• Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics

    From Mikko@mikko.levanto@iki.fi to sci.logic,sci.math.symbolic,comp.theory,comp.ai.philosophy on Wed Jun 24 12:45:51 2026
    From Newsgroup: comp.ai.philosophy

    On 23/06/2026 17:40, olcott wrote:
    On 6/23/2026 12:49 AM, Mikko wrote:
    On 22/06/2026 18:16, olcott wrote:
    On 6/22/2026 2:46 AM, Mikko wrote:
    On 22/06/2026 03:44, olcott wrote:
    On 6/21/2026 7:32 PM, phoenix wrote:
    olcott wrote:
    On 6/21/2026 5:36 PM, phoenix wrote:
    olcott wrote:
    On 6/21/2026 3:18 PM, André G. Isaak wrote:
    On 2026-06-20 04:26, Alan Mackenzie wrote:
    Mikko <mikko.levanto@iki.fi> wrote:
    On 19/06/2026 23:28, Alan Mackenzie wrote:
    In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
    On 18/06/2026 22:35, olcott wrote:
    On 6/17/2026 4:14 PM, olcott wrote:
    https://www.youtube.com/@rossfinlayson
    Making sure to leave out

    Proof-theoretic semantics
    (an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/

    Some people only memorize conventional views and >>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>
    Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>> reject
    alternative views out-of-hand without review.


    Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>> look into proof theoretic semantics.
    https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
    I've spent a couple of hours reading that web page.  It is >>>>>>>>>>>>> abstract in
    the extreme.  One thing is utterly clear: its level of >>>>>>>>>>>>> abstraction is
    well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>>>> who can't
    even understand proof by contradiction.

    That page's level of abstraction is high enough that I >>>>>>>>>>>>> can't be bothered
    to read it any further.  If it actually says anything at >>>>>>>>>>>>> all, that
    something is heavily disguised.  From it's "Conclusion and >>>>>>>>>>>>> Outlook"
    section at the end:

    | Standard proof-theoretic semantics has practically >>>>>>>>>>>>> exclusively been
    | occupied with logical constants. Logical constants play a >>>>>>>>>>>>> central role
    | in reasoning and inference, but are definitely not the >>>>>>>>>>>>> exclusive, and
    | perhaps not even the most typical sort of entities that >>>>>>>>>>>>> can be defined
    | inferentially. A framework is needed that deals with >>>>>>>>>>>>> inferential
    | definitions in a wider sense and covers both logical and >>>>>>>>>>>>> extra- logical
    | inferential definitions alike.

    Does this have any meaning?

    Yes. It means that proof-theoretic semantics is currently >>>>>>>>>>>> and in the
    near future not useful as making it useful requires much >>>>>>>>>>>> time and
    effort if it is possible at all.

    Do its proponents have any idea what PTS ought to be useful >>>>>>>>>>> for? What it
    ought to be able to do that standard logic fails at?  Maybe >>>>>>>>>>> André could
    elucidate.  He seems to have a better grasp of it than >>>>>>>>>>> anybody else here.

    I doubt my understanding of PTS is any better than yours. I >>>>>>>>>> basically only know what is presented in the Stanford
    Encyclopedia article (which you correctly point out is not >>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. What I >>>>>>>>>> am quite certain of, however, is that Olcott lacks any
    understanding of what PTS actually says as he's made a variety >>>>>>>>>> of fairly absurd claims regarding it (for example, that PTS >>>>>>>>>> claims that unproven propositions are 'meaningless' or that >>>>>>>>>> the goal of PTS is to completely overthrow standard truth- >>>>>>>>>> theoretic semantics).

    André


       Proof-theoretic semantics is an alternative to
       truth-condition semantics. It is based on the
       fundamental assumption that the central notion
       in terms of which meanings are assigned to certain
       expressions of our language, in particular to
       logical constants, is that of proof rather than
       truth. In this sense proof-theoretic semantics
       is semantics in terms of proof.
       https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
    In other words it answers the question:
    What happens when truth conditional semantics is
    utterly abandoned and is totally replaced by proof
    theoretic semantics?

    Lastly, and why should we care? Please answer this and other
    questions presented.


    This is the key element to creating the algorithm
    that divides truth was well-crafted lies in real time.

    We can make these lies look foolish at every language
    level from below average kindergarten to profoundly
    brilliant genius with a PhD in everything and we
    can do this before the liar finishes saying their
    sentence.

    It also make the trillion dollar LLM industry more
    than 100-fold more valuable.

    What good does it do to program the LLMs to never admit defeat?

    It is not that they never admit defeat.
    It is that that have a system of essentially infallible reasoning
    that never errs as long as it has all the relevant information.

    It is fairly simple to build a system of essentially infallible
    reasoning that never errs even when it doesn't have all the
    relevant information. The real problem is to construct a system
    that tells something interesting instead of just different
    presentations of the same already known facts.

    It will have the exhaustively complete list of
    every atomic fact of general knowledge of the
    actual world.

    That is impossible. By the time you have all facts of general knowledge
    in your system the general knowledge has grown to inlude more facts.

