So, my question is the following: does ¬∀ have ontological import? How could it not, if it's equivalent to ∃? And if that's so, then does ∀ have ontological import, since it's equivalent to ¬∃? — Arcane Sandwich

Maybe it's just me, but I fail to understand how and why someone would treat ∃ and ∀ differently, as far as the discussion about ontological commitment goes. — Arcane Sandwich

This is what we should probably assess, even though (3) is farcical:

3) ∀x(Sx ∧ Bx) - Everything is a beautiful siren.
4) ∃x(Sx ∧ Bx) - Therefore, some [existing] siren is beautiful.

i.e. "If this is valid, then the universal quantifier must have ontological import." — Leontiskos

I say that neither of them does. — Arcane Sandwich

I’d rather not be accused of making accusations — Wayfarer

In Free Logic or Inclusive Logic, the existential quantifier explicitly asserts existence when paired with a predicate like ∃x(x=t), and existence becomes a property rather than a background assumption tied to the quantifiers. — Banno

Whether such [Meinongian] logics can legitimately be considered free is controversial. On older conceptions, free logic forbids any quantification over non-existing things...

Historically, quantification over domains containing objects that do not exist has been widely dismissed as ontologically irresponsible. Quine (1948) famously maintained that existence is just what an existential quantifier expresses. — 5.5 Meinongian Logics | Free Logic | SEP

Does the statement "All sirens are beautiful" have ontological import, in your view? — Arcane Sandwich

But it's equally the case that Johnson misunderstands Berkeley. Johnson is intending to demonstrate that Berkeley's argument entails that the stone does not really exist, but Berkeley doesn't make such a claim. — Wayfarer

What you are accusing him of is ignoratio elenchus, not begging the question. — Leontiskos

Johnson's exclamation is the historical origin of the expression 'argumentum ad lapidem'. — Wayfarer

Just out of curiosity, how would you handle the claim that the universal quantifier must have ontological import, if the existential quantifier has it? It would seem that whatever import ∃ has, ∀ must have it as well. — Arcane Sandwich

If Ux(Sx⊃Bx) then ∃x(Sx⊃Bx) follows — Banno

It follows because, in classical first-order predicate logic, universal sentences have existential import: ‘∀x φ(x)’ logically entails ‘∃x φ(x)’. If we want to allow ‘∀x φ(x)’ to be true even when there are no φs (because there is nothing at all), then we do not want it to carry any ontological commitment. Ontological commitments should reside entirely with the existential quantifier. Implementing this is easy. We simply do logic so as to include interpretations with an empty domain—so-called, inclusive logic. According to the truth conditions for quantifiers in inclusive logic, all universal sentences are true in an empty domain, and all existential sentences are false. Once we have made the shift to inclusive logic, we can also say, what seems right, that conditional existential sentences—such as, ‘∃x φ(x) ⊃ ∃x y(x)’—carry no ontological commitment. — Inclusive Logic/Free Logic | Ontological Commitment | SEP

Just out of curiosity, how would you handle the claim that the universal quantifier must have ontological import, if the existential quantifier has it? — Arcane Sandwich

If any of the two terms of an affirmative categorical is “empty”, then the term in question refers to nothing. But then, [...] “every affirmative proposition whose subject or predicate refers to nothing is false.” — Gyula Klima, Existence and Reference in Medieval Logic, 3

1) ∀x(Sx ∧ Bx) - All sirens are beautiful.
2) ∃x(Sx ∧ Bx) - Therefore, some sirens are beautiful. — Arcane Sandwich

If Ux(Sx⊃Bx) then ∃x(Sx⊃Bx) follows — Banno

This is nowadays taught as an example of an informal fallacy ('argumentum ad lapidem') — Wayfarer

Appeal to the stone, also known as argumentum ad lapidem, is a logical fallacy that dismisses an argument as untrue or absurd. The dismissal is made by stating or reiterating that the argument is absurd, without providing further argumentation. — Wikipedia

1. If Berkeley were right, *this* would never happen.
2. But it did happen.
3. Therefore, Berkeley is wrong.

That is, it in effect has two domains, one of things that exist and one of things that... do not exist. — Banno

