Preface

In his commentary on Kant’s Critique of Pure Reason, Vaihinger considers the four possible views which result if one combines the epistemological distinction between rationalism and empiricism with the ontological distinction between realism and idealism. He claims that until Kant, rationalism was always connected with realism, empiricism always with idealism. But Kant discovered a new combination: The marriage of rationalism with idealism. And then Vaihinger mentions in parentheses that the fourth possible combination, empiricism with realism, has always been considered to be impossible (see H. Vaihinger, Kommentar zu Kants Kritik der reinen Vernunft, vol. I, p. 52). It is this “impossible” view which I shall defend. That is why I called this book “The Fourth Way.”

Empiricism means different things to different people. I have in mind the view that our knowledge of the external world rests entirely on perception, and that knowledge of our own minds is solely based on introspection. I hold that there is no special faculty of the mind, no Platonic “contemplation,” no Cartesian “understanding,” no Husserlian “eidetic intuition,” by means of which we know external objects. My version of empiricism may be called “radical,” for it insists, not only that we know the familiar objects around us by perception, but also that we know numbers and other abstract entities by means of perception. I hold that the truths of arithmetic ultimately rest just as much on perception as the truths of physics.

It is in regard to this contention that my view differs most profoundly from other theories of knowledge. While many contemporary philosophers accept empiricism in regard to the “natural sciences,” hardly anyone agrees with me that logic, set theory, and arithmetic are a matter of empirical knowledge. But empiricism cannot stand on one leg. An empiricism that claims exception for logic, set theory, and arithmetic is no empiricism at all. Arithmetic, in particular, is the touchstone for any serious attempt to defend empiricism. I shall therefore have to discuss arithmetic knowledge in great detail.

Realism, too, has many meanings. I mean the view that there are such perceptual objects as apples, that these things consist of smaller things like molecules, and that these in turn consist of even smaller objects like elementary particles (or of whatever else the physicist may discover). None of these things is mental. Nor do they depend for their existence or nature on there being minds. But my realism, too, is of a radical sort, for I also hold that there are sets and numbers, and that these things as well do not depend for their existence or nature on minds. Just as an empiricism in regard to science alone can be no more than a paltry evasion of the rationalist’s challenge, so realism only in regard to ordinary perceptual objects can be nothing but a worthless response to the idealist’s taunt. The realist’s work is only half done after he has refuted Berkeley. That an apple is not a collection of ideas is fairly obvious. “That number is entirely the creature of the mind,” however, seems to be an unshakable conviction of even the most realistic philosophers.

But even if we rid ourselves of this idealistic bias, even if we accept numbers and sets as part of the furniture of the world, there remains the formidable task of placing these entities somewhere in the hierarchy of categories. Granted that numbers are nonmental, to what category do they belong? Are they sets? Or are they perhaps properties of properties? This task, I believe, has been so futile up to now because the proper category for numbers was simply not a part of standard ontologies. Philosophers have for generations tried in vain to squeeze numbers into one of the familiar and traditional categories. Until very recently, there was very little to choose from: Numbers had to be either individual things or else properties of individual things. For an idealist, they could only be either intuitions or concepts. A third possibility finally appeared with the reluctant acceptance of the category of set. But this acceptance posed a new challenge: How to reconcile the existence of sets with empiricism.

Vaihinger, as I said, claims that Kant discovered a new combination: the compatibility of rationalism with idealism. I do not think highly either of Kant’s rationalism or of his idealism. But Kant discovered—and proudly insisted on—one crucial truth: arithmetic is necessary and yet synthetic. With this discovery, he challenged all empiricists as well as all rationalists. Empiricists have to explain how arithmetic can possibly be necessary; rationalists, how it can possibly be synthetic. This challenge, I believe, has not been met.

I would like to thank my colleague Romane Clark, who read part of the manuscript and made many helpful suggestions.