TonesInDeepFreeze

Where can I read more about a uniqueness predicate in a second order modal logic? I understand a uniqueness quantification symbol that is followed by ...

Then that opens yet another can of worms. I understand what it means for there to be a unique individual having a certain property: E!xP. And in this ...

Hughes & Cresswell uses just 'E', not 'E!'. And the semantics for 'E' are fixed (in the manner described by Snakes Alive). (I would say that the seman...

Then I understand it this way: It's a primitive symbol, but there are no special logical axioms for it, and it can be interpreted differently in diffe...

'x' is a variable. And 'E!' is being used as a 1-place predicate symbol. So either it is a primitive predicate symbol, in which case it would appear i...

I haven't found a full explication of the argument in a modal logic, with all the terms defined from primitives or previously defined terms. I don't s...

My question was a followup. The previous point is more important: I know the definition of E!xP, but I would like to know the definition of E!x.

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Motivated by the posts of Snakes Alive, I consulted a textbook so that I think I understand what he's saying, which I think is along these lines, even...

Let 'Px' intuitively say "x exists". What is the definition of 'Px' in the form?: Px <-> Fx where 'Fx' is a formula in a given first order language (o...

How do you express that as a modal formula in the object language? I don't quite follow you. In any domain, there is an individual named by 'a'. But t...

Ah, I admit that I am not familiar with a system that has existence as a predicate. For ordinary predicate logic, it's not a formalizable notion. I di...

I don't know what that means. How could I admit it when I don't even know what it means? It depends on a definition of 'philosophy'. Ordinarily philos...

Indeed. I gave an example. And it's basic set theory. For any set S, and individual d, we have that d is not a member of S\{d}.

I'd like to see the logic, the semantics, and the proof explicitly specified. What is the exact sentence that is proved? Is it of the form?: Necessari...

I don't understand the question. One may characterize what logic is "about" in different ways. A common notion is that logic studies entailment and in...

I can't parse that. Good for him! Nor does modern logic. indeed, one of the early notable aspects of modern logic is that it extends past syllogisms. ...

Please provide an example of modern formal modal logic used trying to prove something beyond itself. Of course, a proof may adopt premises that a read...

Right. For example, suppose one universe is the set of even numbers, and suppose 'a' names 2. Then suppose another universe is the set of odd numbers....

I don't know. I'd have to see the specific argument formalized. Perhaps such arguments have additional premises other than the mere proof apparatus of...

I don't know what you intend to mean with that. The a first order theory of course includes non-logical symbols and, if not the pure first order theor...

I'll give the definitions, then I'll address your formulation. Let 'A' notate the universal quantifier. We define 'model for a first order language' a...

I have not claimed that modal logic proves anything in philosophy. And that does not entail that modal logic does not prove anything in philosophy nor...

Yep. With first order logic, every model specifies a universe. For modal logic, we specify a set of universes.

No. That is an hilarious question.

No, it comes from first order logic. Mathematical logic is a field of study. It has no will such that it could will to rule over anything, including a...

Individuals are members in universes. Now, suppose an individual is a member of a certain universe, of course that individual is not a member of certa...

So, still, you've shown nothing specific that Aristotle wrote that would be predictive that he would reject modern modal logic. The fact alone that Ar...

It seems you are wondering how to formalize "there is an individual that exists in every possible world". I don't know at this moment. But I don't thi...

I asked what specific system and what specific theorem you have in mind. Apparently you don't have anything specific in formal modal logic in mind. An...

In Ex a=x 'a' is merely a variable or constant (depending on your specification). It has no specific referent except by assignment to an individual in...

You said you couldn't find mention on the Internet of anything modal logic proves. So those are links were modal logic is used for results in computer...

What system of modal logic and what specific theorem are you referring to?

You said you couldn't find references. I gave you ones.

Ex a=x is a theorem of the pure predicate calculus with identity. So it seems to me that it is the case that necessarily Ex a=x. Am I overlooking some...

What specific theorems of modal logic do you have in mind as "proving something exists from logic structures alone"? And what passages in Aristotle do...

I surmise that I am not mistaken that, ordinarily, physics uses classical mathematics, which has infinite sets and is ordinarily axiomatized by set th...

And contrariwise in other articles. I'm sure you wouldn't want to cherry pick just gainsaying quotes. And the article describes Bridgman's notions as ...

If Aristotle is fine with you, then what particular break between Aristotle and modern modal logic do you object to? That depends on a definition of "...

Whatever you thought you were explaining, you did it by terribly misunderstanding the modal operators in modal logic, thus giving reason to think you ...

Do you have a problem with Aristotle's "traditional philosophy"?

Wikipedia and those articles don't mention that the operators are applied to sentences and don't refrain from saying that the operators are applied to...

"The desk across the room" is a noun phrase, not a proposition. The modal operators are applied to propositions not noun phrases. Would you please tel...

The concepts apply to propositions, or formally - sentences, including propositions about the world. In mathematics, salient uses of modality include ...

I am not informed in physics. So anything I say about axiomatizing physics might very well need to be corrected or qualified. However, I can at least ...

http://tph.tuwien.ac.at/~svozil/publ/1995-set.pdf https://www.sciencedirect.com/science/article/abs/pii/S0960077996000550 and from a set theorist: htt...

I don't know your personal use of the terminology. Of course even without AC every finite set of nonempty sets has a choice function. I don't know whe...

I thought it was obvious that since we don't have in front of us an axiomatization, then my question is hypothetical regarding whatever proposed axiom...

And I have not the least interest in the subject of corporate financing. Go figure. But I do make it a point to go into discussion threads about busin...

I'm not claiming any particular sense of existence. Nor am I disputing any particular sense of existence. In context of the question whether set theor...