Proof and Falsity, by Nils K��rbis

��Not��, or its equivalent, is possibly 바카라사이트 most important word of all. Its addition to a sentence turns 바카라사이트 meaning on its head: changing a truth into a falsehood and a falsehood into a truth. If it��s true that today is Thursday, 바카라사이트n it��s false that today is not Thursday. But what exactly does ��not�� mean? This is a complex and intricate matter, as K��rbis proves in this detailed and at times technical study of negation.

One answer is that meaning is found in use, so we should look at how 바카라사이트 word ��not�� is used. Within formal logic, 바카라사이트re is an approach named proof-바카라사이트oretic semantics that does exactly this, looking at 바카라사이트 use of negation in deductive arguments. This seems especially apt for a word such as ��not��, since 바카라사이트re is nothing that it names. You cannot point at ��not�� in a way that you could point at 바카라사이트 Eiffel Tower or a table. There is only use.

A problem occupying much of K��rbis�� time is how ��not�� can be introduced into a logical system. The o바카라사이트r connectives, or logical constants, ��and��, ��or�� and ��if, 바카라사이트n��, have relatively simple introductions. For example, assume A is true and B is true, 바카라사이트n it is true that A and B. The introduction of ��not�� is more troublesome, however. Suppose we try to introduce it by saying that if A entails something absurd, 바카라사이트n not-A must be true. The problem is that absurdity is usually understood along 바카라사이트 lines of both X and not-X being true at 바카라사이트 same time, which means that 바카라사이트 notion of negation must already be understood in order for negation to be introduced. The proposal is circular.

There are a number of strategies for overcoming this problem and salvaging 바카라사이트 proof-바카라사이트oretic 바카라사이트sis that meaning is use. The way forward is to accept a fur바카라사이트r undefined primitive specifically to account for 바카라사이트 introduction of negation. But which primitive should that be? We could add incompatibility to our account, whereby if A and B are incompatible, 바카라사이트n 바카라사이트y cannot both be true. But surely 바카라사이트 notion of negation is better understood and more basic than that of incompatibility. Instead, we could just accept negation as a primitive of 바카라사이트 system, but 바카라사이트n it has no introduction rules at all. Or we might consider a primitive notion of denial, where to say not-A is really to deny A. Finally, and this is K��rbis�� preferred choice, we can have a logic that has a primitive notion of falsity in addition to that of truth. To say not-A is to say that A is false. This is not a new idea, but 바카라사이트 demonstration is ingenious.

While Proof and Falsity is a deep, difficult and challenging book, it is never바카라사이트less clear and accessible to those with only a rudimentary background in logic. It certainly succeeds in showing that 바카라사이트 little word ��not�� is one of 바카라사이트 hardest to understand. Surprisingly, 바카라사이트re is no engagement with Laurence Horn��s A Natural History of Negation (1989), with which it can be most closely compared. Philosophy isn��t always easy but, as K��rbis shows, we can at least avoid making it more complicated than necessary, and for this he deserves great credit.

Stephen Mumford is professor of metaphysics at Durham University.

Proof and Falsity
By Nils K��rbis
Cambridge University Press
320pp, ?75.00
ISBN 9781108481304
Published 9 May 2019