# 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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### 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
45 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 ...
681 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?
46 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 ...
54 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 ...
916 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 ...
83 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 ...
17k views

### What is the literal meaning of "The only thing that I know is that I know nothing"? (Is not knowing anything a knowledge?)

If a person says, "The only thing that I know is that I know nothing." What exactly does that mean (not metaphorically), literally? If the only thing they know is that they know nothing, ...
69 views

You have probably seen these types of arguments before on incompatibility of omniscience and free will. The question is are these arguments valid and what can be a good refutation? Let G= x is known ...
1 vote
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### 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?
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### Completeness theorem for QML. A doubt about the relation R in the canonical model. (constant domain)

I dont understand this script: wRv iff □−w ⊆ v, where w is a word of W, that is an Lc-saturated set (maximal consistent with the ∀-property, (C is the set of constants that we use to amply the set of ...
640 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 ...
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### 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 ...
58 views

### Fixed/critical points of a nonexistence quantifier/function

Let j(∃0) = 1, and j(∃1) = 1, for a justification function j on ∃-sentences. So far, 0 is the initial critical point of the composite quantifier-function, and 1 is the initial fixed point. So let ...
126 views

### Can someone translate this into quantified modal logic?

So an attempt to translate- its not possible for two necessary beings to exist- in quantified modal logic. Is it correct? ¬◇∃x∃y[[□Nx ∧ □Ny] ∧ x ≠ y]
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### Interpretation of formula with free variables in QML with varying domain

The problem is known, both Huges e Cresswell (p.275) and Fitting e Mendelson (102) mention it. Example of the problem: we have a formula: □ (P(x) v ¬P(x)) that is true in the world w under the ...
1 vote
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### How does Ulrich Meyer treat of an "at eternity" operator in temporal logic?

Something called a "book of abstracts TELS 2022" includes a summary of one Ulrich Meyer's essay on a topic in temporal logic: The challenge is to explain how eternal objects would differ ...
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### What kind of homo/isomorphism, if any, applies to a certain pair of pairs of permission types?

The SEP article on deontic logic mentions at least once or twice that there seem to be two types of permissibility (also a difference between "ought" and "must," to note). Over the ...
111 views

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

If there is a 70% chance a certain occurrence might happen, does it have any chance of happening? There must be a 100% chance that something might occur for it to have any chance of occurring. If ...
46 views

### when A[t/x] it's false? It's to prove UI its valid in quantified modal logic with constant domain

Its for soundness theorem. I need to prove that the axioms (∀x)A -> A[t/x] its valid in constant domain semantics. I assume theres a world in a arbitrary model within (∀x)A -> A[t/x] its false ...
78 views

### A question on quantified modal logic

I originally posted this on math.stackexchange.com, but I’m cross-posting it since I know there are good modal logicians on here too. Also, I already asked a similar question here: Identity in ...
379 views

### Implicit Models and Probability - are degrees of belief/truth/existence a complete free-for-all?

Or, to put it another way, as long as you model your statements using the grammatical framework of our modern logical idioms, is it appropriate practice to assign a probability to any utterance at all,...
909 views

### Are there any established logical symbols for merely possible and contingently true?

In modal logic we have: P → ◇P - If something is true, then it is true at some possible world. ◻P → P - If something is necessarily true, then it is true. However, the reversed conditionals don't hold ...
30 views

### If we used √OB and √𝓐 operations, could we have a demi-is/demi-ought proposition that bridged full "is" with full "ought"?

The insight that the teleological ethicist seems to have is that final causality is a type of the moral law in the Kantian sense (from the second Critique): ... the moral law has no faculty but the ...
23 views

### If existence-tropes would be absurd, does this count against trope theory or the theory of existence-as-a-property?

I advert to the word "trope" as used in philosophy and not as used in narrative analysis (although I can see a reflection of either sense of the word, in the other use). The argument goes: ...
22 views

### Could a being be defined as such that its transworld identity is identical to its in-world identity?

I was reading through Collier[21], which is about Lewisian theism, alongside the SEP article on transworld identity, and have assumed that: The concept of transworld identity (TI) is not necessarily ...
71 views

### Is there a modal modification of the law of excluded middle that may render constructive?

Intuitionistic logic rejects the law of excluded middle, and paraconsistent logic rejects the law of non-contradiction. I wondered whether the rejected laws can still be incorporated, if they're ...
41 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'...
73 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 ...
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### √◊ (or generally √M, for whatever modal operator(s) M)

I tried Googling "demi-possibility demi-negation" and got nothing (just "demi-possibility" gave results mostly related to demisexuality). And my analysis of demi-negation didn't ...
1 vote
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### Does the claim of an is/ought gap presuppose relevance logic (at least for morality-talk)?

