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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Is there some non-classical logic where the van der Waerden theorem does not apply?

The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {...
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118 views

Do sets and the empty set exist?

The original title of this question was supposed to be "Do sets exist?", but it was too short. In philosophy of mathematics we sometimes ask whether mathematical objects exist. I think this ...
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How do mathematical formalists account for unreasonable effectiveness of mathematics?

It will be agreed that mathematical formulae "work" in the sense that we have airplanes, bridges which have been built using mathematical concepts, and they workout in reality as expected. ...
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37 views

Axioms in philosophy

In mathematics one lays an initial sets of axioms and rules of inference, and builds a theory from there: does philosophy, nowadays, proceed like this? if yes, what are other currently "...
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Can we define the notion of an “omnipotent God” in terms of computational power?

A classic omnipotence paradox asks, "can an omnipotent God create a stone so heavy that He cannot lift it?" The problem here is that we take omnipotence to mean "capable of anything ...
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Does Gödel believe in the existence of his rotating universe?

I am wondering whether Gödel believe ain the existence of his rotating universe since he is a mathematical Platonist. I am also wondering in what entities believe mathematical platonists. For example: ...
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Explanation of Littlewood's profound philosophical joke

In "A mathematician's Miscellany", By J. E. Littlewood, I found this piece of conversation between Littlewood and Wittgenstein: "Schoolmaster: Suppose x is the number of sheep in this ...
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What is the connection between Lawvere and Cantor?

Lawvere wrote in a couple papers that Cantors word “menge” which is usually understood as “set” is actually a cohesive type. And the “kardinale” is the abstraction from this by getting rid of the ...
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Philosophy of science: Determinism and indeterminism in statistical methods of science

A variable is modeled as a random variable in a statistical model, often without reference to the question of whether it is random in reality. For example, when the outcome of a coin flip is modeled ...
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Does the following argument about the ontological nature of math exhibit poor reasoning?

Argument P1: Mathematics is the substrate upon which all natural phenomena occur and necessarily governs phenomena in the physical world. P2: One can experience something that is not mathematically ...
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What is the difference between properties and sets?

Is there a difference between properties and sets? To me, it would seem that the property of being non-self-identical is the same thing as the empty set, and the property of being (identical to x OR ...
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264 views

What documented justification is there for using physics to describe the nature of reality?

One of the earmarks of empirical/materialistic research and documentation is its insistence on rejecting and dismissing any subject matter that it deems irrelevant. This has always appeared to me just ...
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What is a set? (Is it possible to define a set?)

I've recently been studying set theory from some introductory textbooks (like Steinhart's "More Precisely" or Open Logic Project's "Sets, Logic, Computation"). I'm interested in ...
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What is the 'axiomatic' or epistemological foundation of Analytic philosophy, what is its practice and purpose?

In researching the origin and purpose of the Analytical Tradition in philosophy, all that appeared was that it traces its origin to the 'Tractatus' offshoots following Wittgenstein and Russell, and ...
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How can we overcome the challenge of the anti statistical philosopher?

Conventional statistical inference has been strongly challenged by the anti statistical philosopher who uses the following example: Imagine a man. Imagine that every time a man opens his front door ...
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What's the role of logic in logical positivism?

I'm reading up on a bit of the ideas of logical positivism. It seems that the main components were the distinction of synthetic and analytic statements, and the verification principle. Without giving ...
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243 views

How can we differentiate between change and progress in the area of math and ethics?

I'm studying epistemology, and I want to use reason and language as tools for carrying an investigation. How do I discuss the subjectivity inherent in change and progress, and also whether change and ...
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205 views

Why is mathematical induction so applicable in mathematics?

Mathematical induction is a way to give finite proofs for (some of the) claims that concern infinitely many objects. For this reason it can be thought of as an approximation of the ω-rule. However, ...
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4answers
213 views

How do we know that this is the truth? [closed]

I am not a philosophy student, academically. But I have watched a lot of videos and studied some of the content regarding the here and there philosophy of the existentialism, religion, relations of ...
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62 views

A same object being analysed by different fields of study

I've been studying Bachelard lately and I haven't been convinced by his propositions that different sciences can't study the same object. I know that "the object of a science" is not a ...
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60 views

Why can unique mathematical objects have “copies” or exist in multiples?

If the empty set is unique, how can it occur twice in a construction like for example the von Neumann ordinal for 2: {{},{{}}}. Or if the number 1 is unique, how is it possible you can add it to an ...
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Is free will compatible with determinism? (Ramsey theorem)

Do we have free will? Or everything is already determined? Are they mutually exclusive? I think they can coexist and have something similar to a proof here and would like to know your thought There is ...
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Books on Philosophy of Mathematics [duplicate]

I want to buy a philosophy of mathematics book. I have three options in mind: Philosophy of Mathematics by Øystein Linnebo, Philosophy of Mathematics: Selected Readings by Paul Benacerraf, or The ...
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Is defining the concept of Probability still an open problem in the Philosophy of Science?

There exist several interpretations of the concept of Probability: https://en.wikipedia.org/wiki/Probability_interpretations Being the assumption of Repeatability an important difference between them. ...
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How would a monistic approach account for these categories of probabilities?

