INTRODUCTION Before Kant almost every philosopher subscribed to the view that truth is some kind of correspondence between ideas and 'what is the case'. ...

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logicalnotions considered we suggest that the "most natural" reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.

Controversies are boiling these days among distinguished men over true and false ideas. This is an issue of great importance for recognizing truth—an issue on which Descartes himself is not altogether satisfactory. So I want to explain briefly what I think can be established about the distinctions and criteria that relate to ideas and knowledge. [Here and in..

IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

Diese Schrift gehört zu den wichtigen Dokumenten der Naturphilosophie von Leibniz und seiner Zeit und stellt das einschlägige Dokument für die Synthese der Lehre von den einfachen Substanzen und derjenigen von den lebendigen Kräften dar.

Descartes’s metaphysics posits a sharp distinction between two types of non-finitude, or unlimitedness: whereas God alone is infinite, numbers, space, and time are indefinite. The distinction has proven difficult to interpret in a way that abides by the textual evidence and conserves the theoretical roles that the distinction plays in Descartes’s philosophy—in particular, the important role it plays in the causal proof for God’s existence in the Meditations. After formulating the interpretive task, I criticize extant interpretations of the distinction. I (...) then propose an alternative at whose core is the idea that whereas the indefinite is a structural, iterative notion, designating the absence of an upper bound, the infinite is an ontic notion, signifying being in general, or what is, without qualification. (shrink)

This thought-provoking classic investigates how the Renaissance spirit fundamentally questioned and undermined medieval thought. Of value to students of literature, political theory, history of religious and Reformation thought, and the history of science.

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the “most natural” reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.