in a disconnected game on paper. Particularly not if we extend the formalism beyond any means of practical connection with the world (irrational numbers). In the latter case we can only hope that certain formal consequences will have a "real-world application". But theorems like the Banach-Tarski paradox show that is not always possible. Even in much simpler cases, we need to be selective in order not to clash with "real-world" sense. (We can extend the domain of natural numbers to the integers, but we cannot extend the concept of the length of a body to include "negative lengths".)

pck said...

I hardly doubt that "the ability to draw distinctions is an elementary feature of human nature." Is this a human ability not shared by other natures? If it is not shared, then, you allude to something distinct about human nature. Is that distinction real, or simply a reflex of our ability to draw distinctions?

An ability could be shared by other natures and still be elementary to humans. It doesn't have to be exclusively human to be distinctly human. "Elementary" just means that it is an ability which cannot be reduced to more basic ones and that it is a necessary ingredient of what it means to be human.

If we accept that it is correct to say that we have an ability to draw distinctions, then that ability is real.

The relation between reality and the distinctions we draw using language is orchestrated in language, not "out there in reality". What counts as "real" (a word which is said in many ways), is determined by how we talk, by rules of representation in language. Whether a "distinction is real" is a conceptual question which cannot be decided empirically. To adjudicate such a question, a normative context must be in place. But a normative context can only exist through certain practiced regularities, and these are what make talk of reality possible in the first place. (Practiced regularities are of course in a sense arbitrary. But this does not imply metaphysical relativism or philosophical nihilism.)

As a linguist [...]

Ok, that explains a lot. (My degree is in math, but I minored in linguistics.) Linguists look for meaning in different ways than philosophers of language do.

one of my chief concerns has been the diversity of languages spoken on the planet, and how their diversity converges with their invariance to tell us something about human nature. As far as that goes, the syntax of human languages is hardly arbitrary

When I say "arbitrary" I don't mean that no regularities in syntax are necessary. Clearly, there could be no communication without certain established linguistic norms and normative contexts. What is arbitrary are the details of these regularities and it is for this reason that syntax gives us no clues with respect to essence. Essence is immanent in the use of syntax. Hence the emphasis on practice. Syntax is a necessary precondition of essence, but it does not reveal essence through its internal relations (grammar). Syntax shows essence in an external sense, through its use within practices ("grammar" in the Wittgensteinian sense).

I'm extremely skeptical with regard to the quest for universals in grammar. Cultural progression across history will produce similar grammatical patterns in certain groups of languages, but a universal grammar, particularly one embedded in our brains as advocated by Chomsky, I regard as a philosophical error (see for example "Computers, Minds and Conduct", 1995, by Graham Button, Jeff Coulter, et al).

I apologize if my comment about "nihilism" came off as an accusation!

No worries, it didn't. I certainly do not deny that there is meaning in the world. I just locate it in a different "place" (it's not literally a location) than you do.

pck said...

It's just that it seems to me that to see all of our formal endeavors as expressions only of our minds, our axiomatizations as "nothing but" designs that suit our pre-theoretical prejudices, then we preclude the possibility of discovery; our "life world" of practice and experience then becomes strangely self-enclosed. Does that make sense?

Yes. My position may not be equal to yours, but its much closer than the "nihilistic" one you describe. I'm not saying that formal endeavors are "nothing but the arbitrary expression of concepts" (although they do have that aspect). I agree that such a notion would indeed be vacuous (and circular). It is precisely because I think that meaning comes into the world via practice that "mere expression" is ruled out here. But for the same reason it does not follow that we can recover meaning or essence just from looking at our expressions. (Just like it is not possible to recover taste from a recipe. The taste of a cake depends on the recipe, but taste and recipe do not stand in any causal relation.) We don't have pre-theoretical prejudices about math, we have concrete practices of counting, ordering, etc., which involve both linguistic and non-linguistic actions. These are neither right nor wrong (and in this sense, they are arbitrary), rather, they provide the framework which makes (arithmetical) judgements of right and wrong possible in the first place. Arithmetic is thus not a formalization of (a part of) the scaffolding (an inherent order) of the world, but part of a net we cast over the world to make it intelligible. (Language use is thus the source of facts and intelligibility. Of course the world has its say in that, but as the ground of the possibility of practices, not as a prescriber of what can be said to be "real".) It is part of a linguistic coordinate system which constitutes the framework that establishes *sense* (again, this happens through practice -- the emphasis is on actions, not on any internal rules of language -- formal endeavour are indeed endeavours).

