Mathematically, Truths have been said to be analytic. Leibniz tried to prove this in a way criticized by frege. The author states: "it is the purpose of this note to exhibit the full force of frege's criticism." frege also attempted to prove the same thing, But concludes the author, In his attempt, Has not "found universal acceptance among mathematical logicians." he finds the value in frege's analysis to be the fact of his attempt at proof and the need for it. (...) (staff). (shrink)

This text unites the logical and philosophical aspects of set theory in a manner intelligible both to mathematicians without training in formal logic and to logicians without a mathematical background. It combines an elementary level of treatment with the highest possible degree of logical rigor and precision. Starting with an explanation of all the basic logical terms and related operations, the text progresses through a stage-by-stage elaboration that proves the fundamental theorems of finite sets. It focuses on the Bernays theory (...) of finite classes and finite sets, exploring the system's basis and development, including Stage I and Stage II theorems, the theory of finite ordinals, and the theory of finite classes and finite sets. This volume represents an excellent text for undergraduates studying intermediate or advanced logic as well as a fine reference for professional mathematicians. (shrink)

The argument of this paper rests on the distinction between two types of what are, loosely speaking, logical claims: A general (speaker-independent) claim that some favoured principle of inference is both truth-preserving, and consistent with certain others. A claim by a particular speaker that he/she has reasonable deductive grounds for concluding that some particular statement is true. The first is a matter of pure logic—a question of what (allegedly) follows from what. The second is a matter of epistemic logic—a question (...) of whether someone has, or more generally, whether there are, reasonable deductive grounds for concluding that something is the case. I shall argue that this distinction has a crucial bearing on the disagreement between classical logicians and non-classical logicians, which is essentially a disagreement about inferential behaviour. The argument is laid out in a manner designed to maximise the chances of any errors being detected. The paper concludes with some considerations of the relevance of relevant logic to the psychologist investigating inference behaviour. (shrink)