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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How to interpret what a set is to see how it could be infinite?
Currently, 'infinite set' sounds oxymoronic to me, so my question is how to interpret what a set is such that it is consonant with it being infinite. I understand that we take it as axiomatic that ...
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Are opinions considered sentences in Logic?
I am beginning to read the book titled forallx An Introduction to Formal Logic by P.D. Magnus. This is an open source book. On page 4 Magnus states:
In this open source book found here: https://math....
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Is there a mathematical notion of "why"?
Is there a mathematical notion of "why"? That is, are there reasons behind the truth of certain mathematical statements? Personally, my belief is that true mathematical statements just are ...
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I don’t know what a natural number actually is
For some context I did a course on set theory where I was taught about ZFC, and the construction of the natural numbers, integers etc.
I think I was far too young to take the course because it’s left ...
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Why do constructive mathematicians claim that mathematical truth is temporal?
It seems to me (and correct me if this is a misconception) that the traditional divide in the interpretation and practice of mathematics is between platonists, who believe that mathematical objects ...
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What is the deal with the bizarre philosophy in historical and current axiomatic set theory? [closed]
Many respectable mathematicians have written about "true axioms" or similar concerns about whether all mathematical theorems are in fact "real" or "true". This seems to ...
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Is there any logic system which ENTIRELY rejects non-contradiction of any kind for any sentence (i.e. all contradictions are true)? Is this possible?
I've recently learned about paraconsistent and intuitionistic logic, and dialetheism.
According to the Stanford Encyclopedia of Philosophy's page on Dialetheism, it states:
Dialetheism is the view ...
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What makes one proof different from another one? [duplicate]
There are around 370 different ways to prove the Pythagorean Theorem, but what does that exactly mean? For instance, if your proof states that $x^2+y^2=z^2$, I could construct a different one by ...
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Why is list of names no more capable of expressing a proposition?
From the Open Logic Project book 2.2, Philosophical reflections (Set theory):
Third: when we “identify” relations with sets, we said that we would allow ourselves to write Rxy for ⟨x, y⟩ ∈ R. This is ...
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Does it make sense to divide mathematical theorems into those susceptible to experimental conjecture and those that are not?
I read the following in a good book: ”let's start from zero", the authors are Vinicio Villani and Maurizio Berni (pisan mathematicians) but I don't know if the book is also marketed outside Italy....
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What is the purpose of mathematical research? [closed]
This is a bit of a soft and philosophical question, but what is the purpose of mathematical research? It seems to me that there is no end goal of mathematical research, because everything can be ...
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What exactly are capture and release?
Motivation:
I'm interested in how different people resolve the Liar paradox and other, related phenomena, like the revenge Liar paradoxes, and so on.
I have a copy of "Formal Theories of Truth,&...
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(Soft Question) Real World Modeling as Understood Through Pure Math
This question is necessarily vague; I'm not looking for an answer so much as I'm checking to see if this is something that has been thought about/discussed before, and if there are any resources out ...
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in modal set theory, why it is issue?
I have been studying the Iterative Set Concept within the context of the paper titled "Modal Set Theory" from Menzel specifically on pages 11-12.
"As we’ve just seen, the iterative ...
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Why do numbers apply to such disparate concepts?
I understand numbers to be defined as objects defined to have certain convenient properties in relation to certain operations. It is very surprising that the exact same group objects should be ...
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