18 research outputs found
aristotle's demonstrative logic
Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogisti
Foundations: Essays in Philosophy, Logic, Mathematics and Economics By F. P. Ramsey Edited by D. H. Mellor London and Henley: Routledge and Kegan Paul, 1978, viii + 287 pp., £9.50
A. N. Prior. Existence in Leśniewski and in Russell. Formal systems and recursive functions, Proceedings of the Eighth Logic Colloquium, Oxford, July 1963, edited by J. N. Crossley and M. A. E. Dummett, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1965, pp. 149–155.
The scientific world-perspective and other essays, 1931–1963, by Kazimierz Ajdukiewicz. Edited and with an introduction by Jerzy Giedymin. Synthese library, vol. 108. D. Reidel Publishing Company, Dordrecht and Boston1978, LIII + 378 pp. - Jerzy Giedymin. Editor's preface. Pp. IX–XII. - Jerzy Giedymin. Ajdukiewicz's life and personality. Pp. XIII–XVI. - Jerzy Giedymin. Radical conventionalism, its background and evolution: Poincaré, LeRoy, Ajdukiewicz. Pp. XIX–LIII. - Kazimierz Ajdukiewicz. On the meaning of expressions. Pp. 1–34. English translation by Jerzy Giedymin of XXXVIII 536(8). - Kazimierz Ajdukiewicz. Language and meaning. Pp. 35–66. English translation by John Wilkinson of 2259. - Kazimierz Ajdukiewicz. The world-picture and the conceptual apparatus. Pp. 67–89. English translation by John Wilkinson of XXXVIII 537(4). - Kazimierz Ajdukiewicz. On the applicability of pure logic to philosophical problems. Pp. 90–94. English translation by Jerzy Giedymin of XXXVIII 536(13). - Kazimierz Ajdukiewicz. On the problem of universals. Pp. 95–110. English translation by Jerzy Giedymin of XXXVIII 536(12). - Kazimierz Ajdukiewicz. The scientific world-perspective. Pp. 111–117. English translation by Wilfrid Sellars of XXXVIII 537(5). (Reprinted from Readings in philosophical analysis
Reviews - Janina Kotarbińska. Pojęcie znaku (The concept of sign). Polish, with Russian and English summaries. Studia logica, vol. 6 (1957), pp. 57–143.
Plural quantifiers: a modal interpretation
One of the standard views on plural quantification is that its use commits one to the existence of abstract objects-sets. On this view claims like 'some logicians admire only each other' involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates-substitutional and set-theoretic-only the latter can provide the language of plurals with the desired expressive power (given that the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability