Wednesday, July 24, 2013

Fifty shades of nothing


Note: The following article is cross-posted over at First Things.

Nothing is all the rage of late.  Physicists Stephen Hawking and Lawrence Krauss have devoted pop science bestsellers to trying to show how quantum mechanics explains how the universe could arise from nothing.  Their treatments were preceded by that of another physicist, Frank Close (whose book Nothing: A Very Short Introduction, should win a prize for Best Book Title). New Scientist magazine devoted a cover story to the subject not too long ago, and New Yorker contributor Jim Holt a further book.  At the more academic end of the discussion, the medieval philosophy scholar John F. Wippel has edited a fine collection of new essays on the theme of why anything, rather than nothing, exists at all.  And now John Leslie and Robert Lawrence Kuhn have published The Mystery of Existence: Why Is There Anything At All?, a very useful anthology of classic and contemporary readings.

Leslie is an emeritus professor of philosophy at the University of Guelph, known for bringing his distinctive brand of Platonism to bear on questions in cosmology and the philosophy of religion.  Kuhn is the creator and host of the PBS series Closer to Truth, whose interviews and roundtable discussions on the big questions have featured an amazingly diverse range of prominent scientists, philosophers, and theologians. 

In an interesting article in the current issue of Skeptic magazine, Kuhn summarizes his own approach to the subject of nothing.  Titled “Levels of Nothing” (and essentially an excerpt from Kuhn’s own contribution to The Mystery of Existence), the article sets out what Kuhn calls a “taxonomy” or “hierarchy” of kinds of Nothing, from least to most absolute.  We are to imagine, first, space and time devoid of any visible objects but containing particles and energy; then space and time devoid of particles, but containing energy; then space and time devoid of that as well; and so forth until we arrive at the notion of there being absolutely nothing whatsoever, not even possibilities, mathematical truths, laws of nature, or abstract objects of any sort.  (Kuhn does not claim each or any level is in fact either physically or metaphysically possible -- he’s just exploring the conceptual territory.)

Physics isn’t everything

The wary reader might fear that what we have here is a rehash of Krauss’s unhappy speculations about “possible candidates for nothingness” in A Universe from Nothing (which I criticized in a review in First Things).   But that is not the case.  Krauss’s book gained notoriety even among some thinkers who share his atheism for its conceptual sloppiness, arrogance, and philosophically ill-informed flippancy.  Kuhn is neither conceptually sloppy, nor arrogant, nor flippant, nor philosophically ill-informed.  Nor does he share Krauss’s unreflective scientism.  Having for the sake of argument described a scenario in which not even space-time or mass-energy exist but the laws of quantum mechanics do -- he calls this “the physicists’ Nothing,” and it is essentially what Krauss and Hawking have in mind in their accounts -- Kuhn writes:

What physicists contemplate -- the sudden emergence or “tunneling” of universes from “Nothing” -- is fascinating and indeed may be cosmogenic, but the tunneling process or capacity is not Nothing.  The Nothing of physicists is thick with the complete set of the laws of physics, and so between the physicists’ Nothing and Real Nothing lies a vast, unbridgeable gulf.

Moreover, Kuhn does not regard the fundamental laws of physics, whatever they turn out to be, as a plausible terminus of explanation.  For to be that, they would have to be either logically necessary or an inexplicable brute fact, and neither supposition is credible.  Writes Kuhn:

I doubt I could ever get over the odd idea that something so intricate, so involved, so organized and so accessible as the laws of physics would be the ultimate brute fact.

I would add that it is crucial to emphasize that the point by no means rests on mere intuition.  For one thing, physicists themselves, including Krauss and Hawking, do not treat the laws of physics as if they were either logically necessary or a brute fact.  For they regard such laws as empirically testable, which would make no sense if they were logically necessary (i.e. the sort of thing the denial of which would entail a contradiction).  If they can in principle be falsified, then they are not necessary.  Physicists also regard each level of laws as something that might at least in principle be explicable in terms of deeper laws -- Krauss even entertains the possibility that for any level there might always be a deeper one -- and if each level might at least in principle be so explicable, then it isn’t a brute fact.

Furthermore, as Lloyd Gerson points out in his book on the Neoplatonic philosopher Plotinus, the suggestion that the world might be an inexplicable brute fact is simply a non-starter as long as a possible explanation is even on the table.  Hence it is quite silly for the atheist or skeptic to say “Well, maybe the fundamental laws of physics have no explanation.”  The Neoplatonist or any other sort of theist can retort: “What are you talking about?  I just gave you an explanation!”  That explanation then has to be evaluated, of course, but the point is that it is no good merely to suggest that there might be no explanation, as if this by itself does anything to rebut some explanation the skeptic doesn’t like.

More than zero

In any event, Kuhn does something Krauss tried but failed to do, which is to propose a philosophically interesting conception of a kind of “nothing” which is something less than what he calls “absolute” nothing or “Real Nothing.”  The idea is this.  As we go through the different possible “levels of nothing” -- and (contrary to the cute title I gave this article) Kuhn thinks there are nine of them -- at each stage deleting more aspects of reality, we reach a point where there are no concrete objects in existence, but where there are still abstract objects.  That is to say, there are no individual substances of either a physical or non-physical sort -- no material objects of any size, no disembodied minds, and so forth -- but there are still universals, numbers, propositions, Platonic forms and the like.  There would be no actual trees or triangles, but there would in some sense still be the property of being a tree and the property of being triangular; there would be no actual concrete objects that could be counted, but the propositions that two and two make four and there are no concrete objects would still be true.  In this scenario, since there would (in a sense) be no things, we would (in a sense) have “nothing,” but it would not be nothing in an absolute sense, since there would still be truths, properties, etc.

Kuhn goes one step further and imagines a scenario in which there are no abstract objects like numbers, universals, or the like, but there are still possibilities.  This would be the “level 8” kind of “nothing.”  Level 9 -- absolute nothing or Real Nothing -- would be reached when we delete even possibilities. 

Could there really have been “nothing” in either the level 8 or level 9 senses?  As Kuhn rightly notes, there are serious problems with the supposition that there could have been.  The domain of abstract objects is the domain of logically necessary truths, truths the denial of which entails a contradiction.  If these truths are necessary, then there could be no scenario in which they are not in some sense real, and thus no level 8 type scenario.  (I would note also that if the level 8 or level 9 scenarios held, then the proposition that the level 8 [or level 9] scenario holds would be true, in which case there would after all be at least one thing that was in some sense real, namely that very proposition.)

Citing his co-editor Leslie, Kuhn also points out that the abstract entities denied by scenarios 8 and 9 are arguably needed in order to explain the world of actually existing concrete things.  (E.g. how could anything actually exist unless it were in some sense a possibility?)  I would add that even Kuhn’s “no concrete objects, only abstract ones” scenario is explanatorily problematic.  For abstract objects are typically regarded as causally inert.  Hence if we need abstract objects in order to explain the realm of concrete things, we would also need at least one concrete thing in order to explain the others.

While Kuhn does not settle on a particular position, he does indicate that he thinks that either the existence of things is a brute fact without explanation, or there is something that is self-existent in the sense that its essence entails that its non-existence is inherently impossible.  The only remaining question in the latter case would be what else we could say about this self-existent reality (e.g. whether we ought to ascribe to it the standard divine attributes).

For the reason given by Gerson, though, I think that if Kuhn is willing to concede even this disjunction -- that either the universe is an inexplicable brute fact, or there is something self-existent -- then he has really implicitly conceded that there is something self-existent.  For the universe could be an inexplicable brute fact only if there were no possible explanation of it, and once it is conceded that it is at least possible for there to be something self-existent, then we have a possible explanation, viz. that that self-existent thing is the cause of the world.  As Gerson says, it is no good for the atheist to say “Maybe there is no explanation” when the theist has just given one. 

Nor will it do for the atheist to retreat into a fallback position according to which there is a self-existent reality, but it is just the basic laws of physics.  For again, by virtue of the facts that he regards them as empirically testable and susceptible of explanation in terms of yet deeper laws, the physicist implicitly acknowledges that the laws of physics do not exist in an absolutely necessary way.  They cannot in that case be self-existent in the requisite sense.  Nor could anything material be self-existent, given that material things themselves depend on the laws of physics.

The classical perspective

Once we allow that there is something self-existent and that it cannot be the laws of physics or anything that depends on the laws of physics, some brand of theism is really unavoidable.  The only remaining question is which brand.  Pantheism?  Panentheism?  The classical theism of Augustine, Anselm, Avicenna, Maimonides, and Aquinas?  The “theistic personalism” or “neo-theism” of contemporary philosophers of religion like Alvin Plantinga and Richard Swinburne?  This question takes us well beyond Kuhn’s article, though it is certainly relevant to the subject matter of his and Leslie’s anthology.  This brings me to a friendly criticism of the latter. 

As I have argued many times (see e.g. the pieces collected here) the “theistic personalism” that characterizes so much contemporary philosophy of religion (the label is one Brian Davies has attached to the group of thinkers in question) is seriously problematic both philosophically and theologically.  And one reason it is is that God as conceived of by theistic personalists simply cannot plausibly be regarded as an ultimate explanation of the world.  Theistic personalists often speak of God as instantiating properties and of being a member of the class of “persons,” and typically deny or at least seriously qualify the doctrine of divine simplicity.  Some theistic personalists would even attribute change to God.  Yet (so the classical theist would argue) whatever instantiates a property requires an explanation of why it does so; whatever is in any way composed of parts requires an explanation of its composition; whatever is a member of a genus has an essence, definitive of the kind of thing it is, which is distinct from its act of existence, so that the fact that it has existence conjoined to that essence requires an explanation; and whatever changes in any way requires a cause of change.  Hence God so construed would not be explanatorily ultimate -- he would either require an explanation of his own or simply be a “brute fact” himself.  Either way he would fail to satisfy the requirements that most classical theists regard as the chief philosophical reason for affirming God’s existence in the first place.  For a classical theist like Aquinas, God is in no way composed of parts, is not in any genus, and is utterly unchangeable.

Now Leslie and Kuhn’s The Mystery of Existence does include readings from some of the key writers of the classical tradition that are absent from too many contemporary anthologies on these matters.  You will find in it selections from Plato on the Good, Aristotle on the Unmoved Mover, Plotinus on the Good, and Aquinas on divine simplicity.  However, the selections are very short -- these four major writers together take up only slightly more than four of the book’s 288 pages -- and while Leslie’s (in my view somewhat eccentric) brand of Platonism naturally gets some space too, the bulk of the anthology is devoted both to theistic personalists like Swinburne and Plantinga, and to other writers approaching things from an essentially modern rather than classical point of view. 

For a classical theist like myself, this is a little like putting out an anthology on dogs that is top heavy with essays about tails.  The classical theistic tradition is the dominant approach to these matters in the history of Western thought.  It is rooted in the metaphysics of Neoplatonism and Aristotelianism, was honed to rigorous perfection by the Scholastics, and is (as I have said) represented by thinkers of the stature of Augustine, Anselm, Avicenna, Maimonides, Aquinas, and many others.  In contemporary philosophy it is represented by outstanding writers like Brian Davies, John Haldane, Brian Leftow, David Oderberg, Gyula Klima, Christopher Martin, Eleonore Stump, and many others -- some of whom have appeared on Kuhn’s Closer to Truth.  Useful as The Mystery of Existence is, it should have contained more from this camp.

Even the classical selections that do appear in the book are in my view not presented entirely fairly.  For instance, the editorial material accompanying the very brief reading from Aquinas on divine simplicity, while treating his view on the subject respectfully, gives it rather short shrift as ultimately merely “puzzling.”  But as I have argued at length in my books The Last Superstition and Aquinas, you cannot properly understand what a classical writer like Aquinas says about the existence and nature of God unless you understand the general background metaphysical theses in which his views are grounded -- theses that are very different from the metaphysical assumptions made by most modern and contemporary philosophers.  In the case at hand, we have to keep in mind that Scholastic writers like Aquinas have a very different understanding of the notions of substance, essence, properties, and predication than modern and contemporary philosophers do.  If you read what he says about divine simplicity through the lens of the usual modern conceptions, then it will indeed seem very “puzzling.”  Not so if you understand it in light of the Scholastic understanding of these notions.