In short, "1+1=2" does not *say* anything about the world. Rather, it is part of how we cope with the world, which includes how we talk about it. "1+1=2" is a rule of language (but not an internal one). The application of it (its use in practice) *shows* something about the world -- namely how human beings classify and use distinctions and quantities. By reflecting on our use of language we may gain greater perspicuity with regard to our linguistic practices and thus new knowledge. (This is where discovery occurs.) The symbols "1", "2", "+", etc., do not point to anything "out there". Rather, the pointing is immanent in the use of the expressions. (If we change their use, we change what they point to and create new meaning.)

pck said...

One more question, if you'll indulge me: what gives you the impression that I have "naturalistic tendencies?" It genuinely concerns me that I might have made such an impression.

Let me start by saying that I never thought you were a naturalist. It was just that some of your remarks struck me as possibly steering towards mistakes commonly found in naturalism, such as the number 4 being somehow "out there" in or with the dog's legs, or the reductionism in the discussion of quantum physics (explaining "the mind" from the behaviour of matter (*), concluding that that isn't possible, and then jumping to a Cartesian picture (**) of a "spiritual soul" independent of matter altogether). I have naturalistic tendencies myself, because my thinking used to be almost exclusively scientific (I started out in physics), even though I knew there had to be something wrong with it when it came to explaining human abilities and behaviour. I couldn't quite put my finger on what exactly was wrong with it though. So I minored in linguistics because I thought that my questions, at least in part, had their origins in how we use words. That hunch turned out to be correct, but it was not until I began studying Wittgenstein that I was able to properly distance myself from naturalism.

(*) You: "The question is whether that freedom can be organized at successively higher levels of organization, and whether the capacity to do so is related to human freedom"

(**) Johannes: "[...] the interface between the spiritual soul and the physico-chemical processes in the brain [...]" (there can be no such interface -- this Cartesian picture contradicts his later remark that the human soul is not created independent of the body)

pck said...

The taste of a cake depends on the recipe, but taste and recipe do not stand in any causal relation.

This should read "causally efficient relation".

pck said...

Likewise, "My soul is not my body's soul" should be amended by "in the sense of efficient causation". I tend to say "cause" when I mean "efficient cause". Naturalistic tendencies are hard to get rid off.

grodrigues said...

@pck:

I do not wish to dive in the main discussion, so just a couple of relatively minor quiblings.

"It's no problem to topologically "complete" the rationals, but it's another thing to define the operations of addition and multiplication on this new set. You'll find no textbook which gives an explicit constructions of those. They silently switch to axiomatics for that. This is the unresolved dirty secret of the irrationals."

I am not sure what you mean by this, but it is *not* difficult to extend the arithmetic operations from the rationals to the irrationals. I can sketch it for you; although it does take a fair number of pages (one of the reasons why many books switch to simply give axioms for the real number system; the other being that the target audience would be unable to digest the construction) several books do it. There is no "dirty secret" going on, much less an "unresolved" one.

"Particularly not if we extend the formalism beyond any means of practical connection with the world (irrational numbers)."

Since the square root of 2 is the length of the diagonal of a square with unit side, it is hardly the case that irrational numbers are "beyond any means of practical connection with the world".

Anonymous said...

"(**) Johannes: "[...] the interface between the spiritual soul and the physico-chemical processes in the brain [...]" (there can be no such interface -- this Cartesian picture contradicts his later remark that the human soul is not created independent of the body)"

No Cartesian picture and no contradiction there. He said that "the human soul, [...] for a theist is spiritual and directly created and infused by God in each human body." If it is spiritual, there must be a way whereby it interacts with the physico-chemical processes in the brain. Call that way "interface" and you are set.

See, there are several such interfaces even between different systems of the body.

pck said...

grodrigues said...
I am not sure what you mean by this, but it is *not* difficult to extend the arithmetic operations from the rationals to the irrationals. I can sketch it for you

You can add and multiply Dedekind cuts (or alternatively equivalence classes of neighbouring Cauchy sequences)? Great. You don't have to sketch it, a reference to a text book will do.

Since the square root of 2 is the length of the diagonal of a square with unit side, it is hardly the case that irrational numbers are "beyond any means of practical connection with the world".

When are where exactly have you ever come across a perfect unit square? ("In my thoughts" does not count as an answer. I said practical connection for a reason.)

pck said...

Anonymous:
He said that "the human soul, [...] for a theist is spiritual and directly created and infused by God in each human body." If it is spiritual, there must be a way whereby it interacts with the physico-chemical processes in the brain. Call that way "interface" and you are set.

How is that not a fully fledged substance dualism?

pck said...

@grodrigues:

You're probably thinking of something like this:

https://www.math.brown.edu/~res/INF/handout3.pdf

But this will of course not satisfy a constructivist.

laubadetriste said...

@grodrigues:

Apropos of nothing on this post, thanks for your earlier Tim Maudlin recommendation. Some of the geometrical concepts are above my pay grade, but it's fascinating. :)

Erich said...


