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Do axioms exist in the natural sciences? Are the fundamental laws the axioms? E.g. principle of least action, conservation of mass/energy, etc.

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Scientific theories have axioms (or: postulates). See en.wikipedia.org/wiki/…, en.wikipedia.org/wiki/…, en.wikipedia.org/wiki/Axiomatic_quantum_field_theory and en.wikipedia.org/wiki/…. However, I don't think the axioms have necessary privileged status over some (other) theorems. Let's see in the answers. :) –  Glen The Udderboat Nov 10 '13 at 18:26
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Causality. Until forever :) –  Asphir Dom Nov 11 '13 at 1:59
    
@Transmissionfrom, your examples are not applicable: they are axiomatic mathematical models of scientific theories, and the question calls for axioms within natural sciences, rather that their mathematical models. Asphir's answer, causality, would be a good example. Another one would be induction. –  Michael Nov 11 '13 at 22:57
    
@Linksku, principle of least action and conservation laws are not the axioms: they are fundamental properties of well-fit mathematical models of certain aspects of reality. One does not assume that these laws hold; one concludes, based on the empirical evidence, that the model with such properties is a good fit. IMO the best answer, causality, is given by Asphir; causality's cousins determinism, reproducibility, and induction are also applicable. –  Michael Nov 11 '13 at 23:05
    
@Michael Thanks for that. Perhaps I was wrong-footed by the use of "in the natural sciences" in stead of "of the natural sciences" as well as by the explication in the body of the question, which provides a couple of mathematical propositions/properties. :) –  Glen The Udderboat Nov 12 '13 at 8:47
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1 Answer

A nice little book on this is "Scientific Method in Practice" by Hugh Gauch. He discusses the critical role of presuppositions in science. He also gives a nice overview of the Science Wars, which, among other things, made heavy use of the idea that science, like all other disciplines, requires presuppositions.

In regards to your question, Gauch gives what I think is the most fundamental presupposition/axiom of science, indeed, in all of rational inquiry:

The world is objective, orderly, and comprehensible

Some unpacking of defintions:

objective - this is bascially a statement of realism. Science presumes there is a single world "out there", independent of perspective or state of perception.

order - in the sense that there is a pattern to existence. It does not imply determinism, merely that there is some order imposed on the universe. E.g., the wave function itself is VERY ordered and puts rather precise restrictions on an experiment. However, it does not determine the outcome, in as much as there are a multitude of possiblities.

comprehensible - Humans have access (albeit imperfectly) to the objective world and have the ability to make reliable conclusions about it.

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I find it fascinating that the general opinion re: Are there laws which govern minds? is 'no', given the very clearly required presupposition you state. :-| –  labreuer Nov 15 '13 at 0:15
    
Yes...the chimera of counter-causal free will is alive and kicking. –  Eupraxis1981 Nov 15 '13 at 0:56
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