Notes On Fregean Existence

– Broadly, the Fregean/post-Fregean concept of existence is that existence is the instantiation (sp?) of a concept. No doubt there are some subtleties here and there but that’s the basic gist. For a horse to exist means that the concept of horse-ness is instantiated.

– Frege noted that there is an odd quality about terms like ‘existence’ – namely, that if existence is a universal predicate (i.e. a predicate which is true of everything) then non-existence is true of nothing.

– This seems to have the consequence that nothing can either exist or not-exist – which is, to say the least, counter-intuitive.

– The consequence of this is that the difference between existence/nonexistence is reduced form ontological to propositional. Surely, though, there are things that don’t exist and things that do, and the difference is more than how they both look when put into formal logic. Perhaps Frege’s logic isn’t equipped to deal with existence?

– It quickly becomes clear that this is a way of speaking about existence, rather than speaking about existence as such (David Bentley Hart points out as much in ‘The Experience of God). Existence is just assumed, rather than explained. And perhaps this is fine – but one certainly does feel that such a conception of existence is thin.

9 thoughts on “Notes On Fregean Existence

  1. Matthew C September 29, 2014 / 3:40 pm

    If correct that view of existence would refute Anselm’s Ontological argument.

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  2. SamL September 30, 2014 / 7:58 am

    I can see why existence being a universal predicate would mean that nothing can not-exist, but not why it would mean that nothing can exist? (Or is the point that if existence is universal then it’s trivial or even contentless to say of a thing that it exists?)

    I don’t think I’d want to go so far as to say that this makes the existence/non-existence distinction purely linguistic, though I do think I see the thought here. What I’d want to say is that there is a certain semantic asymmetry between ascriptions of existence and non-existence — we can say plainly that something exists, but some interpretive work is require to make sense of statements that claim something doesn’t exist. This asymmetry seems to be at the root of lots of things, and in my view is why while it makes sense to talk about necessary non-existence (e.g. square circles) it’s a lot harder to talk coherently about necessary existence.

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    • whitefrozen October 2, 2014 / 7:02 pm

      ‘(Or is the point that if existence is universal then it’s trivial or even contentless to say of a thing that it exists?)’

      Pretty much that.

      ‘I don’t think I’d want to go so far as to say that this makes the existence/non-existence distinction purely linguistic, though I do think I see the thought here.’

      No, it’s not purely linguistic/propositional, but it sure seems to head in that direction.

      ‘This asymmetry seems to be at the root of lots of things, and in my view is why while it makes sense to talk about necessary non-existence (e.g. square circles) it’s a lot harder to talk coherently about necessary existence.’

      How do you mean?

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      • SamL October 3, 2014 / 5:06 am

        Consider this paragraph of Spinoza’s (from the Ethics Part I, proof of Prop XI):

        “Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non-existence – e.g. if a triangle exist, a reason or cause must be given for its existence; if, on the contrary, it does not exist, a cause must also be granted, which prevents it from existing, or annuls its existence. This reason or cause must either be contained in the nature of the thing in question, or be external to it. For instance, the reason for the non-existence of a square circle is indicated in its nature, namely, because it would involve a contradiction. On the other hand, the existence of substance also follows solely from its nature, inasmuch as its nature involves existence.”

        So he’s making an analogy between things that necessarily don’t exist and things which necessarily do. Some things do/don’t exist accidentally, and some things do/don’t exist necessarily. Those things in whose nature it is to exist exist necessarily, and those things in whose nature it is to not exist don’t exist necessarily. The appeal to a symmetry: we’re quite happy to say that square circles are impossible, so by the same token we should be happy to accept proofs that certain things — substance (which for Spinoza was synonymous with God) — as necessarily existing.

        Now I don’t think this makes any sense. In the case of the square circle, it looks like Spinoza is making what’s sometimes called a de re ascription — he is saying *of an existent* that it is in its nature to not exist. Clearly this a contradiction: if square circles don’t exist, then in whose or what’s nature is this non-existence? This is the lesson of Parmenides: de re ascriptions of non-existence are nonsensical.

        To make a statement like “square circles can’t exist” make sense we have to stop interpreting it in a de re manner and start interpreting it in a de dicto manner — we are not saying ‘of a thing’ that it can’t exist, rather we are saying something about the way certain predicates — “is square” and “is circular” — are defined, i.e., they are defined in a way which excludes one another. All it then takes to get from this to the ontological claim that “necessarily square circles don’t exist” is the assumption that there are no true contradictions. Then we can say that necessarily, the set of things that “is square” is true of and the set of things that “is circular” is true of are disjoint: they have an empty intersection, just because they’ve been defined that way. Here we don’t at any point say of an existent that it doesn’t exist, so the Parmenidean contradiction is avoided. To use your phrase, the problem gets solved by moving out of the ontological and into the propositional.

        But this interpretation breaks Spinoza’s symmetry, or rather, to keep it we’d have to make the equivalent move on the opposite side, i.e. we’d have to start interpreting ascriptions of necessary existence as de dicto and not de re. But typically when people are advancing arguments for something’s necessary existence — typically God’s — what they want is a de re ascription, otherwise they haven’t showed anything about a real entity — they haven’t moved from the propositional into the ontological.

        What is always needed in any argument which seeks to establish the necessary existence of something, where this is intended to say something about something real, needs a metaphysical premise. In the case of necessary non-existence this was just the premise that there are no entities with contradictory properties. Given how universal this premise is (and when denied, by, say, dialetheists it is always denied only for very specific instances) that makes talking about necessary non-existence quite straightforward and unproblematic. But in the case of necessary existence things are far murkier. In the case of cosmological arguments / arguments from contingency the key metaphysical premise is always some variant of the principle of reason. In the case of the ontological argument the premise is usually more tacit, but I suggest that it is modal realism (as we discussed on Twitter).

        Urgh – sorry, that was long.

        Sam

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        • SamL October 3, 2014 / 5:10 am

          Urgh — and full of typos.

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        • whitefrozen October 3, 2014 / 12:54 pm

          Good thoughts – for the moment I’m going to zero in on Parmenides, because I do think it was ‘solved’ in an ontological sense (assuming we’re talking about his basic problem – which can be boiled down to: change, which he thought meant being coming from nonbeing etc etc) – Aristotle’s well known act/potency distinction/theory being what I have in mind. This is an answer to Parmenides problem that keeps things firmly in the realm of the ontological – though without really denying one of the basic things that Parmenides has taught us, that even very simple terms like, ‘one’ ‘being’ etc are far from straightforward and can require a heft amount of work to clarify.

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          • SamL October 9, 2014 / 4:33 am

            Sorry – got distracted for about a week there. Just a quick one then:

            I’d agree with the above, though I’d note that Parmenides’ (broad) argument has two stages:

            1. Nonbeing cannot be.
            2. Change requires that nonbeing is.

            Hence change is impossible.

            Aristotle’s retort is a refutation of 2, i.e. the act/potency distinction is a way of showing that change can be made intelligible without running afoul of 1 (both act and potency *are*). So I think we can say that Parmenides’ general argument that change is impossible fails, though his contention about the paradoxical nature of non-being (i.e. 1) is independent of this, and is left in tact.

            Sam

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