Re: Epistemology 201: The Science of Science
From: Jason (jasonstevensNOSPAM_at_free.net.nz)
Date: 01/25/05
- Next message: Jesse Mazer: "Re: A Derivation of Special Relativity without Invoking Group Theory"
- Previous message: Jesse Mazer: "Re: Feynman's fallacy"
- In reply to: robert j. kolker: "Re: Epistemology 201: The Science of Science"
- Next in thread: robert j. kolker: "Re: Epistemology 201: The Science of Science"
- Reply: robert j. kolker: "Re: Epistemology 201: The Science of Science"
- Reply: Neil W Rickert: "Re: Epistemology 201: The Science of Science"
- Reply: mmeron_at_cars3.uchicago.edu: "Re: Epistemology 201: The Science of Science"
- Reply: The Sophist: "Re: Epistemology 201: The Science of Science"
- Messages sorted by: [ date ] [ thread ]
Date: Tue, 25 Jan 2005 15:42:44 +1300
> > I repeat, some mathematical proofs are by empirical means...
>
> A proof is a proof (in mathematics) solely through the logical
> mechanisms that enables one step of the proof to be infered from an
> earlier step or steps. A rigorous proof is strictly formal, even if non
> formal means were used to discover it. Distinguish between discovery and
> justification. Discovery can be very empirical and heuristic, but
> justification (actual proof) is formal.
Maths as a formal system is incomplete, so some statements cannot be proven as
derivations from the axioms. Some of these statements are true or false under
the standard interpretation of the language of mathematics. In these cases,
discovery IS justification. Proof is empirical:
The four colour map problem was finally 'proved' by computer. That is, every
possible combination of neighbouring map shapes were tried and tested. This is
empirical. There is (or at least was at the time) no know formal method to
prove it.
- Next message: Jesse Mazer: "Re: A Derivation of Special Relativity without Invoking Group Theory"
- Previous message: Jesse Mazer: "Re: Feynman's fallacy"
- In reply to: robert j. kolker: "Re: Epistemology 201: The Science of Science"
- Next in thread: robert j. kolker: "Re: Epistemology 201: The Science of Science"
- Reply: robert j. kolker: "Re: Epistemology 201: The Science of Science"
- Reply: Neil W Rickert: "Re: Epistemology 201: The Science of Science"
- Reply: mmeron_at_cars3.uchicago.edu: "Re: Epistemology 201: The Science of Science"
- Reply: The Sophist: "Re: Epistemology 201: The Science of Science"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
