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Critical rationalism is at one with classical empiricism in denying the possibility of synthetic apriori truths, or non-analytic truths knowable independently of experience. A consistent proposition either holds in all possible worlds, in which case it is knowable apriori but analytic, or it holds in some possible worlds but not in others, in which case it is non-analytic and not knowable apriori. But what about pure mathematics? Was Kant wrong to hold that it consists of synthetic apriori propositions? In his 1978 Imre Lakatos distinguished those extra-scientific systems that are deductively organized into "Euclidean" ones where all the axioms are known to be true, and "quasi-empirical" ones where the axioms are not all known to be true and the axiom-set has to be judged by its consequences, as with scientific theories. His thesis was that all serious mathematics is quasi-empirical. In support of this he pointed out that, despite the endeavours of Frege, Russell, Hilbert, and others to "Euclideanize" mathematics, virtually everyone who had worked in this area-pre-eminently Russell himself, but also Bernays, Church, Curry, Godel, Kalmar, Mostowski, Quine, Rosser, von Neumann, and Weyl-had come to recognize, with great reluctance in some cases, the quasiempirical nature of mathematics. That Euclidean geometry itself, with its problematic Parallel Postulate, is not "Euclidean" was shown by the invention of non-Euclidean geometries in the nineteenth century.
What sort of history does critical rationalism expect science to have? The short answer is: a turbulent one. That a theory has been riding high, achieving a wide range of predictive successes, does not mean that it is verified; it is open to daring spirits to construct rivals to it. A rival theory should match or, better, exceed the present theory in explanatory and predictive power; it may proceed from radically different assumptions; if it does, these may lead to predictive implications that diverge, if only slightly, from those of the present theory; these will point the way to crucial experiments from which both old and new theory will be at risk. Karl Popper was famously impressed by the risk of refutation which Einstein ran when he put forward his General Theory of Relativity (henceforth GTR) in competition with Newtonian Mechanics (henceforth NM). The latter had been superbly corroborated by a great variety of experimental observations, and had seemed to Kant, and continued to seem to many others, a grand system of verified truth. But GTR had predictive implications that diverged from those of NM. There were not many such divergences, and they were all small; but in some cases, for instance with regard to the bending of light rays passing close to the sun, they were large enough to be exposed to experimental test.
There had been a rather similar relationship between NM and its predecessors. NM led to small but systematic revisions of the predictive content of Galileo's and Kepler's laws. Galileo's law had freely falling bodies near the earth's surface falling with constant acceleration. NM said that they will fall with a slightly increasing acceleration; for their acceleration varies with the gravitational force, which varies inversely with the square of the distance between the centres of gravity of the earth and the falling body, and hence increases as this distance decreases...
Call a world-view naturalistic if it abides unswervingly by the principle that "Man is a part of nature", where `Man' denotes the whole person, mind and body. Classical empiricists' levelling or eliminative views of freedom generally stayed within the bounds of naturalism. By contrast, classical rationalists' distinctive views generally strayed beyond those bounds. (We shall find this to be true of Spinoza, although "Man is a part of nature" was a main thesis of his.) So the question arises whether critical rationalism, here seen as the mettlesome successor to those once powerful but now moribund classical theories of knowledge, supports a viable view of human freedom that is at once distinctive and naturalistic. This book will offer a positive answer by unfolding such a view.
The plan of the book is as follows. In Part One a naturalistic world-view will be arrived at in the following way. In Chapter 1 the critical rationalist view of human knowledge will be presented with special reference to a recurrent feature of growth of science, a feature that defeats both classical empiricism and classical rationalism and is of decisive importance in several ways. In Chapter 2 guidelines will be laid down to regulate a critical rationalist's science-oriented world-view. Chapter 3 will take up the question of determinism. The above feature will be used as an argument for a kind of indeterminism quite distinct from chance. The above guidelines will call for the inclusion, give-or-take a few revisions, both of classical Darwinism, whose main metaphysical implications will be drawn out in Chapter 4, and of neoDarwinism, or Darwinism with its modern genetic underpinning, whose implications for `Man's Place in Nature' will be examined in Chapter 5.
By the end of Part One we will have taken a down-to-earth look, mainly from a Darwinian or neo-Darwinian viewpoint, at most of the grand metaphysical issues-God, soul, materialism, idealism and, more especially, the mind-body relation. Part Two will turn to the possibility of a distinctive view of human freedom within the naturalistic framework set out in Part One. The investigation will open with an examination of some historically significant views about freedom or autonomy, in the hope of locating mistakes to avoid and leads to follow. The thinkers to be looked into, not in chronological order, are Hobbes and Hume, Descartes, Schopenhauer and Kant, and finally Spinoza who will get a chapter to himself. Although there will be large differences, it will be from two diverging tendencies in Spinoza, to be labelled "Conquer Fortune" and "Transcend Fortune", that our Third View of human freedom will draw most. The philosophical legitimacy of the mind-body relation it presupposes will be considered in the Epilogue.