# 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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### Need help formally translating sentence into modal logic

Can someone please help me formally translate the sentence "it is impossible for x to exist without y existing as well" into modal logic using ~◇? Or, similarly, the sentence "it is impossible for ...
198 views

### 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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### How does the concept of the 'virtual' (Deleuze) relate to 'counterfactuals' (Lewis)?

We read: "[...] Deleuze will reject the notion of the possible in favor of that of the virtual. Rather than awaiting realization, the virtual is fully real; what happens in genesis is that the ...
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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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### How to construct a counter-model of □P --> □◊P in T and K?

I am new to modal logics and would really appreciate it if someone would be able to help me out with this practice question. I’ve established the validity theorem in T with an axiomatic proof, but I ...
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### “Fatalism and Professor Taylor” by Bruce Aune

In this paper Bruce Aune states the following Taylor would probably want to maintain that (p ≺ q) ⊃ — (p → q), where "→" represents physical, or natural, implication So I'm not clear what "...
151 views

### Negation of a E quantifier in a Modal Logic T System?

In System T its possible to conclude: (1) □Ex->Ex Therefore its possible to conclude: (2) Ex->◊Ex But whats the result, if I negate the existence quantifier? Is it: (3) ~Ex->~◊Ex or is it: (4) ~Ex->◊~...
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### How many equivalence classes does the accessiblity relation have in S5?

I'm a math student taking philosophy classes. So I have some math background but am absolutely unfamiliar with metaphysics&c. Recently I've come around the "Nothing Is Impossible" paper as a part ...
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### Natural deduction introduction and elimination rules for modal quantifiers

I've read several papers on modal natural deduction but I've only been able to find one clear explanation of []-Introduction ([]A if A can be proved from no assumptions/premises). But there were no ...
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### In possible-world semantics, what do nested modal quantifiers mean?

I'm trying to learn modal logic and I'm having trouble translating sentences like [][]A and []<>A into natural language using possible-world semantics. The first statement seems to read, "In ...
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### circularity of possibility defined over possible worlds

I have just checked similar questions that have been asked(and answered) before but I am still confused. How is it that the notion of possibility defined over as being True in some possible world not ...
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### introduction to modal logic

I am not entirely sure if we are allowed to ask such questions here but I was wondering if anyone could suggest me a real introductory level textbook on modal logic
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### How to valuate (assign truth values to) a formula in modal logic (Kripke model)

A total novice here, and exasperated at that. I can translate natural language statements into formulae of modal logic, but their valuation in Kripke model seems elusive, as I'm simply unsure how to ...
361 views

### 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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### 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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### 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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### 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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### 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 ...
220 views

### 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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### 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) ...