Questions tagged [philosophy]
Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.
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Which forcing technique implies "every set is countable from some perspective"? Which notion of "the same set" is used between models?
https://plato.stanford.edu/entries/paradox-skolem/ contains this claim:
Further, the multiverse conception leads naturally to the kinds of conclusions traditional Skolemites tended to favor. Let $a$ ...
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Trying to understand how numbers themselves (s0, ss0, sss0, etc) are represented in Gödel numbering
Problem solved: I did not actually read the table given on page 70 of nagel and newman. s does have a Godel number. It's 7. So ss0 would be broken down into 7, 7, and 6, since 0 is given the number 6. ...
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On motivations of continuous geometry
The development of continuous geometry as an abstract field seems to be following a trend of removing the significance of low-dimensional entities from geometry. As classical treatments of geometry ...
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Can the fundamental theorems of real analysis be proven/developed without proof by contradiction?
I've been reading about philosophical debates between mathematicians, and some seemed to reject the ideas of real analysis (such as the extreme value theorem) based on a school called "...
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Mathematical Induction: Strong vs Weak Form
I have a rather naive question: The usual mathematical induction works by the same scheme: Let $n_0 \in \mathbb{N}$ a pos integer and $A(k), n_0 \le k \in \mathbb{N}$ family of statements. Then the &...
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Are there any problems about the difference between set theoretic definitions of polynomials?
I am a novice about this question, so if there is a misunderstanding then I apologize for it.
As for Peano axioms, if I choose Zermelo natural numbers, and you choose von Neumann ones, then this doesn'...
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Why pullback of ideal sheaf should be the conormal sheaf?
I'm sorry that this isn't really a math question, but this gap between my intuition and the truth bothers me. For closed subvariety (for simplicity) with ideal sheaf $\mathcal{I}$, the pullback $i^*(\...
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For every object, is there a unique notion of isomorphism?
Do you think that, according to most mathematicians, the following claim holds?
(Claim) For every object, there is a unique notion of isomorphism.
Perhaps one might think that for some sets, such as $(...
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doesn't the independency phenomenon make a case for non-classical logic? [closed]
alright, this question is philosophical and somewhat fuzzy. i also admit to knowing little about logic. all in all, this question can possibly be easily resolved by either pointing to (perhaps even ...
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What is the logical system of Tractatus Logico-Philosophicus?
Tractatus Logico-Philosophicus states simply that
6 The general form of the truth function is: $[\bar p, \bar\xi, N(\bar \xi)]$. This is the general form of the sentence.
Wikipedia and other sources ...
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Finitists reject the Axiom of Infinity - are there groups who reject the others?
I've seen rejections of the Axiom of Infinity. This is called finitism. Some ultrafinitists even add the negation of the Axiom of Infinity. Definitely doable.
I've seen rejections of the Axiom of ...
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Is there a term for the idea that mathematical objects are defined by their relationships?
In a recent Veritasium video discussing Euclid's Elements, Alex Kontorovich comments that Euclid's definitions of primitive objects (e.g. "A point is that which has no part.") are absurd and ...
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Conceptual Question regarding Shannon Entropy and bits
It is said that the number of "information bits" contained in a certain piece of information can be roughly translated as the number of yes/no-questions that would have to be answered in ...
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Do we ever reason about a non-associative algebra without embedding it in an associative algebra?
This question most certainly contains some errors in phrasing. It is on the subject of the philosophy of mathematics, and it is hard to stay precise when reaching towards the fundamentals of math.
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A philosophical question on the nature of mathematics [closed]
I had a seemingly simply question today, that goes as following.
What do we need for a mathematics to exist in a universe, or a system, more broadly speaking?
Is it a matter of having the ability to ...