Is the question of Lebesgue measurability of projective sets “leaning” one...
A lot of independence results (Continuum Hypothesis, existence of Suslin trees, etc.) can seem (to my mind anyway) a bit “esoteric”, i.e. not impacting in an obvious way to “normal” mathematics (areas...
View ArticleMinimal requirements for Platonist views of the standard model of set theory...
A purported existence of a standard model of such theory as ZFC has been a cause of discomfort for a number of experts. For example, Abraham Robinson wrote:In particular, I will mention here the...
View ArticleGrounds of Stellar Resolution (Transcendental Syntax)
Transcendental Syntax is a program proposed and started by Girard aiming for logic (linear logic, in particular) reconstruction. The idea is to go the "opposite way", forget all the logic rules,...
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Is the mapping between the same scene displayed on screens of different size...
The following is from Analytical Mechanics, by Valter Moretti:Definition 1.11. A metric space is a set $M$ equipped with a function$d:M\times M\to R$, called distance, satisfying:(1)...
View Articlewhy do we remember pictures not videros [closed]
This is probably a question for regular stack exchange but I can't figure out how to post there. Why do we remember pictures not videos, whenever I watch a movie I only remember pictures from what...
View ArticleLogical issues with the weak law of large numbers and its interpretation
In several probability textbooks I have found what amounts to the following argument:Let A be an event in some probabilistic experiment. Let p=P(A) be the probability of this event occurring in n...
View ArticleDid the terms *member* and *element* originally have these different...
I am asking this question out of naive curiosity as well as in a quest to clarify the cognitive processes which are fundamental to mathematical reasoning.I posted a similar question (now deleted)...
View ArticleReference of language aspects of Mathematics.
I occasionally wonder about the language aspects of Mathematics. Like when I read Vilém Flusser, Tractatus Logico-Philosophicus by Wittgenstein and Godel's Proof by Ernest Nagel and James Newman.Some...
View ArticleWhy is it that most mathematical statements that mathematicians tend to study...
This is a bit of a philosophical question. Due to Gödel, we know that there are undecidable statements in ZFC set theory. But why is it that most statements that mathematicians tend to study in...
View ArticleDoes there exist a statement with its relative independence in ZFC being...
I haven't seen a formalisation of "higher order" relative independencies in ZFC, but it probably exists somewhere, I just haven't found it yet. For the sake of this question, let an n-independent...
View ArticleDefinition of definition
I was wondering if there is a good way to "define" what definition means exactly in mathematics. Since the answers may be subjective or philosophical, I want to ask only for references on this topic....
View ArticleHow exactly is Arnauld's Paradox solved in modern mathematics? [closed]
Could you clarify the explanation of Arnauld's paradox in David Graham Wells'The Penguin Dictionary of Curious and Interesting Numbers (p. 6, revised edition, free to read at Internet Archive):A friend...
View ArticleWhat's the meaning of this "tastes," which Whitehead said an object of...
It's a puzzling line for over 20 years for me. The great mathematician A. N. Whitehead said in his "An Introduction to Mathematics"(1911) that:"Now, the first noticeable fact about arithmetic is that...
View ArticleIs there any solution to Frege's criticisms of Hilbert's Geometry without the...
Recently I have come across the interesting Frege-Hilbert Controversy regarding the Foundations of Geometry. It seems to me that the main concern of Frege was on the Logical Consistency of Hilbert's...
View ArticleDo complex numbers really exist?
Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious...
View ArticleWhy linear congruential generator is called random number generator?
As far my understanding linear congruential generator is used to produce pseudo random number. But the algorithm requires four parameters like,def lcg(modulus, a, c, seed): while True: seed = (a * seed...
View ArticleReference books for Foundations of Mathematics (Logic and Philosophy)
I am an undergraduate student. And I want to build solid foundation for Mathematics.I tried google search but could not get proper recommendation.Please suggest books which covers the subject...
View ArticleNatural language examples for failure of double negation elimination
I am trying to explain why double negation elimination $\neg \neg \phi \vdash \phi$ is invalid in intuitionistic logic, but introduction $\phi \vdash \neg \neg \phi$ is valid. The latter is easy: if I...
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 ArticleCan we find a complete and consistent set of axioms for all mathematics with...
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of proving all truths about the...
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