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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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 ...
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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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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, ...
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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 ...
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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 ...
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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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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 ...
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Metaphysical indeterminacy and necessity
This is similar to my last question, but now I am asking about a specific/different interpretation of vagueness.
To fit metaphysical indeterminacy into this picture Barnes and
Williams [claim]... the ...
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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:
(...
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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 ...
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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...
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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 ...
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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 ...
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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 ...
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Could we supply logics make quantification over logical constants?
In first order logic, we make quantification over individuals, and in second order logic, we make quantification over properties. So could we supply logics make quantification over logical constants, ...
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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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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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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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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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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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Is necessary existence a property?
If existence is not a property then doesn't it follow that necessary existence is also not a property? If it is then why?
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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 ...
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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 ...
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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-...
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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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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 ...
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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 ...
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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 ...
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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, ...
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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....
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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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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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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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Completeness theorem for QML. A doubt about the relation R in the canonical model. (constant domain)
I dont understand this script:
wRv iff □−w ⊆ v, where
w is a word of W, that is an Lc-saturated set (maximal consistent with the ∀-property, (C is the set of constants that we use to amply the set of ...
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Fixed/critical points of a nonexistence quantifier/function
Let j(∃0) = 1, and j(∃1) = 1, for a justification function j on ∃-sentences. So far, 0 is the initial critical point of the composite quantifier-function, and 1 is the initial fixed point.
So let ...
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