@pck:

Thanks for your incredibly robust and lengthy comments! Replying point-by-point would probably take more time than I have and you deserve – but I suspect our differences come down to a few key matters, and may not quite be what we thought they were. I'll pull a few points out and we'll see where that goes.

* * *

I don't have a biophysical theory of quadruped locomotion, of course. But that four legs are involved would appear to be elemental to any decent account of it. If you ride a horse, the rhythm of its gait comes in fours; you can hear it. As a biped, when I run I know full well the "twoness" of my contact with the earth. It is essential to my nature. Were I to lose a leg I'd feel somehow imperfect.

The comparison with measures of height is not apt. "Feet" and "inch" are arbitrary units of measure. Numbers associated with them do not inhere in the nature of what they measure. But our having two legs, and the dog's and horse's having four, do inhere in the nature of us creatures.

What about the number "three"? Is "threeness" not crucial to our Christian understanding of a triune God?

* * *

(I'll skip much of what you go on to say, in the hope that your having said it is implicit in the above and the below; correct me if I'm wrong!)

Your points concerning mathematics seem to revolve strongly around the necessity that the natural numbers be "captured," somewhere along the line. Well, yes, but so much mathematics has so little to do with them!

And experience too has not everything to do with them. Take irrational numbers: you refer to their "construction" as one case of "purely formal extensions and analogies," in which one's "semantic anchors" are lost. But they're not lost. They are reconfigured. I have seen triangles drawn on the page, I have seen the Pythagorean Theorem, I have seen lengths that are demonstrably not rational. The "construction" of irrational numbers is not purely formal: it is in fact something closer to what you've been defending: a way of accommodating my concept of number to a formal system, on the basis of experience.

* * *

(cont'd)

Erich said...

@pck

* * *

I don't mean to use Gödel as a trump card. (I'm totally with you on its abuse!) I mean it only as an example, one of many, to show that formal systems surprise us. They show us something. Their consequences, too, become a part of our experience of the world.

Do you, personally, really reject irrational numbers?

* * *

Yes, we learn how to add "in practice." We learn everything in practice. But I am confounded by your claim that the formal consequences of rules and relations "bear no relation to reality," for two reasons: 1. formal consequences" are themselves a part of reality, and 2. we have no a priori reason to expect that every formal system will bear on reality, and thus no reason to claim that those that do not (such as "negative lengths" of physical objects) in any way throw the connection into doubt.

* * *

You said: If we accept that it is correct to say that we have an ability to draw distinctions, then that ability is real.

Agreed! But I didn't make my point well; it slipped by your reply. My point was this: if we believe that any reasonably "formal" statement we make about reality must always already be "axiomatized" to accommodate it, and thus says nothing "real" beyond out own capacity to axiomatize, then isn't your claim about human nature itself (whether shared by other beings or not) already so axiomatized? It seems to me you pull the rug out from under you. What makes it "correct to say that we have an ability to draw distinctions?" Your criteria will have to be your own "axioms." And if having axioms is nothing but our own predilection, then we're lost in infinite regress.

(cont'd)

Anonymous said...


@pck

* * *

I'm a pretty staunch adherent to the Chomskian notion of Universal Grammar; my linguistic work has been in that field. I think it's scientifically as robust as it gets – though I certainly don't agree with Chomsky on many related issues. I don't think the matter has much to do with this discussion, but I'd be happy to discuss it with you in some other forum if you're interested! We have had different experiences with linguistics as a field. (I too started out in physics, by the way.)

* * *

We agree completely that no recipe, no "syntax," confides meaning. Meaning is practiced, it is lived.

But when you say, "In short, "1+1=2" does not *say* anything about the world. Rather, it is part of how we cope with the world, which includes how we talk about it," you remove our "coping with the world" from the world. No! Reason is a part of logos; "1+1=2" is as much a part of it as the trees outside my window, as my love for my beloved. They are all about something.

* * *

Thanks for your comments on (my apparent) naturalism.

My comments to Johannes were merely attempts to clarify what relation he saw between various interpretations of QM and panpsychism. So when I said (as you quote) "The question is whether that freedom can be organized at successively higher levels of organization, and whether the capacity to do so is related to human freedom," I was positing a question that I expected him to have a good answer to; his answer was of no use. (Personally, I find it rather cool that QM might suggest a basic indeterminacy to the way things might turn out in the universe! Perhaps free will is at home here after all!)

Thanks to your description of your own history I see what you mean by "naturalistic tendencies." I suspect we have both encountered the limits of naturalism in different ways, with respect to language: for me, it has been by pushing a Chomskian picture to its limits, for you it has been through a Wittgensteinian picture that would critique Chomsky.


grodrigues said...

@pck:

"You can add and multiply Dedekind cuts (or alternatively equivalence classes of neighbouring Cauchy sequences)? Great. You don't have to sketch it, a reference to a text book will do."

