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Predicate logic, negative existentials and Thomism

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  • Predicate logic, negative existentials and Thomism

    In a discussion on another board, it was put to me that the Aristotelian term logic used by Aquinas et al. escapes the so-called Existential Fallacy as long as no term in a major premise refers to an empty class. My interlocutor also reluctantly allowed that Frege-Russell-style predicate logic is OK for some applications, but he resisted it for arguments about metaphysical principles, for he found it infected by assumptions imported from metaphysical naturalism.

    I think one of the key questions is, what is existence? Aquinas following Aristotle et al. speaks of degrees of being and perfections of being, which is senseless unless existence is a predicate or perfection. In predicate logic, existence is treated as a quantifier, although there is some dispute over whether existence can be a predicate in sentences like "The lamp exists" as opposed to "the lamp is bronze." I am wondering, though, whether in fact Frege-Russell predicate logic and Aristotelian syllogistic/term logic are mutually exclusive, so that Thomism stands or falls depending on the logic that wins the day. Ought the Thomist just reject predicate logic altogether as lethal to his system; on the other hand, does the naturalist have grounds to reject Thomism as entailing rejection of a system of logic more powerful than the Aristotelian syllogistic/term logic?

    I am wondering here, not expounding, about existence's not being a perfection, as Aquinas (and Aristotle) generally treat it.

    Here are two possible test points.

    1. certain Thomistic arguments rely on premises that assert that something exists in an intellect when it is not (yet) actualized in reality. For example, Feser et al. formulate the Fifth Way to include a premise that the end of an operation must preexist in an intellect before it is effected by a natural agent. But on my understanding of the Frege-Russell theory of negative existentials, something's not being actualized in reality cashes out as some F's not being quantified over any x. So an intellect's understanding of, say, the property oak-ness does not give us the existence in the intellect of an oak; we don't know so far whether oakness is instantiated. We only have a property, and someone understands that property; there is no thing even in the intellect that has that property such that the tree gets some kind of mental existence. So arguments that posit that the F exists in an intellect fail. The Fifth Way fails because it needs the end to preexist in a mind before it is effected by an agent cause, but the end doesn't preexist in a mind, only a conception about the end.
    For the reasoning I'm exploring here, see the quotation at the bottom.

    2. If existence is not a perfection, then there are not degrees of being. But the doctrine of analogical predication of names of God, which is necessary for Thomism to work, rests on an analogy of being. And Aquinas talks about perfections of being. So the doctrine of analogical predication will fall if being does not admit of degrees of perfection. A logic that denies that existence is a predicate/perfection will undermine the doctrine of analogical predication, and with it, undermine Thomist discourse about God.

    I don't know enough logic (yet - or ever, perhaps) to be clear about all the above, let alone certain. I hope it's not unintelligible.
    --------------------------------------------------------------------------------------

    Here's a discussion about a non-Thomist argument, the ontological argument, that nevertheless provoked me to think about the consequences for the Fifth of Frege-Russell's theory of negative existentials. They denied that a property's being thought about entails that a thing having that property has a kind of existence in the understanding:

    "If Kant would deny that: (0) God does not exist, means the same as: (1) God exists in the understanding but not in reality, then one might wonder what Kant thinks it does mean, and whether Anselm’s argument could get off the ground under Kant’s interpretation of (0). As an earlier footnote suggested, some commentators (e.g. Byrne (2007), 24, and Forgie (2008)) believe that Kant anticipated the Frege – Russell theory of negative existentials and would hold that (0) means simply that Godhood (the property of being God) is not instantiated. This theory would undermine Anselm’s argument. This is because: (4) If God did exist in reality, then He would be greater than He is, would then no longer follow from: (2) Existence in reality is greater than existence in the understanding, together with the Kant-Frege-Russell interpretation of (0). For (4) to be true, the second occurrence of ‘He’ must refer to something. In Anselm’s original version, it refers to God in the understanding. But given the Kant-Frege-Russell understanding of (0), it has not been established that God exists in any way, even in the understanding. This, of course, is not to say that we don’t understand (0). Kant’s point would be that we do, but that doing so doesn’t require God to have a kind of existence (existence in the understanding). It simply requires that Godhood exist and that we understand it." ~ Chris Heathwood, "The relevance of Kant's objection to Anselm's ontological argument," Religious Studies 47 (2011) 345-57 at 357 n. 12.

  • #2
    I haven´t taken a side on the issue of the nature of existence. So I neither affirm the real distinction or existential eliminativism. I have Vallicellas book on my shelf and he has been a great help in understanding what the question is about in the first place. But I don´t feel knowledgable enough to make an informed commitment yet and after skimming a few pages of Vallicellas book I realized that I need a few calm weeks to really work myself through it and understand it. I think however that Fregean notions of existence and the ones inspired by him are untenable. Carnap drew the consequences out, that if Frege were correct on the nature of existence, then sentences like "I exist" would become meaningless. This should provide enough evidence, that this idea can´t possibly be correct.