No clear way of showing just how words refer to what we take them to refer to? — Janus

What is Quine's intended conclusion? I don't think it is as radical as is being assumed. In a 1970 paper he says that the gavagai example is very limited, and demonstrates the inscrutability of terms rather than indeterminacy of translation of sentences. — Leontiskos

There is an irony in the general analytic tendency to ignore medieval thought (continentals do too, but less). No other period reflects the rigor and professionalization that analytic thought praises, nor the emphasis on logic, semantics, and signification, more than (particularly late) medieval thought. The early modern period has an explosion of creativity in part because philosophy was radically democratized and deprofessionalized (leading to both creativity of a good sort and some of a very stupid sort). — Count Timothy von Icarus

It's unfortunate because so many debates are just rehashes that could benefit from past work, whereas contemporary thought also has a strong nominalist bias that even effects how realism might be envisaged or advocated for, and the earlier period does not have these same blinders. — Count Timothy von Icarus

At the end of the day, it's not about Quine vs Bunge. It's about whether or not we ourselves agree or disagree with what they're saying. Who knows? Maybe they're both wrong. — Arcane Sandwich

There are many key points that I disagree with him, for example I don't accept his dichotomy of conceptual existence and real existence (there's only real existence as far as I'm concerned). — Arcane Sandwich

If all of their dispositions to verbal behavior under all possible sensory stimulations were the same, then what would happen if they started talking to each other? — Apustimelogist

Quine clearly thinks that inscrutability of reference is not a barrier to communication — Apustimelogist

becasue it seems to me to be much the same as what Quine says, but in set-theoretical language — Banno

And here he sensible removes empty sets. Can I point out that this is very close (perhaps identical?) to a set-theoretical version of Quine's "to be is to be the value of a bound variable"?

((P) ≠ ∅) ≡ ∃(x) (Px) — Banno

And the answer given is much the same as that offered by first-order logic. — Banno

The trouble starts when "Some sirens are beautiful" is treated as a non-empty set; — Banno

(i) x exists conceptually = df For some set C of constructs, ECx;
(ii) x exists really = df For some set Θ of things, EΘx.
For example the Pythagorean theorem exists in the sense that it belongs in Euclidean geometry. Surely it did not come into existence before someone in the Pythagorean school invented it. But it has been in conceptual existence, i.e. in geometry, ever since. Not that geometry has an autonomous existence, i.e. that it subsists independently of being thought about. It is just that we make the indispensable pretence that constructs exist provided they belong in some body of ideas - which is a roundabout fashion of saying that constructs exist as long as there are rational beings capable of thinking them up. Surely this mode of existence is neither ideal existence (or existence in the Realm of Ideas) nor real or physical existence. To invert Plato's cave metaphor we may say that ideas are but the shadows of things - and shadows, as is well known, have no autonomous existence. — Bunge (1977: 157)

But if our domain is Greek myths, we are welcome to say that "There are beautiful sirens" — Banno

The idea of existence as quantification is rather, wherever I have seen it presented, that people come with their ontologies, and we can now examine them in terms of quantification (rather than say entailment) in order to determine what their ontological commitments are—not "all philosophers should accept the same set of universal ontological commitments, which include anything we can possibly speak of (but don't worry about this being too broad because ontological commitments now carry no weight at all)". This makes the whole notion of Quine's approach as a "test" between theories meaningless. — Count Timothy von Icarus

Well, at least for Quine there is only one logic (justifying that is another thing.) — Count Timothy von Icarus

...for what is central to Quine's criterion is that one cannot quantify over entities without incurring ontological commitment to those entities. To use quantifiers to refer to entities while denying that one is ontologically committed is to fail to own up to one's commitments, and thereby engage in a sort of intellectual doublethink. Quantification is the basic mode of reference to objects, and reference to objects is always ontologically committing. — Ontological Commitment | SEP

This sounds like the anti-metaphysical movement redux. — Count Timothy von Icarus

