Just one small correction, John. For some theories, like number theory and set theory, there are statements that are true but not deducible. I would think they are entailed by the theory even if not provable, so I would call them part of the theory. Not everyone likes that, but I think we are stuck with that. There are also physical theories (Newtonian mechanics is one, but only in the limit; better cases come in thermodynamic theory in which the energy in a system can change by becoming unavailable). I use this as a criterion for emergence -- true under the theory but not deducible -- in a couple of my papers on my web site). I think these true but non-deducible consequences (entailments) of a theory are not laws, but ironically, as Prigogine (and also David Layzer) showed the existence of these cases is deducible from the theory. Likewise for number theory, as Goedel showed, though they are usually called theorems, not laws, in logic and mathematics. Interestingly, we can test some of these non-deducible consequences even though we can't deduce them from the theory. A relatively simple example is the formation of Bénard cells. We can understand the physics involved, and write the equations of motion, and determine the transformation point, but we can't predict the direction of movement of the cells. Planetary dynamics has many cases, my favourite being the 3-2 resonance of Mercury's rotation period to it revolution period -- it used be assumed that it would 1-1 like the moon. I learned about it from one of the discoverers, who demonstrated a similar phenomenon in class with a piece of aluminium wire loosely couple to a fan rotor. I suspect it was no accident that we were in the same building that Edward Lorenz worked in. The slightest difference in starting conditions could lead to different resonances. My point here is that the issue I am bringing up here has measurable but not predictable consequences in physics. I don't think Peirce was aware of such situations, though it was known in France at the end of the 19th Century that there were possible cases (but they are rather improbable). Lorenz came up with a real case from studying problems in meteorology.
John Collier Emeritus Professor and Senior Research Associate Philosophy, University of KwaZulu-Natal http://web.ncf.ca/collier > -----Original Message----- > From: John F Sowa [mailto:s...@bestweb.net] > Sent: Tuesday, 13 December 2016 5:12 AM > To: peirce-l@list.iupui.edu > Subject: Re: [PEIRCE-L] Peirce and Science (was Democracy) > > On 12/12/2016 1:24 PM, Clark Goble wrote: > > I don’t like the term “legitimate” precisely because it’s ambiguous. > > However I think good theories are theories that allow us to inquire > > about their truthfulness by making somewhat testable predictions. > > I agree with both points. > > I think that some of the objections arise from different uses of the word > 'theory'. Logicians typically use the word 'theory' > for the deductive closure of a set of propositions called axioms. > They impose no constraints the relevance or applicability of the axioms to > any kind of phenomena. > > But scientists make a three-way distinction of hypotheses, theories, and > laws: > > 1. A law is a theory that has been thoroughly tested on some > observable phenomena and shown to be reliable in making > predictions about the future development of those phenomena. > > 2. A theory is a hypothesis that has some relevance to some > observable phenomena about which it makes some testable > predictions. But its reliability has not yet been > sufficiently tested for it to be accepted as a law. > > 3. A hypothesis is any theory in the logicians' sense. > No tests of relevance or reliability have yet been made. > > This distinction allows anyone to suggest a hypothesis at any time -- there is > no penalty for proposing something irrelevant or untestable. Then a > community of inquirers may choose to collaborate in exploring some > interesting hypotheses to determine which might be sufficiently promising > for further development. > > John > >
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