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The 4 logical notions were already described in the paper "Über die Beschränktheit der Ausdrucksmittel deduktiver Theorien”, authored by A.Lindenbaum and A.Tarski, and publish in Ergebnisse eines mathematischen Kolloquiums, fasc. 7, 1934–1935, (published in 1936) pp. 15–22. This paper is related to a talk presented by Tarski June 12, 1935 at the Mathematical Colloquium conducted by Karl Menger in the University of Vienna:
The 4 logical notions were already described in the paper "Über die Beschränktheit der Ausdrucksmittel deduktiver Theorien”, authored by A.Lindenbaum and A.Tarski, and publish in Ergebnisse eines mathematischen Kolloquiums, fasc. 7, 1934–1935, (published in 1936) pp. 15–22. This paper is related to a talk presented by Tarski June 12, 1935 at the Mathematical Colloquium conducted by Karl Menger in the University of Vienna:
The original version of this paper was re-printed in the Collected Papers of Alfred Tarski, originally published in 1986 and reprinted in 2019 (Birkhäuser/Springer).
The original version of this paper was re-printed in the Collected Papers of Alfred Tarski, originally published in 1986 and reprinted in 2019 (Birkhäuser/Springer).
It was translated in English by J.H.Woodger as "On the limitations of the means of expression of deductive theories* and published in A.Tarski, Logic, semantics, metamathematics.
It was translated in English by J.H.Woodger as "On the limitations of the means of expression of deductive theories* and published in A.Tarski, Logic, semantics, metamathematics.
Second edition revised by John Corcoran, and published in 198, by Hackett, Indianapolis, USA, pp.384-392, more details here,
Second edition revised by John Corcoran, and published in 198, by Hackett, Indianapolis, USA, pp.384-392, more details here,
In the 1936 paper by Lindenbaum and Tarski it is written: "Consequently only four binary relations between individuals are definable by purely logical means, namely the universal relation, the empty relation, identity, and diversity (thus the four moduli of Schröder’s algebra of relations)" (p.387 in both editions of the English translation)
In the 1936 paper by Lindenbaum and Tarski it is written: "Consequently only four binary relations between individuals are definable by purely logical means, namely the universal relation, the empty relation, identity, and diversity (thus the four moduli of Schröder’s algebra of relations)" (p.387 in both editions of the English translation)
In the 1986 paper"What are logical notions?" prepared by Corcoram, Tarski says: " ... this is a rather simple meta-logical result, formulated a long time ago (1936) in a short paper by Lindenbaum and myself. Though this result is simple, I think that it should be included in most logic textbooks, because it shows a characteristic property of what can be expressed by logical means." (p,150, in "What are logical notions" (1986)
In the 1986 paper"What are logical notions?" prepared by Corcoram, Tarski says: " ... this is a rather simple meta-logical result, formulated a long time ago (1936) in a short paper by Lindenbaum and myself. Though this result is simple, I think that it should be included in most logic textbooks, because it shows a characteristic property of what can be expressed by logical means." (p,150, in "What are logical notions" (1986)
Adolf Lindenbaum (1904-1941)
Adolf Lindenbaum (1904-1941)
From that we can infer that this result / this charactriztion should be attributed to both of them and since the 1936 paper is authored by Lindenbaum & Tarski in that order, it makes sense to talk about Lindenbaum-Tarski 4 logical notions.
From that we can infer that this result / this charactriztion should be attributed to both of them and since the 1936 paper is authored by Lindenbaum & Tarski in that order, it makes sense to talk about Lindenbaum-Tarski 4 logical notions.
Alfred Tarski (originally Teitelbaum) and Adolf Lindenbaum were close friends and collaborators.
Alfred Tarski (originally Teitelbaum) and Adolf Lindenbaum were close friends and collaborators.
There is a notion wrongly called Lindenbaum–Tarski algebra (or even Lindenbaum algebra) . This notion is due in fact to Tarski himself as he pointed out. So we can infer that if the notion of the 4 logical notions was due to himself, he would not have been afraid to claim that.
There is a notion wrongly called Lindenbaum–Tarski algebra (or even Lindenbaum algebra) . This notion is due in fact to Tarski himself as he pointed out. So we can infer that if the notion of the 4 logical notions was due to himself, he would not have been afraid to claim that.
Alfred Tarski (1901-1983)
Alfred Tarski (1901-1983)
Anita Burdman Feferman and Solomon Feferman, Alfred Tarski (Life and Logic), Cambridge University Press, 2004.
Steven R. Givant, "A portrait of Alfred Tarski", The Mathematical Intelligencer, volume 13, pp.16–32 (1991).
Mario Gómez-Torrente, Alfred Tarski, Stanford Encyclopedia of Philosophy, 2019
Jan Wolenski, “Alfred Tarski (1901–1983)”, in Ángel GarridoUrszula and Wybraniec-Skardowska (eds), The Lvov-Warsaw School. Past and Present, Birkhäuser, Basel, 2018, pp.361-371.
Jan Woleński, “Adolf Lindenbaum”, The Internet Encyclopedia of Philosophy, 2020.
Jan Zygmunt, "Alfred Tarski: Auxiliary Notes on His Legacy", in Ángel GarridoUrszula and Wybraniec-Skardowska (eds), The Lvov-Warsaw School. Past and Present, Birkhäuser, Basel, 2018, pp.425-455.
Jan Zygmunt and Robert.Purdy, “Adolf Lindenbaum: Notes on His Life with Bibliography and Selected References”, Logica Universalis, 8 (2014), pp.285–320.
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