This is not a small lapse.  While Scholastics and other classical thinkers disagreed over certain details concerning divine simplicity, something like Aquinas’s notion is absolutely central to the way Neoplatonists, Aristotelians, Scholastics, and classical theists more generally understand the nature of God and the nature of ultimate explanation.  To write it off in a line or two is simply not to do justice to what is historically the main approach to these issues in Western thought.

Asking the right questions

In his Skeptic article, too, Kuhn seems to me to take insufficient consideration of the richness of classical approaches to these issues.  For instance, regarding the problem of universals and other abstract objects, one might get the impression from his piece that unless one opts for nominalism (which denies the existence of these objects) one has to accept Platonic realism -- the view that universals and the like exist not only apart from the material world but also apart from any intellect whatsoever (which would make them independent of God).   But this neglects the Aristotelian realist view that universals and the like are real, but still exist only either in concrete objects themselves or in a mind which abstracts them.  This was developed by the Scholastics into the view that universals, possibilities, and the like pre-exist as ideas in the divine intellect, and thus are not independent of him (a suggestion that was in fact foreshadowed in Neoplatonism). 

There is also the not insignificant point that the very manner in which the question of ultimate explanation is asked these days is arguably modern rather than classical.  When we ask “Why is there something rather than nothing?” that rather makes it sound as if there could have been nothing and yet isn’t -- a suggestion which, as we have seen, is problematic.  That can give the false impression that theism is an attempt to answer a defective question.  But contrary to what many contributors to the contemporary discussion of these issues seem to assume, Aquinas and other classical writers do not typically begin their arguments for God’s existence by asking “Why is there something rather than nothing?” They don’t assume that there could have been nothing but isn’t; on the contrary, they would deny that there could have been nothing. 

What they do ask is why a world with some of the specific features our world has exists.  For example, they ask, in an Aristotelian vein, how it is that the world undergoes change, and argue that there is no way in principle to account for this unless there is something absolutely unchangeable; or, in a Neoplatonic vein, how it is that there is a world of composite things, and argue that there is no way in principle to account for this unless there is something absolutely simple or non-composite; or, in a Thomistic vein, how it is that there are things that exist but could fail to exist, and argue that there is no way in principle to account for this unless there is something that just is Subsistent Being Itself.

No doubt such notions will be mystifying to many readers with little knowledge of the classical tradition.  And yet that tradition (rather than ideas of the sort you’ll find in writers like Plantinga and Swinburne, Hawking and Krauss) has, as I say, been the dominant approach taken in the history of Western philosophy and theology.  If there is a deficiency here, I would argue that it is not in the tradition but in too many contemporary readers’ understanding of it.  From the classical theist’s point of view, the moderns not only don’t get to the right answers, they often do not even know the right questions, and also lack the right metaphysical tools to answer them even if they knew to ask them. 

All the same, Kuhn and his co-editor John Leslie are to be congratulated for putting forward a valuable and intellectually serious contribution to the recent debate.

This post has been long-winded enough, but readers looking for further commentary on the recent debate over nothing might find the following of interest:

“Mad Scientists” (my review in National Review of Hawking and Mlodinow’s The Grand Design)

“Why are (some) physicists so bad at philosophy?” (a response to some ideas put forward by physicists Ethan Siegel and Vlatko Vedral)

“What part of ‘nothing’ don’t you understand?” (on New Scientist magazine’s recent treatment of these issues)

“Reading Rosenberg, Part III” (on Alex Rosenberg’s discussion of the origin of the universe in The Atheist’s Guide to Reality)

“Greene on Nozick on nothing” (on Robert Nozick’s treatment of the “something from nothing” question in Philosophical Explanations, cited by physicist Brian Greene in his own book The Hidden Reality)

“Not Understanding Nothing” (my review of Krauss’s A Universe from Nothing in First Things)

“Steng operation” (on Victor Stenger’s attempt to defend Krauss against his critics)

“Forgetting nothing, learning nothing” (on some more recent remarks made by Krauss)

237 comments:

  1. And a mirror image of X is certainly partially identical to X. In fact, you can trace the rays of light from X to the mirror image of X. Gregory writes that “human nature is very much like a mirror … When you put gold in front of a mirror, the mirror takes on the appearance of the gold, and because of the reflection it shines with the same gleam as the real substance … thus reproducing in its own substance whatever is placed in front of it” (From Glory to Glory, p. 171). In other words, unless the reflection “shines with the same gleam as the real substance”, it is not a reflection at all.

    He also asks, “how can you see a beautiful image in a mirror unless it has received the impression of a beautiful form? So it is with the mirror of human nature: it cannot become beautiful until it draws near to the Beautiful and becomes transformed by the image of the divine Beauty” (Ibid., p. 186). In other words, there must be an “impression” that is “received” by the mirror of the reflected substance in order for the mirror to actually reflect the substance at all.

    Identity is always the identity of a singular. Something can be identical to itself and to nothing else. We know this because substance is prior to form and matter. Form always appears in a particular, singular way; never identically. When we say that one form is present in two places, we mean that similar forms are present in two places. If these were really the same form, then we would be stating a contradiction. However, your partial identity and partial difference equation requires that one and the same form--not two similar forms--be present in two places.

    First, how can substance be prior to form? There wouldn’t be a substance without a form.

    Second, you keep ignoring the fact that there are different kinds of identity. You focus upon numerical identity as the only kind of identity, and when you cannot reduce some other kind of identity to numerical identity, you refuse to call it identity at all. That is completely unnecessary. For example, there is formal identity, such that the same form is present in different substances. This does not mean the same numerical form, because there are actually two forms, but they are formally the same, because otherwise, the two substances would not be under the same genus at all. It is the formally identical forms that grounds the connection between the two substances. Without it, there is no basis to say that they are both the same kind of thing. In fact, you cannot even say that X is the same kind of thing as Y, on your account. For example, you cannot say that dguller and rank sophist belong to the same species, because that would mean that we are the same human being, which is absurd.

    Third, I agree that formal identity is a kind of similarity, because it is a kind of partial identity. In other words, F-in-X and F-in-Y, both involve the same F, they differ in that F is in different instantiations, i.e. X and Y.

    Weaker kinds of identity reduce to similarity, which means that they can't explain similarity in the way that you argue.

    I think it makes more sense to distinguish between total identity and partial identity in the following way:

    (1) X is totally identical to Y iff X and Y have everything in common iff X and Y do not differ in any way
    (2) X is partially identical to Y iff X and Y have something in common iff X and Y do differ in some way

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  2. The question is whether the “something in common” (which we can call C) in (2) would count as total identity or partial identity. If C is partially identical in X and Y, then you would have an infinite regress. Therefore, C must be totally identical between X and Y at some point in the analysis. Your counter-argument would be that C couldn’t possibly be totally identical in X and Y, because it would differ in some way, i.e. its numerical distinction. Therefore, C cannot be totally identical in X and Y, which means that it must be partially identical, which means that you have an infinite regress, which is impossible. Therefore, the entire account must be rejected as leading to impossibilities.

    My response to this criticism is that C can be abstracted in the mind in such a way that numerical distinction is removed from the concept altogether. Minus numerical distinction, you have C*, and C* is totally identical in X and Y. In other words, once the differences are abstracted away, what is left is totally identical. This is certainly doable by the intellect, which abstracts away particularities in order to arrive at universals, which are shared in common by particulars. Or, to put it in terms that we have used before, you have F-in-X and F-in-Y, and by abstracting away -in-X and -in-Y, one is left with F, which is totally identical in both.

    This is what I'm arguing, sans that last part: "using its own internal resources". This is to confuse the draw of the final cause on the efficient cause with the draw of the formal cause on the material cause. The material cause simply becomes, as a result of the efficient cause placing the form before it, an imitation of the form. Potency is pulled toward act like metal to a magnet. Potency is moved by act; never self-moved.

    But wait. Now you are saying that the efficient cause is drawn by the final cause. I thought the efficient cause (i.e. the agent) draws the patient to transition from potentially P to actually P. What is drawing what to what? And remember, you are saying that the agent only acts as an inspiration for the patient. Nothing else. You explicitly denied that the agent overflows its being into the patient to cause the transition from potency to act in the patient. So, where did this actual being in the patient come from? It didn’t come from the agent. It didn’t come from the patient. Where did it come from? God?

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  3. dguller,

    First, I don’t understand what it means to say that a cause “as a cause” doesn’t change when causing something if the cause changes. Can you elaborate?

    This is simply to say that the substance that causes an effect changes accidentally rather than essentially, i.e. in the order of materiality rather than in the order of causality. Its matter changes as a result of the causal encounter but the form that it presents does not.

    In the context of the causal encounter, the cause is a cause, even if only by entering into a proximity with another substance such that it inspires it to transition from potentially P to actually P. The cause is really inspiring the effect to occur, in that situation, even if the cause never actually intrinsically changes.

    I agree. But we can only locate the cause from its effects, because the only trait that identifies a cause as a cause is the relation of dependence from its effect. "Cause" is simply the word that we use to point to the probable or definite object on which the change (i.e. the effect) depends. Thus we call God a cause because he is the only possible target for creation's relation of dependence, even though "cause" is ultimately a divine name taken from his effects.

    The form is already present in a state of potency in the patient, and only requires the agent to inspire the form to transition to act in the patient.

    Obviously, form must be present in potency before it can be actualized. This is the basis of the concept of prime matter, which contains the potential for all forms. It is also the reason that not every act can actualize every potency: a particular potency for a particular form must be selected if change is to occur.

    When I used the word "transmitted", this shouldn't be taken as the passage of a form from one place to another. Again, this would entail a change in the cause that results in an infinite regress. A transmitted form is simply one that is held up by the efficient cause and copied by the effect.

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  4. So, Clarke’s account of causality as an overflowing of being from agent to patient is certainly possible.

    Again, it depends on how you take what he said. The straight reading, as I can see it, contradicts what Aquinas actually wrote. But I haven't seen the full context, so who knows.

    Act and potency are kinds of being. To have more act is to have more being, because act is a kind of being.

    If potency is a kind of being as well, then it follows that having more potency entails having more being and thus more goodness. As a result, the most potential thing has as much being as the most actual thing. Your argument leads to absurdity. Act and potency are concepts within the thing that really exists, i.e. the substance. Your argument loses sight of substance--which is the only thing to which ontological terms apply--in favor of its actual and potential accidents, which are ontic differences. The substance is what has being, and it can have neither more nor less being than it does. Accidents within the substance can be more or less actual in ontic terms, but this has no bearing on the question of being.

    I think it is more helpful to think that there is a kind of being that admits of degrees and a kind of being that does not admit of degrees.

    Which is where the ontico-ontological divide comes in. Ontic accidents within a substance rely on a more original and unchanging act of existence, but are capable of changing without altering the substance's being. Accidents do not "exist" in any proper sense, but rather attach themselves to the one thing that exists: substance. The reason that they are capable of change is that they have only a semi-existence in the first place.

    Indivisibility and divisibility are both inherent parts of the transcendentals, which means that you cannot rank one as higher than the other.

    I know of no account of the transcendentals that includes multiplicity. If I remember right, Aquinas held that truth, goodness, One, nobility and being were the five transcendentals; others included beauty. But multiplicity is nowhere to be found.

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  5. Second, it ignores the fact that God cannot be the Neoplatonic One, for the very reasons that you cite. The One is undifferentiated, and God is differentiated, but in a virtual fashion, as we discussed before.

