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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?
Ami
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Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

I have always been perplexed by a seeming paradox in probability that I'm sure has some simple, well-known explanation. We say that a "fair coin" or whatever has "no memory." At each toss the odds are once again reset at 50:50. Hence the "gambler's…
Nelson Alexander
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Why is there something instead of nothing?

A simple but fundamental question. The "something" means the whole Universe (known and unknown), it could be represented as the reality version of the set of all sets, which is itself debated. It includes all the Multiverses and such. A better…
Geoffroy CALA
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Is Mathematics always correct?

It seems Mathematical theories/Laws/Formulas are the least questioned in all of the sciences. Is mathematics that good at being closest to the laws of universe, or is it just a logical tool of our own perception of the universe (that being the…
S.D.
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Did Russell understand Gödel's incompleteness theorems?

Russell was active in philosophy (although no longer in math) for many years after the Gödel's 1931 publication. Gödel's paper were not obscure, and Russell would have been aware of their effect on the Principia and his logicism (and Hilbert's…
Artem Kaznatcheev
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Do numbers exist independently from observers?

Do numbers have an objective existence? If life had not evolved on planet earth would there be numbers or are numbers an invention of human minds? Are there any relevant works that discuss this? (I know of Husserl's Über der Begriff der Zahl and…
leancz
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What are the necessary conditions for an action to be regarded as a free choice?

A common philosophical question revolves around the existence of free will, but what I've found is that these debates seem to gloss over the concept of "free will" itself, either taking it as a given that everyone understands what the term really…
Speldosa
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What should philosophers know about math and natural sciences?

My question is whether a lack of knowledge about formal mathematics or theoretical science in general would have an impact on a philosopher's ability to think and make judgments. Why should a philosopher acquire a deeper understanding of natural…
Bob
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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 is that the reality is made up of immeasurable…
Dheeraj Verma
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How is Gödel's incompleteness theorem interpreted in intuitionistic logic?

Classically, one sets up an axiomatic system with a formal deduction system & an interpretation in a model. Generally it is sound, that is: a formally deduced theorem is also true when interpreted in the model. The reverse is called completeness, if…
Mozibur Ullah
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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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Is First Order Logic (FOL) the only fundamental logic?

I'm far from being an expert in the field of mathematical logic, but I've been reading about the academic work invested in the foundations of mathematics, both in a historical and objetive sense; and I learned that it all seems to reduce to a proper…
Mono
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What are the philosophical implications of Gödel's First Incompleteness Theorem?

Gödel's First Incompleteness Theorem states Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that…
Joseph Weissman
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Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will eventually produce the works of Shakespeare, and indeed every text…
Lou
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Is mathematics politically and culturally neutral?

Lately, there have been many people who say that mathematics itself is racist, that it is simply a creation of dead white Greek men. As a mathematician, I strongly disagree, and believe that mathematics transcends any particular culture or political…
user107952
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