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

Filter by
Sorted by
Tagged with
1
vote
1answer
66 views

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 ...
2
votes
1answer
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)...
3
votes
2answers
206 views

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 ...
1
vote
0answers
44 views

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 ...
4
votes
1answer
151 views

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 ...
2
votes
1answer
64 views

“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 "...
2
votes
1answer
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->◊~...
4
votes
2answers
87 views

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 ...
3
votes
1answer
402 views

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 ...
2
votes
3answers
157 views

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 ...
2
votes
2answers
121 views

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 ...
2
votes
1answer
72 views

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
3
votes
1answer
162 views

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 ...
3
votes
1answer
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?
1
vote
1answer
134 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 ...
1
vote
3answers
295 views

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, ...
2
votes
3answers
371 views

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.
1
vote
1answer
141 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 ...
1
vote
1answer
175 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 ...
3
votes
1answer
265 views

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 ...
2
votes
1answer
254 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.
4
votes
1answer
88 views

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?...
7
votes
1answer
379 views

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 ...
0
votes
1answer
93 views

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 ...
6
votes
3answers
258 views

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 ...
3
votes
1answer
286 views

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 ...
3
votes
2answers
214 views

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 ...
-1
votes
2answers
196 views

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 ...
1
vote
2answers
391 views

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 ...
0
votes
1answer
87 views

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 ...
7
votes
2answers
178 views

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 ...
3
votes
2answers
254 views

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 ...
2
votes
1answer
318 views

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, ...
1
vote
1answer
118 views

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 &...
4
votes
1answer
174 views

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 ...
2
votes
1answer
190 views

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 ...
0
votes
0answers
115 views

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 ...
1
vote
1answer
84 views

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 ...
5
votes
1answer
256 views

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 ...
2
votes
0answers
98 views

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 ...
2
votes
1answer
395 views

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 ...
2
votes
1answer
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 ...
1
vote
1answer
122 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/...
1
vote
1answer
82 views

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 ...
8
votes
1answer
332 views

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 ...
3
votes
1answer
401 views

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 ...
5
votes
5answers
222 views

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 ...
2
votes
1answer
477 views

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) ...
3
votes
1answer
276 views

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 ...
1
vote
2answers
223 views

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 ...