It was this second class of analytic statements that caused him to note that the concept of analyticity itself stands in need of clarification, because it seems to depend on the concept of synonymy, which stands in need of clarification.
42.
Using this particular expanded idea of analyticity, Frege concluded that Kant's examples of arithmetical and geometrical truths are analytical " a priori " truths and " not " synthetic " a priori " truths.
43.
So some form of reductionism-" the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience "-must be assumed in order for an empiricist to'save'the notion of analyticity.
44.
In 1965, his doctoral dissertation " Analyticity and Implication " at the University of California, Berkeley was advised by Ernest Adams ( making Pollock an intellectual descendant of Gottfried Leibniz and Immanuel Kant, through Ernest Nagel and Patrick Suppes ).
45.
Then, all the non-analyticity at the critical point, the critical exponents, are because the " equilibrium value " of the order parameter changes non-analytically, as a square root, whenever the free energy loses its unique minimum.
46.
In 1955, he published one of the first monographs on Quantum Electrodynamics, " Kovarijantna kvantna elektrodinamika " ( in French physicists Jacques Bros and Henri Epstein he worked on setting up analyticity properties required for the use of dispersion relations in high energy collisions.
47.
Considering the way which we would test any proposed list of criteria, which is by comparing their extension to the set of analytic statements, it would follow that any explication of what analyticity means presupposes that we already have at our disposal a working notion of analyticity.
48.
Considering the way which we would test any proposed list of criteria, which is by comparing their extension to the set of analytic statements, it would follow that any explication of what analyticity means presupposes that we already have at our disposal a working notion of analyticity.
49.
So the non-analyticity is in the third and in the fourth term ( and maybe it's better to write them with | \ xi | so the expansion is ok for negative \ xi too )-- talk ) 13 : 29, 3 February 2009 ( UTC)
50.
Quine's chief objection to analyticity is with the notion of synonymy ( sameness of meaning ), a sentence being analytic, just in case it substitutes a synonym for one " black " in a proposition like " All black things are black " ( or any other logical truth ).
