Mathematics and science

by Neil Rickert

What is the role of mathematics in science?

This question seems to puzzle some people.  Personally, I never found it at all puzzling.  Much of the development of mathematics was done by scientists, because they needed that mathematics in their science.

Science is not simply a matter of describing or representing nature, as some seem to believe.  Describing is the job of journalists, not of scientists.  Of course, science does make descriptions.  But descriptions do not come for free.  Facts do not just pop into our heads.  Science has had to develop many methodologies, in order to make it possible to describe various aspects of reality.  And that development of suitable methodologies is a large part of science, and a large part of what distinguishes science from other areas of human endeavor.

In a recent post, I suggested that mathematical knowledge was mainly knowledge of the consequences of following methodologies.  I illustrated that by suggesting that arithmetic is a study of the consequences of following the methodology of counting.  I could equally have pointed to traditional geometry (or ruler-compasses geometry) as a study of the consequences of using a portable measuring rod.  The initiative to study these methodologies came from the importance of those methodologies.  And the mathematics thus developed has proved very useful.

More generally, scientists attempt to be as systematic as possible, in their development and use of methodologies appropriate to the area that they are studying.  One could almost say that “Be systematic, young man” is one of the important principles of science.  Mathematics, with its interest in patterns and regularities, is very much the abstract study of systematicity.  So it should be no surprise that mathematics is useful to scientists.  And it should be no surprise that scientists sometimes look to systematic methods studied in abstract mathematics, so as to see if those systems can be adapted for use by science.

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2 Comments to “Mathematics and science”

  1. I’ve read your three posts concerning the relationship between mathematics/mathematical knowledge and scientific knowledge, and for the most part we are in agreement. The one area, though, that needs revision is with respect to mathematical platonists/realists. The point of contention between many philosophers about the role that mathematics plays in the sciences is not its application, not its indispensable use, nor even the idea of abstract entities existing – the problem arises when philosophers of science take a scientific theory, break it down to first order logic, and declare that because the existential quantifier quantifies over ‘mathematical objects’ that therefore those mathematical objects are ontologically just as real as that which they are being used to describe/explain. This is the main contention between the mathematical platonists and their adversaries – their opponents agree with them all they way until the mathematical platonits say that numbers, mathematical objects, or what have you, deserve the same ontological commitment as do, say, electrons, germs, or plate tectonics. In addition, mathematical platonists say that such mathematical objects play an explanatory role, and how numbers can explain I just don’t see how when they are non-spacial and non-temporal. If numbers describe, though, that’s another story… but… I would also say that the sciences do much more describing than you give it credit for (and no, just because a journalist is said to describe, or a child, or a scientists, does not mean that the descriptions are all of the same kind and or validity). Not to be too nit-picky, when you say:
    “The mistake is to treat mathematical statements as if they were descriptions. Mathematics is not descriptive; it is methodological. Mathematical statements are statements about important methods that are used. And, among other things, those methods are often used to form factual statements (descriptions).”
    you are saying that its a mistake to treat mathematical statements as if they were descriptions, and then you conclude that (among other things) those methods (referring to that which mathematical statements are about) are used to form factual statements, i.e. descriptions….

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