8
votes
Difference between how a physicist and mathematician approach science?
Mathematicians need not practice science at all, except as a personal hobby unrelated to their profession. If you search Physics SE for the inverse of this question - "how does the physicist's ...
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8
votes
Difference between how a physicist and mathematician approach science?
Sweeping generalisation alert. Physicists tend to be very pragmatic. If they can find a mathematical technique that predicts the results of experiments, they're happy- they won't have sleepless nights ...
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5
votes
Why do numbers apply to such disparate concepts?
You should not be surprised. Numbers were conceived to model concepts such as length, area, angles and so on. Any qualities that vary by extent can be compared in an analogous way. For example, the ...
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3
votes
Accepted
A problem I noticed with if-then-ism in the philosophy of mathematics
Originally, if-then-ism was an approach to the philosophy of mathematics defended by Bert Russell. Russell held that mathematical truths are necessarily true, but that no existential statement is ...
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3
votes
Is mathematics based on formal logic, or vice versa?
Historically, mathematics and logic evolved independently, though mathematicians have always used forms of logical inference. Euclid, for example, proved things by reductio ad contradictionem which is ...
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3
votes
Difference between how a physicist and mathematician approach science?
Alright, this question begs for some clarification since it seems to equivocate a little on 'science'.
The demarcation of science, as Karl Popper called it, is a question about determining what is and ...
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2
votes
Why do numbers apply to such disparate concepts?
I think that the more fundamental question is "why is our world so free" in the mathematical sense of free. For example, as others have pointed out, the natural numbers can be generated from ...
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2
votes
Why do numbers apply to such disparate concepts?
There are a host of different philosophical positions on what math is. The philosophy of math has positions such as Platonic realism, constructivism, structuralism, etc. Numbers are by some defined to ...
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2
votes
Why do numbers apply to such disparate concepts?
The so-called real numbers are based on the natural numbers, which in turn are based on the primitive notions of first and next as follows:
Let '1' symbolize the first object in some collection of ...
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2
votes
Why do numbers apply to such disparate concepts?
Number is a formal abstraction created specifically to do what they do. What I mean by formal abstraction is sometimes illustrated by parallel lines. What parallel lines have in common is that they ...
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2
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Did Gödel think certain math could only be understood if platonism is correct? (and correspondence and nominalism)
We do not have a definition for existence.
Take a naïve (read best possible) notion of existence:
x is perceivable -> x exists (fails because of hallucinations)
x exists -> x is perceivable (...
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2
votes
Difference between how a physicist and mathematician approach science?
It is similar to the difference between a designer and a mechanical engineer working on a merry-go-round. The designer (or physicist) is concerned ultimately with some observable phenomena and general ...
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2
votes
Difference between how a physicist and mathematician approach science?
Is a theoretical Physicist a physicist? Is an applied mathematician a mathematician?
If so, then I believe there isn't a formal distinction in how either approach problems.
Now, there are general, ...
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2
votes
Is mathematics based on formal logic, or vice versa?
While Bumble's answer is authoritative, I'd like to reason from what we know about the relationship of mathematics and logic to the human brain and language. The human brain, of course is at least the ...
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2
votes
Does the incomputability of kolmogorov complexity imply that we will never have a final theory of everything?
No, the incomputability of Kolmogorov complexity merely means that we probably won't know for sure if we have the right TOE. We may indeed one day have a theory that explains the whole universe in a ...
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2
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Can this be an example of sophism?
Start with any even number. Adding/subtracting 2 should take you to the next higher/lower even number.
8 - 2 = 6, 6 - 2 = 4, 4 - 2 = 2, 2 - 2 = 0. O is an even number.
Doing the same for odd numbers ...
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1
vote
Accepted
Can this be an example of sophism?
If you are taking sophism to mean a type of fallacy, then no.
The extension of even numbers from outside the naturals to the non-negative integers is an example of a technical definition in ...
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1
vote
Do some philosophers-of-mathematics give priorities to different epistemologies of math, rather than (over)committing to one epistemology?
You use the terminology of "epistemology" but in fact what you are talking about is closer to "ontology" than epistemology. Benacerraf famously distinguished between ontology and ...
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1
vote
Accepted
Does the incomputability of kolmogorov complexity imply that we will never have a final theory of everything?
Let's start with some comments. You say:
I'm putting this question here and not in computer science or math because the incomputability of Komlogorov Complexity and the validity of the Curry-Howard ...
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1
vote
Gödel's Incompleteness Theorem
The problem lies with your definition of G. Your G is explicitly self-referential and says of itself that it is not provable. There are many objections to doing this, including the simple one that it ...
- 22.2k
1
vote
Difference between how a physicist and mathematician approach science?
Looking at Dyson's quote in context (from the talk "Missed opportunities", Bull. Amer. Math. Soc., 1972), it appears he thought that the divorce had happened as early as the 1860s. One of ...
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1
vote
Did Gödel think certain math could only be understood if platonism is correct? (and correspondence and nominalism)
The passage from Shapiro does not mention nominalism at all, whereas four out of your five conclusions deal with nominalism. One wonders how they are derived from Shapiro's passage.
As far as Gödel ...
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1
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Are numbers noumena?
As Guambra Feo has pointed out, metaphysical presupposition play a role in determining an answer. For instance, the term 'noumenon' invokes the term 'real' or 'objective' indirectly by referencing '...
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