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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.

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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Was mathematics invented or discovered?

What would it mean to say that mathematics was invented and how would this be different from saying mathematics was discovered? Is this even a serious philosophical question, or just a meaningless, tautological linguistic ambiguity? In the context…
Ami
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How does mathematics work?

If I am given a parking lot with ten thousand cars and I want to determine whether one of the cars is orange, the only way I can do this is go through the parking lot examining each car until I find one that is orange or I examine each car and…
Craig Feinstein
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What would happen if suddenly, 1+1=2 is disproved?

Would the universe be thrown into chaos were the most fundamental equation proved to be wrong?
Peter Johnmeyer
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Does Math use the scientific method?

I've reading many entries about whether Math uses the scientific method and the dominant opinions seems to be "no", e.g. from "Is Mathematics a science?" and other websites. James Moosh, PhD in Pure Maths 1) The use of the scientific method of…
Pablo
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Are numbers real?

I am confused as to what numbers are. Numbers are defined to be what they are, so numbers aren't real? But numbers are found in nature, right? So if we invented them, how can they be found in nature? How can everything be based on something that is…
Wobblester
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If there were only one single mathematician in the world, would they be able to produce a mathematical proof?

If there were only one single mathematician in the world, would they be able to produce a mathematical proof? This question was motivated by the Math stackexchange question: Should a mathematical proof be 'convincing'? I thought it would be more…
Stephen
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Is there a notion of "because" in mathematics?

Sometimes, in math classes, we are asked to give justification for our mathematical assertions. We say that mathematical statement X is true because Y is true. However, I don't know if "because" is the right word to use. Mathematical objects and…
user107952
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What is mathematical existence?

When I make a claim in a proof that a mathematical entity exists, is this no more than saying that the theory I'm working within is consistent, and that all the steps upto that point in the proof are allowed moves in the theory? By mathematical…
Mozibur Ullah
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Can mathematics be separated from the physical world?

I am a math enthusiast, with very little interest in physics. In fact, today I thought to myself how can I expel the physical world from mathematics completely. However, this has proved to more difficult than I had previously thought. The notion of…
JimmyJackson
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What is the philosophical status of category theory?

In the philosophy of mathematics, some attempts have been made to give it ultimately secure foundations; a notable example is the Hilbert Program. Goedel's Theorems show that it is not quite possible, but there are some partial results. Most such…
Jakub Konieczny
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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 1 abstract. For me to figure that out, I must also…
novice
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What are the major philosophical interpretations of probability?

Are there important philosophical interpretations of probability? What are the major "schools" or frameworks? What is their relation to formal systems of probability (for instance - the orthodox axiomatic system of Kolmogorov)? And how do they…
Jordan S
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What is the difference between formalism and logicism

What is the difference between logicism and formalism? Is there a conflict in being a formalist and logicist?
Amr
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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 middle, and therefore proof by contradiction,…
Martin C.
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Should I trust mathematics?

First of all I'm not an expert in this field, please correct me if I'm lacking relevant knowledge here. A few hundreds years ago mathematics was largery based on intuition. People realised we need to make mathematics more rigorous. Axioms and…
user107986
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