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Questions tagged [modal-logic]

a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality

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3 votes
0 answers
39 views

what is the definition of a necessary fact in the contingency argument?

how can we define a necessary fact in the contingency argument in a way which does not lead us to the ontological argument? (exists in all possible worlds) the contingency argument is: A contingent ...
2 votes
2 answers
66 views

could the set of all contingent facts be necessary?

I was thinking about the PSR. when it comes to the set of all contingent things, it seems that the set must also be contingent and could fail to exist because each member could fail to exist. but ...
1 vote
0 answers
46 views

What papers or books should I read in order?

I have been reading literature on modal set theory and am currently reading Putnam's "Mathematics Without Foundations," which is known for being one of the earliest presentations of this ...
3 votes
10 answers
1k views

Does this modal ontological argument prove the existence of God?

What are some objections to this form of the argument? It seems like the only premise that can be disputed is premise 1, but nobody has successfully disproven the possibility of a maximally great ...
3 votes
0 answers
53 views

In the usual modal logics, are there tautologies of the form ◊¬X or ¬☐X?

And not when, "Possibly not X," or, "Not necessarily X," are implied by, "Impossibly X," already. But so is it possible to have a tautology be a statement of mere ...
9 votes
1 answer
183 views

What is Dummett's narrow/wide scope objection to Kripke's modal argument against descriptivism?

I just cannot wrap my head around this concept, if anyone can make it clear for me I'd be greatly appreciate it. I've tried reading the literature, but the papers I read invariably start putting the ...
-4 votes
1 answer
67 views

What does it mean to say "possible in reality?" [closed]

Consider the following truth table. I am hungry My eyes are closed 0 0 0 1 1 0 1 1 Each row is possible. But that seems to me like an incomplete statement. Instead, I think it makes more sense ...
1 vote
3 answers
124 views

If a proposition is necessarily true, does it follow that it's a tautology?

If □P, does it follow that P is a tautology? I know in K modal logic, the law of NEC states ⊢ P; therefore □P. The corresponding conditional of the previous argument is If ⊢ P then □P. Now ⊢P iff P is ...
2 votes
1 answer
72 views

deontic logics without agency

Standard deontic logics are agentless. That is, obligations in the logic are not assigned to agents; instead, they are made sort of general and ephemeral. This strikes me as rather fraught with all ...
0 votes
2 answers
130 views

How do you prove transitivity of equality?

There are only two axioms of equality in SQML, reflexivity (RX), and substitution (II). Obviously you can prove transitivity of equality, but how does the proof go? Reflexivity (RX) ∀x[x = x] ...
0 votes
1 answer
35 views

Is there a counterpart of "merely possible"/"merely permissible" in temporal logic?

It might not be too bad to say that, in modal and deontic logic, possibility and permissibility are like "ground states," having the lowest "logical energy." At least we think ...
2 votes
0 answers
21 views

Can 𝐅𝐑 be taken for a deontic negation operator (rather than just a specified negation of 𝐎𝐁)?

Presuppositions of the question: beliefs about the ambient structure of negation: I was rethinking the following in light of questions about supervenience, grounding, alterity, and identity: A ...
0 votes
0 answers
24 views

Question regarding modal logic version of disjunctive syllogism

Is the following theorem provable in SQML? ⊢ (A ∨ B) ∧ ~◊A → ☐B Here's how far I got. ⊢ (A ∨ B) ∧ ~A → B [Prop.] ⊢ ☐(A ∨ B) ∧ ~A → B [1;NEC] ⊢ ☐[(A ∨ B) ∧ ~A] → ☐B [2;Dist.,MP] ☐(A ∨ B) ∧ ☐~A → ☐B [3;...
1 vote
0 answers
60 views

Was Gödel actually convinced that his ontological proof was correct?

The proof is obviously logically valid, but it is as obvious that it isn't logically sound. For instance, the second axiom states that ¬P(φ) ⟺ P(¬φ), take φ(x) ⟺ x is a male human being. Then either ...
5 votes
2 answers
378 views

How can I derive ~a=b→☐~a=b in SQML?

I have been thinking about this question for a long time but didn't seem to make any progress. Here are the axioms of SQML:
-1 votes
1 answer
63 views

Question regarding conjunction and necessity in modal logic

I've been learning SQML, and I have a question regarding conjunction and necessity. How do you prove the following theorem, or is it not generally true? ⊢ □(A ∧ B) → □A ∧ □B
1 vote
0 answers
40 views

Can the modal logic S5 be reduced to Rosser's system for a first order function calculus?

