Jagdish Hattiangadi

I. Ian Hacking asks an intriguing question, and answers it in an interesting way. Why, he asks, does language matter to philosophy? It is a simple question. But his answer is not quite so simple, though its main feature is simple: Language matters to philosophy today for the same reason that ideas were important to philosophy in the seventeenth and eighteenth centuries. Each in its time has been the “interface” between the knower and the known. There is much truth to this answer of his, though we may note that it is somewhat incomplete: we would still like to know how ideas then and language now have come to occupy this position.

If, as it is usually understood, incommensurable theories must be compatible then one need never choose between two such theories. But if theories were incompatible and incommensurable one would have to choose between them. What if they are incompatible only outside the domain of observation? The fact that Darwin's biology can clash with Kelvin's physics (each with their respective auxiliary assumptions) regarding the age of the earth shows how commensurable theories may yet be incompatible. But it also shows that they need not be alternatives--i.e. that one may not be able to simply and satisfactorily replace the other in our world view. But standard examples of scientific revolutions consist of the replacement of one theory by another in one's world view. These alternative theories must therefore be more than merely incompatible--what do they share if not content? (I.e. they must be commensurable.)

SummaryThe clash between rationalism and humanism presupposes a radical and optimistic view of reason, with science taken as the archetype. Popper's theory of reason as critical of tradition seems to offer a new direction. But Kuhn's discovery that scientists normally are uncritical of some basic ideas makes it vacuous. An improvement upon Duhem's analysis of tests gives us a new epistemology, however where viable alternative views which are not believed nevertheless influence the organization of research. The tacit debate can be regarded as an organized escape rather than as progress towards the Truth.We can thus admit tradition in science, and maintain that it is rational, even if scientists might be agreed on some basic issues during some periods

Scientists apply Bacon’s investigative induction by first cataloguing experimental discrepancies among apparent natures of things. Induction begins by multiplying discrepancies, thus creating a puzzle with multiple clues. Solved puzzles thus give us power to produce those unusual, discrepant effects. Bacon’s experimental method, however, is not empiricist. Grasping things empirically, like receiving impressions on a wax tablet, presupposes that our senses cannot deceive us whenever we are deceived: we err in our interpretations. Empiricism thus leaves no objective discrepancies to resolve, as deception resides in our interpretation. Scientific induction, for all its success, becomes invisible to modern empiricist methodologists.

This paper addresses the problem of understanding what mathematics contributes to the exceptional success of modern mathematical physics. I urge that we give up the Kantian construal of the division between mathematics and physics, and that we ask instead how algebra helps synthetic a posteriori mathematics improve our ability to study the world. The theses suggested are: 1) Mathematical theories are about the empirical world, and are true or false just like other theories of empirical science. 2) The air of artificiality in mathematics lies exclusively in the use of algebraic method. 3) This method is constructive much like all fiction is, but this construction is for the purpose of experimental investigation of the physical world to the extent that anything in the world has objects like those in the fictional world of a particular algebra. 4) This is why algebraic techniques are successful even when the assumptions of the system are false: they may still be applicable to some things considered from some perspective. 5) The success of mathematical physics is also due to Descartes' discovery of a remarkable truth: we live in space and time which can be described as a whole. 6) Therefore, what distinguishes modern science from earlier and later philosophy is not a general method of science, but the fact that it happened to find a truth, and a particular way of studying reality which bore fruit.

Locke’s liberal democratic theory advocates toleration, to broker a peace among faiths. Secular common knowledge, including science, is used to adjudicate neutrally in disputes across all faiths. Some politicized religious groups have now begun to question the possibility of neutral arbitration, by denying any common knowledge. Secularism instead seems to be a rival to their faith. The belief in viable knowledge fracture, however, relies on a mistaken philosophy of science which allows that any general result in science is only a matter of opinion because theory is ever empirically underdetermined. True, but it may not be experimentally underdetermined. Religious politicians need to rethink their priorities, for they are losing their youth as we speak and fast giving up on a precarious peace.

The book sets an ambitious goal. It devises a new account of scientific methodology that makes it possible to explain how scientists manage, at least occasionally, to find true models of reality. The new methods may be contrasted with all those currently available that employ “coherence theories” of knowledge. Under this designation are grouped positions that can seem very different (such as those of Poincaré, Duhem, Popper, Hempel, Quine, Kuhn, and Feyerabend) but are united by the idea that the most general statements of science are merely hypotheses. They may be conjectures, opinions, conventions, posits, paradigms, or even myths. The most we can claim to know from such generalities is that they are internally consistent and coherent with empirical data. Consistency is insufficient to establish the truth of a conceptual system because many different systems, perhaps an infinite number, can be logically consistent and cohere with recorded data. Such is the well-known problem of the empirical under-determination of theories. Francis Bacon’s Skeptical Recipes for New Knowledge suggests a new methodology that solves this fundamental problem of knowledge.