It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...) as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text. (shrink)

Bertrand Russell’s 1906 article ‘The Theory of Implication’ contains an algebraic weak completeness proof for classical propositional logic. Russell did not present it as such. We give an exposition of the proof and investigate Russell’s view of what he was about, whether he could have appreciated the proof for what it is, and why there is no parallel of the proof in Principia Mathematica.

The principal differences between the contemporary philosophic traditions which have come to be known loosely as analytic philosophy and phenomenology are all related to the central issue of the interplay between predication and perception. Frege's critique of psychologism has led to the conviction within the analytic tradition that philosophy may best defend rationality from relativism by detaching logic and semantics from all dependence on subjective intuitions. On this interpretation, logical analysis must account for the relationship of sense to reference without (...) having recourse to a description of how we identify particulars through their perceived features. Husserl' s emphasis on the priority and objective import of perception, and on the continuity between predicative articulations and perceptual discriminations, has yielded the conviction within the phenomenological tradition that logical analysis should always be comple mented by description of pre-predicative intuitions. These methodological differences are related to broader differences in the philosophic projects of analysis and phenomenology. The two traditions have adopted markedly divergent positions in reaction to the critique of ancient and medieval philosophy initiated by Bacon, Descartes, and Hobbes at the beginning of the modern era. The analytic approach generally endorses the modern preference for calculative rationality and remains suspicious of pre-modern categories, such as formal causality and eidetic intuition. Its goal is to give an account of human intelligence that is compatible with the modern interpretation of nature as an ensemble of quantifiable entities and relations. (shrink)