From the SEP In propositional logic, a valuation of the atomic sentences (or row of a truth table) assigns a truth value ( T or F ) to each propositional variable p . Then the truth values of the ...
2 votes
2 answers
151 views

Question regarding disjunction and necessity in modal logic

I have a question regarding disjunction and necessity. Is the following theorem provable in any system of modal logic, or is it not generally true? ⊢ A ∨ B → □A ∨ □B I was thinking about using the ...
2 votes
1 answer
246 views

Can natural deduction be incorporated into SQML?

EDIT - From the SEP 3.4 Propositional Modal Logic (S5) (1) □(φ → ψ)→ (□φ → □ψ) (2) □φ → φ (3) ◇φ → □◇φ Rule of Necessitation (RN): □φ follows from φ (3) is precisely what I have in my demonstration, ...
1 vote
1 answer
85 views

Can modal logic be used to define the notion of an “arbitrary constant” in FOL?

I was wondering if first-order logic can be reduced to propositional calculus if we eliminate quantification. For example, instead of saying “for all x in a domain D, P(x)”, we could state “P(x)” for ...
3 votes
1 answer
79 views

Can vague concepts have a modality?

Can vague concepts, which I am thinking of as concepts without boundaries, though there are I assume other ways of thinking about them, be necessary, especially if that modality changes? Supposing it'...
0 votes
1 answer
99 views

What is the reason behind the fourth axiom in Gödel's ontological proof?

In Gödel's ontological proof, axiom 4 goes like this: And I'm not sure about what it means. If that P(φ) is true, then isn't it necessarily true as well? There's some basic concept about modal logic ...
4 votes
0 answers
82 views

What would we gain by allowing quantification over logical constants?

In first-order logic, we quantify over individuals, and in second-order logic, we quantify over properties. However, could we extend this idea to include quantification over logical connectives, ...
2 votes
0 answers
55 views

Does Kripke endorse a view of free logic?

Considering Kripke's reluctance to accept Barcan's formula in its changed form in free logic, especially given his essentialism, one possible solution is to adopt free logic.
4 votes
3 answers
236 views

Kripke against Lewis

In Kripke 's Naming and Necessity, there is a footnote says that "Lewis's elegant paper also suffers from a purely formal difficulty: on his interpretation of quantified modality, the familiar ...
2 votes
0 answers
47 views

Do universals exist in all possible worlds?

Exactly what it says on the tin: Do abstract objects, like universals for instance, necessarily exist in all possible worlds? To my knowledge, David Lewis held to the opinion that they did (And that ...
0 votes
0 answers
52 views

Is B(p) V B(~p) an instance of LEM in doxastic logic?

So in classical logic either p is T or p is F. But is it same in doxastic logic, ie, is B(p) V B(~p) an instance of LEM? And the second issue, is it equivalent to B(p) V ~B(p)?
6 votes
3 answers
164 views

Can you help me understand the masked man paradox?

The masked man fallacy (or paradox) is roughly: Premise 1: I don't know who the man wearing the mask is. Premise 2: The man wearing the mask is my father. Premise 3: I know who my father is. ...
4 votes
1 answer
88 views

Understanding possible world semantics and time

In possible world semantics, statements of the form "It is possible that P" are interpreted as meaning "There is some 'possible world' in which P is true". And if you're a modal ...
0 votes
1 answer
66 views

If Zalta objects exist, would there be a contingently abstract obligation?

One of the posits of Zaltaesque object theory (let's call it that, since there is something vaguely Kafkaesque about logicist realism) is that for every set of assertible encoding relations there is ...
4 votes
2 answers
310 views

When is the proposition expressed by "I am here" necessary?

I'm currently reading Kaplan's On The Logic of Demonstratives (1979). He considers the example (1) I am here now. and on page 84 he argues that (b) In almost (if not all) contexts, an utterance of (...
1 vote
0 answers
61 views

Proof that the single variable fragment of first order logic is equivalent to an S5-like modal logic

I think I read that a single sorted logic is a logic in which there is only one unique variable symbol permitted. In other words, there is only one “parameter of variation” amongst all sentences of ...
4 votes
0 answers
82 views

Can there be nested possible worlds semantics?