Landau's "Foundation of Analysis" has all the details from the natural numbers to the complex numbers (via Dedekind cuts). The hardest part is the definition of multiplication. Mendelson's "Number systems and the foundation of analysis" is another reference. The construction with Cauchy sequences is, imho, much more natural but off the top of my head, I do not know any textbook reference. The catch here is that you cannot simply borrow the results of metric spaces (especially the universal property of the completion) as they rely on already having the real numbers on hand. But otherwise, it is a perfectly doable, albeit laborious, task. Both constructions are important because they generalize in different directions.

"When are where exactly have you ever come across a perfect unit square?"

So by "means of practical connection with the world" you meany the literal existence of perfect squares? Then I misunderstood you.

"But this will of course not satisfy a constructivist."

This is a different kettle of fish, depending on the constructivist strictures you impose yourself. Bishop has done a lot of analysis in a constructivist setting, and topos theorists (Banaschewski, Mulvey, etc.) have been making progress since the 1970's.

pck said...

@grodrigues:

The construction with Cauchy sequences is, imho, much more natural but off the top of my head

Yes, I agree. Although proving simple things like every positive real number having a square root is a tremendous amount of work. (I have very little experience with Dedekind cuts, I don't suppose it gets simpler.)

The catch here is that you cannot simply borrow the results of metric spaces (especially the universal property of the completion) as they rely on already having the real numbers on hand.

Right. The nice thing about Cauchy sequences is that they turn the problem (of not necessarily having limits) into a solution in a rather straightforward way.

This is a different kettle of fish, depending on the constructivist strictures you impose yourself.

But that was what I was talking about. *Explicit* constructions of addition and multiplication. A Dedekind cut (A,B) consists of two infinite sets of rationals. A concrete instance of a D-cut needs some algebraic expression(s) to define it, such as q^2 < 2 for the square root of 2. But there are only countably many such expressions, since they are finite strings constructed from a finite amount of different symbols. However, there are uncountably many irrationals. Thus almost every irrational cannot be given or characterized explicitly. (Hermann Weyl compared this situation to "paper money" with no gold in the bank to back up its value.)

Thanks very much for the references to Bishop and the topos theorists.

From https://en.wikipedia.org/wiki/Errett_Bishop#Quotes:
Bishop described what he perceived to be a lack of "meaning" in classical mathematics, a condition he described both as "schizophrenia" and a "debasement of meaning", and expressed the sentiment in 1968 that its demise is "very possible".

I wouldn't go as far as calling it "schizophrenia" -- and I don't think classical math needs to go away either -- but the problem of meaning is exactly what I was concerned with in my original post.

pck said...

@grodrigues:

So by "means of practical connection with the world" you meany the literal existence of perfect squares?

Yes, my point was simpler than I may have made it sound. We learn to count in "practical connection with the world" with no references to formalisms. (We initially have no use for these, just like a child learning to say "mom" and "dad" has no use for a dictionary explaining these words.) Practices of counting and ordering thus remain our semantic anchors, even later on when we learn to use formalisms and theories. (We could of course learn those as purely formal games of symbol manipulation. But then we could not talk about meaning at all and mathematics would be exactly like chess. I often use the example of botanists not being able to afford not to know what a tree is, even though the word "tree" nowhere occurs in botany.)

The construction with Cauchy sequences is, imho, much more natural but off the top of my head

Yes, I agree. Although proving simple things like every positive real number having a square root is a tremendous amount of work. (I have very little experience with Dedekind cuts, I don't suppose it gets simpler.)

The catch here is that you cannot simply borrow the results of metric spaces (especially the universal property of the completion) as they rely on already having the real numbers on hand.

Right. The nice thing about Cauchy sequences is that they turn the problem (of not necessarily having limits) into a solution in a rather straightforward way.

This is a different kettle of fish, depending on the constructivist strictures you impose yourself.

But that was what I was talking about. *Explicit* constructions of addition and multiplication. A Dedekind cut (A,B) consists of two infinite sets of rationals. A concrete instance of a D-cut needs some algebraic expression(s) to define it, such as q^2 < 2 for the square root of 2. But there are only countably many such expressions, since they are finite strings constructed from a finite amount of different symbols. However, there are uncountably many irrationals. Thus almost every irrational cannot be given or characterized explicitly. (Hermann Weyl compared this situation to "paper money" with no gold in the bank to back up its value.)

Thanks very much for the references to Bishop and the topos theorists.

From https://en.wikipedia.org/wiki/Errett_Bishop#Quotes:
Bishop described what he perceived to be a lack of "meaning" in classical mathematics, a condition he described both as "schizophrenia" and a "debasement of meaning", and expressed the sentiment in 1968 that its demise is "very possible".