    It can be reasonably approximated pretty quickly.
    We start with all of the textbooks.

    That is a lot of reading, though those for the same topic area tend
    to say the same, and the old ones add very little to the new ones,
    mainly some now obsolete technology.
    --
    Mikko

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  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math.symbolic,comp.ai.philosophy on Thu Jun 25 10:09:19 2026
    From Newsgroup: comp.ai.philosophy

    On 24/06/2026 23:19, olcott wrote:
    On 6/24/2026 3:23 AM, Mikko wrote:
    On 23/06/2026 17:29, olcott wrote:
    On 6/23/2026 12:39 AM, Mikko wrote:
    On 22/06/2026 16:13, olcott wrote:
    On 6/22/2026 2:13 AM, Mikko wrote:
    On 22/06/2026 02:51, olcott wrote:
    On 6/21/2026 4:57 AM, Mikko wrote:
    On 20/06/2026 23:03, olcott wrote:
    On 6/20/2026 2:17 PM, dbush wrote:
    On 6/20/2026 3:02 PM, olcott wrote:
    On 6/20/2026 12:40 PM, André G. Isaak wrote:
    On 2026-06-19 20:40, olcott wrote:
    On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
    [ Followup-To: set ]

    In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
    On 18/06/2026 22:35, olcott wrote:
    On 6/17/2026 4:14 PM, olcott wrote:
    https://www.youtube.com/@rossfinlayson
    Making sure to leave out

    Proof-theoretic semantics
    (an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/



    Some people only memorize conventional views and >>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>
    Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>> reject
    alternative views out-of-hand without review.


    Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>> look into proof theoretic semantics.
    https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/

    I've spent a couple of hours reading that web page.  It is >>>>>>>>>>>>>> abstract in
    the extreme.  One thing is utterly clear: its level of >>>>>>>>>>>>>> abstraction is
    well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>> Olcott, who can't
    even understand proof by contradiction.


    What superficially looks like contradiction
    "This sentence is not true"

    Once again, you're responding to people's posts with
    irrelevancy.

    The Liar's Paradox has absolutely nothing to do with proof >>>>>>>>>>>> by contradiction. The LP isn't a contradiction; it's a >>>>>>>>>>>> paradox. The two are different things. A contradiction is a >>>>>>>>>>>> statement which is necessarily false. A paradox is a
    statement to which no truth value can be consistently assigned. >>>>>>>>>>>>
    André


    Then I have never spoken of anything where proof by
    contradiction applies,

    False, as that is exactly the method uses by the halting
    problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>> which you've been attempting (and failing) to refute for years. >>>>>>>>>>

    Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>> to the operational semantics of the C programming language.

    That only means that your DD is not a strictly confoming C program. >>>>>>>
    The exact operational semantics of C conclusively
    prove that the input DD to HHH is ungrounded in
    these operational semantics because this input
    specifies non-terminating recursive simulation
    to HHH.

    Because DD is not strictly conforming the exact operational semantics >>>>>> do not fully specify the behaviour of DD. In order to prove that DD >>>>>> halts you also need additional operational spemantics provided by the >>>>>> C implementation you have used. When DD iss executed in that
    environment
    it halts, which is sufficient to prove that in that environment DD >>>>>> halts. In some other environment its execution might be aborted or it >>>>>> could be rejected by the compiler.

    Proof Theoretic Semantics provides the correct way
    to handle pathological self-reference (PSR).

    This would be dead obvious if you were not totally
    clueless about Prolog.

    % This sentence is not true.
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Nice to see that you don't disagree.

    Not nice to see that everyone continues to
    totally ignore my best validation of proof
    theoretic semantics.

    Unfortunately that is unavoidable as long as your best presentation
    of the validation and of your version of proof theoretic semantics
    are not good enough.

    Is is dead obvious and completely clear example
    of the final resolution of the Liar Paradox using
    generic proof theoretic semantics implemented in
    Prolog.

    Except that it is not final -- others will continue presenting
    different views about it -- and not even a resolution.

    Anyway, nice to see that you still don't disabree.

    This is understandable for anyone that has no
    idea what a directed graph is.

    Your understanding of understandability is far from the real thing.

    This has been completely rewritten just now.
    https://github.com/plolcott/x86utm/blob/master/README.md

    The description is updated. The described is not updated.

    It always was a proof theoretic halt prover
    I just didn't have those terms until recently.

    It is not a prover. It does not prove.

    It proves that no canonical proof of DD reaching
    its own final halt state exists within the operational
    semantics of the C programming language for PTS halt
    prover HHH.

    Irrelevant. That DD halts when executed is sufficient for a reasonable
    person to conclude that it halts. To formulate that inference as a
    formal proof is trivial to anyone who knows the formal rules.

    It produces some execution trace
    but may end before termination, and presents its conclusion or crashes.

    Perhaps you have no idea what cycles in directed graphs are?

    Doesn't really matter, especially when they are not even mentioned.
    The words are well known and the definitions can be found on the
    web.
    --
    Mikko
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