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    • #3
      Originally posted by Kwlsk View Post
      if Frege were correct on the nature of existence, then sentences like "I exist" would become meaningless. This should provide enough evidence, that this idea can´t possibly be correct.
      Some authors I have read would say that a Fregean take on "I exist" is that it's grammatically formed but that existence is a quantifier not a property. So they would translate the sentence so it will fit into a universal predicate logic - i.e. "I exist" cashes out as "there exists an x such that it is [fill in properties here]".

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      • #4
        Originally posted by ficino View Post

        Some authors I have read would say that a Fregean take on "I exist" is that it's grammatically formed but that existence is a quantifier not a property. So they would translate the sentence so it will fit into a universal predicate logic - i.e. "I exist" cashes out as "there exists an x such that it is [fill in properties here]".
        But how does it preserve the intelligibility of the existence of x? The consequence is either that my existence is necessary or a brute fact. I know the attempts of the Quineans, but they are, in my view, merely reformulating rather than answering. Or as Vallicella puts it: "Calling it an existential quantifier is completely question-begging."

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        • #5
          Originally posted by Kwlsk View Post

          But how does it preserve the intelligibility of the existence of x? The consequence is either that my existence is necessary or a brute fact.
          In the above you write as though existence is a predicate. That is the point in question.

          I shall be grateful for any link you can provide to Vallicella on this.

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          • #6
            Originally posted by ficino View Post

            In the above you write as though existence is a predicate. That is the point in question.

            I shall be grateful for any link you can provide to Vallicella on this.
            Can´t give you specific quotes, his entire career is full of works on that high abstract level. His book is the hardest on my shelf to work through. I´d got to his blog maverickphilosopher.typepad.com and look into the Quine, Frege, Heidegger and van Inwagen category.I downloaded several articles I found on PhilPapers, too.
            Last edited by Kwlsk; 10-06-2019, 05:58 AM.

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            • #7
              Originally posted by ficino View Post

              1. certain Thomistic arguments rely on premises that assert that something exists in an intellect when it is not (yet) actualized in reality. For example, Feser et al. formulate the Fifth Way to include a premise that the end of an operation must preexist in an intellect before it is effected by a natural agent. But on my understanding of the Frege-Russell theory of negative existentials, something's not being actualized in reality cashes out as some F's not being quantified over any x. So an intellect's understanding of, say, the property oak-ness does not give us the existence in the intellect of an oak; we don't know so far whether oakness is instantiated. We only have a property, and someone understands that property; there is no thing even in the intellect that has that property such that the tree gets some kind of mental existence. So arguments that posit that the F exists in an intellect fail. The Fifth Way fails because it needs the end to preexist in a mind before it is effected by an agent cause, but the end doesn't preexist in a mind, only a conception about the end.

              This kind of idea could be questionable; I starting thinking about using computer programs like Zbrush to sculpt models which are later produced physically by 3D printers, but the general idea is that it is possible to know and to hold in the mind a concept of a thing that includes a large number of its properties, maybe most of them if it is a simple object.

              It seems minds much more powerful than a human mind are conceivable, the kind of mind which could hold a much more detailed knowledge of an object's properties such that knowledge of its properties was complete or exhaustive.

              It doesn't seem clear that an oak tree known or conceived in this could be said to be non-existent, even if it wasn't yet an object with mass extended in space. Would this type of criteria for existence make something being extended in space and having mass a necessary condition of being existent?

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              • #8
                Originally posted by FZM View Post


                It doesn't seem clear that an oak tree known or conceived in this could be said to be non-existent, even if it wasn't yet an object with mass extended in space. Would this type of criteria for existence make something being extended in space and having mass a necessary condition of being existent?
                I don't know about Zbrush, but I think people who say existence is a quantifier and not a first-order property would say that you run into trouble when you talk about "an oak tree" conceived in the mind vs. "an oak tree" extended in space, as though "oak tree" has a single reference. It doesn't. The term "oak tree in the mind" refers to a concept (or pick some other cognition-word), while "oak tree extended in space" refers to what we call an actual oak tree. The people who deny that existence is a first-order predicate would say that what's instantiated in the first case is a concept and in the second case, a tree.

                As far as I understand it, talk of something's existing in the mind but not in reality, and of something else's existing both in the mind and in reality, is Meinongianism. I haven't read Meinong himself and probably never shall. His ontology doesn't seem successful, as far as I've read about it.

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                • #9
                  Originally posted by ficino View Post

                  I don't know about Zbrush, but I think people who say existence is a quantifier and not a first-order property would say that you run into trouble when you talk about "an oak tree" conceived in the mind vs. "an oak tree" extended in space, as though "oak tree" has a single reference. It doesn't. The term "oak tree in the mind" refers to a concept (or pick some other cognition-word), while "oak tree extended in space" refers to what we call an actual oak tree. The people who deny that existence is a first-order predicate would say that what's instantiated in the first case is a concept and in the second case, a tree.
                  Yes, but I would be interested to know if they are right to say this. And, I seem to remember Anthony Kenny has written about this topic (a book?) in relation to Aquinas already.
                  Last edited by FZM; 10-06-2019, 10:11 PM.

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