By Irving M. Copi
This reissue, first released in 1971, presents a quick historic account of the speculation of Logical varieties; and describes the issues that gave upward push to it, its quite a few assorted formulations (Simple and Ramified), the problems hooked up with each one, and the criticisms which have been directed opposed to it. Professor Copi seeks to make the topic obtainable to the non-specialist and but offer a sufficiently rigorous exposition for the intense pupil to determine precisely what the speculation is and the way it really works.
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Extra info for The Theory of Logical Types
Sample text
Of course it may be urged that admitting a transfinite type is already to postulate an axiom of infinity. But if one did not put infinity into the system one way or another, one could scarcely hope to find it there. Objection 3 A frequently expressed objection to the Simple Theory of Types is that it is itself involved in contradiction. The Theory states that nothing can be said about all properties, all relations, all classes, or all functions. But to say this the Theory itself must say something about all properties, relations, classes, functions.
There are several replies, of varying degrees of persuasiveness, that can be made to this objection. After discussing the problem, Ramsey (1931, 78f) remarked: It would appear then impossible to put forward analysis except as a consequence of the Axiom of Infinity; nor do I see that this would in general be objectionable, because there would be little point in proving propositions about infinite series unless such things existed. And on the other hand the mathematics of a world with a given finite number of members is of little theoretical interest, as all its problems can be solved by a mechanical procedure.
Two words of different types can occur in inverted commas in such a way that either can replace the other, but cannot replace each other when the inverted commas are absent (Russell, 1944, 692). But one cannot characterize a language by giving an account, however detailed, of its syntax alone. A language has a semantical dimension at least as important as its syntactical one. And when the meaning relations involved in its semantical rules are formulated, it will be found that what is said formally about the linguistic structure must be stated materially about the interpretation.