The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Synopsis

Charles Chihara gives a thorough critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world--the universe in which we live--is just one. The striking success of possible-worlds semantics in modal logic has made this ontological doctrine attractive. Modal realists maintain that philosophers must accept the existence of possible worlds if they wish to have the benefit of using possible-worlds semantics to assess modal arguments and explain modal principles. Chihara challenges this claim, and argues instead for modality without worlds; he offers a new account of the role of interpretations or structures of the formal languages of logic.

Excerpt

This is a book about Modal Realism--roughly, the ontological doctrine that our universe (the world we live in) is just one among many possible worlds. My book will supply a detailed exposition of Modal Realism, as well as a thorough examination and evaluation of the principal grounds that have been advanced in support of it. I shall also take up some of the outstanding objections that have been levelled at the view, and I shall assess various criticisms of these objections thrown up by the defenders of Modal Realism.

This book also investigates several possible worlds semantical systems, which have been devised to study the logic of the modal operators. One reason that my investigation into Modal Realism involves a study of possible worlds semantics is this: the fact that possible worlds semantics is such an effective instrument for evaluating and validating reasoning involving the modal operators is widely regarded as a strong argument for accepting some form of Modal Realism. in this work, the cogency of such an argument will be evaluated.

Also within the scope of these investigations are areas of philosophy of mathematics. Some arguments for Modal Realism are similar to those put forward for Mathematical Realism--the ontological doctrine that there are mathematical objects. This is suggested by David Lewis when he writes:

[S]ystematic philosophy goes more easily if we may presuppose modal realism in our analysis. I take this to be a good reason to think that modal realism is true, just as the utility of set theory in mathematics is a good reason to believe that there are sets. (Lewis 1986: vii)

Utilitarian arguments of this sort will be investigated in some detail.

There are other reasons why topics in the philosophy of mathematics will be examined in this work. in a previous book (Chihara 1990), I developed a system of mathematics utilizing the notion of constructibility quantifiers--a notion that was explained in part by means of possible worlds semantics. This has led some scholars to infer that my system of mathematics presupposes the existence of possible worlds. One goal of this work is to assess the cogency of such an inference.

This book grew out of my "Perspectives in Philosophy" lectures given in March of 1991 at the University of Notre Dame. Some of the ideas in this work have found their way into lectures that I have delivered at the following: the Fifteenth International Wittgenstein Symposium held in Kirchberg am Wechsel; the University of California, Davis; the University of California . . .

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