Imagine Hume's remarks but with reference to the usual disjunction introduction: In every system of conjunction, which I have hitherto met with, I have always remarked, that the author proceeds for ...
1 vote
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### Does "ought-implies-can" have to be taken for a universal material implication?

I was thinking of Quine's "change the logic, change the subject," saying, and thought over "change the deontic logic, change the deontic subject," and so then I wondered if deontic ...
1 vote
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### Is Aquinas' ethics a case of a supererogation-first system?

Section 2.2 of the SEP article on modal epistemology differentiates possibility-first from necessity-first systems. Per modal logic, one can take these as metaphysical readings of the order-of-...
76 views

### Computer Graphics Imagery (CGI) & Modality (Possibility)

The trend is obvious ... CGI is here to stay. Many movies wouldn't stand a chance in the box office sans computer generated images and I don't mean just the slew of superhero movies (DC & Marvel ...
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### Can something be logically necessary now but not in the future?

Can something be logically necessary now but not in the future? I probably always assumed it couldn't, that it followed from the laws of logic alone, and that these are immutable etc.. I don't think ...
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### Can we effectively (or at least plausibly) argue from a (3+)-valued set of deontic charges to 3+VL?

Suppose we defined an honest agent as one who intends to focus on stating truths, with liars as those who intend to focus on stating falsehoods. But if there are other relations an agent can bear ...
1 vote
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### Can physical universes nontrivially embed themselves into themselves?

Sometimes our world is said to be a "Big Conjunctive Contingent Fact" or that other possible worlds are "recombinations" of available propositions for some actual world. So model-...
2k views

### Is there a system of logic which denies DNI?

From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE. DNI: p -> ~~p DNE: ~~p -> p and denies DNE ...
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### Modal system K - prove ⊢ (□p ∨ □q) → □(p ∨ q)

I am trying to prove the following: ⊢ (□p ∨ □q) → □(p ∨ q) However, I think that I am lacking the knowledge of a tautology in classical logic that would help me prove this. I tried something, but it ...
53 views

### Modal Companions and Trivially Strict Conditionals

The classical material conditional is given a truth-functional definition that can be determined with truth-tables. Intuitionistic implication is a kind of strict implication that can be translated to ...
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### Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K

This time I have a more "complex" problem at first glance. I need to create a direct proof using the axioms of system K and rules of inference, but I have been unable to do so. □(A ∨ ¬B), ¬□...
286 views

### Proof of □P ⊢ □¬¬P in modal logic system K

I need to prove the aforementioned formula in modal logic system K, which I am having trouble to do. Of course, this should be easy to prove if I had access to axiom T, but since it's system K, we can ...
1 vote
71 views

### Infinitary modal logic

Let 'L' and 'M' denote the necessity and possibility operators. In Modal Logic, the following theorems hold: L(p and q) <--> (Lp and Lq) (Lp or Lq) --> L(p or q) M(p or q) <--> (Mp or ...
52 views

### platinga's actualism and introduction of essences

I am reading Plantinga's "Actualism and Possible Worlds" and I am struggling to see why he needs to introduce his idea of essences to resolve the following issue: The actualist holds that: (...
1 vote
52 views

### A question about David Lewis's refutation of taking possibility as consistency

I’m reading a chapter from David Lewis’s counterfactuals. He says something which I’m confused about, wondering if any of you guys can explain what he's saying... “ We might take…. ‘Possibly P’ [to ...
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### Are there "generalized Barcan formulas" in combining logic?

I did a search for "epistemic Barcan formula" and got only one result, with the sample being: An example with the Barcan formula in an epistemic context shows that our intuitions are much ...
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### Entry points from philosophy into mathematics at higher levels?

Everytime I look up of the link between philosophy and mathematics, I see the topics only of the most foundational levels discussed. As in logic, and stuff. When I study higher mathematics theories, ...
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### What is a “possible” event?

Things seem to happen or they don’t. If a dice rolls on 6, does this mean that it could have been possible for it to land on 1-5? We seem to differentiate this kind of event from an “impossible” kind ...