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Together, they wrote a paper, “An Outline of a Theory of Semantic Information.” This paper suggested the computability of linguistic meaning. Sentences had a handful of kinds of “atomic” logic.⁷¹ Syntax is logical, which is why “in practice, every logician since Aristotle, in laying down rules, has dealt mainly with sentences.”⁷²

Carnap and Bar-Hillel’s thesis was unlike Chomsky’s to the extent that Carnap and Bar-Hillel did not dismiss semantics outright. “The semantic information carried by a sentence … may well be regarded as the ‘ideal’ pragmatic information which this sentence would carry for an ‘ideal’ receiver whose only empirical knowledge is formulated in exactly this class of sentences. By an ‘ideal’ receiver we understand, for the purposes of this illustration, a receiver with a perfect memory who ‘knows’ all of logic and mathematics, and together with any class of empirical sentences, all of their logical consequences.”⁷³

As we have been arguing, such an ideal sender-to-receiver relation never exists. The logic of communication in practice always is the opposite – differentials without end, or what Bakhtin would call “heteroglossia.”^§AS2.1.2b So, we must turn our analysis to patterns in the differentials. However, this critique of basic assumptions is not our point for the moment, which is to trace foundational thinking about mechanisms for the computability of sentences and their meanings.

Carnap and Bar-Hillel mention two fundamental components, “empirical knowledge,” and “logic.” During the years of the Vienna Circle, the years when Wittgenstein was building his sister’s house and when the Circle was so interested in his Tractatus,^§MS2.1.1a Carnap had set an agenda for defining “the logical structure of the world.” Its assumption: that a synthesis was possible between the work of empiricists and rationalists, and where “[t]he senses provide the material of cognition, [and] reason synthesizes the material so as to produce an organized system of knowledge.” These two halves, the sensible and the rational, Carnap and others fused into an amalgam that he and others in the Circle called “Logical Positivism.”⁷⁴

Otto Neurath^§MS1.1.3h called the program “empirical rationalism,” and set up a committee to guide the development of the International Encyclopedia of Unified Science which would lay out a full agenda. As well as Neurath this included Carnap, John Dewey,^§AS1.1 C.K. Ogden,^§AS1a and Bertrand Russell.^§MS1a Neurath also planned to create an Isotype Thesaurus to support the project, with system of “unified visual aids.”⁷⁵

Setting aside the empirical half of the program, Carnap focused on “pure syntax,” something that is “wholly analytic, and is nothing more than a combinatorial analysis.”⁷⁶ Reduced to their logical essence, a robot even might be able to operationalize such mechanisms.⁷⁷

Bar-Hillel for a time also focused on the analytic side of the Vienna Circle’s agenda, “a real challenge for structural linguists” because of “their thesis that language can be exhaustively described in non-referential terms” – that is, stripped of empirical or semantic specifics.

Though Carnap’s work on the logical syntax of language seemed to point in the right direction, it was not yet the right grammar for machine translation. “To my knowledge, no sufficiently complete operational syntax of any language has thus far been produced, mainly because the importance of such a syntax has not been recognized.”⁷⁸ What was needed, Bar-Hillel said, was a “quasi-mathematical notation for syntactic description” capable of implementation in “a completely mechanical procedure” such as “mechanical translation.”⁷⁹ This is why he had been so excited to read Chomsky’s dissertation.

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⁷¹ Rudolf Carnap and Yehoshua Bar-Hillel, 1952, “An Outline of a Theory of Semantic Information,” Cambridge, MA: Research Laboratory of Electronics, p. 4.

⁷² Rudolf Carnap, 1934 [1937], The Logical Syntax of Language, translated by A. Smeaton, London: Routledge and Kegan Paul, pp. 1–2.

⁷³ Rudolf Carnap and Yehoshua Bar-Hillel, 1952, “An Outline of a Theory of Semantic Information,” Cambridge, MA: Research Laboratory of Electronics, p. 3.

⁷⁴ Rudolf Carnap, 1922–25 [1967], The Logical Structure of the World, translated by R.A. George, Berkeley, CA: University of California Press, p. vi.

⁷⁵ Otto Neurath, Rudolf Carnap, and Charles Morris, 1938 [1955], International Encyclopedia of Unified Science, Volume 1, Chicago, IL: University of Chicago Press, pp. 24–25.

⁷⁶ Rudolf Carnap, 1934 [1937], The Logical Syntax of Language, translated by A. Smeaton, London: Routledge and Kegan Paul, p. 7.

⁷⁷ Rudolf Carnap, 1956, Meaning and Necessity: A Study in Semantics and Modal Logic, Chicago, IL: University of Chicago Press, p. 244.

⁷⁸ Yehoshua Bar-Hillel, 1953a, “Some Linguistic Problems Connected with Machine Translation,” Philosophy of Science 20:217–25, pp. 217, 218–19.

⁷⁹ Yehoshua Bar-Hillel, 1953b, “A Quasi-Arithmetical Notation for Syntactic Description,” Language 29(1):47–58, p. 47.

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Kalantzis, Mary, and Bill Cope. 2020. Adding Sense: Context and Interest in a Grammar of Multimodal Meaning. Cambridge UK: Cambridge University Press. pp. 211–213. https://doi.org/10.1017/9781108862059

Yehoshua Bar-Hillel’s “Mechanical Translation” §AS2.2b