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Thursday, June 15, 2006

History of Logic at HOPOS

I'm at HOPOS, which is loads of fun. All my history of analytic/history of logic buddies are here. But more to the point:

Paolo Mancosu just gave the most amazing talk about the debate within the Vienna Circle about Tarski's theory of truth, in particular, the opposition that Neurath had voiced against it from the mid 1930s onward. I had always thought that the Vienna Circle wholeheartedly accepted Tarski's theory, and that Tarski's paper made truth an "acceptable" notion (from a logical empiricist standpoint). What Paolo showed, using correspondence between Carnap, Neurath, Tarski and others from 1935 and later, was that there was a debate raging over it. Neurath was opposed not, as one might suppose, because of the set theoretic metalanguage in which Tarski's theory was couched, but because he feared that people would use Tarski's theory in areas where it wasn't applicable, i.e., in non-formalized languages, and that it would lead people to return to "metaphysics". (I guess, that has actually happened decades later in the whole thing about deflationary conceptions of truth!) Moreover, we now know why no-one is aware about the tensions within the Vienna Circle around the theory of truth: at the Congrès Descartes in Paris in 1937, there was a private meeting with Carnap, Tarski, Neurath, Naess, Lutman-Kokoszynska, Hempel, and others where the proponents and opponents of Tarski's theory put forward their arguments. It was agreed (or, decreed by Carnap) that noone was to bring up the differences within the Circle regarding this issue in print.

Paolo's talk was followed by Johannes Hafner on the origins of model theory in Hilbert and Tarski. Johannes' main point was that whereas Tarski's notion of interpretation of an axiom system was a lot clearer about the syntax of the language (precise recursive definition of syntax in meta-language), Hilbert's notion of interpretation was a lot closer to the modern one--Tarski's notion of truth in the 1935 paper did not allow for varying domains. It wasn't until the 1950s in Tarski's and Vaught's work on model theory that the modern notion of truth in a structure emerged.


At June 15, 2006 6:28 PM , Anonymous Anonymous said...

I'd like to second your endorsement of Paolo's work on this topic -- the documents are fascinating, and Paolo's treatment of them is excellent. (From what I understand, this paper will be coming out in a collection of articles on Tarski edited by Douglas Patterson, from OUP.)

I just wanted to make one tiny remark. People often say, as you do, that the modern notion of truth in a model dates to Tarski and Vaught's work in the mid-fifties. In at least one important sense, this bit of conventional wisdom is not right. The notion of truth in a model appears in exactly its current form in a March 1948 article in JSL  by John Kemeny, entitled "Models of Logical Systems." It may be the case that this work fell on deaf ears, and that, historically speaking, it was Tarski and Vaught's mid-50's work that served as the source for the logico-mathematical community's notion of truth in a model. But at least conceptually, Kemeny preceded them in print. (I don't know whether there was someone before Kemeny; his above-mentioned article made it sound like there's not, but he may have overlooked something.) 

Posted by Greg Frost-Arnold

At June 15, 2006 7:12 PM , Anonymous Anonymous said...

wow, cool!
that seminar we took back in '93 was so half-assed! 

Posted by libby

At June 16, 2006 3:13 AM , Anonymous Anonymous said...

Thank's Greg! That's interesting. BTW, Paolo mentioned that the "position papers" of the two sides written up after the 1937 meeting were going to be published, but I forgot to ask where. Also: even if you don't care about the history in this, you should get the paper, because the quotes from the letters were so funny . Logical empiricists calling each other names: Neurath to Carnap: "You're like Thomas Aquinas". Carnap to Neurath: "I recall our debate in 1937 and that you were pigheaded and had no rational arguments. I'll still talk to you, though." (I'm paraphrasing.) 

Posted by Richard Zach


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