The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism: that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable'. Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us (...) understand the difficulties of the problems which we try to solve. This is how we become better acquainted with our problem, and able to propose more mature solutions: the very refutation of a theory - that is, of a tentative solution to our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows, even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason here for despair of reason. And since we can never know for certain, the can be no authority here for any claim to authority, for conceit over our knowledge, or for smugness. The essays and lectures of which this book is composed apply this thesis to many topics, ranging from problems of the philosophy and history of the physical and social sciences to historical and political problems. (shrink)

Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw (...) upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject. (shrink)

A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They should abandon the relation and (...) replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)

I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

Popper formulates and explains his non-justificationist theory of knowledge. Science--empirical science--aims at true explanatory theories, yet it can never prove, finally establish, or justify any of its theories as true, not even if it is in fact a true theory. Science must continue to question and criticize all its theories, even those which happen to be true.

The paper offers a new analysis of the difficulties involved in the construction of a general and substantive correspondence theory of truth and delineates a solution to these difficulties in the form of a new methodology. The central argument is inspired by Kant, and the proposed methodology is explained and justified both in general philosophical terms and by reference to a particular variant of Tarski's theory. The paper begins with general considerations on truth and correspondence and concludes with a brief (...) outlook on the "family" of theories of truth generated by the new methodology. (shrink)

This paper argues for a conditional claim concerning a famous argument—developed by Church in elucidation of some remarks by Frege to the effect that the bedeutung of a sentence is the sentence’s truth-value—the Frege–Gödel–Church argument, or FGC for short. The point we make is this :if, and just to the extent that, Arthur Smullyan’s argument against Quine's use of FGC is sound, then essentially the same rejoinder disposes also of Davidson's use of FGC against ‘correspondence’ theories of truth. We thus (...) dispute a contention by Professor Davidson that it is coherent to accept that Smullyan’s rejoinder takes away the force of Quine’s version of FGC, while still consistently using FGC to establish that if true sentences (or utterances) correspond to anything, they all correspond to the same thing. We show that the differences between the cases discussed by Smullyan and Davidson’s version of FGC on which Davidson relies for his contention are irrelevant to the point under dispute. (shrink)