    I'm not sure things are this clear-cut. While I agree that the One was seen to be wholly undifferentiated (hence the problem that it can only create one thing, which is a lesser copy of itself), I don't believe that Pseudo-Denys and Aquinas posited something that radically different. It was taken for granted in the ancient world that lower things represented higher things, which in some way contained and surpassed lower things. This is what made the concept of the One possible in the first place. Augustine (who, I believe, first posited the divine ideas) simply added to this concept the possibility that the One could know and create all individual things without a demiurge.

    If you think about it, it's not that unnatural of a leap. Aquinas makes the case simply in ST I q15 a2: since God's knowledge is his being, and his being is the ultimate principle of all things (again, still in territory compatible with the One), he will understand and contain all things. God is wholly one, but, by understanding his own oneness, he knows the multiplicity that relies on it. That's all it means for creation to be virtually contained within God: lower represents higher; higher in some strange way contains and surpasses lower. The One is very similar in this respect, even though the Neo-Platonists failed to reach Augustine's conclusions.

    If the One has no differentiation, distinction or composition, then how can it be represented “in some respect”?

    In the respect that lower always represents higher in ancient metaphysics. There is no partial identity and partial difference equation here. There is no F-in-X with respect either to the One or to God, because neither of them is differentiated. They simply contain and surpass that which is lower than themselves, which in turn acts as a symbol for higher things. The similarity here is vague, basic and impossible to hash out in a rationalistic manner. But we know that it must be there, because that which relies always resembles the thing(s) on which it relies.

    The virtual distinction is how Aristotle and the Scholastics tackled the issue of the lower being in the higher, but, even then, you have to remember that the virtual distinction is nothing like a real distinction. The way the higher contains the lower is ontologically vague and basic, and only notionally clear. Recall that the virtual distinction is a notional distinction that relates to a real whole, which is not ontologically distinct. We can, somehow, pick apart the higher in our minds to comprehend how it contains the lower; but this does not mean that our notional distinctions are anything real. Once again, the resemblance of higher and lower things is a basic concept that cannot be cashed out in the way that you want it to be.

    For this analogy to make sense, there would have to be something present in both God and the soul, much like the form is present in the carving and in the wax.

    What you're proposing is straight-up onto-theology that reduces God to the level of a supreme being. God and man would have to exist in the same sense and have properties in the same sense for this analogy to work. That clearly is not what Gregory is saying. Rather, he's saying that the lower contains the stamp of the higher. This is totally different than isomorphism.

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  6. What makes the representation of X a representation of X is an isomorphism between X and the representation of X, which typically involves the presence of F in both X and the representation of X.

    The re-presentation of X is a dimmed reflection of X-as-X, rather than of F-in-X.

    In other words, there must be an “impression” that is “received” by the mirror of the reflected substance in order for the mirror to actually reflect the substance at all.

    Indeed. But Gregory was a Neo-Platonist, and so his words don't translate that directly into Aristotelian language. He is not referring to the presence of a substantial or accidental form in two places, but rather to what I described above: the re-presentation of X-as-X. Neo-Platonism, to my knowledge, did not spend much time hashing out a virtual distinction. Resemblance was a holistic representation of substance, rather than a reduced discussion of forms in multiple locations. That language, in fact, was essentially just an attempt to rationalize what the Platonists had always believed.

    First, how can substance be prior to form? There wouldn’t be a substance without a form.

    And there wouldn't be a substance without matter, but matter is not prior to substance. Form and matter are smaller concepts that are placed within the wider context of substance, which is larger than either form or matter. I didn't mean that forms didn't create substances; I just meant that substance was prior in nobility to form, as Aquinas affirms:

    Now it belongs to such a nature to exist in an individual, and this cannot be apart from corporeal matter: for instance, it belongs to the nature of a stone to be in an individual stone, and to the nature of a horse to be in an individual horse, and so forth. Wherefore the nature of a stone or any material thing cannot be known completely and truly, except in as much as it is known as existing in the individual.

    For example, you cannot say that dguller and rank sophist belong to the same species, because that would mean that we are the same human being, which is absurd.

    I understand that what I'm saying can hint at nominalism, but it's really the core of Aquinas's beliefs on form. As I quoted above, the individual substance is what really exists. And the form possessed by an individual substance is in turn individualized. We can only talk about the identity between dguller and rank sophist after we have moved into the realm of universals, which is an abstraction fundamentally separate from what really exists. In fact, you mention this below. However, in reality, what exist are individual substances with vague similarities. We can mentally ground this similarity in the absolute identity of form, but this, again, is simply abstraction. It can tell us certain things about the real individuals--natural law, for instance--, but it fails to provide the concrete ground for similarity that you want it to. Similarity is what really exists; partial identity and partial difference is a mental construct that does not really exist. Even you admit below that partial identity is an impossible idea until we head into abstraction.

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  7. In other words, F-in-X and F-in-Y, both involve the same F, they differ in that F is in different instantiations, i.e. X and Y.

    F-in-X and F-in-Y does not reflect ontological reality, though. X and Y are what exist; both are whole substances with ontological similarities. The grounding of this similarity in the total identity of form is a mental abstraction that cannot be carried over into reality without a contradiction.

    Minus numerical distinction, you have C*, and C* is totally identical in X and Y. In other words, once the differences are abstracted away, what is left is totally identical. This is certainly doable by the intellect, which abstracts away particularities in order to arrive at universals, which are shared in common by particulars.

    Indeed. But you cannot then re-project C* on to X and Y without qualification. C* is an abstraction from the concrete reality of X and Y; it only partly reveals the proper object of knowledge, which is the individual substance. You can't explain the ontological reality of analogy by appealing to a distinction between partial identity and partial difference that is only valid in the mind.

    But wait. Now you are saying that the efficient cause is drawn by the final cause. I thought the efficient cause (i.e. the agent) draws the patient to transition from potentially P to actually P. What is drawing what to what?

    The way the final cause draws the efficient cause is different from the way that the efficient cause draws the material cause. The final cause is the precondition for any activity whatsoever. Without it, the proximity between the efficient cause and material cause would have no result. What the final cause does is to allow the efficient, formal and final causes to do their work, in the manner of a drawing that removes impediments and that determines the result. It moves nothing in the sense that we use the term "move", as was argued a few comboxes ago by others. (This has support in the actual texts of Aristotle and Aquinas, by the way.) It simply draws the efficient cause to move other things (read: to present other things with the standard to imitate), in a manner that does not involve motion.

    To put it succinctly, the final cause non-movingly draws the efficient cause to movingly draw the material cause. The final, formal and efficient causes do not change; they act together to bring about change in the material cause.

    So, where did this actual being in the patient come from? It didn’t come from the agent. It didn’t come from the patient. Where did it come from? God?

    I have no idea what you're saying.

    There is an unfathomable moment when potency becomes act as a result of act's presence. The form presented to the potency is suddenly copied in the potency, and the potency transitions into act. It is fundamentally strange and unique, but it is not contradictory.

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  8. @RS


    >I know of no account of the transcendentals that includes multiplicity. If I remember right, Aquinas held that truth, goodness, One, nobility and being were the five transcendentals; others included beauty. But multiplicity is nowhere to be found.

    Transcendental Multiplicity is a term used by Aquinas in Trinitarian theology(which many scholastics believe is not compatible with a Christian Platonist view of The One). In case you haven't noticed RS your so called opponent mixes and matches and equivocates between Natural Theology, Revealed Theology(which involves the Trinity), Natural Philosophy and even Mystical Theology at the drop of a hat.

    You sane person that you are know enough to keep them separate & confine a discussion on causality to natural Theology. You opponent doesn't have such scruples & will pettifog this issue to keep from having a rational discussion(like pulling concepts from Revealed and Mystical Theology out of left field).

    Just thought I'd warn you.

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  9. Ben,

    Thanks for the heads-up. I've never heard that term before. In any case, you're definitely correct that pulling the concept of transcendental multiplicity from Trinitarian theology into the realm of transcendental being is an equivocation. Esse has no transcendental multiplicity, even if God does.

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  10. RS,

    NP.

    It's like Richard Dawkins arguing with a Young Earth
    Creationist who is claiming "The second law of Thermal Dynamics refutes or contradicts the claims of evolution". The YEC is just making a bad argument & mixing concepts that belong in Biology with those that belong is Physics & trying to justify it by saying "Well they are both part of Science so what I say must be true."

    In such a case I have a rare sympathy for Dawkins.

    Equivocating between different spheres of Theology is just as illegitimate.

    Anyway this essay by Rocca on analogy & God-Talk might prove useful.
    http://www.ts.mu.edu/readers/content/pdf/54/54.4/54.4.2.pdf

    Tell me what you think about it when you get the time or not.

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  11. Ben,

    I checked out Rocca's essay. In my opinion, it wasn't totally off the mark, but it still failed to place analogy in its wider Christian context. Aquinas said absolutely nothing original on the subject of analogy: all of it was taken from Pseudo-Denys, Gregory of Nyssa and the other Church Fathers. Rocca seems to insinuate that Denys was a negative theologian in the same vein as Maimonides, which could not be further from the truth. He quotes some seriously apophatic passages of Denys's to support his view, but he fails to incorporate Denys's radical statement about God being "beyond every denial" into his argument. Aquinas follows Denys on this point. Nothing absolutely true or false can be said about God for the simple reason that God is prior to (i.e. he precedes and surpasses) every reality that we understand, including existence. Rocca suggests that there is a positive theology underneath this, but I don't think that's correct. He seems to think that Aquinas believes the Five Ways to make positive statements about God when they do no such thing: they simply extend creaturely concepts to their logical conclusions and state that, if they are to be explained, some kind of transcendent reality analogically similar to them must exist. Analogy is presupposed in the proofs of God's existence, rather than derived from them. Rocca's argument that analogy is always presented after arguments for God in Aquinas's work falls flat: before presenting the Five Ways, Aquinas defends analogy in ST I q2 a2 as a means of talking about what could stand beyond creation.

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  12. Rank:

    If potency is a kind of being as well, then it follows that having more potency entails having more being and thus more goodness. As a result, the most potential thing has as much being as the most actual thing. Your argument leads to absurdity.

    I don’t know if potential being and actual being can be quantified in such a way, i.e. one unit of potential being = one unit of actual being, but I would agree that the most potential thing has more being than non-being, and that potential being, by virtue of being a kind of being, is also good, by virtue of the interconvertibility of the transcendentals.

    Act and potency are concepts within the thing that really exists, i.e. the substance. Your argument loses sight of substance--which is the only thing to which ontological terms apply--in favor of its actual and potential accidents, which are ontic differences. The substance is what has being, and it can have neither more nor less being than it does. Accidents within the substance can be more or less actual in ontic terms, but this has no bearing on the question of being.

    First, act and potency are transcendentals that are operative upon everything that exists under the categories, including substances. Remember that a transcendental is “something above every genus, common to all beings, and thus not restricted to any category or individual” (Feser, Aquinas, p. 33). Act and potency certainly qualify under that description.

    Second, I think that you have to be clear about your terms. I think that when Heidegger uses the terms “ontic” and “ontological”, he is speaking about particular beings and their specific characteristics as “ontic”, and their underlying transcendental conditions (i.e. their grounds) that allow those particular beings to manifest themselves in the way that they do as “ontological”. That is why every ontic investigation presupposes an underlying ontology, and every ontology can only be discovered through ontic phenomena. That is why he had to investigate the underlying ontology of Dasein in order to understand how ontic phenomena can manifest themselves at all, i.e. as they appear to Dasein. After all, to understand why X manifests itself in the way that it does, one must understand what X is manifesting itself to, i.e. Dasein, and what it is about Dasein that allows X to manifest itself in that way. So, “ontological terms” would not apply “only” to substances, but would rather apply to Dasein and its existential structures in their relationship of concern towards particular entities in the world as they disclose and reveal themselves to Dasein within that broader context as particular ontic phenomena. Perhaps you should clarify your terms, because you are not using them according to Heidegger’s understanding.

