Questions tagged [philosophy-of-mathematics]

Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

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What is the nature of proof in mathematics?

Preamble: I think we have this sort of questions, where we are required to find a solution for them. For example, what is the area of a circle?. I think the way to solve these problems is to try to ...
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The mathematical language of the brain

This question is similar, but not identical, to one I posted to the mathematics SE some time ago. I was originally unsure of where to post it. I believe this question is sufficiently different to ...
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Is it true that modern statistics was created to prove eugenics? [closed]

Karl Pearson, Francis Galton, R.a Fisher were all prominent figures in the development of modern statistics and were all proponents of Eugenics. Is this true that it was a scientific/mathematical ...
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Badiou vs. Deleuze - Set Theory vs. Differential Calculus - Limits vs. Infinitesimals

My question is triggered by a quote from Manuel DeLanda which I find difficult to unpack as it is probably not only that they prefer different mathematical tools but that there is a profound ...
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If-then syllogisms

We have a sentence like this: If you are right above 85/100 then you can enter a university. Does this sentence presuppose that a university exists in order for it to be true?
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Thoughts on an article by Danielle Macbeth

I'm just starting to learn about the philosophy of mathematics, and was asked to read this paper for a course: Danielle Macbeth, Seeing How it Goes: Paper-and-Pencil Reasoning in Mathematical Practice,...
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Philosophical feminism and logic

Are there any resources to study about academic works on philosophical feminism and logic?
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Probabilty of a coin head on nth toss after a few coind head tosses? [closed]

Suppose, you have been flipping a fair coin and got coin head 5 times in a row. Now, what is the probability of getting 6th? On the one hand, it is said that probability is 1/2. On the other hand, ...
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Quantum Mechanics and Logic [closed]

I heard several times that the results of quantum mechanics (double-slit experiment for instance ) challenge our logic. One example of that is the famous physicist Lawrence Krauss. He keeps ...
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Higher-order probability

How does one assign a probability to statements that are themselves probabilistic? For example, how would one assign a probability to the statement, "There is an 80% chance that it will rain on ...
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1answer
235 views

Are propositions in mathematics synthetic or analytic?

I'm reading Kant's Critique of Pure Reason and I understand that he thought that "Mathematical Judgements are all synthetic". I would like to know where does this debate lies or if it is of interest ...
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1answer
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Do morphisms and their compositions capture the essence of “having a structure”?

As you may have guessed from the title I'm talking about category theory (CT). It's a fascinating subject to me. It can beautifully describe the essence of what it means to "have a structure" and it'...
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Why is the complex number an integral part of physical reality?

In modern physics, the quantum wave distribution function necessarily uses complex numbers to represent itself. If physics defines the physical reality, then what we are saying by the statement above ...
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Can a physicalist be also realist about mathematical objects?

Is it possible to believe that mathematical objects enjoy some kind of mind-independent existence while holding physicalism? And if they are mind-dependent, should one embrace constructivism ...
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Questioning determinism (example)

Questioning the world's deterministic behaviour, I shall present an example which seems to defy any certainty about the recurrence of events and is (obviously) a result of faulty logic, but I would ...
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Theory of Chaos

One example given by my philosophy teacher in highschool to explain the chaos theory was this : Take this sequence of numbers : 1, 2, 4, 8, 6, 2, 4, 8, 6, ... Built following these rules : Take ...
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1answer
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How does a Bayesian respond to the Grue-hypothesis?

According to Bayesian inference/confirmation theory, your confidence in a hypothesis increases as you observe more and more evidence predicted by that hypothesis (according to bayes theorem and the ...
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Is mathematics founded on beliefs and assumptions?

Note: I originally posted the question in meta.math.stackexchange.com but I reckon this would suit a more philosophical audience so I am posting it here. Background: I am a 28 year old ...
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Why did ancient Greeks not regard the negative numbers as numbers?

The Ancient Greeks famously rejected the conception of irrational numbers or rather refused to treat them as numbers - they regarded them as geometrical magnitudes. While I understand why this was the ...
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3answers
114 views

If you can “divide” anything other than numbers [closed]

I am wondering about a system with division defined for non-numbers. From what I have encountered so far, it seems division is only applied to numbers. For example: 4 * 6 = 24 You can then take the ...
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Information of a sentence

Someone rolls a six-sided die, but before he rolls it he says, "the outcome can be 1 or 2." Is he lying because he didn’t refer the other possible outcomes?
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What would happen if suddenly, 1+1=2 is disproved?

Would the universe be thrown into chaos when the most fundamental equation is proved to be wrong?
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Does one have to become a Platonist to refuse to be a Platonist?

I believe the answer is no, but Scott Aaronson on his blog just gave in interesting argument to the contrary. This is in connection with the now famous paper Undecidability of the Spectral Gap, and ...
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Is this a good argument that mathematics was invented?

The Black-Scholes equation describes the price of a stock option over time. Since the concept of stock options, financial markets et cetera were invented, not discovered by humans, does that suffice ...
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What is the intuitive notion that ZF minus Extensionality minus Regularity plus Collection capture?

