New answers tagged philosophy-of-mathematics
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if there is less than 100% chance that X might occur, can it occur?
The probability of something happening when added to the probability of it not happening always comes out to be one.
Probabilities tell you what the odds are for a certain outcome in a trial which ...
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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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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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Do mathematicians always agree at the end?
No. There are schools of thought, with many a disagreement about fundamental and philosophical / metaphysical questions regarding what maths is about etc.
However, they do tend to agree on those ...
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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 ...
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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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Is mathematics based on formal logic, or vice versa?
Mathematics is all-encompassimg per a specific definition, that math is the study of patterns. One could argue-reply that math is about arithmetico-geometric-etc. properties of patterns. From my ...
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Is mathematics based on formal logic, or vice versa?
Definitions provide the answer. This couple of definitions, useful for philosophy, are my synthesis, based on the work of others.
To start, there's no "formal logic" or "informal logic&...
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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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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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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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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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Difference between how a physicist and mathematician approach science?
I wonder if:
Physics studies what is observable.
Mathematics studies what is establishable *) **).
*) Maybe a subset of all that is establishable, but it does not study anything that is directly ...
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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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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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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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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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Implicit Models and Probability - are degrees of belief/truth/existence a complete free-for-all?
It makes sense to distinguish between what is true/false about the world and what we as reasoning agents believe about the world. Our beliefs are based on partial information. This does not mean that ...
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Implicit Models and Probability - are degrees of belief/truth/existence a complete free-for-all?
Well, actually assigning consistent probabilities to everything in a way that conforms to the Kolmogorov axioms is, in practice, impossible. Humans cannot do it. Computers can't do it. It's too hard.
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Are there different forms of rigor, and if so, are some forms of rigor more rigorous than others?
The SEP article on vagueness includes these two passages (early on):
Inquiry resistance recurses. For in addition to the unclarity of the borderline case, there is normally unclarity as to where the ...
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Does significance testing contain a logical flaw or not?
In frequentism probability applies to the observed data given a probability model, but not to the model or its parameters itself. There is no well defined probability for a null or alternative ...
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Is mathematics an art?
I'm wanted to answer this duplicate: Is Mathematics an art or a science?
I would say that Mathematics is a plutonic discipline. Mathematicians are trying to discover something that exists outside of ...
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Does significance testing contain a logical flaw or not?
It is not so much that the hypothesis is improbable if we see significant observations, but that the frequentist considers that the hypothesis merits rejection. If the distinction seems subtle, see if ...
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