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*To*: dinosaur@usc.edu*Subject*: Math vs. Science*From*: "A.P. Hazen" <a.hazen@philosophy.unimelb.edu.au>*Date*: Sun, 25 Jun 2006 20:12:37 +1000*Reply-to*: a.hazen@philosophy.unimelb.edu.au*Sender*: owner-DINOSAUR@usc.edu

Four thoughts:

(1) The line that started this discussion ("...or they're mathematicians deluded into thinking that math IS science: it isn't") is ambiguous: the "math IS science" COULD mean that ONLY mathematics (or, a bit more plausibly, what is mathematicized, as physics is) counts as science. This is a familiar prejudice: the "science divides into physics and stamp-collecting" attitude. But subsequent discussion has interpreted it the other way.

"Logic [Russell thought mathematics and logic were the

same thing] is concerned with the real world just as

truly as zoology is, though with its more abstract and

general features." (p. 169 of Dover edition)

1+1=2 applies whether you are counting apples or rocks or dinosaurs(*), but ONE of the goals of science is to state the GENERAL principles ("laws") that it finds in the worls, so it would be inadequate make separate statements about what happens when you count apples, and rocks, and dinosaurs. Hence the abstract version referring to numbers. (If you think numbers are too imaginary, one of the things Russell showed was that the relevant reference to NUMBERS can be interpreted as a shorthand reference to SETS of things, or to the PROPERTIES of things.) ... Obviously there's more to be said, and there is no guarantee that ALL parts of mathematics are "about" the same thing. But the parts of mathematics-- combinatorics, probability theory over finite sample spaces-- that seem to be involved in pylogenetic reconstruction strike me as among the parts for which Russell's "logicism" is most plausible.

--

(**) The names have a history, and their meaning is not transparent. "Constructivists" in THIS sense are not the same as the people who call themselves constructivists in math education, and certainly not the same as what are called "social constructivists" elsewhere.

--

Allen Hazen Philosophy Department University of Melbourne

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