Equality1 gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift I assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = (...) b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names ‘a’ and ‘b’ designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign ‘a’ is distinguished from the sign ‘b’ only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true.. (shrink)

Chomsky proposes a reformulation of the theory of transformational generative grammar that takes recent developments in the descriptive analysis of particular ...

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

Thoughts and other mental states are defined by their role in a functional system. Since it is easier to determine when we have knowledge than when reasoning has occurred, Gilbert Harman attempts to answer the latter question by seeing what assumptions about reasoning would best account for when we have knowledge and when not. He describes induction as inference to the best explanation, or more precisely as a modification of beliefs that seeks to minimize change and maximize explanatory coherence. Originally (...) published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

It has been maintained that we need not tolerate such entities as pains, events, tasks, and obligations. They are indeed not required in connection with sentences like ‘Jones has a pain’, ‘the event of the sun’s rising occurred at eight’, ‘Jones performed at eight the task of lifting a stone’, or ‘Jones has the obligation to give Smith a horse’, which can be paraphrased without reference to the entities in question—for instance, in the case of the second example, as ‘the (...) sun rose at eight’. (shrink)

In this paper I argue that human pattern recognition can be simulated by automata. In particular, I show that gestalt recognition and recognition of family resemblances are within the capabilities of sufficiently complex Turing machines. The argument rests on elementary facts of automata and computability theory which are used to explicate our preanalytic, informal concepts concerning gestalt patterns and recognition. The central idea is that of a machine which "knows" its own structure. Although the paper thus aims to support mechanism, (...) especially as a framework hypothesis for perception, it contains suggestions for philosophy of science and philosophy of language as well. Some of these suggestions are sketched in the final section. (shrink)

The purpose of this book is to develop a terminological structure in which private perceptions can be discussed publicly without bringing into existence the usual unnecessary philosophical problems of confused usage of language. chisholm displays an appraisive, quasi-ethical use of language, whereby he claims that a thing has some particular sensible property is to have adequate evidence that it actually does have that property. (staff).

Classic text considersgeneral theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.