    Third, I will provisionally agree that a substance, once it exists, cannot have more or less being, because it is simply the actualization of a substantial form. However, even granting this, the powers of that substance as delineated by its substantial form can be actualized in varying degrees, and it is precisely the actualization of a substance’s powers via secondary actuality that determines how good an instantiation of its kind it is. It is only in reference to this latter kind of being that degrees of actuality and goodness makes any sense. And just because it pertains to secondary actuality and accidental being, and not to substantial being, does not mean that it has nothing to do with the being of a substance. In fact, that substance would not be what it is unless it had such powers and accidental properties.

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  13. Which is where the ontico-ontological divide comes in. Ontic accidents within a substance rely on a more original and unchanging act of existence, but are capable of changing without altering the substance's being. Accidents do not "exist" in any proper sense, but rather attach themselves to the one thing that exists: substance. The reason that they are capable of change is that they have only a semi-existence in the first place.

    First, if you want to say that the kinds of being in which there is no degrees of being correspond to “ontological”, and the kinds of being in which there are degrees of being correspond to “ontic”, then that is fine. But that doesn’t change the fact that they are both different kinds of being, much like act/potency and substance/accident are different kinds of being. In fact, the different kinds of being – i.e. substantial being, accidental being, actual being, potential being, etc. – are all analogous to one another, and thus exist in relationships of similarity to one another. As long as being is not understood as a genus, there is no problem here, and thus, there is no problem with saying that ontic being admits of degrees such that a particular being can have more (ontic) being than another being, which ends up corresponding to the former being closer to the ideal set by the being’s nature than the latter.

    Second, I think that you are simplifying the dependencies involved. Yes, accidents could not exist without substances to inhere in, but substances cannot exist without accidents, either. It is impossible for a material substance, for example, to exist without some accidents. In fact, only God exists without accidents. So, in that case, the material substance depends upon its accidents in order to be a material substance to begin with. There is a co-dependency involved.

    I know of no account of the transcendentals that includes multiplicity. If I remember right, Aquinas held that truth, goodness, One, nobility and being were the five transcendentals; others included beauty. But multiplicity is nowhere to be found.

    Aquinas discusses transcendental multiplicity in the context of trying to understand the plurality of the divine persons in God, because numerical counting is impossible when it comes to God, and any numerical terms of plurality can only be used metaphorically to denote excess or greatness. One cannot literally say that God is three or one, because numerical counting involves quantity, which is an accident, and thus inapplicable to God. The only kind of plurality that can literally be predicated of God is transcendental multiplicity which is just that one individual is divided from another individual. He discusses this at ST 1.30.3, and at QDP 9.7, if you want to read about it. Transcendental multiplicity is necessarily a transcendental, because it is a condition under which any differentiation is possible inasmuch as transcendental unity is a condition under which unity is possible, which is beyond the categories, and is, in fact, presupposed by them, thus making it a transcendental.

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  14. I'm not sure things are this clear-cut. While I agree that the One was seen to be wholly undifferentiated (hence the problem that it can only create one thing, which is a lesser copy of itself), I don't believe that Pseudo-Denys and Aquinas posited something that radically different. It was taken for granted in the ancient world that lower things represented higher things, which in some way contained and surpassed lower things. This is what made the concept of the One possible in the first place. Augustine (who, I believe, first posited the divine ideas) simply added to this concept the possibility that the One could know and create all individual things without a demiurge.

    But when Augustine made that addition, he added differentiation to the One, which completely contradicted the original Neoplatonic understanding of the One as undifferentiated. That is why Plotinus described the One as “the all-transcendent, utterly void of multiplicity” (Enneads 5.3.15). And remember why this was so: differentiation is a necessary condition of intelligibility, and only that which is undifferentiated is beyond intelligibility. As Perl writes: “Being as a whole, therefore, is intelligible, and so is, only in virtue of the internal differentiation of the forms from one another, and this differentiation is constitutive of being itself. The differentiation of one being from another is what makes all thigns to be intelligible, and so be” (Theophany, p. 10).

    If you think about it, it's not that unnatural of a leap. Aquinas makes the case simply in ST I q15 a2: since God's knowledge is his being, and his being is the ultimate principle of all things (again, still in territory compatible with the One), he will understand and contain all things. God is wholly one, but, by understanding his own oneness, he knows the multiplicity that relies on it. That's all it means for creation to be virtually contained within God: lower represents higher; higher in some strange way contains and surpasses lower. The One is very similar in this respect, even though the Neo-Platonists failed to reach Augustine's conclusions.

    That’s all fine, as long as we are clear that God necessarily involves differentiation, at the very least in the virtual differentiation between the divine ideas, the divine attributes, and the divine persons, which is impossible for the Neoplatonic One. They may be “very similar”, but nonetheless are clearly different in important ways.

    In the respect that lower always represents higher in ancient metaphysics.

    What does it mean for a lower X to represent a higher Y in “ancient metaphysics”? Everything that I’ve read involves an isomorphism of some kind between X and Y that grounds the representation. You have explicitly denied that this is going on, which leaves me with no idea what you mean when you say that “X represents Y”.

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  15. They simply contain and surpass that which is lower than themselves, which in turn acts as a symbol for higher things. The similarity here is vague, basic and impossible to hash out in a rationalistic manner. But we know that it must be there, because that which relies always resembles the thing(s) on which it relies.

    So, similarity, even if “vague, basic and impossible to hash out in a rationalistic manner”, must be true, because if X is lower than Y, then X is dependent upon Y, and if X is dependent upon Y, then X must “resemble” Y. You seem to claim that it all comes down to X resembling Y, which I think is synonymous with X being an image of Y, X being similar to Y, X being a representation of Y, X being an effect of Y, and so on. These are all just different ways of describing the same underlying reality. It does no good to say that these are all just different ways of talking about dependence and inferiority, because then your account is completely circular. You have to pick some point in the circle as the foundation, and explicate it, insofar as you can, possibly with examples to demonstrate the overall principle. I think that you are right to focus upon resemblance, but now you have to explain what it means to say that X resembles Y without talking about similarity, image, dependence, inferiority, and so on, because all of these terms are parasitic upon resemblance.

    The virtual distinction is how Aristotle and the Scholastics tackled the issue of the lower being in the higher, but, even then, you have to remember that the virtual distinction is nothing like a real distinction. The way the higher contains the lower is ontologically vague and basic, and only notionally clear. Recall that the virtual distinction is a notional distinction that relates to a real whole, which is not ontologically distinct. We can, somehow, pick apart the higher in our minds to comprehend how it contains the lower; but this does not mean that our notional distinctions are anything real. Once again, the resemblance of higher and lower things is a basic concept that cannot be cashed out in the way that you want it to be.

    Here’s how I understand things.

    Say that you have X and Y, and X and Y are both in Z.

    One the one hand, X is really distinct from Y iff (a) in reality, X is different from Y (i.e. not notionally), (b) in reality, X and Y are both in Z, and (c) X could exist separately from Y and Z. For example, in a material being (= Z), you have form (= X) and matter (= Y). In reality, the form is different from matter (i.e. not notionally), which satisfies (a). In reality, the form and matter are both in the material being, which satisfies (b). The form could exist separately from matter and the material being, i.e. following abstraction into an immaterial intellect, which satisfies (c). Therefore, form is really distinct from matter.

    On the other hand, X is virtually distinct from Y iff (d) in reality, X is different from Y (i.e. not notionally), (e) in reality, X and Y are both in Z, and (f) X cannot exist separately from Y and Z. For example, in the divine intellect (= Z), there exists the divine idea of human nature (= X) and the divine idea of dog nature (= Y). In reality, the divine idea of human nature is different from the divine idea of dog nature, which satisfies (d). In reality, the divine idea of human nature and the divine idea of dog nature are both in the divine intellect, which satisfies (e). The divine idea of human nature cannot exist separately from the divine idea of dog nature and the divine intellect, which satisfies (f). Therefore, the divine idea of human nature is virtually distinct from the divine idea of dog nature.

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  16. Ultimately, real distinction and virtual distinction are differentiated from notional distinction in that the former affirm (a) (= (d)) and (b) (= (e)), whereas the latter denies (a) (= (d)) and (b) (= (e)). And real distinction is differentiated from virtual distinction in that the former affirms (c) whereas the latter denies (c) (= affirms (f)). So, the virtual distinction is not a kind of notional distinction at all, because the notional distinction between X and Y is only in the mind, and not rooted in reality at all, whereas the virtual distinction between X and Y is rooted in reality, and thus not only in the mind.

    Now, to relate this to your account above, I think that the higher (cause) virtually contains the lower (effect) in the sense that the higher contains the forms of the lower in a virtual mode of being that becomes an actual mode of being in the effect. In a sense, the higher becomes manifest in the lower via the shared form that subsequently becomes limited by particularity, and thus becomes manifest in a limited and finite fashion that still contains the representation of the higher via the shared form. The formal identity between the two forms is what grounds the connection between them. As Aquinas writes: “It is according to the form of the effect pre-existing in the agent that the effect attains likeness to the agent, for an agent produces its like with respect to the form by which it acts” (SCG 2.46).

    What you're proposing is straight-up onto-theology that reduces God to the level of a supreme being. God and man would have to exist in the same sense and have properties in the same sense for this analogy to work. That clearly is not what Gregory is saying. Rather, he's saying that the lower contains the stamp of the higher. This is totally different than isomorphism.

    But that is what Gregory is implying with his examples. He talks about the reflection in the mirror being the same as what is reflected. He talks about the imprint that something makes in the wax. In both examples, there is an isomorphism which grounds the connection between them. You cannot say that two things are connected without affirming something in common between them, and that commonality must be a kind of isomorphism between the two. In a mirror image, the commonality is the shared light rays between the object and its mirror image. In the wax, the commonality is the physical shape and spatial orientation of the object that is imprinted in the wax. If you claim that X and Y are connected, but they have nothing in common between them, then I’m afraid that you are talking nonsense.

    Furthermore, it depends upon what you take “onto-theology” to mean. To me, onto-theology is the reduction of all reality into a form that is consistent with human conceptual and semantic resources and demands. Ontology must be reduced to being, which is coextensive with (human) thought and intelligibility; theology must be reduced to a supreme being that is causa sui, and that serves as the source and ground of all other beings, which is necessary for reality to be intelligible to us. It is ultimately about us and our need to know and control, which is what leads Marion to declare that onto-theology is ultimately a form of idolatry in which God must conform to and be reduced to human horizons of meaning and significance. As he writes:

    “The idol must fix the distant and diffuse divinity and assure us of its presence, of its power, of its availability. Just as our experience precedes the face of the divine, so our vital interest proceeds from it: the idol fixes the divine for us permanently, for a commerce where the human hems in the divine from all angles … These gods, therefore, conform first to us, or, less summarily, to the modalities of our multiform perception of the divine. The idol reflects back to us, in the face of a god, our own experience of the divine” (Marion, The Essential Writings, p. 44).

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  17. To overcome onto-theology and such idolatry, according to him, is to allow God to reveal himself on his own terms and in such a way that he exceeds our concepts and semantics that simply cannot contain him at all:

    “the unthinkable enters into the field of our thought only be rendering itself unthinkable there by excess, that is, by criticizing our thought. To cross of Gxd, in fact, indicates and recalls that Gxd crosses out our thought because he saturates it” (Ibid., p. 70).

    Anyway, it is perfectly fine if you want to affirm the mystery and incomprehensibility of your position as an intrinsic feature of it. That would fully explain why it makes absolutely no sense to me on conceptual terms, i.e. it exceeds the capacity of the intellect to contain it within its finite scope and power. (But notice that it leaves open the possibility that the mind is enfolded in darkness, not due to excess (i.e. too much), but due to deficit (i.e. too little).) However, this opens you to someone objecting to any argument to yours in the exact same way. After all, a materialist can say that it is an incomprehensible mystery how consciousness arises from the material brain, but it is affirmed nonetheless, which would leave you with no further response, because logic and reason have been left outside as inapplicable within. In fact, it leads to a radical relativism with no ability to decide between competing positions, because once a logical contradiction or incoherence is derived, your interlocutor could simply say, “mystery!”, and leave you silent.

