Introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols.
Dialogues Concerning Natural Numbers advances a thesis made several years ago by Rudolph Carnap: The sentence «There are numbers» is a trivial truth if construed as an assertion from within mathematics. As such it cannot possibly divide philosophers of mathematics. It lacks sense if construed as an assertion outside of mathematics. Unfortunately, the truth and importance of Carnap's thesis has not been fully appreciated by philosophers of mathematics. The six dialogues that compose Dialogues Concerning Natural Numbers were formed to bring attention and praise to Carnap's theory.
Introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols.
This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one central debate in the philosophy of mathematics. Non-realism, i.e., the view supported by Hugly and Sayward in their monograph, is an original position distinct from the widely known realism and anti-realism. Non-realism is characterized by the rejection of a central assumption shared by many realists and anti-realists, i.e., the assumption that mathematical statements purport to refer to objects. The defense of their main argument for the thesis that arithmetic lacks ontology brings the authors to discuss also the controversial contrast between pure and empirical arithmetical discourse. Colin Cheyne, Sanford Shieh, and Jean Paul Van Bendegem, each coming from a different perspective, test the genuine originality of non-realism and raise objections to it. Novel interpretations of well-known arguments, e.g., the indispensability argument, and historical views, e.g. Frege, are interwoven with the development of the authors’ account. The discussion of the often neglected views of Wittgenstein and Prior provide an interesting and much needed contribution to the current debate in the philosophy of mathematics.
Dialogues Concerning Natural Numbers advances a thesis made several years ago by Rudolph Carnap: The sentence «There are numbers» is a trivial truth if construed as an assertion from within mathematics. As such it cannot possibly divide philosophers of mathematics. It lacks sense if construed as an assertion outside of mathematics. Unfortunately, the truth and importance of Carnap's thesis has not been fully appreciated by philosophers of mathematics. The six dialogues that compose Dialogues Concerning Natural Numbers were formed to bring attention and praise to Carnap's theory.
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