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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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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 ...
Johnathan Green's user avatar
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Truth/actuality as an operator

Frege claimed that "it is true that" adds nothing to the actual meaning of an assertion, and following him along this line are prosentential theories of truth. However, I wonder if this is ...
Kristian Berry's user avatar
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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, ...
AnduinWilde's user avatar
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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 ...
Kristian Berry's user avatar
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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'...
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Are there modal operators that don't take a proposition as an argument?

All of the modal propositions I can think of are most reasonably analyzed as a modal operator applied to a proposition, and possibly other arguments. In the following examples, I'll write the ...
David Gudeman's user avatar
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Propositions that can't be used to distinguish possible worlds

Are there known ways of formalizing the notion of propositions that can't be targeted by counterfactuals in a coherent way? Or of propositions that are outside the scope of the framework in question? ...
Greg Nisbet's user avatar
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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 ...
Kristian Berry's user avatar
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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 ...
Johnathan Green's user avatar
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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 ...
PW_246's user avatar
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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 ...
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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: (...
zzz's user avatar
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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, ...
Babu's user avatar
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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 ...
David Gudeman's user avatar
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How to prove that: ⊢/k ◻p v ◻¬p

My though it that we can refer to completeness. So just argue that ◻p v ◻¬p does not have a corresponding model. But I am not sure...
luyang sun's user avatar
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Are there "merely necessary" worlds?

If whatever is actual is possible, but not everything that is possible is also actual, and if everything that is necessary is actual (and hence possible), it looks like it might not make sense to talk ...
Kristian Berry's user avatar
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Questions about truth in deontic logic

I'm currently studying a bit of deontic logic due to a course in modal logic that I'm taking and I have some questions. My main question is regarding truth value in deontic logic. Initially, I ...
melosomelo's user avatar
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How to accomodate hyperintensionality in a Bayesian framework?

Generally, propositions are modelled as sets of possible worlds, and Bayesians define a credence function on the set of those propositions. They then adopt new credence functions in response to new ...
Rando McRandom's user avatar
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What is 'expendable' in logic and how to explain 'tautology' given this image?

This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
Abdul Muhaymin -Free Palestine's user avatar
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How to do indirect proof (reductio ad absurdum) using natural deduction for modal logic?

I have been using Garson's Modal Logic for Philosophers, 2nd edition, to learn how to use natural deduction with modal logic. (BTW, does anyone know where there's an answer key for chapters 1 and 2 of ...
richard cameron's user avatar
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Proof that uniform substitution is validity preserving in modal system K?

I'm reading "A new Introduction to Modal Logic" by Hughes and Cresswell. I've encountered this proof and I can't make sense of it: I'll try to break down what I don't understand about it. ...
Nick Doe's user avatar
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What is the distinction between A-intension and C-intension?

I'm having a really hard time understanding a concept discussed in “Qualia and Analytic Conditionals” by Braddon-Mitchell and "Why We Need A-Intensions" by Jackson. Here's my extraction of these ...
Jeremy Hadfield's user avatar
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Did Quine change of opinion towards quantified modal logic?

Willard Van Orman Quine was a strong opponent to quantified modal logic calling it unreasonable and useless. But, did he always think like that? Or did he relax his attitude towards it with time? Did ...
vengaq's user avatar
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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.
AnduinWilde's user avatar
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Can a Rigid Designator still exist if there is only one possible world?

According to Kripke, a rigid designator is a pronoun (but not all pronouns are rigid designators) and they pick out the same unique individual in each possible world. I understand this, however, if ...
user39914's user avatar
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Modal logics - philosophical paradoxes using modeling by possible worlds

I'm searching for "paradoxes" in classical modal logics, meaning lines of reasoning which give a counterintuitive conclusion if performed in classical logic, which can be modelled by the (semantical) ...
blub's user avatar
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De Re, Counterfactuals, and rigidity

This is going to come off as vague or obscure; but, I hope the idea is performatively expressed: Two questions: Do you think that Kripke would argue that the impossibility of de re counterfactuals ...
Wallows's user avatar
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Does ◻(∀x)[Px ≡ ◻(E!x → Qx)] and ◻(∀x)(Qx → ◻E!x) entail ◻(∀x){Px ≡ ◻[E!x & (E!x → Qx)]}?