    The re-presentation of X is a dimmed reflection of X-as-X, rather than of F-in-X.

    But this just pushes the matter one step further, because then you have to explain what a “dimmed reflection” is. What makes X a reflection of Y? What makes X a dimmed reflection of Y?

    Indeed. But Gregory was a Neo-Platonist, and so his words don't translate that directly into Aristotelian language. He is not referring to the presence of a substantial or accidental form in two places, but rather to what I described above: the re-presentation of X-as-X. Neo-Platonism, to my knowledge, did not spend much time hashing out a virtual distinction. Resemblance was a holistic representation of substance, rather than a reduced discussion of forms in multiple locations. That language, in fact, was essentially just an attempt to rationalize what the Platonists had always believed.

    First, again, the issue is this “resemblance”. The examples that are used to explain and justify resemblance all involve isomorphism of some kind. To say that resemblance can also not involve isomorphism of any kind is simply to negate resemblance itself. It would be like explaining triangularity with multiple three-sided figures, and then saying that there can be a triangle that is not three-sided at all, and yet still a triangle. I don’t think that there can be any sense to such a position.

    Second, he may not be talking specifically about Aristotelian forms, but he is still talking the language of isomorphism. There is something that is common between the object, and its image, its mirror image, its representation, its resemblance, and so on, which is what makes all the latter about the former at all. Without that commonality, which Gregory references when he says that “when you put gold in front of a mirror, the mirror takes on the appearance of the gold, and because of the reflection it shines with the same gleam as the real substance”. When you put gold in front of a mirror, the mirror takes on the appearance of the gold, and because of the reflection it shines with the same gleam as the real substance. It is precisely because there is “the same gleam” that the reflected image in the mirror “takes on the appearance” of the object in question.

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  18. I understand that what I'm saying can hint at nominalism, but it's really the core of Aquinas's beliefs on form. As I quoted above, the individual substance is what really exists. And the form possessed by an individual substance is in turn individualized. We can only talk about the identity between dguller and rank sophist after we have moved into the realm of universals, which is an abstraction fundamentally separate from what really exists. In fact, you mention this below. However, in reality, what exist are individual substances with vague similarities. We can mentally ground this similarity in the absolute identity of form, but this, again, is simply abstraction. It can tell us certain things about the real individuals--natural law, for instance--, but it fails to provide the concrete ground for similarity that you want it to. Similarity is what really exists; partial identity and partial difference is a mental construct that does not really exist. Even you admit below that partial identity is an impossible idea until we head into abstraction.

    First, you are contradicting yourself. On the one hand, you say that “individual substance is what really exists”, and on the other hand, you say that “similarity is what really exists”. Unless you want to claim that similarity is a substance, then you have made a mistake somewhere. The truth is that similarity is a relation between substances that is grounded upon something in common between the substances and something not in common between the substances. That relation would remain true even if no mind existed to think about the relation as a mental proposition of some kind.

    Second, I think that you are equivocating on “mental construct”. There are different kinds of mental constructs, which correspond to different referents, which either actually exist, potentially exist, virtually exist, previously existed in the past, will exist in the future, or do not exist at all in any sense of “exist”. When you say “mental construct” you seem to implying only the non-existent kind of referent, when the reality is that all our thoughts are necessarily “mental constructs”, even when they are about actual, potential, virtual beings. After all, “existence” is manifold and multifaceted, and is quite rich. Reducing “existence” to a single kind was Parmenides’ mistake, i.e. if you only admit actual being, then you get stuck in bizarre paradoxes. Once you admit different kinds and degrees of being, then you avoid such paradoxes. Similarly, by reducing existence to actual substantial being makes it inconceivable how a core and fundamental relation like similarity is even possible. My account explains how similarity works, and your main objection is that it is impossible upon your impoverished ontology. My response is that ontology is far richer than you assume.

    Third, if you look at what Aquinas wrote about similitude, he writes at SCG 2.46:

    “Now, the likeness of one thing is found in another thing in two ways: first, as regards natural being-the likeness of heat produced by fire is in the thing heated by fire; second, cognitively, as the likeness of fire is in sight or touch.”

    To me, this means the following. Say you have X and Y, and claim that X is like Y. Aquinas says that there are two ways that this could be true. First, if X and Y share a commonality that exists outside of a knowing mind. For example, when a flame is heating wax, the flame is like the wax in that they are both hot. “Heat” is what is in common between the two, and which grounds the likeness between them. Second, if X and Y share a commonality that exists inside of a knowing mind. For example, seeing fire is like touching fire in that both involve the perception of fire by a knowing mind. “Perceiving fire” is what is in common between the two, and which grounds the likeness between them. In both cases, the likeness presupposes a commonality, which can exist in the mode of esse naturale or the mode of esse intentionale, as we discussed in a previous thread.

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  19. F-in-X and F-in-Y does not reflect ontological reality, though. X and Y are what exist; both are whole substances with ontological similarities. The grounding of this similarity in the total identity of form is a mental abstraction that cannot be carried over into reality without a contradiction.

    First, the contradiction only occurs if you assume that identity can only mean numerical identity. If you admit other kinds of identity, e.g. formal identity, then there is no contradiction at all.

    Second, if you claim that only substances exist, then God does not exist. God is not a substance. To be a substance necessarily requires having a substantial form. However, God does not have a substantial form, because to have a form is to have an essence defined as distinct from existence. God’s “form” or “essence” is subsistent being itself, which is ultimately not an essence at all. Therefore, God is not a substance. Now, if you want to predicate some kind of existence of God that is different from substantial existence, then you have opened the door to different kinds of being, all of which are appropriate for their respective entities, which should also include the existence of the metaphysical components of substances.

    Third, you still assume that mental abstractions necessarily do not correspond to anything real, which ultimately reduces everything that isn’t a substance to unreality.

    Indeed. But you cannot then re-project C* on to X and Y without qualification. C* is an abstraction from the concrete reality of X and Y; it only partly reveals the proper object of knowledge, which is the individual substance. You can't explain the ontological reality of analogy by appealing to a distinction between partial identity and partial difference that is only valid in the mind.

    Again, there seems to be an inconsistency here. On the one hand, you dismiss abstraction as a mental construct that misses the concrete reality by virtue of being an abstraction. On the other hand, you admit that abstraction can partly reveal the concrete reality, and thus it must correspond to something real within the concrete reality of an individual substance. It is not exclusively a mental construct in the sense of having no correspondence to anything in reality, such as different names and ideas for the same thing. Instead, it is something really in a substance that the mind is equipped to understand via abstraction, even though the form itself does not exist outside of a substance or an intellect. It is true that dguller and rank sophist have a formally identical human nature that is numerically distinct, which is what makes them both human beings. This is not just something the mind is projecting upon reality on the basis of its own needs and capacities, but rather something that the mind has discovered in reality by its intellectual powers. And if that is true, then one certainly can say that C* is present in both X and Y, even if this came at the end of a process of abstraction and ratiocination that required cognitive processes.

    There is an unfathomable moment when potency becomes act as a result of act's presence. The form presented to the potency is suddenly copied in the potency, and the potency transitions into act. It is fundamentally strange and unique, but it is not contradictory.

    But wait. I thought that the form was already in the patient, but in a potential mode of being. The form was not “copied” by the patient when the agent is in proximity to the patient. It simply transitions from potency to act. What copying is going on? Perhaps what you mean is that the patient copies the form in act in the agent, which is different from copying the form per se, which already exists in the patient in potency.

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  20. In any case, you're definitely correct that pulling the concept of transcendental multiplicity from Trinitarian theology into the realm of transcendental being is an equivocation.

    But remember that transcendental multiplicity is not a divinely revealed term that is locatable in the Bible or early Christian tradition. It is a philosophical term that is brought to bear upon the doctrine of Trinity to better understand it. If you want to say that this is necessarily an equivocation, then all revealed theology involves equivocation, because all revealed theology involves the use of human intellectual resources to understand revelation. Rather than equivocation, it would be better to say it is involves analogy such that human intellectual resources can be used to understand revelation, because they have something in common between them that grounds the connection, and thus justifies the applicability of those resources to understand revelation in the first place.

    Esse has no transcendental multiplicity, even if God does.

    It depends upon what you mean by “esse”. Do you mean ipsum esse subsistens? If you do, then it most certainly has transcendental multiplicity, because ipsum esse subsistens is God. Do you mean esse commune? If you do, then it also has transcendental multiplicity, because one can coherently describe this esse in this particular ens as distinct and different from that esse in that particular ens. Remember that act is limited by potency, which means that esse is limited by essence into a particular ens. Once that esse has been limited by essence into a composite ens, it assumes the characteristic of transcendental multiplicity, which is applicable to every composite ens.

    Rocca seems to insinuate that Denys was a negative theologian in the same vein as Maimonides, which could not be further from the truth

    His book provides more nuance, I think. He writes: “Dionysius’ negative theology is primarily mystical and nonconceptual; and when it occurs as an element within affirmative theology it appears as a gift from a higher region and takes in affirmative theology the form it does due to the constraints of the imaginative or notional context, and as a concession to human weakness” (Rocca, p. 22). He affirms the tension in his thought between the need for silence in the face of the incomprehensible, but also the need for constant talk about the divine as manifest in creation, albeit with never-ending denials and negations in a dialectic between affirmation and negation.

    he fails to incorporate Denys's radical statement about God being "beyond every denial" into his argument

    He specifically cites this passage on p. 16 of his book.

    Rocca suggests that there is a positive theology underneath this, but I don't think that's correct. He seems to think that Aquinas believes the Five Ways to make positive statements about God when they do no such thing: they simply extend creaturely concepts to their logical conclusions and state that, if they are to be explained, some kind of transcendent reality analogically similar to them must exist. Analogy is presupposed in the proofs of God's existence, rather than derived from them.

    First, you are correct that he argues that the negative theology can only make sense on the basis of positive affirmations about God. God is incomprehensible, because his essence is unavailable to our intellects in this life. Why? Because God is simple such that his essence is subsistent being itself, which makes it impossible for our intellects to abstract his essence from his existence as would be necessary to know him in a natural fashion. Now, you could argue that divine simplicity is a negative doctrine, i.e. the negation of composition, but the further implication of the negative doctrine of divine simplicity in which God’s essence is subsistent existence itself becomes a positive doctrine itself.

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  21. Second, you should know that he agrees with you that the epistemology and semantics of analogy presupposes an ontological scheme involving likeness and representation (Ibid., p. 308). It is only on the basis of an ontology of causality such that lower effects resemble their higher causes by virtue of the fact that the lower effects pre-exist in a more eminent fashion in their higher causes.

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  22. dguller,

    Comment moderation has been enabled, so, as usual, this will be my last response.

    I don’t know if potential being and actual being can be quantified in such a way, i.e. one unit of potential being = one unit of actual being

    It can't be quantified in that way without undermining the entirety of Aristotelian metaphysics. That was my point.

    First, act and potency are transcendentals that are operative upon everything that exists under the categories, including substances.

    For Aquinas, there are five transcendentals: being, One, goodness, nobility and truth. Act and potency are not in there. You can say that act and potency apply to everything that has to do with substance of any sort, which is true. However, this does not make them transcendental concepts.

    Remember that a transcendental is “something above every genus, common to all beings, and thus not restricted to any category or individual” (Feser, Aquinas, p. 33). Act and potency certainly qualify under that description.

    If act and potency were transcendentals, then it would follow that act and potency were interconvertible. This leads us to the contradiction that something can be potential and actual in the same way at the same time. Potency and act are not common to all being: they are kinds of being.

    Perhaps you should clarify your terms, because you are not using them according to Heidegger’s understanding.

