The origin of the logical positivist’s distinction
ΟΙ ΛΙΓΙΚΟΙ ΘΕΤΙΚΙΣΤΕΣ ΣΥΜΦΩΝΗΣΑΝ ΜΕ ΤΟΝ KANT ΟΤΙ … ΟΙ ΜΑΘΗΜΑΤΙΚΕΣ ΠΡΟΤΑΣΕΙΣ ΕΙΝΑΙ A PRIORI.
(The logical positivists agreed with Kant that we have knowledge of mathematical truths, and further that mathematical propositions are a priori.)
ΑΝΤΙΘΕΤΑ ΜΕ ΤΗ ΣΥΝΘΕΤΗ ΜΕΤΑΦΥΣΙΚΗ ΠΟΥ Ο ΚΑΝΤ ΠΡΟΣΕΦΕΡΕ ΟΙ ΛΟΓΙΚΟΙ ΘΕΤΙΚΙΣΤΕΣ ΙΣΧΥΡΙΣΤΗΚΑΝ ΟΤΙ Η ΓΝΩΣΗ ΟΛΩΝ ΤΩΝ ΚΡΙΣΕΩΝ ΕΙΝΑΙ ΙΔΙΑ: ΟΛΕΣ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΤΗ ΓΝΩΣΗ ΤΩΝ ΣΗΜΑΣΙΩΝ ΤΩΝ ΟΡΩΝ Ή ΤΩΝ ΣΥΜΒΑΣΕΩΝ ΤΗΣ ΓΛΩΣΣΑΣ.
(However, they did not believe that any complex metaphysics, such as the type Kant supplied, are necessary to explain our knowledge of mathematical truths.
Instead, the logical positivists maintained that our knowledge of judgments like “all bachelors are unmarried” and our knowledge of mathematics (and logic) are in the basic sense the same: all proceeded from our knowledge of the meanings of terms or the conventions of language.)
[FN, TODO] “Since empiricism had always asserted that all knowledge is based on experience, this assertion had to include mathematics. On the other hand we believed that with respect to this problem the rationalists had been right in rejecting the old empiricist view that the truth of “2+2=4” is contingent on the observation of facts, a view that would lead to the unacceptable consequence that an arithmetical statement might possibly be refuted by new experiences. Our solution … consisted in asserting empiricism only for factual truth. By contrast, the truths of logic and mathematics are not in need of confirmation by observations”.[Carnap, R. The Philososphy of Rudolf Carnap]
Logical positivist definitions
Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, named it the “analytic/synthetic distinction.” They provided many different definitions, such as the following:
– analytic proposition: a proposition whose truth depends solely on the meaning of its terms
– analytic proposition: a proposition that is true (or false) by definition
– analytic proposition: a proposition that is made true (or false) solely by the conventions of language
(While the logical positivists believed that the only necessarily true propositions were analytic, they did not define “analytic proposition” as “necessarily true proposition” or “proposition that is true in all possible worlds.”)
Synthetic propositions were then defined as:
– synthetic proposition: a proposition that is not analytic
These definitions applied to all propositions, regardless of whether they were of subject-predicate form. Thus, under these definitions, the proposition “It is raining or it is not raining,” was classified as analytic, while under Kant’s definitions it was neither analytic nor synthetic. And the proposition “7 + 5 = 12” was classified as analytic, while under Kant’s definitions it was synthetic.