×

zbMATH — the first resource for mathematics

The taming of the true. (English) Zbl 0929.03001
Oxford: Clarendon Press. xvii, 465 p. (1997).
One common sense platitude about truth regards truth as a basically wild thing which can never be confined within human knowledge. Such a common sense realism about truth is expressible as: The truths are what they are independently of whether or not human beings ever do or can know them. Neil Tennant “tames the True” by showing that nothing worth wanting as true in mathematics or natural science ranges beyond the limits of human knowledge. Any thing worthy of the name true in mathematics or natural science is in principle knowable. Tennant’s position is called semantic anti-realism because it denies that truths “are really there” independently of human knowledge. However, terms such as ‘anti-realism’ and ‘irrealism’ can evoke suspicion of anti-rational, ill-argued positions parading under the banner of postmodernism. So it is best to avoid such terms in a short synoptic review. Indeed Chapters 2 and 3 of Tennant’s book make a significant contribution with their careful analyses of philosophical terms such as ‘realism’, ‘anti-realism’, and ‘irrealism’. Those who follow discussions about realism in mathematics initiated by Michael Dummett and extended by Crispin Wright will profit from these two chapters. Those who work in these areas need to study all of Tennant’s book for it moves the arguments and issues significantly forward.
The book offers a comprehensive philosophy of mathematics and natural science whose orientation the author expresses with “Logical empiricism was almost right!” Note a few of the important moves in the construction of a viable logical empiricism for the 21st century. Against Quine, Kripke et al. he argues that meanings are determinate and that peoples’ grasp of meaning is manifested by being able to specify what it is like to be in a position to assert a claim. With meaning so interpreted bivalence must be abandoned. Without bivalence he needs to abandon classical logic and so we find a case for a relevant intuitionistic logic as the correct logic for mathematics and natural science. He can reconstruct an analytic/synthetic distinction and effectively set aside A. Church’s old argument that all verification criteria of cognitive meaningfulness will be too broad. Many more important theses are analyzed and evaluated.
It is a demanding book which can be understood only by those with knowledge and appreciation of mathematics. The author draws on sophisticated mathematics for many of his examples. Fortunately, the introductory chapter guides readers through the details with a chapter by chapter synopsis and statement of author’s stand on crucial issues. Working through Tennant’s book in a reading group or advanced course on the philosophy of mathematics or natural science would be the way to gain most from it.

MSC:
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
PDF BibTeX XML Cite