    I wasn't trying to mirror Heidegger's use of ontological and ontic--I wasn't even aware that my post would give this impression. By "ontic", I was referring to beings and their characteristics, accidents, forms, matter and suchlike. All of these concepts presuppose ontology, which addresses being-as-such. Ontology therefore considers the essences and esse of substances that ground all ontic components. Your argument confuses ontology with the actuality and potentiality of ontic accidents, which results in strange contradictions such as the concept of "more being". Being is presupposed by the ontic world: it does not even enter into its consideration. You can have more potential being or more actual being, but you cannot have more being-as-such. No matter how much your ontic actuality increases, you will never exist more.

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  23. And just because it pertains to secondary actuality and accidental being, and not to substantial being, does not mean that it has nothing to do with the being of a substance.

    If by "the being of a substance" you mean literally the esse of a substance, then it has nothing at all to do with it. But if you mean the ontic "existence" of the substance in the world, then certainly. Just don't confuse transcendental goodness with ontic goodness: ontic goodness is an attempt to mirror transcendental goodness; it is not transcendental goodness proper.

    First, if you want to say that the kinds of being in which there is no degrees of being correspond to “ontological”, and the kinds of being in which there are degrees of being correspond to “ontic”, then that is fine. But that doesn’t change the fact that they are both different kinds of being

    Ontology deals with being-as-such: the concepts of esse and essence. Esse and essence are not kinds of being. Rather, they are that in which being consists, and so ground all "kinds of being". The existence of a real tree, for example, is an ontic condition that presupposes essence and esse at every level. There isn't tree-being and esse-being; there is tree-being and esse.

    there is no problem with saying that ontic being admits of degrees such that a particular being can have more (ontic) being than another being, which ends up corresponding to the former being closer to the ideal set by the being’s nature than the latter.

    We are agreed, then. As long as you mean by "ontic being" things like tree-being or human-being, whose accidents and powers can be more or less actual. In that case, though, it's kind of an equivocation to say that one thing has more being than another. Ontic being is not esse; it presupposes esse. Ontic being is the semi-existence of the components of substance that presupposes the true act of existence that allows it to be.

    So, in that case, the material substance depends upon its accidents in order to be a material substance to begin with. There is a co-dependency involved.

    Accidents inhere in substance; substance does not inhere in accidents. This is not co-dependency.

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  24. He discusses this at ST 1.30.3, and at QDP 9.7, if you want to read about it. Transcendental multiplicity is necessarily a transcendental, because it is a condition under which any differentiation is possible inasmuch as transcendental unity is a condition under which unity is possible, which is beyond the categories, and is, in fact, presupposed by them, thus making it a transcendental.

    I haven't read this section of the Summa before. Very interesting. However, I think you've misinterpreted Aquinas here. He does not say that multiplicity is a transcendental, in the sense that it may be placed alongside being, truth, etc. He derives multiplicity from the concept of One:

    So when we say, the essence is one, the term "one" signifies the essence undivided; and when we say the person is one, it signifies the person undivided; and when we say the persons are many, we signify those persons, and their individual undividedness; for it is of the very nature of multitude that it should be composed of units.

    Multiplicity is simply an abstract collection of "One" units. It is not itself a transcendental. Aquinas is arguing that the concept of One can entail multiplicity, which is a very novel way of looking at it. With this position, he is able to affirm the Trinity's multiplicity simply by affirming the existence of its members in their "individual undividedness", which is analogous to One.

    As cool as this is, though, it has very little to do with our argument. My claim was that One is the ground of the idea that the whole is greater than the part, and that, in its convertibility with goodness, it is the ground of superiority-inferiority relations. The Trinity is neither a whole nor a part, nor is One applicable to it except analogously. As a result, your argument did not address my claim.

    But when Augustine made that addition, he added differentiation to the One, which completely contradicted the original Neoplatonic understanding of the One as undifferentiated.

    I don't believe you're correct here, but I haven't read enough of Augustine's work to comment.

    That’s all fine, as long as we are clear that God necessarily involves differentiation, at the very least in the virtual differentiation between the divine ideas, the divine attributes, and the divine persons, which is impossible for the Neoplatonic One.

    Virtual differentiation is applicable to the Neo-Platonic One. This is because virtual composition is only in our minds, as they relate to really undifferentiated wholes.

    You seem to claim that it all comes down to X resembling Y, which I think is synonymous with X being an image of Y, X being similar to Y, X being a representation of Y, X being an effect of Y, and so on.

    Actually, I would argue that the relation of dependence is what ultimately grounds resemblance--a word that I would also use synonymously with "being an image", "being similar", "being a representation" and so forth. But I would not argue that resemblance can be explained in rational terms: I think it's a basic concept that cannot ultimately be divided.

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  25. It does no good to say that these are all just different ways of talking about dependence and inferiority, because then your account is completely circular. You have to pick some point in the circle as the foundation, and explicate it, insofar as you can, possibly with examples to demonstrate the overall principle. I think that you are right to focus upon resemblance, but now you have to explain what it means to say that X resembles Y without talking about similarity, image, dependence, inferiority, and so on, because all of these terms are parasitic upon resemblance.

    Here's what I think.

    If X depends upon Y, then X will resemble Y. What does "resemble" mean? This is impossible to explain clearly in ontological terms. The finite simply suggests the infinite; created beauty simply suggests uncreated beauty. Particular instantiations of fire suggested fire-as-such to ancient scientists. The conclusion that "Socrates is mortal" suggests the premise "All men are mortal". The only way to make resemblance intellectually clear is to move from ontology into our own minds and employ the virtual distinction. In this way, we can somehow point to the way that the higher contains the lower, even though the distinctions we make do not reflect real distinctions. Ontological resemblance remains vague no matter how many clear virtual distinctions we make about it.

    My conclusion is twofold: first, resemblance is a basic feature of ontology that cannot be explained further in ontological terms; second, the virtual distinction allows us to analyze ontological resemblance in such a way that it becomes intellectually clear. The danger is when we confuse virtual distinctions with ontology, which I believe is the root of our long argument about analogy.

    On the other hand, X is virtually distinct from Y iff (d) in reality, X is different from Y (i.e. not notionally), (e) in reality, X and Y are both in Z, and (f) X cannot exist separately from Y and Z.

    Your first two points show that you are not talking about the virtual distinction. A virtual distinction is when a real whole is seen by our minds to contain a multitude of forms. The core of the virtual distinction is that it does not exist in reality. As a result, X (virtual part) would be virtually distinct in Y (real whole) iff (a) X was not really different from Y in reality (only notionally) and (b) X did not really exist in Y (only notionally).

    In reality, the divine idea of human nature is different from the divine idea of dog nature, which satisfies (d).

    In reality, there are no divine ideas, because God is wholly one. Virtual distinctions do not relate to real distinctions; they relate to real wholes.

    In reality, the divine idea of human nature and the divine idea of dog nature are both in the divine intellect, which satisfies (e).

    This is false as well. The only thing that exists in the real world is the divine intellect. Nothing is, properly speaking, "in it" at all. The divine ideas exist only virtually, i.e. notionally. What really exists is an undivided whole, which we notionally analyze.

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  26. Ultimately, real distinction and virtual distinction are differentiated from notional distinction in that the former affirm (a) (= (d)) and (b) (= (e)), whereas the latter denies (a) (= (d)) and (b) (= (e)).

    Not at all. The differences between the three types of distinctions are as follows:

    1. A logical distinction is real iff it relates to a real distinction in the real world.
    2. A logical distinction is notional iff it relates only to a being of reason.
    3. A logical distinction is virtual iff it relates to a really indistinct whole in the real world.

    The virtual distinction is a combination of the notional and real distinctions: its distinctions are notional but are related to real wholes.

    Now, to relate this to your account above, I think that the higher (cause) virtually contains the lower (effect) in the sense that the higher contains the forms of the lower in a virtual mode of being that becomes an actual mode of being in the effect.

    In other words, the cause is really indistinct and contains the effect in an ontologically vague way, even though our minds can analyze it in clearer terms.

    He talks about the reflection in the mirror being the same as what is reflected. He talks about the imprint that something makes in the wax.

    He is making the fairly standard point that there is a vague ontological resemblance between the dependent and that on which it depends.

    To me, onto-theology is the reduction of all reality into a form that is consistent with human conceptual and semantic resources and demands.

    I would agree with this definition. And this is what isomorphism entails. If there is an isomorphism between the form that is "in" God and in us, then it follows that God has been reduced to a supreme being that falls into the same categories we do. But isomorphism is clearly not what Gregory or any of the other great writers of Christianity have in mind.

    Anyway, it is perfectly fine if you want to affirm the mystery and incomprehensibility of your position as an intrinsic feature of it.

    There is nothing mysterious or incomprehensible about vague ontological resemblance. We see it everywhere. Anything that virtually contains another thing is an example.

    What makes X a reflection of Y? What makes X a dimmed reflection of Y?

    X is a reflection of Y because X relies on Y, which results in (again) vague ontological resemblance. This is (again) a simple, basic concept that cannot be analyzed further in ontological terms. Virtual distinctions allow us to make logical sense of it, even though these do not relate to real distinctions.

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  27. There is something that is common between the object, and its image, its mirror image, its representation, its resemblance, and so on, which is what makes all the latter about the former at all.

    There is nothing between the two things that can be said to be totally identical, for two reasons. First, total identity in two places is a contradiction. Second, the resemblance that Gregory is talking about is fundamental: it simply happens when certain conditions (i.e. the creation and sustenance of one thing by another) are met. The virtual distinction is an attempt to rationalize this event, but even those who use it acknowledge that it does not reflect the real distinctions and real isomorphism that you believe are necessary.

    On the one hand, you say that “individual substance is what really exists”, and on the other hand, you say that “similarity is what really exists”.

    Both exist. The individual substance is what has esse, and the individual substance is fundamentally similar to other individual substances.

    The truth is that similarity is a relation between substances that is grounded upon something in common between the substances and something not in common between the substances.

    If something is common between the substances, then it is either partially identical or totally identical. If it is partially identical, then there must be something fully identical to ground that partial identity. But if something is fully identical in two places, then we have a contradiction. Your account cannot maintain coherence.

    Similarly, by reducing existence to actual substantial being makes it inconceivable how a core and fundamental relation like similarity is even possible.

    Existence is actual substantial being for Aquinas. Other forms of being (i.e. accidental being, beings of reason, etc.) rely on this more original existence.

    For example, when a flame is heating wax, the flame is like the wax in that they are both hot. “Heat” is what is in common between the two, and which grounds the likeness between them.

    Heat-in-wax and heat-in-flame are either partially or totally identical. You know the rest.

    The solution to this problem, to which Aquinas subscribes, is that heat-in-flame (like health-in-medicine) is only virtually distinct from flame itself. Flame as a totality heats wax, which copies a particular form (heat) from flame. This form existed virtually but not really within flame. In other words, there is a vague ontological resemblance between flame and the form of heat that appears in wax. The virtual distinction makes this resemblance mentally but not actually clear.

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  28. If you admit other kinds of identity, e.g. formal identity, then there is no contradiction at all.

    Formal identity does not exist in the actual world. Again, only individual substances with individualized forms exist. Formal identity (i.e. the total identity of a form in two places) is an abstraction of the possible intellect.

    Second, if you claim that only substances exist, then God does not exist.

    He doesn't. From the Sentences as quoted by Rocca: "Lastly, however, we even remove from him his very existence, as it is in creatures, and then our understanding remains in a certain darkness of ignorance".

    Third, you still assume that mental abstractions necessarily do not correspond to anything real, which ultimately reduces everything that isn’t a substance to unreality.

    Anything that isn't a substance or in some way reliant upon a substance cannot be said to exist. This is Thomism 101.

    Anyway, our mental abstractions relate to components within substances that are similar, but similarity is not one-to-one identity--i.e. isomorphism. Humans are always particular humans, and "formal identity" is never simply one-to-one identity. In other words, it isn't a total identity that could ground your partial identity regress. The correct answer to this mess is to reject the partial identity-partial difference distinction as meaningless and to acknowledge that the vagueness of similarity is fundamental.