Donald Gillies, in his book "Philosophical Theories of Probability," draws a distinction between monistic views and dualistic views of probability, the latter of which, at least in his ...
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122 views

Mathematical universe hypothesis: Why shouldn't all imaginable universes exist?

In his paper on mathematical universe hypothesis, Max Tegmark only responses with a single paragraph to this assumption: The MUH and the Level IV multiverse idea does certainly not imply that all ...
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Good texts on logicism

I'm trying to learn about the logicist programme by myself so I was wondering, what are some good book/papers/articles on logicism? I'm looking for introductory to medium level texts, nothing very ...
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What separates mathematics from logic? Can “mathematical” operations be applied to logical systems?

In my 'Introduction to Logic' class, my professor told us that half of the class will be based on "mathematical" operations withing logic. After looking through the textbook, I realized that ...
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Does science require the exclusion of the “infinite”?

And if so, are there any interesting implications? According to the storyline, Galileo launched modern science by declaring the necessity of rendering physical events countable. What is countable must ...
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Possible reason for the exponential development of Mathematics

The history of Mathematics shows a peculiar pattern of progress. The development was quite steady but one-sided during the Greek times and then was almost very slow during the Roman and Byzantine ...
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326 views

Logical Interpretations of Probability

According to Wikipedia's page on probability interpretations... Logical probabilities are conceived (for example in Keynes' Treatise on Probability) to be objective, logical relations between ...
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Why Frege thinks geometry is synthetic?

Frege believes that arithmetic is analytical. Why not Frege thinks geometry can be reduced to arithmetic by coordinate system or something else?
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160 views

Is it possible to create an axiomatic system where 1+1 doesn't equal 2? What would be the consequences of such a system? [closed]

1+1=2 is a result (perhaps arguably more of a definition than a theorem?) of Peano Arithmetic, as well as other systems such as ZFC. I understand that 1+1 doesn't necessarily have to equal 2 if we ...
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What are the limitations of the language of mathematics?

I was told that mathematics cannot express qualitatively what the elements of a set are, such that you cannot say for example that the members of a set consists of white tigers. So mathematics cannot ...
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What makes mathematical ideas provable but philosophical ideas unprovable?

Assuming that math is the the study of relationships between quantities and sets, why are those entities provable while more qualitative abstract ideas such as beauty or consciousness in philosophy ...
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Statements about real world

We make statements like "This table is composed from atoms". This statement must be true or false. But what if tomorrow the atomic theory is completely abandoned and we work with another ...
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129 views

Is logic part of Philosophy or Mathematics?

Is logic part of Philosophy or Mathematics? I asked this question "Does programming use logic more or mathematics more" and users on some site insisted that logic was part of mathematics, I ...
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Are axioms more important than definitions?

To prove a theorem in mathematics we usually use our axioms, definitions and other already proved theorems. Suppose we wante to prove a specific theorem and we haven't prove any other theorem and also ...
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1answer
124 views

Do mathematical objects exist after their definition? [duplicate]

Suppose we have a system with a set of axioms. Now we begined to define new terms. E.g. in maths we have a particular set of axioms and then we define what a function is. But do all the functions ...
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162 views

Does truth exist without proof?

When we prove something (e.g. in maths) we show that a particular statement is true. But if we couldn't prove that statement that doesn't mean that the statement would be false right? So is proof a ...
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Could the axiom of infinity be in itself inconsistent?

I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
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Do all paradoxes of naive set theory have something in common?

If P(x) is the formula "x ∉ x", then ... the assumption that a set h has P(x) purity ... (i.e. the assumption that for all t, if t∈h then P(t)) ... implies that there exists a set k, where ...
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Is tautology for logic what theorems are for mathematics?

Consider the following statements. "If x is an integer then 3+2=5" and "If x is not integer then 3+2=5". Constructing truth tables for the above statements show that there is no ...
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Epistemological Basis of Mathematics Debate

In the following link: https://plato.stanford.edu/entries/intuitionism/ in the last paragraph in Section 1, there is mention of the "lack of epistemological and ontological basis for Mathematics.&...
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Is there a Physics-limited-mathematics?

For example,how about in this mathematics if If we calculate to the 80th power of 10 and still don't have a single counterexample, we can say that we have "proved" Goldbach's Conjecture, ...
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Do mathematicicans care about implications where the hypothesis is always false?

Suppose we want to prove the implication P implies Q. Now we can use proof by contradiction and show that there is no case were P is true and not Q is true. But this does not imply that there is a ...
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Validity/Soundness of an argument from R. Carrier

This is about training in argumentation. I use a text from R. Carrier: https://www.richardcarrier.info/archives/468, where he claims that from nothing everything follows. (Don't get shocked, the ...
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What are the differences in belief between the Mathematical Universe Hypothesis and platonism?

The beliefs are very similar in nature, but they have some different ideas. I am confused where the line of distinction is between MUH and platonism; therefore, I would like to know if anyone has ...
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What are the best books in defense of Platonism in Philosophy of Mathematics?

I am interested in the subject and was recently doing some research about literature to read about it, but it seems that there aren’t many books on the topic. Some suggestions for books in defense of ...
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Is pure math invented or discovered? [duplicate]

I know that many people believe that math is discovered, but here I want to know if pure mathematics, in specific, is discovered or invented and why. There are definitely many arguments to both sides. ...

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