In order to clarify my questions I'll here introduce the concept of intuitive completeness of an axiomatic system, an axiomatic set A of a consistent theory would be said to be intuitively complete if ...
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journal for mathematics of philosophy/mythology

I have been working on research involving the use of mathematical formulas and reasoning in order to philosophical concepts, specifically concepts concerning mythology, the Jungian model of the psyche,...
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A Question Regarding Russell's Paradox

Consider the 'set' behind Russell's Paradox: R = { x | x is a set and x ∉ x } in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO ...
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Why do mathematical Axioms work so well in science? [closed]

Axiom, an established rule or principle or a self-evident truth. Better yet, An Axiom is a mathematical statement that is assumed to be true Why does math apply so well to science? Why is 1 atom+1 ...
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How is 0 defined?

I know that the naturals are assumed by the axiom of infinity, but the relationship between them (eg 1+0=1), must be rule based or defined at the very least. Basically I want to know what makes 0 or ...
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Can any correct logical reasoning in natural language sentences be translated into a formal mathematical proof?

Since natural languages (e.g. English) are prone to ambiguities and misunderstandings due to their constant evolving nature and lack of rigorous formalization, and given an arbitrary philosopher X who ...
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What is the difference between mathematical reasoning and philosophical reasoning?

Please see question in title. Why isn't philosophy considered to be a branch of mathematics? Is study of anything not a branch of mathematics, vague and imprecise?
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Ontological status of Axiom of Choice

Mathematical facts are necessary truths, either in a Platonic sense or by way of axioms. In the latter sense I mean that the Peano Axioms prove that 2+3=5, for example. In other words, "PA ⊨ 2+3=5"...
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Will McDuck go bankrupt?

The present question is of interest because it is answered in very different ways by different groups (mathematicians, physicists, students, professionals of non-mathematical occupations). I ask here ...
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Quote of Russell on Mathematics

My memory seems to be failing me at the moment, but I seem to recall Russell saying something like the following on some occasion: The consistency of mathematics does not show that it is true but ...
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Was Bishop Berkeley part of the Enlightenment and if so - how did it fit his adherence to religion?

In his The Analyst Berkeley argued, among other things, that mathematicians must not "submit to Authority, take things upon Trust" and so expressed a view of the Enlightenment. This made me think: if ...
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The tags for the 21st century philosophy [closed]

What are the tags, if I'd like to read something about 21st century philosophy? Where do I find the list of the greatest philosophers of the 21st century? Is it true that the pure philosophy is in ...
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Gödel's incompleteness theorem and non-standard logics/foundational systems

I am amateur in the field of mathematical logic, so sorry for any confusing parts of this question. It is well known that Gödel's incompleteness theorem shows there are great limits to what first-...
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1answer
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Nature of Logic and Mathematics, and its relationship with God and materialism

I believe that logic is infallible, mathematics is true and that an entirely mathematical description of the entire universe is possible. Are these inconsistent with materialism and atheism? Can ...
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1answer
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In which publication does Bertrand Russell define “philosophy”?

I've personally read a book or an article by Bertrand Russell where he defines philosophy. The definition --- IIRC --- is that philosophy is the study of the unknown. If it becomes a matter of fact, ...
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Is the couplet about mathematics and poetry about logocentricism and deconstructionism?

I find this couplet really interesting: Mathematics is the art of giving the same name to different things Poetry is the art of giving different names to the same thing The first one is made ...
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Is it possible to visualize higher dimensional space?

This might seem like a trivial question, but it may be more complicated than it seems. I'm wondering if it would be technically possible to visualize higher dimensional space. By that I mean seeing ...
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Can we compare the believe that mathematics refers to an objective reality with the believe in god(s)?

Some people think mathematics is not an invention of man, but that mathematics exists independently of human beings, no matter what we think about it. Some people think god(s) is (are) not an ...
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Is anything truly continuous?

The idea that there is some space between any two spaces is somewhat related to continuity, but the mathematical term for this is "dense". The rationals are dense, as there is some rational between ...
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Two questions about logic/mathematics

1: Why do we say that there can't be other logics/mathematics than those we have? 2: Logic and maths are independent of reality. Then, if we have invented a logic/math based on reality, would it be ...
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What factors could affect the resolvability of disputes over knowledge claims (within a discipline in an area of knowledge)?

I am considering the area of knowledge of History but it has so many disciplines that I don't really understand fully. As for answering the question, I already thought of one factor: the lack of data ...
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Why are true and false the only truth values used in mathematics?

Why do we use only true and false? It is possible to have many states in-between in fuzzy logic and other many-valued logics. If we assign numbers to true and false, such as 1 and 0 respectively, ...
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Validity of mathematical induction

Are there philosophical positions that reject the validity of mathematical proofs by induction? If so, what are the implications? I know that mathematical intuitionists reject the law of the excluded ...
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Do whole numbers other than zero actually exist?

Think about counting up: you start from 0. There are many decimals in between 0 and 1, actually, an infinite amount of decimals are there. So in the same way that there is no last number there is no ...
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Does God need to create mathematics?

If someone knows the detail of everything and has endless life, did s/he need to create mathematics to describe the world?
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Which philosophers considered mathematics an experimental science?

Which philosophers considered mathematics an experimental science (as opposed to a theoretical/speculative science)? It seems Kant thought that mathematics (or at least geometry) is purely a priori, ...