    On the one hand, you dismiss abstraction as a mental construct that misses the concrete reality by virtue of being an abstraction. On the other hand, you admit that abstraction can partly reveal the concrete reality, and thus it must correspond to something real within the concrete reality of an individual substance.

    I reject the idea that correspondence is isomorphism, and so this is not a problem. As Aquinas puts it, the intelligible species is a "likeness". He does not cash out likeness in any more fundamental terms. The intelligible species is simply similar to that which it relates: not partially identical and partially different. Since I believe similarity to be a basic concept, I'm not bothered by this vagueness.

    It is true that dguller and rank sophist have a formally identical human nature that is numerically distinct, which is what makes them both human beings.

    If the formal identity is numerically distinct, then it is not absolute but only (in your words) partial identity. And partial identity cashes out in two ways: as an infinite regress or as a contradiction of total identity. The solution, again, is to say that formal identity is a kind of similarity rather than a partial identity.

    And if that is true, then one certainly can say that C* is present in both X and Y, even if this came at the end of a process of abstraction and ratiocination that required cognitive processes.

    C* itself is numerically distinct from X and Y, which are numerically distinct from each other. It cannot be present in X and Y except through similarity and likeness.

    Perhaps what you mean is that the patient copies the form in act in the agent, which is different from copying the form per se, which already exists in the patient in potency.

    That would be a better way of putting it, yes.

    He affirms the tension in his thought between the need for silence in the face of the incomprehensible, but also the need for constant talk about the divine as manifest in creation, albeit with never-ending denials and negations in a dialectic between affirmation and negation.

    Which is analogy properly understood, yet Rocca does not seem to refer to it as such.

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  29. Rank:

    For Aquinas, there are five transcendentals: being, One, goodness, nobility and truth. Act and potency are not in there. You can say that act and potency apply to everything that has to do with substance of any sort, which is true. However, this does not make them transcendental concepts.

    Why not? A transcendental is just something that is beyond the categories, and yet applies to the categories and everything under the categories. Since act and potency “apply to everything that has to do with substance of any sort”, then they are transcendentals, under my definition, which is also Feser’s. And if act and potency are not transcendentals, then what are they? They are not categories. They are not transcendentals. Do they fit anywhere?

    If act and potency were transcendentals, then it would follow that act and potency were interconvertible. This leads us to the contradiction that something can be potential and actual in the same way at the same time. Potency and act are not common to all being: they are kinds of being.

    That would be true only if all transcendentals were interconvertible. Maybe some are, and some aren’t? Maybe there are two kinds of transcendentals: convertible and non-convertible.

    Your argument confuses ontology with the actuality and potentiality of ontic accidents, which results in strange contradictions such as the concept of "more being". Being is presupposed by the ontic world: it does not even enter into its consideration. You can have more potential being or more actual being, but you cannot have more being-as-such. No matter how much your ontic actuality increases, you will never exist more.

    And your argument limits “being” to only the esse of a substance. If being exists in different modes, then why is only one mode called “being”, and the other modes “non-being”? Why can’t they all be kinds of being, and thus “being”? So what if accidental being depends upon substantial being. Dependence does not nullify being, or else created being would not be being either. Only God would exist, and nothing else would exist, which is absurd. Sure, God exists in a higher and incomprehensible fashion, but it does not follow that nothing else exists, or can be said to have “being” or “existence”.

    We are agreed, then. As long as you mean by "ontic being" things like tree-being or human-being, whose accidents and powers can be more or less actual. In that case, though, it's kind of an equivocation to say that one thing has more being than another. Ontic being is not esse; it presupposes esse. Ontic being is the semi-existence of the components of substance that presupposes the true act of existence that allows it to be.

    It isn’t an equivocation, unless you assume that only substantial being counts as being. If ontic being is a kind of being, then more ontic being counts as more being, even if it doesn’t count as more substantial being.

    Accidents inhere in substance; substance does not inhere in accidents. This is not co-dependency.

    A substance would not be a substance without accidents. And you cannot cite God as an example of a substance without accidents, because God cannot be a substance by virtue of transcending the categories, one of which is substance.

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  30. I haven't read this section of the Summa before. Very interesting. However, I think you've misinterpreted Aquinas here. He does not say that multiplicity is a transcendental, in the sense that it may be placed alongside being, truth, etc.

    I never said that it was interconvertible with other transcendentals. And this actually puts to the question whether all transcendentals are interconvertible. If transcendental multiplicity is a transcendental by virtue of applying to the categories and what exists under the categories, then not all transcendentals are convertible. If transcendental multiplicity is not a transcendental, then it must be a category, which is impossible, because then it cannot be applicable to God, and thus cannot shed light upon the Trinity. So, again, the question is where transcendental multiplicity fits in this scheme, if it fits anywhere at all.

    Multiplicity is simply an abstract collection of "One" units. It is not itself a transcendental. Aquinas is arguing that the concept of One can entail multiplicity, which is a very novel way of looking at it. With this position, he is able to affirm the Trinity's multiplicity simply by affirming the existence of its members in their "individual undividedness", which is analogous to One.

    First, unity and division are presupposed by all the categories, and thus transcends them, which I think would fit the definition of a transcendental, as Feser defined it.

    Second, transcendental multiplicity does not necessarily follow from transcendental unity. It requires an additional negation of indivisibility to arrive at divisibility. In other words, if you start with transcendental unity, then you must further negate the indivisibility associated with transcendental unity to arrive at the divisibility of one from another.

    My claim was that One is the ground of the idea that the whole is greater than the part, and that, in its convertibility with goodness, it is the ground of superiority-inferiority relations. The Trinity is neither a whole nor a part, nor is One applicable to it except analogously. As a result, your argument did not address my claim.

    One is the source of unity and indivisibility. Indivisibility could be taken in two senses: X has no parts, and thus is indivisible, because that without parts cannot be divided, or X has parts, but they are inseparable without destroying X as X, such as the esse-essence composition in an ens, which cannot be separated without destroying the ens. If you are talking about the former sense, then your argument doesn’t work, because there is no whole, because there are no parts at all. If you are talking about the latter sense, then your argument still doesn’t work, because it assumes that transcendental unity is superior to transcendental multiplicity. Since they are both transcendentals, you require some other standard to derive the former’s superiority to the latter.

    Virtual differentiation is applicable to the Neo-Platonic One. This is because virtual composition is only in our minds, as they relate to really undifferentiated wholes.

    Not according to the Neoplatonists.

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  31. Actually, I would argue that the relation of dependence is what ultimately grounds resemblance--a word that I would also use synonymously with "being an image", "being similar", "being a representation" and so forth. But I would not argue that resemblance can be explained in rational terms: I think it's a basic concept that cannot ultimately be divided.

    But some account must be provided to explain why if X is dependent upon Y, then X resembles Y. Why would anyone agree with this conditional? How would you show them that it is true? I don’t think it stands in the same level of primacy as the law of non-contradiction, for example, which is presupposed by all rational and coherent thought whatsoever, and thus any account of it would have to presuppose it to give an account at all. So, some account must be provided, which would have to be supported by examples in which you have X in a state of dependence upon Y, which always leads to X resembling Y, and even better to explain why dependency necessitates resemblance at all.

    If X depends upon Y, then X will resemble Y. What does "resemble" mean? This is impossible to explain clearly in ontological terms. The finite simply suggests the infinite; created beauty simply suggests uncreated beauty. Particular instantiations of fire suggested fire-as-such to ancient scientists. The conclusion that "Socrates is mortal" suggests the premise "All men are mortal". The only way to make resemblance intellectually clear is to move from ontology into our own minds and employ the virtual distinction. In this way, we can somehow point to the way that the higher contains the lower, even though the distinctions we make do not reflect real distinctions. Ontological resemblance remains vague no matter how many clear virtual distinctions we make about it.

    First, every example that you gave involved a limitation placed upon an unlimited X. The finite is a limitation placed upon the infinite; created beauty is a limitation placed upon uncreated beauty; particular instantiations of fire are limitations placed upon fire-as-such; Socrates is mortal is a limitation placed upon the claim that all men are mortal. In other words, the resemblance is between an unlimited X and a limited X. They are both X, but the former is a limited kind of X and the latter is an unlimited kind of X. That is what explains the resemblance involved, and it certainly wasn’t “impossible” to explain.

    Second, remember that we are trying to explain why X depends upon Y iff X resembles Y, which you are now trying to explain on the basis of a higher Y containing a lower X. So, there is now a grounding connection between a higher Y contains a lower X and X resembles Y. How exactly did you go from the former to the latter? What is the intermediary steps that justify the connection itself? It certainly isn’t clear. I can think of examples of containment that imply neither resemblance nor dependence. A ball in a box, for example. So, what is it about a higher containing a lower that explicates why the lower must resemble the higher?

    Your first two points show that you are not talking about the virtual distinction. A virtual distinction is when a real whole is seen by our minds to contain a multitude of forms. The core of the virtual distinction is that it does not exist in reality. As a result, X (virtual part) would be virtually distinct in Y (real whole) iff (a) X was not really different from Y in reality (only notionally) and (b) X did not really exist in Y (only notionally).

    First, this account is incorrect. The divine persons are virtually distinct from one another, according to G-L, but the divine persons are not “a multitude of forms”.

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  32. Second, we conceive of X as distinct from Y in our minds, and the question is whether this conceptual distinction corresponds to anything in reality. This can be understood in a variety of ways, depending upon how you understand “reality”. If by “reality”, you only understand independently existing substances, then if X cannot exist as an independently existing substance, then X does not really exist. But this condition holds for both notional and virtual distinction, because in both cases, X cannot exist as an independently existing substance. So, there must be something more to a virtual distinction that distinguishes it from a notional distinction. Your account does not explain what differentiates a notional distinction from a virtual distinction. I recall that G-L wrote that a virtual distinction is “grounded in reality”. But what could that mean, according to you? If “reality” is an independently existing substance, then it would mean that X is “grounded” in an independently existing substance. But what does this “grounded” mean? Even a notionally distinct X would be “grounded”, because it is about Y. So, you would have to explain “grounded” without making any reference to reality, and yet without the grounding being solely a byproduct of our minds. I don’t think that this is possible.

    In reality, there are no divine ideas, because God is wholly one. Virtual distinctions do not relate to real distinctions; they relate to real wholes.

    But if the virtual distinctions are grounded in reality, then they must correspond to something real, other than the whole substance that contains the virtual distinctions. Otherwise, there is no difference between a virtual distinction and a notional distinction at all.

    This is false as well. The only thing that exists in the real world is the divine intellect. Nothing is, properly speaking, "in it" at all. The divine ideas exist only virtually, i.e. notionally. What really exists is an undivided whole, which we notionally analyze.

    But then there is no difference between a notional distinction and virtual distinction. In fact, you seem to imply that they are one and the same, “only virtually, i.e. notionally”.

    Not at all. The differences between the three types of distinctions are as follows:

    1. A logical distinction is real iff it relates to a real distinction in the real world.
    2. A logical distinction is notional iff it relates only to a being of reason.
    3. A logical distinction is virtual iff it relates to a really indistinct whole in the real world.

    The virtual distinction is a combination of the notional and real distinctions: its distinctions are notional but are related to real wholes.


    First, you haven’t defined “real distinction” at all.

    Second, I don’t see the difference between (2) and (3). If all that exists is the “really indistinct whole in the real world”, then any distinction that you make within the whole will necessarily be a “being of reason”. After all, the distinction does not correspond to anything in reality, and thus is nothing but a projection of the human mind upon the “really indistinct whole in the real world”. Thus, if you are correct, then (2) = (3).

    He is making the fairly standard point that there is a vague ontological resemblance between the dependent and that on which it depends.