Say we are working in a free quantified modal logic system S5. Would the following argument be valid: ◻(∀x)[Px ≡ ◻(E!x → Qx)] (Premise) ◻(∀x)(Qx → ◻E!x) (Premise) ◻(∀x){Px ≡ ◻[E!x & (E!x → Qx)]}...
James McGraw's user avatar
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Is there a symbolic formulation of modal realism?

Is there a symbolic formulation of modal realism, i.e. the doctrines of modal realism captured in some formal system?
Michael Smith's user avatar
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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 ...
Elvis's user avatar
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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 ...
lee pappas's user avatar
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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 ...
Julius Hamilton's user avatar
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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 ...
Kristian Berry's user avatar
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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 ...
Kristian Berry's user avatar
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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 ...
Kristian Berry's user avatar
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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-...
Kristian Berry's user avatar
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Actual content of Gettier cases

I'd not rewrite here classical Gettier cases. Each of cases hinges on a crucial fact: after obtaining "knowledge" from observable facts via disjunctive introduction or entailment, the ...
Denis T's user avatar
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Zero-one laws Model Logic, question regarding significance of domain size

Wikipedia informs me that: Essentially (correct me if I'm wrong) the result states that as the domain of objects (domain of discourse) grows (n->inf), a static first order sentence (S) will be ...
help-me's user avatar
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Zero-one laws and Modal logic, question regarding statement of result

Wikipedia informs me that the probability that a given structure (G-subN) with Domain {1,...,n} models S where 'S' is a first order sentence converges to either 0 or 1 as n->inf. I have two ...
help-me's user avatar
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Is modality always involved when we talk about the future?

When I make statements about causes in the future like "Cold causes frost to form on the window.", am I unavoidably involving modality even though i'm not using modal auxiliaries? Can ...
r0k1m's user avatar
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Is division of propositions by their modality comprehensive?

I call division of any concept comprehensive if the combination of concepts received by such division has a scope congruent (containing exactly the same objects) to the scope of the divided concept. ...
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What does this phrase mean according to the Modal Epistemic Model of logic?

According to the modal epistemic theory of logic, what does the statement P over P...ie p/p = p Np? To clarify, I am asking in the context of this document, because it seems to use Np meaning not p, ...
brigadier's user avatar
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Modal logic for absoluteness

Modern modal logic has the modalities of necessity and possibility. However, both of these can be seen as relative to the set of possible worlds and the accessibility relation chosen for the semantics....
Avi C's user avatar
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Axiom 4 in epistemic logic

In epistemic logic, axiom 4 says that if I know p, then I know that I know p. What is the philosophical value of such an axiom?
LJGC's user avatar
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How to define ‘impossible’ using propositional modal logic?

I am trying to define impossibility using the symbols we have in propositional modal logic. I got ‘negation diamond alpha’ in mind as equivalent to ‘it is impossible that alpha’. It that correct and ...
Eva's user avatar
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Is there a non-transitive frame in which schema 4 is true? Or an irreflexive frame in which schema T is true?

So, I know that I can construct a frame {W, R, I} which is not transitive and in which schema 4 is not true (more specifically, Axiom Schema K and Axiom Schema 4 are not both true). I also know that I ...
Lazarus Jones's user avatar
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Yablo's condition on "Truth about a subject matter"

In section 2.4 of "Aboutness" Yablo offers the following analysis of what does it mean that a statament is true about a certain subject matter/topic: So, what is the proposition we are ...
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Inference Rules of Modal Logic

I'm currently reading the book "An Introduction to Non-Classical Logic." Currently, I'm being introduced to modal logic for the first time. This book seems to prefer to present the reader with the ...
N. Bar's user avatar
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Boethius, Logical Necessity, and Accidental Necessity: A Solution to Free Will and Foreknowledge?

In his classic book, the Consolation of Philosophy (Book V), Boethius attempts to make an argument that libertarian free will and [divine] foreknowledge are not incompatible. His argument goes ...
brightlySalty's user avatar
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Modal Logic: Proving Schema Validity

When faced with a question of the sort, "Is schema X valid in class of frames C?", we usually go about proving or disproving this by assuming the antecedent of X and showing that the consequent ...
nbogs's user avatar
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