Yes and no. What I would rather is that "existence/being" should be declared meaningless, dead by the thousand cuts of equivocation and ambiguity. — J

"Now I completely agree that this [Quine's motto] tells us next to nothing. [i.e. it is trivial.] (In particular, it is neutral about some of the uses of "exist" that traditional metaphysics wants to privilege as "real existence" or "what being means" or some such.). But nor should it be controversial." — J

no matter what words we use for our labels — J

What it shows is that structure -- which is what we care about — J

Quine clearly thinks that inscrutability of reference is not a barrier to communication — Apustimelogist

So where is Quine going wrong? — Apustimelogist

Still, if we take the conclusion to be inscrutability of reference, then anyone who accepts (1) and (2) must admit that the argument fails, at least if (1) and (2) are more certain than the counter-premises in an argument for inscrutability. — Leontiskos

(i) x exists conceptually = df For some set C of constructs, E_Cx;
(ii) x exists really = df For some set Θ of things, E_Θx. — Bunge (1977: 157)

• "I found a weakness in your theory, therefore your theory is wrong or unacceptable."

Shorter: I can distinguish Pegasus from a phoenix. They're not the same fictional creature. Neither of them exists, so how is it even possible for me to distinguish them? Most of the time, reference is far from being inscrutable. And even in those cases in which it is, it can cease to be inscrutable. Unknown references are not the same thing as unknowable references. — Arcane Sandwich

It sounds as if one agrees with anything that Aquinas said, then one has magically converted to Catholicism. But this makes no sense to me. — Arcane Sandwich

Note: The "R" in "ERx" is meant to be a subscript, but this forum doesn't seem to have the option for subscripts. — Arcane Sandwich

E[sub]R[/sub]x

Surely most contemporary philosophers hold that ∃ formalizes both the logical concept "some" and the ontological concept of existence. I shall argue that this is a mistake. — Bunge (1977: 155)

...However, as I have argued in detail elsewhere,[3] Kenny’s objection fails on several counts.

In the first place, Aquinas simply does not have a notion equivalent to the Fregean notion of an existential quantifier. In fact, a notion that would come closest to this notion in Aquinas’s conceptual arsenal would be regarded by him not as a concept of existence, but as a signum quantitatis, namely, a signum particulare, the syncategorematic concept expressed by the Latin terms ‘quidam’, ‘aliquid’ or their equivalents, which render a proposition to which they are prefixed a particular, as opposed to a universal, singular or indefinite proposition (as in, ‘Quidam homo est animal’ = ‘Some man is an animal’, as opposed to ‘Every man is an animal’, ‘Socrates is an animal’ or ‘A man is an animal’, respectively). In any case, Kenny’s reason for holding that Aquinas would have to use in his argument the notion of specific existence, and, correspondingly, the notion of nominal as opposed to real essence,[4] is his unjustified assumption that Aquinas would take a phoenix by definition to be a fictitious bird as we do... — Gyula Klima, Aquinas' Real Distinction and Its Role in a Causal Proof of God's Existence

We needed some kind of "foothold", — Moliere

But until you have that it's a nothing, right? If we don't even recognize something as a language, for instance... — Moliere

Eventually, through trial and error, you can learn it! Even if you knew nothing of it!

Which is kind of the puzzle.... in a way. — Moliere

First, the inscrutability of reference applies even to our own language. — Moliere

Second: I'd take it that since we're talking to one another we can't ever deny that we're communicating, unless we're communicating about when we're not communicating to correct communication. So if we can connect a philosophical belief that we're not communicating that'd be damning for it -- not that'd it be false, but it'd indicate we're not communicating and thereby, in spite of all of our efforts, we're linguistically solipsistic. — Moliere

"Reference", as a philosophical concept, is the target of the "gavagai" criticism -- as well as various metaphysical theses people might have drawn from various notions of reference.

It's not so much that we can't communicate or learn. It's that there's no fact of the matter, in the sense of a true sentence which refers to the world in the same way that "gavagai' refers to the world, which will decide how "gavagai" refers. — Moliere

Is there a particular bit you want me to discuss? — Moliere

Most people want to avoid the thesis that existence is a property, and that it can be represented with a first-order predicate, such as "E", instead of the existential quantifier, "∃".