Fairly straightforward question, I'd think: Usually, when we do Modal Logic, we think of propositions as sort of embedded within a framework of possible worlds. What, then, do we make of propositions ...
0 votes
2 answers
574 views

What does the "⊢" symbol mean in ⊢ p ⇔ (p & p)?

⊢ p ⇔ (p & p) what means the right part of these Entailments?
2 votes
2 answers
300 views

What is the modality of a statement that follows from a necessary statement?

Let □P. Suppose □P => Q. What can be said about the modality of Q? □P <=> P holds in every possible world. Thus it is available as a premise to derive Q in every possible world. Suppose Q is ...
-5 votes
1 answer
144 views

If there is less than a 100% chance that X might occur, can it occur? [closed]

The key word is might. If there is a 100% chance that a thing might occur, that does not mean there is a 100% chance it will occur! It might not occur, even though there is a 100% chance it might ...
1 vote
3 answers
124 views

A question on the belief operator in Doxastic Logic

Let Bp be the statement "it is believed that p". Why is ~Bp not equivalent to B~p? in words it amounts of saying that: "it's not believed that p" equivalent to "it's believed ...
2 votes
3 answers
356 views

Questioning the category of the “moral”

Briefly: it occurs to me that taking as given the pre-existence of the terms “morality” and “ethics” structures our thinking preemptively and heavily. In the manner of discursive analysts like ...
1 vote
1 answer
52 views

Do the incompleteness theorems need the provability predicate to be expressed, or can they be expressed via just ⊢?

In his "Epistemic Set Theory," William Reinhardt says: It is the purpose of this paper to formulate axioms for Gödel's modal operator B for provability (see [3], [8]) in the context of set ...
2 votes
1 answer
96 views

Metaphysical indeterminacy and necessity

This is similar to my last question, but now I am asking about a specific/different interpretation of vagueness. To fit metaphysical indeterminacy into this picture Barnes and Williams [claim]... the ...
2 votes
3 answers
87 views

Question about eliminating parentheses

Are '□(p → q)' and 'p → □q' semantically equivalent? Specifically, does eliminating parentheses in the former gives us the latter?
6 votes
4 answers
674 views

General sentence operators

There are lots of operators that act on sentences. Here are a few examples: P and Q not P forall x.P necessarily P eventually P x believes that that P it is obligatory that P etc. The first two ...
1 vote
0 answers
22 views

Modal dualism: is there a combination of counterpart and transworld-identity theory classifying objects based on which relation they enter into?

Theorists love to be competitive, but often enough we find out that they don't have to be like that. The SEP article on infinitesimals, for example, notes at one point: It is of interest to note that ...
3 votes
3 answers
120 views

Is necessary existence a property?

If existence is not a property then doesn't it follow that necessary existence is also not a property? If it is then why?
4 votes
2 answers
117 views

Tautological Many Worlds?

this is my first question here so I hope I'm following the guidelines correctly. I recently found a relatively obscure physicist/philosopher who asserts that the concept of Many Worlds is ...
1 vote
1 answer
51 views

Trying to avoid a modal explosion: if anything can be obligated, and ought-implies-can, then would everything be possible?

Where by "anything"/"everything" I mean atomic propositions (and I am quantifying over atomic propositions). The argument would seem to be something like: ◊OBA, ∀anyA OBA → ◊A ◊◊A ...
5 votes
4 answers
775 views

According to modal realism, how many possible worlds are there?

Modal realism tells us there is an infinity of possible worlds, but how many are there exactly? Is it countable infinity ℵ₀, uncountable infinity 𝖈, or some other, bigger uncountable infinity?
3 votes
3 answers
61 views

Does Necessity Mandate Uniqueness?

Suppose there is a nonzero number of contingent entities and a nonzero number of necessary entities. For example, the law of non-contradiction is probably a plausible candidate for something that ...
2 votes
4 answers
950 views

Is Fermat's last theorem a logical necessity or a different kind of necessary truth?

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The question was, is this a logically necessary ...
-1 votes
1 answer
106 views

Proof verification of god existence theorem

NB: My question was closed on math stack exchange. They advised me to post it here, but due to the lack of LaTeX formatting, I had to upload it as images. Apologies for that. I am a first year student ...

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