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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 mathematics invented or discovered?
discovery = finding something that existed before, for the first time (e.g., a frog, black holes)
invention = intellectual creation of something that did not exist before (e.g. a system, concept, ...
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Why is the gambler's fallacy a fallacy?
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" has "no memory."
At each toss, the ...
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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 ...
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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 G?del's 1931 publication. G?del's paper were not obscure, and Russell would have been aware of their effect on ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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What are the philosophical implications of Gödel's First Incompleteness Theorem?
G?del's First Incompleteness Theorem states
Any effectively generated theory
capable of expressing elementary
arithmetic cannot be both consistent
and complete. In particular, for any
...
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What is the difference between a statement and a proposition?
I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
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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 ...
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What are some works that apply an axiomatic method to something other than mathematics?
The axiomatic method is today mostly associated with mathematics. However, historically there have been some works, as for example Spinoza's Ethics, that have applied axiomatic method to philosophy, ...
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What was Cantor's philosophical reason for accepting the infinite but rejecting the infinitesimal?
I have begun inquiring recently into mathematical aspects of Georg Cantor's theory of transfinite numbers and sets, which he developed between the years of 1874 and 1897. Throughout his theory, Cantor ...
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Why is Aristotle's objection not considered a resolution to Zeno's paradox?
It seems to me, perhaps na?vely, that Aristotle resolved Zenos' famous paradoxes well, when he said that,
Time is not composed of indivisible nows any more than any other magnitude is composed of ...
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