I wouldn't go as far as calling it "schizophrenia" -- and I don't think classical math needs to go away either -- but the problem of meaning is exactly what I was concerned with in my original post.

pck said...

Erich:
But that four legs are involved would appear to be elemental to any decent account of it.

Yes, I'm not denying that. In fact I explicitly affirmed it earlier, when I said that the number four essentially belongs to how we talk about dogs. What I deny is that the number four can be treated like a thing or object in the world. It's connected to reality through our use of it, not because it's a name for a Platonic idea "out there".

The comparison with measures of height is not apt. "Feet" and "inch" are arbitrary units of measure. Numbers associated with them do not inhere in the nature of what they measure.

An example of what I meant would be to lay out 6 rulers, each one foot long, to measure a length of 6 feet. It is in this way that the number 6 figures in the practice of measuring. Yes, measures are arbitrary in a sense which is quite obvious. But once a practice/norm of measuring has been fixed, the practice is real and thus my height really is 6 2". With respect to an established norm, the data 6 2" is no longer arbitrary.

What about the number "three"? Is "threeness" not crucial to our Christian understanding of a triune God?

I'm not actually a Christian, but that is not important here. What I was alluding to was not about whether the number 3 figures in important ways in how we think and talk. It does, and clearly so. (But it doesn't do so all by itself. You have to specify 3 of what you are talking about.) My question was about the status of the expression "the number 3" and whether it allows for reification as "threeness". And I don't think it does. We can still use the term "threeness", but should regard it as a metaphor for possible transformations of propositions. There is no property of threeness in God (or anywhere else), even for those who understand God as a trinity. Nor can you have a dog with its four legs and separate the legs from the number of the legs.

Your points concerning mathematics seem to revolve strongly around the necessity that the natural numbers be "captured,"

I would say "formalized" instead of "captured". One of my points was that the notion of "capturing" easily misleads one into reifying mathematical "objects".

Well, yes, but so much mathematics has so little to do with them!

True, but everything in mathematics starts out with the practice of counting. Eventually we go beyond it and that's where we lose the semantic connection to our experience. This is not inherently bad, but important to keep in mind when we go on to claim that nature is in some way "essentially mathematical" (which I think lacks sense).

pck said...

I have seen triangles drawn on the page, I have seen the Pythagorean Theorem, I have seen lengths that are demonstrably not rational.

Right, but you have not literally seen any lengths. You have come across practical and formal notions of length within practical and formal systems. In formal systems there are practices of symbolic transformation, perhaps inspired, in part, by geometric drawings. You can relate these formal notions to the world because you have previous knowledge of practices of counting, measuring, etc. The formalisms "speak" to you only because of these previous experiences. Thus they *say* nothing about the world in and of themselves. It is only against a previously established background of practice and experience that they mean more to you than, say, the rules of chess do.

The "construction" of irrational numbers is not purely formal: it is in fact something closer to what you've been defending: a way of accommodating my concept of number to a formal system, on the basis of experience.

The starting point for the construction of irrationals is rooted in experience, and so is the formalism of the natural numbers. But nobody can construct actual infinities or an infinite decimal expansion (or experience or measure it). We have to characterize irrationals using finite, algebraic means. And these are problematic, since there are too few of them (see my post in answer to grodrigues above). Most irrationals are conjured into "existence" simply by allowing ourselves to talk about elements of a set we cannot explicitly describe. The reason why we can expect not to run into too much immediate trouble with them is that their "construction" involves a formal extension of the notion of addition. "Infinite sums" cannot literally be carried out, but they can be understood as the limits of sequences of finite sums. It's a bit like having raspberry and strawberry flavoured candy and adding a fantasy flavour called "zoolberry". Zoolberry is just like any other flavour, except nobody has ever tasted it. Also, the store is always out of zoolberry and they can never order it, because they cannot describe it to their candy supplier, who would need a description or recipe in order to make zoolberry candy. Other than that, they are perfectly confident zoolberry "exists", because they have no problem imagining selling and eating zoolberry candy. It does not logically clash with the two actual ones.

formal systems surprise us. They show us something. Their consequences, too, become a part of our experience of the world.

I agree, but my point was that 1+1=2 *says* nothing about the world. It's not a factual statement. Rather, it shows how we divide the world up using mathematical language.

(Btw, if a formal system surprises me, then that is always a sign that I haven't fully understood it yet.)

Do you, personally, really reject irrational numbers?

There doesn't seem to be much of a choice between me rejecting them and me, personally, really, rejecting them. Kidding aside, it's not that I get sick whenever I write down "sqrt(2)". More kidding aside, I reject the idea that irrational numbers are on the same level as the naturals with regard to their meaning. Irrationals stand in a similar relation to the natural numbers as the technical terms of a theory stand in relation to the terms of ordinary ("naturally learned") language. For example, I may experience kinetic energy, but I cannot experience E_kin=1/2*m*v^2. (Which is not to be confused with experiencing the calculation of E_kin.)

pck said...

