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Mauro Murzi's pages on Philosophy of Science
Logical positivism - page 5
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With respect to the method of ascertaining their truth or falsity, the statements of a scientific theory are divided in two sets:

  1. Analytic a priori statements, whose truth is based on the meaning of the terms of the language. They include logical statements, whose truth is based only on the rules of logic and mathematics.
  2. Synthetic a posteriori statements, which are the not-analytic statements.

Another distinction is between:

  1. P-true or P-false statements, which are either a logical consequence of the axioms of the theory or incompatible with the axioms (that is, their negation is a logical consequence of the axioms).
  2. Contingent statements, which are independent from the axioms of the theory.

The following table represents the diverse kinds of statements.

True
False
P-true
Contingent
P-false
Analytic a priori true
Synthetic a posteriori
Analytic a priori false
Logical true
Possible
Logical false

(From: Rudolf Carnap, Analiticità, significanza, induzione, ed. Alberto Meotti and Marco Mondadori, il Mulino, Bologna, 1971, pag. 114)

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