Joe and Rich, (01)
Joe
> I get a 404 -- File not found -- when I click the provided link. (02)
I'm sorry. I cited that file so often, that I forgot to check it.
I omitted the 'i': http://www.jfsowa.com/talks/micai.pdf (03)
Rich
> Here is another relevant quote from PG:
>
>> However, it became apparent that the methodology of the positivists
>> led to serious problems in relation to the problem of induction...
>> What we need is a non-logical way of distinguishing those predicates
>> that may be used in inductive inferences from those that may not. (04)
The logical positivists read very little, if anything, by Peirce.
If they had, they wouldn't dream of searching for purely logical
criteria for induction and abduction. (05)
Basic point: The word 'formal' implies reasoning that depends only
on the *form* or syntax. Every method of reasoning other than
deduction -- induction, abduction, and analogy -- must be informal. (06)
Even mathematics requires a large amount of informal background
knowledge to support the discovery processes of induction and
abduction. See below for the citations to books by George Polya. (07)
Two of the many mathematicians quoted by Polya:
> Euler: "The properties of the numbers known today have been mostly
> discovered by observations... long before their truth has been
> confirmed by rigid demonstrations."
>
> Laplace: "Even in the mathematical sciences, our principal
> instruments to discover the truth are induction and analogy." (08)
I discuss these issues in http://www.jfsowa.com/talks/ppe.pdf (09)
John
_______________________________________________________________________ (010)
Pólya, George (1945) How to Solve It, Princeton: University Press. (011)
Pólya, George (1954) Mathematics and Plausible Reasoning, Volume I:
Induction and Analogy in Mathematics, Volume II: Patterns of Plausible
Inference, Princeton: University Press. (012)
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