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I don't think that logic is at the root of most sciences, if at all. The statistical tools which science employs may have logical underpinnings, but the theorie

I don't think that logic is at the root of most sciences, if at all. The statistical tools which science employs may have logical underpinnings, but the theories formed by science aren't axiomatic. For example, there is hardly any enthusiasm for axiomatizing physics by either mathematicians or physicists. Science is also very comfortable with holding competing theories, whereas in conventional logic that would be "explosively" destructive.

boris_m 5y ago
Not necessarily, you have competing theories based on the same kind of logic - it is just that every theory would be based on different set of postulates and will reside in a different logical space (i.e. a different category). But the fact that that two theories don't agree with each other does not mean that one of them is illogical. Actually, I'd argue that they have to both be logical in order not to agree with each other at all i.e. logic is the common ground which enables you to express the differences. Also, I do think that physics is pretty axiomatic right from it's roots. Newton's main inspiration for forming his theory is the work of Euclid, i.e. first formal system that was ever created.
- threatofrain 5y ago
  For science, competing theories exist within the same universe of discourse. That's because scientific theories find their basis in their ability to generate new or better predictions from existing empiricism. And in terms of modern physics, I reiterate that there is no enthusiasm from either mathematicians or physicists to axiomatize physics.
  - boris_m 5y ago
    There is some: https://arxiv.org/abs/quant-ph/0101012 https://arxiv.org/abs/quant-ph/0101012 And according to the first sentence of the summary the current formulation is axiomatic as well...
roenxi 5y ago
Science can't be logically inconsistent. If a system is logically inconsistent then you can prove anything from it, so there would be nothing for science to explain - everything would follow from the inconsistency. Science is comfortable with uncertainty, but not with things that are illogical. It has to be logical, and the scientists have to accept some sort of logic to give theories a better-worse hierarchy.
- Koshkin 5y ago
  > then you can prove anything from it Except most of sciences take experiment as the criterion of truth rather than logical inference. Real-world science can almost always be expected to be inconsistent - simply because each scientific theory is a "local" approximation, and theories developed for different areas of the same science are not required to be mutually consistent in order to be useful. One (in)famous example is quantum mechanics and general relativity.
  - boris_m 5y ago
    It's not "experiment rather than logical inference" it's experiment and logical inference.
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    - coolgeek 5y ago
      There seems to be a markdown error (and a grammatical error) in: > This is it about axiom schemas and *rules of inference are almost the same thing except they allow us to actually distill the conclusion from the premises.
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boris_m 5y ago

Not necessarily, you have competing theories based on the same kind of logic - it is just that every theory would be based on different set of postulates and will reside in a different logical space (i.e. a different category). But the fact that that two theories don't agree with each other does not mean that one of them is illogical. Actually, I'd argue that they have to both be logical in order not to agree with each other at all i.e. logic is the common ground which enables you to express the differences. Also, I do think that physics is pretty axiomatic right from it's roots. Newton's main inspiration for forming his theory is the work of Euclid, i.e. first formal system that was ever created.

threatofrain 5y ago
For science, competing theories exist within the same universe of discourse. That's because scientific theories find their basis in their ability to generate new or better predictions from existing empiricism. And in terms of modern physics, I reiterate that there is no enthusiasm from either mathematicians or physicists to axiomatize physics.
- boris_m 5y ago
  There is some: https://arxiv.org/abs/quant-ph/0101012 https://arxiv.org/abs/quant-ph/0101012 And according to the first sentence of the summary the current formulation is axiomatic as well...

roenxi 5y ago

Science can't be logically inconsistent. If a system is logically inconsistent then you can prove anything from it, so there would be nothing for science to explain - everything would follow from the inconsistency. Science is comfortable with uncertainty, but not with things that are illogical. It has to be logical, and the scientists have to accept some sort of logic to give theories a better-worse hierarchy.

Koshkin 5y ago
> then you can prove anything from it Except most of sciences take experiment as the criterion of truth rather than logical inference. Real-world science can almost always be expected to be inconsistent - simply because each scientific theory is a "local" approximation, and theories developed for different areas of the same science are not required to be mutually consistent in order to be useful. One (in)famous example is quantum mechanics and general relativity.
- boris_m 5y ago
  It's not "experiment rather than logical inference" it's experiment and logical inference.
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  - coolgeek 5y ago
    There seems to be a markdown error (and a grammatical error) in: > This is it about axiom schemas and *rules of inference are almost the same thing except they allow us to actually distill the conclusion from the premises.
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