But I am confounded by your claim that the formal consequences of rules and relations "bear no relation to reality," for two reasons: 1. formal consequences" are themselves a part of reality, and 2. we have no a priori reason to expect that every formal system will bear on reality, and thus no reason to claim that those that do not (such as "negative lengths" of physical objects) in any way throw the connection into doubt.

X can depend on Y without standing in a relation to it (like the taste of a cake stands to the cake recipe). That's why I explained that by "relation" I mean a causally efficient connection. The shape of my body doesn't efficiently cause its height, but of course my height depends on the shape of my body. But I cannot read the existence of "heights" off of the shape of my body. I have to introduce a practice of measuring to get heights. Since *I* introduced the practice, I cannot automatically claim that I have discovered heights. Just because measuring and using heights "works", I cannot deduce that heights metaphysically existed before I invented the measuring practice. (They may have, but I would need additional arguments to show that.)

So I cannot read what the world is like off of the syntax I use in formal systems. Our formal systems are practices of "measuring" -- of dividing up -- the world, using language.

isn't your claim about human nature itself (whether shared by other beings or not) already so axiomatized? It seems to me you pull the rug out from under you. What makes it "correct to say that we have an ability to draw distinctions?" Your criteria will have to be your own "axioms." And if having axioms is nothing but our own predilection, then we're lost in infinite regress.

As I said, the relationship between reality and the truth or falsity of our propositions is orchestrated in language, not in reality. "In reality" being a meaningless term until we have created normative practices (involving language, but not only language), which constitute the meaning of "real" in a given context (I deliberately avoided saying "which define what 'real' means" here, because the definition of a word requires a previous mastery of language and is thus restricted to theories -- normative practices (including linguistic ones) by contrast don't need (formal) definitions, if they did, language could never get off the ground). The criteria for saying "the wall is really red" and "he can really drive a car" are categorically different. "Being real" -- attributing "reality" -- does not come down to a single, homogeneous process or notion. At the bottom of it, there are no axioms, only regularities of human actions and abilities. These make criteria possible, but nothing makes it correct to say that "we can draw distinctions". Rather, we introduce regular uses of the expression "to draw distinctions" in our speech (alongside non-linguistic actions).

The idea that there must be something (a fact F) in the world which makes the proposition P(F) true is another reification and an epistemically useless one at that, because we can then ask "What makes it true that whenever F obtains, the proposition P(F) is true?". And then we are truly lost in a regress. (This is part of the reason why Wittgenstein said that philosophy should not attempt to theorize.) So does this mean there are no facts in the world? No. It is just that facts are immanent in our use of factual language instead of being language-external targets of propositions which are their logical pictures. (Consider that it does not add anything to a proposition P if we say "it is true that P". To assert P is the same as to assert the truth (or "factuality") of P.)

pck said...

I'm a pretty staunch adherent to the Chomskian notion of Universal Grammar; my linguistic work has been in that field. I think it's scientifically as robust as it gets – though I certainly don't agree with Chomsky on many related issues.

It is certainly to Chomsky's credit to have brought scientific methods to linguistics. It's not that I think that linguists should stop looking for common properties in different languages. But even if universals were found in grammar, it would at best show something about certain technical restrictions humans are subject to as users of language. It would be similar to looking at how the tongue can move and concluding that certain restrictions apply to the forms of utterances. Inhowfar this would allow conclusions with regard to the content of what we say is unclear to me.

But when you say, "In short, "1+1=2" does not *say* anything about the world. Rather, it is part of how we cope with the world, which includes how we talk about it," you remove our "coping with the world" from the world. No! Reason is a part of logos; "1+1=2" is as much a part of it as the trees outside my window, as my love for my beloved. They are all about something.

I think that's the naturalistic tendency talking again. I don't see how coping with the world is "removed from the world", when it is precisely the application of 1+1=2, not the mere uttering of it, which gives it its meaning. Where is this abstract "fact" 1+1=2 and how can it give meaning to "1+1=2"? Nobody has ever experienced the "naked fact" 1+1=2.

When you say "Hello!" in a greeting, what is that about? Is there a metaphysical greeting out there somewhere that your utterance refers to (is about), which *makes* it a greeting?

Personally, I find it rather cool that QM might suggest a basic indeterminacy to the way things might turn out in the universe! Perhaps free will is at home here after all!

To be sure, if determinism was true, then there could be no free will. Indeterminism does not logically imply free will, it merely leaves room for it. But I don't think that free will can be explained from laws of physics, deterministic or not. The view of physical laws as generative operations is one of the biggest sources of philosophical confusion. I think we're much better off looking at physical laws as constraints on what *can* happen instead of as "commanding" what *must* happen. Thus we free ourselves from the spectre of materialism and exclusively reductive explanations.

grodrigues said...

