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Extra resources for Carnap’s Logical Syntax of Language
69 10 One language? In §18, Carnap introduces Part II of LSL in the following way: Up to the present, we have differentiated between the object-language and the syntax-language in which the syntax of the object-language is formulated. Are these necessarily two separate languages? [. ] we intend to show that, actually, it is possible to manage with one language only; not, however, by renouncing syntax, but by demonstrating that without the emergence of any contradictions the syntax of this language can be formulated within this language itself.
According to the thesis of Physicalism, which will be stated later (p. 320) but which will not be established [begründed] in this book, all terms of science, including those of psychology and the social science, can be reduced to terms of the physical sciences. [. ] For anyone who takes the point of view of Physicalism, it follows that our Language II forms a complete syntactical framework for science. (LSL, pp. 150–1) 34 Carnap’s Logical Syntax of Language 9 General syntax In Part IV, Carnap undertakes the construction of a general syntax, one which may be applied to any language.
129) and he uses it to construct an undecidable sentence which is the analogue in Language II to the sentence constructed by Gödel in the proof of his ﬁrst incompleteness theorem. In a footnote added to the 1965 edition of his Princeton Lectures, Gödel credits the general self-reference lemma to Carnap (Gödel 1934/1965, p. 63). The ﬁnal paragraphs of Part III (§§37–40) give an outline of some further possible developments of Language II. They suggest ways of treating classes, cardinal numbers, real numbers, and physical concepts in the framework of this language.