All Questions
Tagged with philosophy math-history
79
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What are the criteria for a subject to be under the domain of mathematics [duplicate]
It is to my understanding that mathematics is in some way the domain of all logical systems. However unconventional, as long as certain criterias are met, they could be considered as part of ...
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Proof by Contradiction: "Bad Form" or "Finest Weapon"? Reconciling Perspectives [duplicate]
G.H. Hardy famously described proof by contradiction as "one of a mathematician's finest weapons." However, I've encountered claims that some schools of thought consider proof by ...
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On motivations of continuous geometry
The development of continuous geometry as an abstract field seems to be following a trend of removing the significance of low-dimensional entities from geometry. As classical treatments of geometry ...
- 1,528
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Does it make sense to divide mathematical theorems into those susceptible to experimental conjecture and those that are not?
I read the following in a good book: ”let's start from zero", the authors are Vinicio Villani and Maurizio Berni (pisan mathematicians) but I don't know if the book is also marketed outside Italy....
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Reference request: which theorems are "interesting" to mathematicians?
Disclaimer: this question is more about philosophy of mathematics than technical mathematics.
Mathematicians always need to choose what to focus their work on. Many pure mathematicians like to say ...
- 143
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Is the term "category" in Category theory entirely different from the category in topological spaces?
$(X, \tau) $ be a topological space.
$A\subset X$ is said to be first category (meager) if it can be expressed as a countable union of nowhere dense sets. Otherwise we call the set $A$ second ...
- 13k
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Philosophical/Historical question on the word "kernel" in Algebra
My question is little philosophical/historical, and it came to mind due to some natural curiocity.
The word kernel appears in many contexts in abstract algebra. (It also appears in other branches of ...
- 3,047
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Why does Hadamard claim that Pascal could have discovered non-Euclidean geometry
In The psychology of invention in the mathematical field, p. 53, Hadamard makes the following claim:
Is his point that there must, in any axiomatic theory, be undefined terms, and if you write the ...
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Paradigm Shifts in Mathematics [closed]
in physics there were several clear revolutions or paradigm shifts which fundamentally changed the field. One example is the copernican revolution and the encompassing shift from the ptolemaic to ...
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Is there a relation between the ZFC set axioms and our intuitive notion of sets?
A question about history.
When I took my first course in set theory, I had the perception that ZFC axioms weren't the most intuitive thing in relation to what common people would usually call a set. ...
- 80
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Non-associativeness of composition in deductive systems?
WARNING: The first three and last two paragraphs of this question concern historical/philosophical matters related to a secondary aim of the question. If you are more interested in the properly ...
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If we didn't have examples of irrational numbers, would we know they exist?
Irrational numbers are very easy to find. Square roots require only a little bit more than the most basic arithmetic. So it might be that this question is impossible to answer because it presupposes a ...
- 199
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Can you convert a categorical proposition into a zeroth order proposition?
I am a student learning mathematical logic as a hobby. When I say "zeroth order" I mean "not predicate logic".
Question: Is it possible to convert a categorical proposition into a zeroth-order ...
4
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Is there criticism in literature of Euclid's fifth common notion ("The whole is greater than the part")?
In Book I of Euclid's Elements, the fifth common notion says "The whole is greater than the part".
For Euclid, magnitudes are objects that can be compared, added, and subtracted, provided they are of ...
- 841
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What are the arguments of the mathematicians who objected against the ontological proof Gödel offered?
Q:
What are the arguments of the mathematicians who objected against the ontological argument/proof Gödel offered?
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