And why do most people want to avoid that thesis? Because they somehow believe that to treat existence as a property is naive... — Arcane Sandwich

20th Century thinkers like Mario Bunge — Arcane Sandwich

reference is inscrutable — Moliere

Sorry for diverting the thread too much, tho — Moliere

We need the mean, but disagree upon what the mean is. — Moliere

"But how can you include something in the domain if you haven't even conceived of it?" Well, we just did. — Banno

...that an entity can figure as a value of a bound variable in his theory is, according to Quine, equivalent to the assumption that such an entity exists; it is impossible to quantify over entities of which existence is not, eo ipso, assumed. Put more precisely: according to Quine the notion of existence just means the capability of featuring as a value of a bound variable. To assume that something exists is to assume nothing less, and nothing more... — Lukáš Novák, Can We Speak About That Which Is Not?, 159

Thus theories that allow their variables to take non-existent individuals as their values are automatically understood as possibilist, to the effect that those who share Quine’s dislike towards the overpopulated Meinongian slum feel under pressure to construe their theories so that they enable reference to actual entities only. That results in various technical problems (the Barcan Formula[50] and the like) requiring sophisticated workarounds, which however tend to introduce various ersatz-entities into the actualist systems like individual essences (Plantinga) or bare individuals “in limbo” (Transparent Intensional Logic), in effect barely distinguishable from the abhorred possibilia.

[50] If it is possible that there is an F, then (actually) there is something that is possibly an F: ◇∃x(Fx) → ∃x◇(Fx). — Lukáš Novák, Can We Speak About That Which Is Not?, 159

And why do most people want to avoid that thesis? Because they somehow believe that to treat existence as a property is naive, if not outright scholastic. After all, didn't Kant refute the ontological argument by pointing out that existence is not a predicate? — Arcane Sandwich

In many places today, for example, no one bothers any longer to ask what a person thinks. The verdict on someone's thinking is ready at hand as long as you can assign it to its corresponding, formal category: conservative, reactionary, fundamentalist, progressive, revolutionary. Assignment to a formal scheme suffices to render unnecessary coming to terms with the content — Joseph Ratzinger, Conscience and Truth

How about we start by analyzing these completely irrational themes that underlie these sorts of discussions, instead of digging our heals and just blurting out nonsensical accusations such as "You don't really understand Quine's point." — Arcane Sandwich

...I think it is worth noticing in the second [criticism] the smooth transition from “the description has/does not have a referent” to “the referent of the description does/does not exist” [...] What is interesting in the smoothness of this transition is how easy it is nowadays to have an unreflected, and accordingly deep conviction that whatever more restricted meanings existence may have, the full scope of being is that of the possible range of reference of the expressions of our language.[7] — Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding, 2

So if we insist on using "existence" and asking what it means for something to exhibit this feature, all we can do is point to the one characteristic they have in common, "being the value of a bound variable." — J

I'm recommending we drop the word entirely — J

but I am not seeing how this "solution" resolves any of them — Count Timothy von Icarus

quantifier variance — J

From this Buridanian perspective, one cannot make claims about the relationships between language and reality from some external, God-like position, from the position of the user of a meta-language, who has a certain “context-free” or “context-neutral” access to the object-language and “the world”, both as it is in itself and as it is conceived by users of the object-language, that is to say, the totality of semantic values of items in that language. — Gyula Klima, Quine, Wyman, and Buridan: Three Approaches to Ontological Commitment, 10

Not really, since "I think" as a attributer/weakener dominates English usage, any other use is very unusual and requires clarification. Far from being learned in either philosopher's work, I nonetheless see two possibilities for a "philosophical" "I think". — hypericin

What I am really doing, by my lights, is making an argument from contingency and necessity as it relates to composition; basically by way of arguing that an infinite series of composition is impossible because it would be an infinite series of contingent things of which each lacks the power to exist themselves. — Bob Ross

Yes and no. If you were to take a dead frog and “sew it back to together”, then yes you are right; but if you configure the frog’s pieces to be exactly as it were when it was alive; then it must now be alive again….no? — Bob Ross

What’s the problem with that? Are you saying that it doesn’t account for a soul? — Bob Ross

That’s true, but I say that because Aristotle’s proof only works if we think of a thing having the potential to remain the same through time and that potential being actualized through time. Otherwise, the argument fails to produce a being that would fit classical theism which is the perpetual sustainer of everything; instead, we just get a kind of ‘kalam cosmological argument’ where this being starts everything off moving.