@pck:

"Although proving simple things like every positive real number having a square root is a tremendous amount of work."

Yes, but this is pretty much inevitable. If you are dabbling in foundations, then you cannot appeal to a library of already proved results. What you do have, at this late stage of mathematical history, is your experience as a mathematician with the abstract theories that formalize the type of reasonings you have to make (abstract theories themselves motivated by their more or less concrete examples). When confronted say, with constructing the reals from the rationals, an algebraist will say to himself something like "Want to add the limits to all Cauchy sequences. So start with the set of Cauchy sequences; prove it is a ring for the pointwise operations; prove that the subset of null sequences is an ideal; then prove it is maximal; etc. and etc. Easy peasy."

For the specific case you mention, probably just easier to first prove the intermediate value theorem and then that the function x |-> x^2 is continuous.

"But that was what I was talking about. *Explicit* constructions of addition and multiplication. A Dedekind cut (A,B) consists of two infinite sets of rationals. A concrete instance of a D-cut needs some algebraic expression(s) to define it, such as q^2 < 2 for the square root of 2. But there are only countably many such expressions, since they are finite strings constructed from a finite amount of different symbols. However, there are uncountably many irrationals. Thus almost every irrational cannot be given or characterized explicitly."

There are different questions here. If the reals are defined by Dedekind cuts, then addition of reals just is an operation on Dedekind cuts and it is as explicit as you could wish it. The fact that a countable language only has a countable set of distinct names to name things is a different question altogether, and I do not quite understand why anyone should be bothered by that. After all, a countably infinite language is as much a "mathematical fiction" as an uncountable one -- the big jump is from finite to infinite, not from countably infinite to uncountable. If you already stomach sequences, you should have no qualms swallowing sequences of sequences, and it is well known that a large chunk of (classical) mathematics, including much of real analysis, can be done in (fragments of) second order arithmetic.

If on the other hand you are homing in on the fact that only a countable set of real numbers is computable, once again that is a different, mathematically valid question, and only a problem if you insist on some very strong form of constructivity. And one should remember that constructivism has its own share of "misgivings". To mention just two, on the Brower topos every real function is continuous and on the effective topos every (total) function on the natural numbers is recursive. I imagine that seen from a certain angle, this is as "paradoxical" as Banach-Tarski.

pck said...

grodrigues:
Yes, but this is pretty much inevitable. If you are dabbling in foundations, then you cannot appeal to a library of already proved results.

I know, I wrote my master thesis about different concepts of finiteness.

There are different questions here. If the reals are defined by Dedekind cuts, then addition of reals just is an operation on Dedekind cuts and it is as explicit as you could wish it.

I should perhaps restate that the context from which the debate evolved was about the question of what an existence quantifier signifies.

By "explicit" I mean that the existence quantifier should be "semantically abused" as little as possible, given that natural number arithmetic is not understood to be a purely formal game like chess, but inspired by our pre-formal abilities to count, add, etc. One question was whether we should be surprised that math has so many successful applications (unlike chess). Some claim we should take this as a hint that the world is in some sense "mathematical in nature", but I think that is false, or rather, nonsensical, given Wittgenstein's ideas about how meaning is created through the use of language. The whole issue is a non-issue if we ignore any connections which mathematical formalisms have to practices outside of mathematics.

When I said there was a dirty secret about the irrationals, I didn't mean that the formalism of Dedekind cuts left something to be desired in and of itself, but that, because of its characteristics, it is a lot harder to ontologically and epistemically map onto "real-world" practices (like actual measurements) than the natural numbers or even the rationals are. Conceptually, the worst part may be that the continuum in classical mathematics is always a point-set. Nevertheless I am told that the "real world contains irrationals". To even begin to make sense of such a statement, something like Weyl's "werdende Folge" (emerging sequence) may be needed, and with those we are headed towards finitism and Brouwer's concept of the reals (which are no longer a point-set and can better represent a "connected" continuum).

After all, a countably infinite language is as much a "mathematical fiction" as an uncountable one -- the big jump is from finite to infinite, not from countably infinite to uncountable.

Well, fiction or not, it's still a lot easier to contemplate a countable infinity than it is to think of an uncountable but well-ordered one. How much goes on between the cardinals aleph0 and c depends on the model of ZF, so it's not as if the only big hurdle is to introduce infinity and it's all smooth sailing from there.

To mention just two, on the Brower topos every real function is continuous

Actually, not every real function, but every function whose domain is the whole of R.

I imagine that seen from a certain angle, this is as "paradoxical" as Banach-Tarski.

