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: :
: : : Induction is not logically compelling
: : : Science is based on induction
: : : therefore science is not logical.: : Induction is not totally compelling, but it has worked to date.
: Piper: Induction is NOT logically compelling in the sense that inductive conclusions do not follow necessarily from a premise.
: : This does not mean that it is always going to work; but the same can be applied to any posited axiom you care to mention.
: Piper: Induction is (at best) rational. I.e. it is rational to believe in something concluded from a strong inductive inference. Similary it is irrational not to believe something derived from a strong inductive inference. It is not however alogical not to believe something derived from an inductive conclusion (as the conclusion is not necessary).
This is only the case if you believe in synthetic a priori. If you believe that logic has no dependence on induction, then, yes, an inductive conclusion is alogical. If, however, you hold that logic is the offspring of induction, then something that is not demonstrable inductively is also alogical.
: : Will you therefore take the path of Russell's lunatic?
: Piper: To do that i would, i believe, have to deny thta induction is rational. Although i have yet to see a satisfactory proof that shows induction is in facvt rational (the inductive proof of induction is the best i have seen and i am not sure that this shows induction to be rational), i do think it is so.
: : If you accept that the world exists, as you do, then the inductive method is the one with the fewest unproveables; it is entirely self-consistent.
: : This might not satisify the logical purist seeking the Platonic Form he or she calls 'logic'; but a moderately logical model is logically more sound than a totally alogical one.
: : Define 'compelling'; define 'logic'
: : If you want to be totally consistent, try defining them without reference to any physical observation point.
: : You can't. Logic is based on science; it's an abstraction of observed science.
: Piper: logic is mathematical, not an abstration of science. Observed science is inductive. I do not understand how you could even put this forward gideon. Deductive logic originated with the greeks. Induction, the basis of modern science had its (articulated) origins in the writings of Bacon and Descarte.
Because logic; the 'deduction' you speak of, is ultimately formalised and abstracted induction. It is inherently just reliabilist treatment of inductive maths.
When Leucippus and Democritus first formulated the idea of atoms, they called them atomos - 'little pebbles'; they were applying their perception of the physical world and extending it beyond their physical perception; induction is not merely a product of the Age of Enlightenment.
: : So *of course* science isn't perfect in logical terms; in the same way that a real-world circle is never perfectly round; the concept of 'roundness' is an abstraction of a concept from physical observation.
: : Science is the act of making models that describe the observed world; the logic is the mechanism on which the model is based.
: The mechanism is based on induction which is rational, not logical.
The mechanism on which logic is based on is ultimately inductive; the a priori is itself still founded on induction.
: : When a model is shown to be faulty, it is revised or discarded; this process occurs in what Kuhn calls a 'crisis in science'; the competing models are weighed in the balance and the lesser is found wanting.
: Piper: "Kuhn? *spits*". (I don't mind what you'cve said there too much, just don't start going on about 'incommensuarability' etc...)
: : (Of course, as Kuhn and Lakatos pointed out, this isn't always the case in the sociological human world, but...)
: : The best scientific model is the one that most simply explains all scientific observations.
: Piper: Yes, as long as you realise that it is only rational, not logically necessary.
If I think I am a flea; then it is entirely logical that I should think of fleas as bipeds and ~2 metres tall; logic without some reference to the real world is conceptual rather than reliable.
: : (Examine Popper's answer to the Quine-Duhem thesis.)
: : Induction comes before logic; not after it. So your three lines should read;
: Piper: yes, it is true that most deduction can be traced back to induction via the premises.
All deduction can.
: : 1. There appears to be a 'real world'. This is inductive.
: Piper: Yes.
: : 2. Distillation of what appear to be common 'rules' leads to a system of 'logic'
: Piper: No, the truths of mathematics are a priori. Distillation of common rules is induction.
Nothing is 'a priori'; when it comes down to it, you are still ultimately assuming the a posteriori results of someone else's inductive observations. Euclid could not have formulated mathematical laws without a model of 'the real world' to match his ideas against.
This does not mean that either logic or rational induction are useless; ultimately, the yardstick by which a theory is measured is by its reliability and completeness.
What you call 'a priori' is merely an inductive theory that has been confirmed so many times that no-one bothers to check it any more.
1+1=2; you don't check this every time you do it; even though it is only an observed correlation; it is accepted as 'a priori' true.
Surely there is a defineable point at which you can say 'look, we've tested this axiom enough times to be reasonably sure, so let's accept it as such until such time as a better theory comes along'.
Of course, to do this, you have to subject your theory to rigorous testing; mere circular reasoning and vague generalizing are not sufficient; either you take your experiment down to the scale of testing the precise nature under inquiry; as Popper suggested; or you build a model of the whole thing, as Kuhn suggested.
However, any testing you submit such a theory to are themselves subject to induction; pace Goodman's problem; the famous example of 'grue' and 'bleen'; if 'grue' described something that was 'green' before 1/1/2000 and 'blue' thereafter; and you examined the set of gemstones on the paradigm of 'greenness' on 31/12/1999 and 1/1/2000, you would find that your method of testing was no longer sufficient; it would have shown itself to be inductively invalid; even if it had worked up until then.
Logic is no less subject to induction; just because 1+1 = 2 yesterday, we have no a priori reason to believe it will tomorrow. After all, as Gödel showed, there are logical propositions which cannot be described in a logical system.
So reliablism is ultimately the best yardstick we have in the physical world; if you accept the general validity of logic and mathematics as a priori, then you can use them in construction and validification of your epistemological model; which is what Deborah Mayo effectively says in her attempts to build a statistical 'provenness' for scientific induction.
All in all, I would still hold that Judge Overton's judgement in the Arkansas creationism/evolutionism trial had a passable definition of what differentiates 'science' and non-science;
A theory is scientific if and only if;
1. It is guided by (apparent) natural law.
2. It has to be explicable using (apparent) natural law.
3. It is testable against the empirical world.
4. Its conclusions are tentative; not final.
5. It is falsifiable.
Anyway; it's 23:30; I'm going to bed.
Gideon.
