Unanswered Questions
55 questions with no upvoted or accepted answers
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Are Quine atoms counterexamples to the irreflexivity of grounding?
It seems commonplace enough in the literature on grounding to find the claim that x grounds {x}. It is also a commonplace that grounding is irreflexive. But what about a Quine atom, then? For this is ...
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Minimal assumptions to believe ZFC is consistent
Introduction
ZFC (Zermelo-Fraenkel set theory with the axiom of Choice) cannot be shown to be consistent using finitary arguments (unless it is inconsistent) and thus in order to justify to ourselves ...
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Is there a counterpart semantics available for the multiverse standpoint in set theory?
I've been working on something that might be usefully denoted "the Dual Continuum Hypothesis," which is based on the following from Asaf Karagila on the Math Stack Exchange:
We know that ...
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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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For "⊰" = "grounds" and {C, D} = {~A, ~B}, does (C | D) ⊰ ~(~A ∧ ~B) ⊰ (A ∨ B)?
One paradigmatic example of grounding is supposed to be that of conjunctions-in-their-conjuncts and disjunctions-in-their-disjuncts. But per the duality of classical conjunction and disjunction, and ...
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what's means scope of further modal operators?
I am reading page 315 of Parsons' Sets, Classes, and Truth.
He presents the comprehension principle in the following form, but at the same time, he argues that this does not prevent Russell's paradox....
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What papers or books should I read in order?
I have been reading literature on modal set theory and am currently reading Putnam's "Mathematics Without Foundations," which is known for being one of the earliest presentations of this ...
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Would "to avoid the class/set distinction" be, or not be, an ad hoc reason to propose a couniversal set?
Once upon a time, von Neumann proposed the axiom of limitation-of-size, which says that any class "too large to be a set" is then a "proper class," meaning that there is a ...
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Is there a difference between "is an intensional element of" and "is an extensional element of"?
There is a version of set theory according to which there are two flavors (types? categories?) of elementhood relation, and if it's ultimately coherent, it does offer a solution to Russell's paradox (...
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What is the connection between Lawvere and Cantor?
Lawvere wrote in a couple papers that Cantors word “menge” which is usually understood as “set” is actually a cohesive type. And the “kardinale” is the abstraction from this by getting rid of the ...
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Does Reflective Set Theory "RfST" fulfill the requirements of founding Category Theory and Mathematics?
On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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How does Badiou analyze natural situations?
I'm having trouble applying Badiou's method of looking at situations as sets (EDIT: specifically sets in a model of ZFC). The following example was in the introduction to one of his books, Infinite ...
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Using paraconsistent logic, can we construct a conceptually stable set theory where proper classes both are and are not sets?
Suppose that the superclass problem is the problem of defining a new infinite hierarchy of set-like concepts over the concept of proper classes. For example, some superclass types in the literature ...
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how to solve Russell's paradox in modal set theory?
I am currently reading Nil Barton's "Iterative Set Theory." at pp.42-45.
It explains that modal set theory resolves Russell's paradox, but I don't fully understand it.
If a set x satisfies ...
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Why is this argument valid?
I m reading Linnet's paper 'pluralities and set' where his claim said that collapse principle lead contradiction if we didn't assume 'it is possible to quantify over absolutely everything'
He uses ...
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