    But look at some other things that Gregory writes:

    “Now as the image bears in all points the semblance of the archetypal excellence, if it had not a difference in some respect, being absolutely without divergence it would no longer be a likeness, but will in that case manifestly be absolutely identical with the Prototype” (On the Making of Man, 16.12)

    You have a prototype and an image of the prototype. He says that the image “bears in all points the semblance of the archetypical excellence”, but that “if it had not a difference in some respect”, then “it would no longer be a likeness”, but would be “absolutely identical with the Prototype”.

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  33. He also writes:

    “For that which is “made in the image” of the Deity necessarily possesses a likeness to its prototype in every respect; it resembles it in being intellectual, immaterial, unconnected with any notion of weight, and in eluding any measurement of its dimensions; yet as regards its own peculiar nature it is something different from that other. Indeed, it would no longer be an “image” if it were altogether identical with that other” (On the Soul and the Resurrection)

    Again, the image must have something in common with the prototype, i.e. “a likeness to its prototype in every respect”, and yet differ in some way, i.e. “something different from that other”, because otherwise, the image would not be similar to the prototype, but rather identical to the prototype.

    Note that Gregory does not throw his hands in the air, and say that resemblance is inexplicable, because ontologically prior, but rather gives examples and explanations that describe resemblance as partial identity and partial difference. He even explicitly distinguishes resemblance from identity by virtue of the former having a partial difference despite having “a likeness to its prototype in every respect”, which I would construe as partial identity. To say that X is like Y in every respect is identity, which Gregory concedes by saying that only “a difference in some respect” differentiates resemblance from identity. Therefore, he effectively is affirming my account of partial identity and partial difference as the underlying ground of any resemblance.

    I would agree with this definition. And this is what isomorphism entails. If there is an isomorphism between the form that is "in" God and in us, then it follows that God has been reduced to a supreme being that falls into the same categories we do. But isomorphism is clearly not what Gregory or any of the other great writers of Christianity have in mind.

    I know. That is the crux of the problem. Gregory cannot help but affirm isomorphism in any account of resemblance, and yet all such affirmations end up affirming onto-theology and idolatry, because they reduce God to a conceptual level that can be assimilated to the human intellect and understanding.

    There is nothing mysterious or incomprehensible about vague ontological resemblance. We see it everywhere. Anything that virtually contains another thing is an example.

    But that is the problem. If we “see it everywhere”, then what are its distinguishing properties? It is clearly distinct from identity, which even Gregory admits. What makes resemblance different from identity? There must be some account of this difference, and if there is no account, then how do you differentiate between the two?

    There is nothing between the two things that can be said to be totally identical, for two reasons. First, total identity in two places is a contradiction.

    That is only true if the only kind of identity is numerical identity. A form F can exist in two places, and yet be the same F in each location. F is only different in terms of its particular instantiation. In every other respect, it is the same. This is the same as Gregory saying that the image of God in human beings is the same in every respect to the prototype in God, and yet must differ in some way to avoid an identity relationship. He is tacitly using the idea that X = Y iff X and Y are the same in every respect. This account is certainly amenable to abstracting differentiating properties from X and Y until you achieve an identical commonality between them.

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  34. Second, the resemblance that Gregory is talking about is fundamental: it simply happens when certain conditions (i.e. the creation and sustenance of one thing by another) are met. The virtual distinction is an attempt to rationalize this event, but even those who use it acknowledge that it does not reflect the real distinctions and real isomorphism that you believe are necessary.

    I disagree.

    Both exist. The individual substance is what has esse, and the individual substance is fundamentally similar to other individual substances.

    But why? Why is the individual substance similar to other individual substances? Why isn’t the individual substance identical to other substances? Why isn’t the individual substance different from other substances?

    If something is common between the substances, then it is either partially identical or totally identical. If it is partially identical, then there must be something fully identical to ground that partial identity. But if something is fully identical in two places, then we have a contradiction. Your account cannot maintain coherence.

    It is totally identical in its partial identity. In other words, it is partially identical, because certain particularities have been abstracted away, and thus it cannot represent the totality, but rather only a part of the totality, i.e. the part that remains after the other parts have been abstracted. However, that part can be totally identical to another part, which has also been abstracted and stripped of its particularized features, including its numerical identity. For example, say that you have F-in-X and F-in-Y. You abstract away the –in-X and –in-Y, which leaves only F and F. You then abstract away numerical identity, and that only leaves F, which is totally identical to itself.

    Existence is actual substantial being for Aquinas. Other forms of being (i.e. accidental being, beings of reason, etc.) rely on this more original existence.

    But if dependence necessarily means the absence of “existence”, then creation does not “exist”. Only God “exists”. So, even substances do not “exist” on your account, which undermines the entire account, because it is based upon the fundamental “existence” of substances.

    The solution to this problem, to which Aquinas subscribes, is that heat-in-flame (like health-in-medicine) is only virtually distinct from flame itself. Flame as a totality heats wax, which copies a particular form (heat) from flame. This form existed virtually but not really within flame. In other words, there is a vague ontological resemblance between flame and the form of heat that appears in wax. The virtual distinction makes this resemblance mentally but not actually clear.

    But it doesn’t copy a particular form at all. Say that you have F-in-X such that F is virtually distinct from X. You claim that F is copied by Y to result in F-in-Y. But to say that F is copied from X to Y presupposes that F maintains its identity through the copying process. Otherwise, how can you say that F is copied from X to Y? You would have to say that F is in X, and then F* is in Y. What is the relationship between F and F*? They are not identical, which means that they must differ in some respect. I would say that they only differ in terms of F being in X and F* being in Y, which ultimately means that other than that sole difference, F = F*. You would disagree, which means that F is not the same as F*, and thus what sense is there a copy?

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  35. Formal identity does not exist in the actual world. Again, only individual substances with individualized forms exist. Formal identity (i.e. the total identity of a form in two places) is an abstraction of the possible intellect.

    Again, formal identity abstracts something grounded in the reality of individual substances. Otherwise, you have nominalism, because there is nothing in reality that corresponds to the abstractions of the human intellect. Unless there is something that really corresponds to the abstraction, you have undermined all human knowledge into solipsism.

    He doesn't. From the Sentences as quoted by Rocca: "Lastly, however, we even remove from him his very existence, as it is in creatures, and then our understanding remains in a certain darkness of ignorance".

    That is equivocal and ambiguous. When you say that God does not exist, that could mean either (a) God does not exist at all, in any sense, or (b) God does not exist according to a creaturely mode of existence. Aquinas would never affirm (a), but rather would affirm (b), because he writes that God does exist, but in a higher and more eminent fashion that is distinct from “as it is in creatures”.

    Anything that isn't a substance or in some way reliant upon a substance cannot be said to exist. This is Thomism 101.

    Then God cannot be said to exist, even in a higher and more eminent fashion. After all, if existence is exclusively associated with substances, and God cannot be a substance, then God cannot exist at all in any sense.

    Anyway, our mental abstractions relate to components within substances that are similar, but similarity is not one-to-one identity--i.e. isomorphism. Humans are always particular humans, and "formal identity" is never simply one-to-one identity. In other words, it isn't a total identity that could ground your partial identity regress. The correct answer to this mess is to reject the partial identity-partial difference distinction as meaningless and to acknowledge that the vagueness of similarity is fundamental.

    But formal identity is “one-to-one identity”. It is the same form instantiated in different particular substances. If it wasn’t, then you could not draw conclusions about the nature of the substances in question, because what applied to one wouldn’t necessarily apply to the other. That would result in nominalism, unless formal identity was a reality in substances.

    I reject the idea that correspondence is isomorphism, and so this is not a problem. As Aquinas puts it, the intelligible species is a "likeness". He does not cash out likeness in any more fundamental terms. The intelligible species is simply similar to that which it relates: not partially identical and partially different. Since I believe similarity to be a basic concept, I'm not bothered by this vagueness.

    First, Aquinas does cash out likeness in “more fundamental terms”. He does so in his analysis of analogy as partial identity and partial difference in his commentary on the Metaphysics (7.3.2197), but we disagree about the implications of that passage. He also writes:

    “There is a twofold likeness between God and creatures. One is the likeness of the creature to the divine mind, and thus the form understood by God and the thing itself are homogeneous, although they have not the same mode of being, since the form understood is only in the mind, while the form of the creature is in the thing” (QDP 7.7).

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  36. Notice that Aquinas explains the “likeness of the creature to the divine mind” in terms of the form as “understood by God” and in “the thing itself” being “homogeneous”. I think that “homogeneous” does not mean “similar”, but rather “identical”. This is clear when he writes that “in every homogeneous whole, the whole is made up of parts having the form of the whole; as, for instance, every part of water is water” (ST 1.11.2). He does not say that a “homogeneous whole” is such that the whole and its parts have similar forms, but rather that the parts have the exact same form as the whole, i.e. “every part of water is water.” What that means is that when Aquinas describes the likeness of the divine intellect to the created entity as based upon a “homogenous” form, he is talking about formal identity. That means that the form in the divine intellect is the same as the form in the created entity, but in a different “mode of being”, i.e. F-“in the mind” versus F-“in the thing”. However, it is still the same F in both instances, despite F’s existence in two different modes of being.

    Now, you can reply that when Aquinas talks about “homogeneous” forms, he is not talking about formal identity, but rather is talking about similarity and likeness instead. However, that response will not work. He writes:

    “… we find that some are numerically the same, as are Socrates and this man in the Socrates now pointed out; others are numerically diverse and specifically the same, as Socrates and Plato who, although they differ numerically, have the same human species; others differ specifically but are generically the same, as man and ass have the same genus animal …” (DPN 45).

    Notice that Aquinas does not say that the forms are “similar”, but rather are “numerically diverse and specifically the same”, or “differ specifically but are generically the same”. He specifically uses identity and sameness as part of the defining aspects of the similarity between particular entities (e.g. between Socrates and Plato, man and ass). That negates your claim that similarity cannot be further analyzed into more basic components, and is ontologically primary and fundamental.

    Second, your account has absurd consequences, such as the complete negation of univocal meaning. For example, Aquinas writes that univocal meaning is where “one term is predicated of different things with absolutely one and the same meaning” (In Meta 7.3.2197). Now, you would object that this is metaphysically impossible, because two different terms cannot possibly have “absolutely one and the same meaning”. After all, they necessarily differ in that one meaning is associated with one term, and another meaning is associated with a different term, and thus they cannot be exactly the same in every respect. It thus follows that univocal meaning is impossible, which means that all meaning is either analogical or equivocal.

    Third, similarity admits of degrees such that if X and Y are both similar to Z, it stands to reason that X could be more similar to Z than Y. I would explain this by saying that X and Y both share Z in common, but that X actualizes Z to a greater degree than Y does, and thus is closer to approximating the ideal set forth by Z. How would you explain this phenomenon? Since similarity is a “basic concept”, you cannot point to any deeper analysis to explicate degrees of similarity. So, what do you do here?

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  37. If the formal identity is numerically distinct, then it is not absolute but only (in your words) partial identity. And partial identity cashes out in two ways: as an infinite regress or as a contradiction of total identity. The solution, again, is to say that formal identity is a kind of similarity rather than a partial identity.

    It depends upon your frame of reference. Say that you have F-in-X and F-in-Y. From the standpoint of F-in-X and F-in-Y, F is not totally identical, because F is associated with X in the former and F is associated with Y in the latter, and thus they differ in some respects. However, once you abstract away F’s particularized features that are associated with X or Y, which are the basis for its numerical distinction, then you are only left with F, which is what formal identity is. Yes, in reality, F cannot exist independently of an individual substance, whether material or immaterial, but F can be considered intellectually as abstracted from all characteristics of numerical distinction, and thus be considered formally identical.

    C* itself is numerically distinct from X and Y, which are numerically distinct from each other. It cannot be present in X and Y except through similarity and likeness.

    No, because C* is stripped of all particularizing features that would form the basis of any numerical distinction. Just because in reality, C* exists with particularizing features does not change the fact that C* can be considered in isolation by an intellect.

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