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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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? ...
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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) ...
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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 ...
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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 ...
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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 ...
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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 ...
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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) ...
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60 views

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 ...
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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)]}...
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Axioms for modal logics based upon counterfactuals

Suppose we have a logic for counterfactuals as with David Lewis. I here use ⇛ for the counterfactual conditional. So suppose we have: Rules: (1) If A and A→B are theorems, then B is a theorem. (2)...
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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?
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What's the difference between logical modalities and physical modalities?

I am just wondering what's the difference between the two. I would say that there is something different, but honestly I can't define what it is exactly. What do you think?
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How to prove, in modal logic, that □A→A is valid (T axiom) iff R is reflexive?

How to prove, in modal logic, that □A→A is valid (T axiom) iff R is reflexive? I'm not sure how to prove axiom in reverse?
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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?
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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 ...
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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 ...
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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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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. ...
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Does Kripke hold a view of free logic?

if Kripke doesn't want to accept Barcan's formula(the changed form in free logic) - given his essentialism - one solution is free logic. So does Kripke say that he accepts free logic or?
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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 ...
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138 views

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 ...
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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 ...
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Did Carnap propose some kind of Modal Realism?

I have read in several pages that Rudolf Carnap, just as David Lewis (The creator of Modal Realism philosophical hypothesis) proposed that every logical proposition exists as a universe But is this ...
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How and why Aristotelian essentialism is a problem for Quine?

I cannot understand how and why the Aristotelian essentialism is problematic for Quine. I have tried to read articles on the theme but probably I am not smart enough to understand them. Could you ...
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Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a)...
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Does Sosa's modal definition of knowledge beg the question?

In his 1999 paper "How to Defeat Opposition to Moore", Ernest Sosa argues that sceptical, Nozickian tracking, relevant-alternative, and contextualist accounts of the sceptical paradox rely on the ...
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Proving validity/invalidity of a modal argument

□(A v B) → (□A v □B) ...(1) This symbolic argument is intuitively invalid. In (1), if we replace B with ~A, then we see that though the antecedent is necessary, the consequent is a contradiction since ...
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can S5 be the weakest logic?

If we were to prove that an argument is a logical truth only in S5 logic out of (K, T, S4, and S5). does that make S5 the weakest of these four logics in which the argument is a logical truth?
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"Where" does the counterpart relation subsist?

AFAIK, according to the counterpart theory, it is true of me that I could have lived a different life, if my counterpart in another possible world did live a different life. But where is it true that ...
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66 views

Prove that p → □p is not derivable in system K?

The only way I could think of doing this is to show that p → □p with the K axioms would imply a contradiction, but I don't think that's true. Not sure how to get started on this. Do I just have to ...
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Possibly necessarily P → Necessarily P?

So I saw this proof for ◊□p → □p but I don't know if it's true. ◊~p → □◊~p (5 axiom) ◊~p → ~◊~◊~p (Definition of □) ~~◊~◊~p → ~◊~p (Contraposition) ◊~◊~p → ~◊~p (Double negation) ◊□p → □p (Definition ...
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Is there a moral to the deontic-logic story?

In alethic modal logic, it is arguably conventional (or metaphysically thematic) to start with a possibility or a necessity operator. For example, you can start with possibility and get not-possibly (...
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What is basically at stake in contemporary discussions regarding essentialism and essential properties?

Modern discussions of " essentialism" ( 17th century) can be associated with the empiricism / rationalsit debate. By denying that we have acces to " real essences" , Locke also denies that we can know ...
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Alphabetic Substitution, Barcan, and Strict Implication

Context: I'm stuck on Axiom 8 from the introduction to Barcan 1946, "A Functional Calculus of First Order Based on Strict Implication." My instinct is that I'm missing a basic, perhaps obvious concept-...
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Proving the Modal Logic S5-Theorem ♦□ϕ ↔ □ϕ

As above (http://gki.informatik.uni-freiburg.de/teaching/ss15/ml/script.pdf page 59), and in many other sources, the formula ♦□ϕ ↔ □ϕ is considered a theorem in modal logic S5. However, the paper ...
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Is this valid in first-order modal logic?

(∀x)(∀y){(xEy) --> (∀z)[Tz --> (C(x,z)Ey)]} (Premise) {(∀y)[Ty --> (∃x)(Tx & xEy)]} --> {(∀y)[Ty --> (∃x)(Tx & xEy & ◻(Tx --> Ty))]} (From (1)) I'm trying to work this out in a quantified ...
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Real impossible worlds

What is the name of a/the metaphysic that affirms the reality of all worlds including impossible worlds? Actualism denies the reality of all non-actual worlds, possibilism affirms the reality of all ...
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Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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How to make sense of " I know that p but I could be wrong as to p"? ( Faillibilism)

There is a well known modal fallacy regarding knowledge which says that if some subject s knows that p, then p cannot be false, and therefore , p is a necessarily true proposition. Source : [ by ...
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Modal Logic Proof in System T

I need to provide an axiomatic proof of the following formula in System T of modal logic: ◇(A→□B)→(□A→◇B). Any advice on how to start would be great!
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A question about possibility

If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...