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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:
 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.
 Synthetic a posteriori statements, which are the notanalytic statements.
Another distinction is between:
 Ptrue or Pfalse 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).

Contingent statements, which are independent from the axioms of the theory.
The following table represents the diverse kinds of statements.
True 
False 
Ptrue 
Contingent 
Pfalse 
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)
