Philosophical ability, so that the principles chosen for formalization are not trivial or absurd.

An argument opposing the unrestricted use of quantification in modal logic has been put forward by Quine. Central to this argument are the two phrases, The Morning Star, The Evening Star.One form of the argument is obtained by considering the following two statements: It is necessary that the Morning Star is identical with the Morning Star. It is not necessary that the Evening Star is identical with the Morning Star.

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, (...) and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that Every man loves some woman is implied by, but does not imply, Some woman is loved by every man, since the latter is taken to mean the same as Some woman is loved by all men. Also, Jack knows which woman came is implied by Some woman is known by Jack to have come, but not by Jack knows that some woman came. (shrink)

Metaphysics is self-critical in a way and to an extent not to be found in any other field of study. This is an outcome of its extreme generality. Its subject-matter includes all subject-matters and hence all methodologies. Therefore metaphysics is also concerned with its own methodology. There is no more inclusive or more general study of methodology which might take upon itself the authority to criticize the methodology of metaphysics. Any such study would have to concern itself with all concepts (...) and subject-matters, and so would itself be simply metaphysics. Any general denial of metaphysics is itself a metaphysical theory, and therefore self-contradictory. (shrink)

Mathematical continuity, in the technical sense, is a precisely definable mathematical notion which refers to certain properties of numbers and number sequences. The continuity of the physical world, on the other hand, is rather different from mathematical continuity, since it is a directly experienced attribute of nature and does not require, for being understood, any mathematical theory of properties of numbers.