Rudolf Carnap @CarnapSpeaks
Applied Mathematician. ‘Prospectus to a Homotopic Metatheory of Language’ (self-published). ‘Prolegomenon to a Treatise’ on @BauerVerlag. Views my own. after8books.com/reihe-no.-3-pr… Joined August 2022-
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This latter may sometimes be a genuine object-sentence (that is to say, not a quasi-syntactical sentence); and, in that case, no material mode of speech occurs. Otherwise it must be possible to give the interpretation by means of translation into a syntactical sentence.
That is, if S 3 is derivable from S 2 , and © 2 from S i, then S 3 is also derivable from S x; for this derivation can be obtained by placing the first two derivations one after the other. If S x is demonstrable, and S 2 derivable from S x, then S 2 is also demonstrable.
For the purpose of indirect proof, let us suppose the contrary, namely: 9 3 4 and 9 3 6 are given in such a way that neither — S 6 nor any sentence of ft4 is contradictory in respect of 9 34+9 36.
Later on we shall show how very easily the neglect of this rule, and the failure to differentiate between symbols and the objects designated by them, leads to error and obscurity (§§ 41, 42). § 5.
Just arrived! I thought this was a three-volume set, but apparently I bought only one book of the set.
An © Q x, to which ^ 3r, or © are suitable as arguments, is called extensional if every full sentence of S g x with closed arguments is extensional in relation to every argument. Correspondingly for every © fiix or ^Jtx to which ^ 3r, $U, or © are suitable as arguments.
The word- language employs as variables words (‘ a ’, ‘ some’, ‘ every’, ‘ all’, ‘ any ’, and so on) to which no particular genus is correlated as their realm of values.
Richard, J. , 213, 219, 222, 270. Richards, I. A. See Ogden. Rosser, J. B. *A Mathematical Logic without Variables. I. Ann. of Math. 36,1935. II. Duke Math. Journ. I, 1935. See also Kleene. Rustow, A. , 213. Der Liigner. Theorie , Geschichte und Auflosung. Diss. Erlangen, 1910.
Ali Enayat: Tarski's undefinability of truth theorem strikes again youtu.be/QKXSJIIfvxU
physicists when two matrices can be simultaneously diagonalized
If only every matrix was diagonalizable
https://t.co/iKh8q8fABp
*B eitrage zur lo g isc h e n Analyse d e s W a h rsch ein lich ke itsb egriffe s. Diss. , Berlin, 1934. * Analyse Logique de la Psychologie. Rev. Synthese , 10, 1935. *tJber den Gehalt von Wahrscheinlichkeitsaussagen. Erk. 5,I935«With P. Oppenheim.
We define a pr ‘ P ’ :§ 8. THE DEFINITIONS 25P(*) = (G r(*,y). G r(y,5)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (i) (1). . . . . . . . (Gr(7,6). G r(6,5))D P(7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Gr(7,6).
c- T erm sWe shall now define a number of c-terms, beginning with 4 consequence ’, one of the most important syntactical terms. In what follows the R are always sentential classes.
The final sentence of a proof is called a demonstrable sentence. §11. T he Pr im it iv e Se n t e n c e s o f La n g u a g e IWe shall give here, not the individual primitive sentences, but a series of schemata of primitive sentences.
For instance, certain sentential forms (such as unlimited existential sentences) and rules of inference (such as the Law of Excluded Middle), have been eliminated by certain authors.
Further, given an appropriate rule, the sentence “ A karulizes elatically” can bededuced from the original sentence and the sentence “ A is a Pirot”— again provided that the type to which the individual words belong is known.
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Didrik Lundberg @LundbergDidrik
96 Followers 147 Following I work with formal methods in computer science.@CarnapSpeaks My view is that Lawvere's theorem itself is pretty uninteresting it's the application to foundational questions that gives it the mystique. I'd be happy to be proven wrong though. I'm always looking for hidden dialectical complexities
@CarnapSpeaks Interested to hear your thoughts. In my opinion the mysticism around diagonal arguments seems unwarranted once you peal away the admittedly very interesting particulars of its various applications.
Ali Enayat: Tarski's undefinability of truth theorem strikes again youtu.be/QKXSJIIfvxU
physicists when two matrices can be simultaneously diagonalized
When navigating tech xitter, it’s important to tell the difference between people sharing a decent advice and pushing their agenda. Practice your skills on these: “Go will prevail, Rust will die” “Everyone needs to learn C” “FP is superior to OOP” “OOP is superior to FP”
If only every matrix was diagonalizable
Okay, this is high! I have to talk to @CarnapSpeaks and @pseudoSergius regarding this after two years when I have a working understanding of category theory!
As someone who has spent years in the trenches of analytic philosophy, I now feel able to articulate what strikes me as a flaw in its method--namely to commit too soon to a formal discourse without working through the informal bases which philosophical thought demands.
Category theory for computing science is a classic, in my opinion, and the most beginner friendly text on categories that i have ever read. The best thing about this book? It's available for free on McGill University's website.
The Popper cult and the Wittgenstein cult should have a fanatical-devotion-off to see who really solved all of philosophy in the 20th century.
@CarnapSpeaks I have a very strong feeling about people having to be in the same room.
@CarnapSpeaks Congratulations man, I adhere to your mathematics as passion, good luck for a great journey ahead
@RitchieTorres I mean... yeah I do got it. Why does performative stupidity help you here? Why would it make her look bad that you don't know stuff?
@CarnapSpeaks Congratulations and good luck!
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