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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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The difference between indicative conditional and counterfactual

I was confused about the difference between indicative conditionals and counterfactuals. Could someone please offer an elaboration?
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133 views

Why isn't 4 a theorem of K? and Can I use Show boxes in modal logic?

In my basic logic course if I want to prove A ⊃ B then I would do the following: 1 Show A ⊃ B 2 A Assumption for Conditional derivation. 3 Stuff..... 4 Show B 5 More stuff.... 6 B [or some ...
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Are all logically necessary statements self identity claims?

When we say that x is necessarily P, are we not asserting that this is the case regardless of all contingent facts, so regardless of what x and P are? And if x was P regardless of what x and P are, ...
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What is necessity in modal logic?

I understand that something that is necessary must exist. However, what is the exact definition of necessity? Thank you.
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135 views

Quantified Logic and Unquantified Modal Logic

Is there a need to study unquantified modal logic if one knows the quantified PC logic very well? There seems to be an obvious connection between Possibility and the Existential Quantifier, and ...
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163 views

Is this a contradiction in system K?

I'm trying to prove that M(p implies p) implies (Lq implies Mq) where M is possibility and L is necessity. So obviously p&~p is a contradiction but is L(p&~p) a contradiction? At first ...
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Quine on Necessity

Lately, I have been reading some of Quine's works on modality. I can't help but feel that many of his pronouncements on modality are wrong/misguided, although pinpointing exactly where is goes wrong ...
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226 views

What the main reason for Bertrand Russell's skepticism and rejection of modal logic?

It seems to me that Bertrand Russell was somewhat hostile to the idea that modality plays a role in logic.
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The converse to the C modal logic axiom - has it been studied?

There is a C axiom as mentioned at https://plato.stanford.edu/entries/logic-modal/#MapRelBetModLog in Section 8. My question is: what can be said about the formula which is the converse of the C axiom?...
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Why substitutivity doesn't work in an intensional context?

I was trying to grasp some more insights on the difference between intensional and extensional. I started reading this article by Melvin Fitting on intensional logic. It seems interesting but I ...
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Truth that requires two possible worlds not causally linked

There is a clear example I have in mind of a modal transformer. The primary winding is in possible world, W1. The secondary winding is in possible world, W2. W1 and W2 are not causally linked in any ...
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Has any philosopher ever claimed that possibility can't really be tensed?

Has any philosopher ever claimed that possibility can't really be tensed? So that whatever will be possible is possible now. I really have no idea, and would love an answer. I'll add my motive, so ...
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What is Plantinga's “trivial property”?

I have seen the term "trivial property" used several times, and some authors seem to be attributing it to Plantinga, but I cannot find his definition. I have seen others define it as a property ...
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Getting started with reading papers in (philosophical) logic

I have worked through some textbooks thus far, but would like to get started reading papers in the field of logic. Can anyone recommend any papers or how I could get started? I found that many papers ...
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Why does this reductio ad absurdum work?

A is something which we do not know the truth value of, for example: A = It will rain tomorrow. It might happen, it might not. So possibly A is true, and possibly ~A is also true. What is wrong with ...
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Are statements in modal logic true or false?

A bit new to modal logic. I believe that it is the case if we say "It is possible that P is true in world w", then this statement is "true". This is not the same as saying P is true. Just that P is ...
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In what ways are formalisms like modal logic Eurocentric?

I mean this as a linguistic question, not a cultural one. Operators in modal logic, like must and should exist in English, and many other languages -- but not in all of them. I mean: Modality is not ...
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What is the explanation for inferring existence in every possible world from existence in some in Plantinga's Ontological Argument?

I found the following version of the Ontological Argument online (I'm pretty certain its Plantinga's but I couldn't find an exact source). Here is how it goes: It is possible that a maximally great ...
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A problem with Modal Logic (necessary truths)

I have this problem with Modal Logic that I am not sure I see which propositions in this logic are necessary besides tautological propositions. I mean metaphysically, something is necessary if it's ...
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What is the fallacy in deriving necessity of an event from God's foreknowledge of it?

Here is the form: If God knows I will eat lentils tonight, then necessarily I will eat lentils tonight God knows I will eat lentils tonight Therefore, necessarily I will eat lentils tonight. Now, ...
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Proving ¬Lp ∨ Lp

I want to prove this using only Necessitation Rule, Distribution Axiom and Reflexivity Axiom from modal logic (their combination is sometimes called modal system T). As I can't conclude that ¬Lp &...
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Is it provable that epistemically possible (possible for all I know) does not imply possible?

Here is an argument that it is not. Let's start with some equivalences: X is epistemically possible iff X is possible for all I know iff not (X is impossible given what I know) iff X is not ...
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Why do “L” and “M” name the strong and weak modal operators in modal logic?

Though the box and diamond are the more common representations of the strong and weak modal operators in modal logic, “L” and “M” are also used. I suspect that those letters were chosen because they ...
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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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Validity of: ◻◇◻p → ◇p in transitive frames

How can I show the (in)validity of: ◻◇◻p → ◇p in a transitive frame? Proof method: I want to do this by showing in a transitive frame that ◻◇◻p holds and that ◇p doesn't hold. (I think that ◻◇◻p ...
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Does semantic externalism imply modal realism?

