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- From: mclean@itd.nrl.navy.mil (John McLean)
- Subject: Re: Natural Kinds (was re: Are all crows bl
- Message-ID: <BxBB5J.54w@ra.nrl.navy.mil>
- Sender: usenet@ra.nrl.navy.mil
- Reply-To: mclean@itd.nrl.navy.mil
- Organization: Information Technology Division, Naval Research Laboratory
- References: <1992Nov5.171453.22237@CSD-NewsHost.Stanford.EDU>
- Date: Fri, 6 Nov 1992 20:48:54 GMT
- Lines: 58
-
- From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt):
- >In article <1992Sep23.094901.1@sscvx1.ssc.gov> doctorj@sscvx1.ssc.gov writes:
- >>pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
- >>How about: Physics is science, while math is not. By science, I mean
- >>the sequence:
- >> 1: Look at the existing data and formulate a theory which explains it.
- >> 2: Use that theory to predict new results.
- >> 3: Perform experiments (ie, collect more data) to test the theory.
- >> 4: Go to 1.
- >>Math does not follow this sequence. It does not contain falsifiable theories
- >>in the way that physics does.
- >>...
- >>This use of the word "experiment" is ill conceived. Computer calculations
- >>are not experiments. Neither are slide rule or hand calculations.
- >
- >Let me not dispute your sequence here, but rather opine:
- >
- >(A) Math is perfectly capable of following your sequence.
- >
- >(B) Hypotheses can be falsified in math.
- >
- >(C) Falsification isn't all it's cracked up to be in either math or
- >physics.
-
- I have to admit that I'm a bit unclear who is saying what in the
- above exchange, but let me make two comments.
-
- First, I largely agree with claims (A)-(C) and recommend reading
- Lakatos' multi-part article "Proofs and Refutations" which
- originally appeared in the British Journal of the Philosophy of
- Science and was later reprinted as a book.
-
- Second, although I largely agree with (A)-(C), I think that math and
- physics do differ in degree. What sequence (1)-(4) leave out is proof
- in the sense of derivation. Physical theories are usually established
- by inference to the best explanation and are not usually derived from
- other theories. (Note I say "not usually". Many important statements
- of physics are derived from theories. E=mc^2 comes to mind if I
- remember my freshman mechanics course correctly.) Mathematical
- statements are usually justified by derivation or by finding a
- counterexample to its negation (which can also be viewed as a
- derivation). Nevertheless, when evaluating axioms, one often
- experiments with their consequences and makes what resembles an
- empirical judgement about the truth of the axioms. Witness the
- discussion on set theory.
-
- Let me go out on a limb and say that the emphasis on derivation in
- mathematics is why mathematicians spend so much time looking at
- derivationally elegant, but nevertheless false, sets of axioms. For
- example, Euclidean geometry is still extensively studied although
- Einstein showed that it is not true. (My doubt about this last
- observation is that one could say that physicists do the same when they
- study Newtonian mechanics and that the underlying reason is the same in
- both cases: both Newtonian mechanics and Euclidean geometry provide
- useful approximations to the way the world is.)
-
- John McLean
-
-