Cf: Abduction, Deduction, Induction, Analogy, Inquiry • 31
Re: Scott Aaronson ( https://scottaaronson.blog/ )
::: Explanation-Gödel and Plausibility-Gödel
( https://scottaaronson.blog/?p=6754 )
A general heuristic in problem solving suggests priming the pump
with a stronger hypothesis. Applying that strategy here would
have us broaden the grounds of validity, our notion of validation,
from purely deductive proofs to more general forms of inference.
Along that line, and following a lead from Aristotle, C.S. Peirce
recognized three distinct modes of inference, called abductive,
deductive, and inductive reasoning, and that way of thinking has
even had some traction in AI from the days of Warren S. McCulloch on.
At any rate I think it helps to view our questions in that ballpark.
There’s a budget of resources and running thoughts on the matter
I keep on the following page.
• Survey of Abduction, Deduction, Induction, Analogy, Inquiry
( https://inquiryintoinquiry.com/2020/12/16/survey-of-abduction-deduction-ind… )
Cf: Theme One Program • Exposition 5
Lexical, Literal, Logical
Theme One puts cactus graphs to work in three distinct but related ways,
called their “lexical”, “literal”, and “logical” uses. Those three modes
of operation employ three distinct but overlapping subsets of the broader
species of cacti. Accordingly we find ourselves working with graphs, files,
and expressions of lexical, literal, and logical types, depending on the task
The logical class of cacti is the broadest, encompassing the whole species
described above, of which we have already seen a typical example in its
several avatars as abstract graph, pointer data structure, and string
of characters suitable for storage in a text file.
Being a “logical cactus” is not just a matter of syntactic form —
it means being subject to meaningful interpretations as a sign of
a logical proposition. To enter the logical arena cactus expressions
must express something, a proposition true or false of something.
Fully addressing the logical, interpretive, semantic aspect of cactus graphs
normally requires a mind-boggling mass of preliminary work on the details of
their syntactic structure. Practical, pragmatic, and especially computational
considerations will eventually make that unavoidable. For the sake of the
present discussion, however, let’s put a pin in it and fast forward to the