Unanswered Questions
91 questions with no upvoted or accepted answers
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What are some noteworthy consequences of a deontic logic extended with the axiom “Ob(A) → Ob(◊A)”?
I think one unsuccessful attempt to construct a form of deontic logic in which the “ought” modal operator implies the “can” modal operator was to include the axiom OBA → ◊A, for an “obligation” ...
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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 ...
CommunityBot
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Can there be nested possible worlds semantics?
Fairly straightforward question, I'd think: Usually, when we do Modal Logic, we think of propositions as sort of embedded within a framework of possible worlds. What, then, do we make of propositions ...
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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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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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In set theory: What is the motivation for transitioning from first-order language to plural logic language?
I am reading Burgess's paper titled "Plural Logic and Set Theory." In this work, the motivation for transitioning the language of set theory from first-order logic to plural logic is based ...
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In the usual modal logics, are there tautologies of the form ◊¬X or ¬☐X?
And not when, "Possibly not X," or, "Not necessarily X," are implied by, "Impossibly X," already. But so is it possible to have a tautology be a statement of mere ...
CommunityBot
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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 ...
CommunityBot
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What would we gain by allowing quantification over logical constants?
In first-order logic, we quantify over individuals, and in second-order logic, we quantify over properties. However, could we extend this idea to include quantification over logical connectives, ...
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How to understand connecessity(?)?
Not quite following Messina and Rutherford[??], I assume that compossibility for propositions/factsF A and B is when:
A, B are compossible when A ∧ B is possible.
So I assume there is a slot to be ...
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Do ⊢ and ⊣ (as "demitrue" and "demifalse") conform to the classical, or to neo-Hegelian, absorption rules for disjunction and conjunction?
The use of the word "absorption" in a logical and/or mathematical context is varied. Per the examples on Wikipedia, the uptack and the downtack are absorbing elements modulo conjunction and ...
CommunityBot
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Challenging the distinction between a validity and a tautology
I know that there is a formal difference between a validity and a tautology. On the one hand, a validity is any formula of First-Order Logic that is true in all interpretations. A tautology is a ...
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Can 𝐅𝐑 be taken for a deontic negation operator (rather than just a specified negation of 𝐎𝐁)?
Presuppositions of the question: beliefs about the ambient structure of negation: I was rethinking the following in light of questions about supervenience, grounding, alterity, and identity:
A ...
CommunityBot
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Was Gödel actually convinced that his ontological proof was correct?
The proof is obviously logically valid, but it is as obvious that it isn't logically sound.
For instance, the second axiom states that ¬P(φ) ⟺ P(¬φ), take φ(x) ⟺ x is a male human being. Then either ...
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Do universals exist in all possible worlds?
Exactly what it says on the tin: Do abstract objects, like universals for instance, necessarily exist in all possible worlds? To my knowledge, David Lewis held to the opinion that they did (And that ...
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