Frege’s ideas exerted a deep influence on Carnap.
Carnap had lost the plot.
Schlick even assisted Carnap in locating a publisher for the work.
Carnap also touches on theoretical languages in several parts of the Schilpp volume (1963).
One strong disanalogy with formalism is that Carnap takes this line with all areas of discourse, not just mathematics.
It would be another decade, though, before Carnap came to see Frege’s logic as the key to a new way of doing philosophy.
With Reichenbach, Carnap founded a periodical, Erkenntnis (1930–39; refounded 1975), as a forum for the new “scientific philosophy.”
Carnap stressed that usually such tests cannot provide strict proof or disproof but only more or less strong “confirmation” for an empirical statement.
Carnap introduced a distinction between questions that are internal to a framework and questions that are external to a framework (Carnap 1950).
Interestingly, he mentioned Carnap only in a footnote: ‘Professor Carnap has a similar definition of logical necessity in terms of what he calls “state-descriptions”’ (ibid).
Carnap and his followers (Carnap 1980; Kuipers 1988; Niiniluoto 1988; Maher 2000; Romeijn 2006) have formulated principles of analogy for inductive logic, using Carnapian λγ rules.
Carnap was well aware of this challenge and addressed it using a sentence that became labeled later on the Carnap sentence of a scientific theory (Carnap 1958; 1966: ch. 23):
And in a talk Carnap gave about the Aufbau project in Vienna in January 1925, we find a new guiding principle: “Overcoming subjectivity” (Carnap 1925a, 1925b, as quoted in Carus 2007a: 168; 2016).
Rudolf Carnap took things further with his method of intension and extension, and provided a semantics in which quite specific model-theoretic entities are identified with intensions (Carnap 1947).
Goodman’s predecessor in studying a constitutional system by the means of modern formal logic is, as we already said, Rudolf Carnap, who follows a very similar project as Goodman in his Der logische Aufbau der Welt (Carnap 1928).
It is much less clear whether Quine is right to attribute a weaker form of reductionism to the later Carnap, as Carnap regards the confirmation of scientific hypotheses to be holistic and theory-relative from the Logic Syntax at the latest.
The dates here are relevant because by the time of this essay Carnap had already decided (Carnap 1936–37) that theoretical terms could not in general be given explicit definitions in the observation language even though the observation reports were already in a physicalist vocabulary.
An important instance of probabilistic logic is presented in inductive logic, as devised by Carnap, Hintikka and others (Carnap 1950 and 1952, Hintikka and Suppes 1966, Carnap and Jeffrey 1970, Hintikka and Niiniluoto 1980, Kuipers 1978, and Paris 1994, Nix and Paris 2006, Paris and Waterhouse 2009).
One interesting view about the relationship between formal languages, ontology, and meta-ontology is the one developed by Carnap in the first half of the 20th century, and which is one of the starting points of the contemporary debate in ontology, leading to the well-known exchange between Carnap and Quine, to be discussed below.
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One interesting view about the relationship between formal languages ontology and meta-ontology is the one developed by Carnap in the first half of the 20th century and which is one of the starting points of the contemporary debate in ontology leading to the well-known exchange between Carnap and Quine to be discussed below