Semantic externalism, or more broadly externalism about mental content, is the idea that propositions, intentions, attitudes, etc. derive their meaning from the external world as opposed to internally ...
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What is the difference between Herbrand Logic and Relational Logic or Predicate Logic?

I am learning a course from Stanford University, and it introduces the notion of Herbrand Logic. However in Wikipedia I cannot find a definition specifically for "Herbrand Logic", only for Herbrand ...
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Existence as a predicate and Godel's ontological argument

I am referring to this paper https://github.com/FormalTheology/GoedelGod/blob/master/GodProof-ND.pdf which has formalized the ontological argument. If I am not mistaken, watered down, the argument ...
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Consistency in Modal Metaphysics

I read this article Modal Metaphysics weeks ago, but one thing that struck and perplexed me was the definition of consistency offered in this article. According to this article, it seems that one ...
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110 views

Reasons to think that metaphysical theories express contingent truths

In a paper I read recently, the author claims that metaphysical theories such as Determinism or Materialism/Physicalism may be regarded as contingent truths. I take Determinism and Materialism/...
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Is there any way to represented nested modalities in alethic modal logic?

It is possible to represent simple statements involving possibility and necessity in alethic modal logic and possible world semantics. But consider a statement like "It is possible that it is ...
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Is it possible to not know that one knows p?

An axiom that is often included in standard modal logic is Kp => KKp If we use epistemic modal logic, so that K translates as 'he knows', then recalling p stands for a proposition, we have that Kp ...
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Is there anyone who believes that all modal statements are meaningless or trivial?

It is often useful to interpret statements in various modal logics using possible-world semantics. For instance "it is necessary that P" means "P is true in all possible worlds", "it is possible that ...
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Is Modal Logic Logic?

What makes "Modal Logic" Logic? Why are symbols that stand for "necessary", for example, taken as symbols of Logic (of the same level of symbols that stand for "exists")? What are the limits that ...
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Prove ◇(p ∨ q) → (◇p ∨ ◇q) and ◇(p ∧ q) → (◇p ∧ ◇q) in Modal Logic K

I would really appreciate a rundown of a proof of one of the formulas or both: 1) ◇(p ∨ q) → (◇p ∨ ◇q) 2) ◇(p ∧ q) → (◇p ∧ ◇q) I'm allowed to use following proof procedures of modal logic K: 1) ...
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Classes of frames in Modal logic

In Modal logic, a frame is defined as a pair (W,R), where W is a non-empty set (of possible worlds, states, or other terminology), and R is a binary relation on W. However, what exactly is a 'class ...
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Skepticism and Belief in Doxastic Logic

It seems to me that the proposition: "I am skeptical of everything" is synonymous with "I don't believe in anything". But obviously in Doxastic logic there must be some form of axioms that say that ...
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If everything is possible, is it possible for something to be impossible?

If everything is possible, is it possible for something to be impossible? Possibility and impossibility are modal notions; and are dual in the usual formulation; the SEP remarks: It would seem to ...
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Defining logical possibility without circularity

In explaining logical possibility (broad), I tend to say that a thing is logically possible if it exists in some possible world, some possible description of reality, but in what sense is such a world/...
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Why does a blind inaccessible world verify, but not falsify, 𝓐 ↣ 𝓑?

Picture 1: Last example on the 'Additional Examples' website for Chapter 11. (Not in the textbook) Picture 2: p 319, Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, ...
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Can one be a Modal Realist without also having to incorporate the existence of impossible worlds?

I know Modal Realism well enough itself, and have read many of the objections (and subsequent responses) that David Lewis himself took up in relation to the philosophical position. My question is, do ...
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The definition of a possible world

I have a two-part question about the definition of a possible world. I will make the assumption that time is tensed. First of all, is a possible world a complete list of all propositions that are ...
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Exercise 2.2b from A New Introduction to Modal Logic

I am kind of stuck on page 48 on exercise 2.2b in Hughes and Cresswell; In case you don't have the book at hand here's the question: Let K** be K but with N and K replaced by LT: L( p→ p), ...
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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?
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What is the difference between ∃ (existence) and A (actuality)?

The existential quantification can, it seems, be used with modal logic. Now excuse my naivety, but: if so, what is the difference between being actual and existential quantification? I'm just asking ...
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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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Necessity and possibility (again)

My question is inspired by the following post: Necessity in relation to possibility It seems that necessity does not entail possibility in every modal logic. In order to do so, one may require the ...
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Necessity in relation to possibility

(1) Does necessity (materially) imply possibility? (2) Does possibility (materially) imply necessity? From a logical point of view: If by material implication (A -> B), we mean (-A or B), then it ...
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Can the square that ends a proof (similar to QED) be considered to claim the same thing as “necessarily” from modal logic?

I've only thought of this because superficially they look the same, and seem to be making similar claims. When you prove a statement P=>Q ◻, then is it the same as writing ◻P=>Q in modal logic?
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Is there modal logic without possible worlds?

Would it be desirable to carry out a deflationary research programme in modal logic? In other words, would it be desirable to re-think modal logic without the possible worlds semantics? The original ...