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Results tagged with philosophy-of-mathematics
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user 38198
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.
15
votes
How does mathematics work?
The math solution is, to find out properties of the things we work with, and prove those. Then we re-search those properties for more properties we can now prove. And on those more intricate propertie …
56
votes
Accepted
Falsification in Math vs Science
In math, we define stuff like numbers and operators, then we go on to prove other stuff from those premises.
When you ask: "Is 1 + 1 = 0?", a mathematician will just ask back: "With what definition o …
0
votes
Is the fact that ZFC implies that 1+1=2 an absolute truth?
First you need to define what it means for something to be true. The simple fact is, that you are always making implicit assumptions, like the meaning of the words you use. You cannot formally define …
3
votes
Can all truths be scientifically verified?
Even in pure math, the answer is a firm "no".
This is proven since around 1930 by Kurt Gödel (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems). The gist of the theorem is, that wi …
1
vote
Why can't numbers be 'used up'?
The closest answer to this question that has been posted already, is that of Mankka, which states that numbers are names. However, this does not take it far enough. My answer is that the existence of …