19 votes

Is there a notion of "because" in mathematics?

It seems like the type of "because" statements you are talking about can be equated to "is implied by" (or perhaps more precisely "is derivable from"). For example 3+4=7 ...
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  • 545
6 votes

Is there a notion of "because" in mathematics?

The answer is actually quite trivial once you understand formal proofs. Take for example this Fitch-style system. Each line in a proof in this system must be deduced from preceding lines. If you skip ...
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  • 630
4 votes

Is there a notion of "because" in mathematics?

I believe “because” in the sense you want enters at the foundational level of mathematics, as in how one views mathematical objects beyond the formalism. Why does 3+4=7? Because it somehow represents ...
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4 votes

is the theorem of Pythagoras right?

First of all, it is 'Pythagoras', not 'Pithagoras'. Second, the theorem has nothing to do with units of measurement, as @joseph seems to think. Third, we always assume we -can- draw our diagrams ...
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  • 41
2 votes
Accepted

Unique-ness in the languages of Math and Physics?

The sort of example you provide is based on the idea of a normal form. "In a rewriting system, a term is said to be of normal form if it does not admit any further rewrites." source When we ...
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  • 189
2 votes
Accepted

Which philosophy topics are necessary for philosophy of mathematics?

Returning... The available anthologies are replete with excellent papers. Nevertheless, with regard to single authors, next are probably Pierce and Frege. I have not read much Pierce. But, I keep ...
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  • 36
2 votes

Which philosophy topics are necessary for philosophy of mathematics?

First, I would strongly advise that you pick up anthologies of translated (or not) original sources. Ewald has a two-volume set, "From Kant to Hilbert." Another is "From Frege to Goedel&...
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2 votes

Is there a notion of "because" in mathematics?

Yes, almost(?) every mathematical proof has one or more "because" in it, but (according to my experience) usually the word "since" (which, you will certainly agree, is equivalent ...
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  • 121
2 votes

Is there a notion of "because" in mathematics?

You can rephrase "x=1 because x+1=2" to "x+1=2 therefore x=1" or x+1=2 ∴x=1
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2 votes

Do concepts transcend reality?

I don't think anybody has reached a definitive answer to the question you asked. However, there have been various attempts to grapple with this problem. One is Hegel's idea of dialectic. I'm not Hegel ...
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  • 189
2 votes

Necessity of arithmetic truths into Godel sentences

"But it seems like any sentence can be laid upon mathematical structure. It doesn’t matter that Godel found/made one that speaks of truth outside the formalism. Any and every sentence is possible ...
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1 vote

Do concepts transcend reality?

Many professionals in philosophy of math, ethics, and probably logic too are open to pluralism. To me this allows concepts to have the free range we want them to have, while never positing they go ...
1 vote

Do concepts transcend reality?

The relevant meaning of "abstract" is: to extract or remove (something). By which I mean the following. An abstract concept is one that has started with some collection of existing things (...
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  • 176
1 vote

Is there a notion of "because" in mathematics?

Yes. The symbol is: ∵ which is an upside down "therefore".
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1 vote

Is there a notion of "because" in mathematics?

Because means either: by reason of or by cause of (as in cause and effect, a temporal relation). We can formalise the first notion by qualifying propositional logic into modal logic with the ...
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1 vote

Is there "empirical" distance without "mathematical" distance?

Is there "empirical" distance without "mathematical" distance? Absolutely. I would argue that "empirical" distance has been the primary metric for nearly all of the ...
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1 vote

Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism?

Short Answer Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism? No. Structuralism is defined in terms of isomorphisms, and there are not ...
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1 vote

Why should universal generalization work for abstract objects?

Here is another way of looking at the matter. Let a,b,c... be of type "people with brown hair". Let x,y,z.... be of type "natural number". Lets use your coffee example: Say that ...
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1 vote

Space and time in Kant and space and time in physics

Let's imagine everyone viewed the world, for the sake of argument, through hyperbolic geometry rather than Euclidean geometry. Then our mathematical and physical models of the world would have to ...
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1 vote

Statements about real world

We make statements like "This table is composed from atoms". This statement must be true or false. But what if tomorrow the atomic theory is completely abandoned and we work with another ...
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