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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1Scientific 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. :)– user3164Commented Nov 10, 2013 at 18:26
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1Causality. Until forever :)– Asphir DomCommented Nov 11, 2013 at 1:59
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@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.– MichaelCommented Nov 11, 2013 at 22:57
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@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.– MichaelCommented Nov 11, 2013 at 23:05
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@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. :)– user3164Commented Nov 12, 2013 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. :-|– labreuerCommented Nov 15, 2013 at 0:15
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Yes...the chimera of counter-causal free will is alive and kicking.– user4634Commented Nov 15, 2013 at 0:56