Hello CG-list,
Thanks to László Babai graph isomorphism is known to be quasi-polynomial.
Original paper : https://arxiv.org/abs/1512.03547
Live exposition : https://www.youtube.com/watch?v=r-nCYbX_Au0
This result generalizes well to hyper-graph isomorphism.
Does that mean one could imagine a CoGUI version based around a weaker CG
subsumption ?
What would be the value of such a platform ?
Regards,
- damien
--
Cet e-mail a été vérifié par le logiciel antivirus d'Avast.
www.avast.com
Cf: Zeroth Law Of Semiotics • Discussion 2
http://inquiryintoinquiry.com/2022/10/27/zeroth-law-of-semiotics-discussion…
Re: Zeroth Law Of Semiotics
https://inquiryintoinquiry.com/2015/07/30/zeroth-law-of-semiotics/
Re: FB | Charles S. Peirce Society
https://www.facebook.com/groups/peircesociety/posts/2757776511024990/
::: Joseph Harry
https://www.facebook.com/groups/peircesociety/posts/2757776511024990?commen…
<QUOTE JH:>
“Meaning is a privilege not a right” would seem to be
a meaningless proposition, since ‘privilege’ and ‘right’
are third-order evaluative, symbolic terms, while ‘meaning’
is a neutral second-order term, implying only existential
individualized dynamic activity or process. Driving (a car)
is a privilege not a right, but meaning is neither.
</QUOTE>
Dear Joseph,
That may be too literal a reading for Zero‑Aster's poetic figure.
If I read the oracle right, the contrast between “privilege” and
“right” serves merely to mark the distinction between meanings
optional and obligatory. Whether any hint of “private law” or
“law unto itself” is intended or involved is something I would
have to spend more time thinking about.
Regards,
Jon
Cf: Abduction, Deduction, Induction, Analogy, Inquiry • 31
https://inquiryintoinquiry.com/2022/10/14/abduction-deduction-induction-ana…
Re: Scott Aaronson ( https://scottaaronson.blog/ )
::: Explanation-Gödel and Plausibility-Gödel
( https://scottaaronson.blog/?p=6754 )
All,
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… )
Regards,
Jon
Cf: Theme One Program • Exposition 5
https://inquiryintoinquiry.com/2022/06/23/theme-one-program-exposition-5/
All,
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
at hand.
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
logical substance.
Regards,
Jon
Basal Ingredients Of Society • Prologue
https://inquiryintoinquiry.com/2015/09/01/basal-ingredients-of-society-prol…
All,
I settled on the acronym BIOS to suggest the vital elements of life in society,
a life in association with others, and not just any association but one whose
flickers of life are sustained for more than a few vicissitudes of history.
Sustainability in that life requires democracy, a society based on
a distinctive form of social compact.
Best Regards on this Day of Contemplation,
Jon
Jeff,
Your questions about Peirce's proof of pragmatitiicsm are important.
Jeff> I tend to think the later writings often build on the earlier. As
such, I wonder what the later proof borrows by way of premisses from the
arguments developed in the 1903 Harvard Lectures on Pragmatism. Once that
is clearer, we can then ask what might have been added to the later
argument by way of additional premisses.
Peirce's ideas were constantly evolving up to the very end. He frequently
went back to earlier ideas, but always with some new insights or directions
from his later developments. For pragmaticism, his 1903 Harvard and
Lowell lectures were an important starting point. And the word
'prolegomena' in 1906 is an important clue.
An interesting occurrence in December 1902: Carus published a new English
translation of Kant's "Prolegomena to any future metaphysics" and Peirce
published a notice of it in the Nation in June 1903. -- he must have been
reading (or rereading) it around the same time as he was preparing those
Lectures.
Peirce must have read it (in German) during the time that he and his father
were studying Kant. After Kant finished the first edition of KdrV (or CdrV
as Peirce preferred to refer to it), he wrote the short Prolegomena as an
intro and overview of the questions that he tried to answer in the first
edition of the K(C)drV. Those questions were the prelude to his second
edition, which he finished a few years later. Although Peirce had
criticized some of Kant's fundamental assumptions, he always had a high
regard for Kant, and he cited him frequently throughout CP. And he had a
very high regard for Kant's questions, which are the main topic of his own
Prolegomena. If you (a) read Kant's questions and (b) read Peirce's
writings from 1903 onwards, you can see a strong influence of Kant's
questions on Peirce. In fact, Peirce's 1903 classification of the sciences
seems to be part of Peirce's answers to K's three transcendental questions.
Even stronger evidence for Kant's influence is Peirce's 1906 Apology for
Pragmaticism, which is written as a prelude to a series of articles he
planned for the Monist. Unfortunately, he ran into difficulties around
1909, which led him to the series of ten MSS on "Assurance" (R661 to R670)
from 1910 to 1911.
There's much more to be said about all these issues. I recommend an
article about Peirce's Apology by Max Fisch (1982) and reprinted in a book
by Fisch in 1986. In that article, Max F. wrote that methodeutic is a key
topic that Peirce was addressing in his planned proof. I agree.
And I also believe that there were two reasons why Peirce stopped in 1909:
(1) problems with phaneroscopy as a science egg (R645) and (2) problems
with logic, which were the reason for his ten studies (R661 to R670) from
1910 to 1911. These are the reasons for major revisions that Peirce made
in 1911 and 1912. It's sad that he was converging on important new ideas
just when he had that accident in 1911 followed by the cancer.
There is, of course, much more to say about all these issues. And as Max
Fisch also said, that's why we need all of Peirce's late MSS available in
suitable formats. As Peirce's late letters show -- he was thinking very
hard about all these issues. And he didn't hesitate to make major
revisions when necessary.
John