(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...
View ArticleHow do we prove a set axioms never lead to a contradiction?
How can we be sure that a set of axioms will never lead to a contradiction? If there's a contradiction, we will find it first or later. But if there's no one, how can we be sure we choosen reasonably...
View ArticleWhat 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," by Beall...
View ArticleWhy do we have different sets of axioms? (metamathematics reference request)
For example, ZFC and ZF.I have come across the notion of pure and applied mathematics, and how the development of the former can (and is usually intended to) lead to the furtherance of the latter. In...
View ArticleWhat 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...
View ArticleDoes it make sense to divide mathematical theorems into those susceptible to...
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.I...
View ArticleWhy 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...
View ArticleWhat 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...
View ArticleIs there any logic system which ENTIRELY rejects non-contradiction of any...
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 that...
View ArticleWhat is the deal with the bizarre philosophy in historical and current...
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 make a great deal of non-sense...
View ArticleWhy 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...
View ArticlePrinciple of mathematical induction
In his book “Introduction to Mathematical Philosophy” Bertrand Russell seems to reach the conclusion that mathematical induction is a definition and not a principle. In essence he states that...
View ArticleI don’t know what a natural number actually is, and it’s making me sad :(...
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 me...
View ArticleIs 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 true. There...
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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:...
View ArticleHow does one refute this ultrafinitist argument?
From Wikipedia: Edward Nelson criticized the classical conception of natural numbers because of the circularity of its definition. In classical mathematics the natural numbers are defined as $0$ and...
View ArticleProbability - Interview Question - Hidden Assumptions and Phrasing Issues
I’ve encountered the following seemingly simple probability interview question in my workplace:Two reviewers were tasked with finding errors in a book. The first had found 40 errors and the other had...
View ArticleHow 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...
View ArticleSet theory and model theory: which set is ZFC?
I have yet another post about what is model theory doing and why is it valid; I hope I can be coherent.(1) https://mathoverflow.net/questions/23060/set-theory-and-model-theory(2) What exactly is the...
View ArticleIs there a mathematical or physical, real world use for numbers passed I? Who...
I is the Square root of -1, such that I * I = -1. Through this, I can be considered like a "Half Negative."Why hasn't this been taken further? Why don't we make a quantity such that I^3 is -1, such...
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