If one doesn't understand intuitionist logic, it's not just paradoxical but completely incomprehensible. It's a wholly different kind of "paradox" compared to B.-T., which merely tricks the intuition by leaving and returning to the domain of measurable sets without calling attention to it.

Anonymous said...

@pck:

Sorry for the delay, I've been traveling. Hope you're still there. Here's what I've got for you!

What I deny is that the number four can be treated like a thing or object in the world. It's connected to reality through our use of it, not because it's a name for a Platonic idea "out there".

How is the number four any different from any other ascription, then? How is the word "dog" any different? These are both concepts we use when we talk about the world. Does a dog lack "dogginess" any more than it lacks "fourness"? If not why not? And if so, and you really mean that our language is entirely a code of our own with no capacity to reflect essences of things, why believe there are essences of things? (This is what smacks of nihilism to me.)

We could not, after all, ever really point to things, since every pointing would be nothing but the expression of our code for them.

* * *

Mathematics may start out with the practice of counting (though this is debatable), but no more than it starts out with the practices of seeing, naming, drawing, identifying, and so on. Many practises and intuitions are involved here. If you believe that mathematics expresses concepts like number only by virtue of our pre-theoretic affinity toward number, and that therefore number is not a property to be found in the world but only in our use of it, then the same goes for shape, identity, constructability – indeed every way you can think of that we ascribe properties to things.

* * *

Most irrationals are conjured into "existence" simply by allowing ourselves to talk about elements of a set we cannot explicitly describe.

Well, two objections: 1. We can explicitly describe them, as the Greeks did, without appeal to sets at all; 2. If you don't think even the natural numbers "exist" as aspects of (mind-independent) reality, then the irrationals hardly suffer from being merely "conjured" into existence by the mind; even the natural numbers are "conjured," from your perspective; they're just there, given by the human mind "doing its thing," and even the set-theoretical system we use to formalize them is axiomatized in such as way as to yield the desired results, i.e. it too is conjured into existence.

* * *

Your comment that "if a formal system surprises me, then that is always a sign that I haven't fully understood it yet" makes my point: it is there to be understood. It surpasses your experience of it. It is not a function of your practice: your understanding of it is a function of your practice, which is constrained by it.

* * *
(cont'd)

Erich said...

@pck
(cont'd)

* * *

I cannot read the existence of "heights" off of the shape of my body. I have to introduce a practice of measuring to get heights. Since *I* introduced the practice, I cannot automatically claim that I have discovered heights. Just because measuring and using heights "works", I cannot deduce that heights metaphysically existed before I invented the measuring practice.

Well, dig a little deeper. You cannot read the existence of "shape" off of your body either, by your logic. You have to introduce the practice of discerning shapes. Since *you* introduced the practice, just because the idea of shape "works" does not mean you can deduce that "shapes" metaphysically existed before you invented the various concepts of "shapes." Shape, like number, is just an artifact of the human mind, right? This is my point above: it is not only number that begins in the human mind (through the practice of counting), but every concept we apply.

So we can go a level deeper: what is this "body" of yours that would have a shape or a height to be ascertained? There is only some practice of discerning bodies, by your logic, from which we cannot conclude their metaphysical existence. Bodies too are artifacts of the mind.

And we can continue: What about other minds? Should we recognize their existence? Or do they only exist in our practice of discerning them, and are not metaphysically prior?

* * *

the relationship between reality and the truth or falsity of our propositions is orchestrated in language, not in reality. (etc.)

How can any orchestration, in language or anywhere else, not be "in reality?" Language is a part of reality. Your claim swings both ways.

At the bottom of it, there are no axioms, only regularities of human actions and abilities.

You empiricist, you! :-) If that's the case, then we don't really ever understand anything in a principled way. Except, curiously, what lies at "the bottom of it" all: that there are no axioms. Of course, what it meant by "regularities of human action" is unclear unless we have some criterion of regularity. If it is a numerical notion, then any regularities, for you, will be artifacts of the human mind, and not real aspects of human action and behavior.

* * *

But even if universals were found in grammar, it would at best show something about certain technical restrictions humans are subject to as users of language. It would be similar to looking at how the tongue can move and concluding that certain restrictions apply to the forms of utterances.

I think you've captured it quite well. We are innately subject to certain "restrictions," i.e. fundaments of linguistic structure, around which – and by virtue of which – particular syntactic patterns emerge in different languages. A theory of Universal Grammar shows us what that fundamental structure is in human cognition (which is what's meant by "universal"). It says nothing about the use of language, about reference or meaning. It is quite like looking at the shape of the tongue, in that respect.

I would differ with you only in asserting that universals have certainly been found; there's no "if" here.

Inhowfar this would allow conclusions with regard to the content of what we say is unclear to me.

It makes no conclusions with regard to the content of what we say.

* * *

I've got to stop writing – apologies for not addressing everything, and thanks for your discussion! More soon, I hope.