By ‘motion’, Aristotle is not just talking about, e.g., an apple flying in the air: he is talking about the change which an apple that is just sitting there is undergoing by merely remaining the same. That’s the only reason, e.g., Ed Feser’s “Aristotelian Proof” gets off the ground in the first place. — Bob Ross

To be is to be the value of a bound variable. Which is Quine's approach. — Banno

My preferred solution, as many of you know. I've seen you refer to this as Quine's "joke" about being, but it's about time we took him seriously. — J

isn't there a way of posing the question "What are beliefs?" — J

What is interesting in the smoothness of this transition is how easy it is nowadays to have an unreflected, and accordingly deep conviction that whatever more restricted meanings existence may have, the full scope of being is that of the possible range of reference of the expressions of our language.[7]

In medieval thought, this certainly was not the prevailing idea. According to the medieval view, inspired originally by Aristotle’s Perihermeneias, reference, following meaning, is a property of linguistic expressions only insofar as they express thoughts, i.e., mental acts of users of the language. Accordingly, linguistic expressions refer to what their users intend by them to refer to in a given context, that is, what they think of while using the expression either properly, or improperly.[8] So referring was held to be a context-dependent property of terms: according to this view, the same expression in different propositional contexts may refer to different things, or refer to something in one context, while refer to nothing in another. As it was spelled out systematically already in the freshly booming logical literature of the 12th century in the theory of ampliation[9], terms that are actually not true of anything may have referents, or in the current terminology, supposita, in the context of intentional verbs, such as “think”, “want”, “imagine” and the like. But, to be sure, these referents are not to be construed as beings (entia), or objects, simpliciter, but as objects of thought — according to 13th century terminology, beings of reason, entia rationis.[10] — Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding, 2

So, it might seem that Buridan’s semantics, represented by this semantic system, is equally committed to mere possiblia, that is to say, Quine’s possible charges are justified. But the tricky thing about Buridan’s semantics is that it makes no distinction comparable to the modern distinction between object-language and meta-language, so it has no meta-language comparable to the meta-language in which we see Quine’s charges justified.

Buridan has only one language to talk about the world as well as about the language and its semantic relations to the world. And in that one language we cannot truly say that there are mere possibilia, or that something that is merely possible exists. Accordingly, from this Buridanian perspective, the issue of ontological commitment in terms of a meta-linguistic description of the relationship between language and the world is radically ill-conceived.

From this Buridanian perspective, one cannot make claims about the relationships between language and reality from some external, God-like position, from the position of the user of a meta-language, who has a certain “context-free” or “context-neutral” access to the object-language and “the world”, both as it is in itself and as it is conceived by users of the object-language, that is to say, the totality of semantic values of items in that language. We only have this one language we actually speak (where, of course, it doesn’t matter which particular human language we take this one language to be), and we can speak about those semantic values only by means of the context-dependent ways of referring that are afforded to us by this language. — Gyula Klima, Quine, Wyman, and Buridan: Three Approaches to Ontological Commitment, 10

For one, self-consciously thinking p would be rendered as something like "I'm thinking about thinking p", not "I think p". — hypericin

A good rule of thumb for everyone is to keep in mind that, during a conversation, if it just so happens that good common sense needs to be praised, then something about the conversation has gone terribly wrong. — Arcane Sandwich

I have in mind speaking in a language you don't understand. Speaking on a subject you don't understand. Lying. — hypericin

accurately notating that you are indeed thinking-p, and reflecting on your own thought, can both be represented as "I think p" in English. — hypericin