Logic Geometry, Information@LGcommaI

Professional mathematician. Doctorate in (a subarea of) mathematics from a German university.

 Germany
Joined July 2018
84,662 Photos and videos
»..diligite homines, interficite errores, sine superbia de veritate praesumite, sine saevitia pro veritate certate, orate pro eis quos redarguitis atque convincitis.« St. #Augustine(354–430), Contra Litteras Petiliani, Book 1, Chapter 29 #Christianity #ChristianCulture #Europe
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#KreiselObituaryForGoedel-20 [Psychiatry Psychology] "After Gödel’s first visit to Princeton (1933/34) he had a nervous breakdown. It began with severe anxiety when he got off the boat. .. Wagner-Jauregg was called in, a Nobel Prize winner [then] more famous than Freud, >
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[Extremely relevant to the above: Wagner-Jauregg seeing Gödel is mentioned in the interview with Hao Wang and Robin Gandy (v=hnBSRxHDxBk).] > , at least in Austria. No indications of psychosis were found. >
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Logic Geometry, Information retweeted
Logic Geometry, Information@LGcommaI
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Pohlers' valuable 1999 Proof-Theory-lecture notes appear to have vanished from uni-muenster.de/Logik/en/Stu… (and from the non-deep web in its entirey)! Today I managed to retrieve the pdf from the Internet Archive! One good deed a day. 😊

Lecture Notes

uni-muenster.de
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To repeat myself: it is embarrassing (to humanity) that it is only ONE (freely accessible) internet-archive. It should go without saying that there ought to be several such archives on several continents. This kind of centralization is intolerable.
Internet Archive
@internetarchive
Jan 28
The internet's memory isn’t a cloud—it’s heat, power, and hard drives 🔥💾 Inside the Internet Archive’s trillion-page fight against digital forgetting, from PetaBox servers to legal battles over memory itself ⚙️📚 Learn more ⤵️ hackernoon.com/the-long-now-… @zbruceli #InternetArchive #DigitalPreservation #WebHistory #Infrastructure #Engineering
The Internet Archive headquarters: a large white neoclassical building with columns, stands on a street corner in San Francisco.

ALT The Internet Archive headquarters: a large white neoclassical building with columns, stands on a street corner in San Francisco.

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Pohlers' valuable 1999 Proof-Theory-lecture notes appear to have vanished from uni-muenster.de/Logik/en/Stu… (and from the non-deep web in its entirey)! Today I managed to retrieve the pdf from the Internet Archive! One good deed a day. 😊

Lecture Notes

uni-muenster.de
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#FefermanWhatLogicTellUs-1 [CoquandNeuwirth #KreiselObituaryForGoedel Outreach #TaitNoCounterexample Teaching] The Mathematical Intelligencer 2, pp. 20–24 (1979) What Does Logic Have to Tell us about Mathematical Proofs? Solomon Feferman (Stanford University)
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'Der Mensch ist ein der Idee nach Unendliches, das jeweils in endliche Bedingungen eingespannt ist und nur in diesen, indem es sie ergreift, Substanz gewinnt. [In] dieser [Lage] kommt es für jeden Menschen darauf an, in ihnen frei zu werden.' Jaspers: Idee der Universität (1961)
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#KreiselObituaryForGoedel-64 'In short, formalization and purity of method is just much subtler than suggested by generalities about mathematical rigour.. A corollary to this is that the significance of Gödel’s incompleteness theorem is a subtle business too. For if we were to >
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#KreiselObituaryForGoedel-63 "[It] is often neglected [that] (i) [the] actual reliability or ‘security’ [of impure proofs] is obviously unaffected by the possibility of pure proofs if that possibility has not been realized (ii) impure methods are not only used heuristically, >
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>, as..logical hygiene. But also there is the void created by simply not saying out loud what (knowledge) is gained by impure proofs, for example by analytic proofs in number theory: knowledge of RELATIONS BETWEEN THE NATURAL NUMBERS AND THE COMPLEX PLANE or, more fully, >
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>between arithmetic and geometric properties. It is precisely this knowledge which provides effective new means of checking proofs: if this conflicts with some ideal of rigour, so much the worse for the ideal (which is being tested)."
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Uhm, thanks...
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"Lindström had an exceptionally clear and concise style in writing mathematical logic. His 1997 book, Aspects of Incompleteness, remains a perfect example: it provides a systematic introduction to his work in arithmetic and interpretability. The book is short .." [Teaching]
Logic Geometry, Information@LGcommaI
14 May 2023
#DawsonGoedelToLindstroem-1 [#LindstroemElementaryLogic #HistoryOfMathematics] History and #Philosophy of #Logic 14(1), 15-37 (1993) The Compactness of First-Order Logic: From Gödel to Lindström John W. Dawson, Jr. M.t. Die Kompaktheit der Logik erster Stufe: von Gödel bis >
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>of propositional logic) while in fact this inference requires the Substitution Lemma of of Modal Logic (which isn't hard but definitely nontrivial). Smoryński treats this lemma right in [9780387962092; p. 77]. The (admitted by Lindström) fact that he was copying this from >
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>Smoryński's book makes this expository error even more severe.
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It is a commonplace worth repeating that superhuman intellects have existed for a long time (and the world did not change dramatically because of it): any technical forum constitutes a superhuman intellect. Both they and putative machine-solutions have finite resources, too.
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(Similarly, any moderately disciplined research team is a superhuman intelligence, i.e., more intelligent than one human being.)
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new and relevant:
doomslide
@doomslide
Oct 2
Broke: AI consciousness Woke: AI personhood Bespoke: Corporate personhood Bewoked: Corporate consciousness
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New and relevant:
doomslide
@doomslide
Oct 2
Broke: AI consciousness Woke: AI personhood Bespoke: Corporate personhood Bewoked: Corporate consciousness
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"Fast allen Bildungsidealen ist gemeinsam der Sinn für - Disziplinierung - Form - Selbstbeherrschung" Karl Jaspers: Die Idee der Universität (1923)
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#KreiselObituaryForGoedel-62 "Defects of ideals are generally seen most clearly in areas where they have been realized, and so the results can be compared both with earlier expecta­tions and with alternatives >
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"the typesetter's nightmare is the reader's delight"
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