My new book, ‘A Wittgensteinian way with paradoxes’, out today https://rowman.com/ISBN/9780739168967, is an attempt to look at why and how philosophers, including oneself – and using the word “philosophers” in the broadest sense possible, to refer to anyone who is doing philosophy, whether or no they know it – get stuck in paradoxes, how they can be helped to get unstuck, and how, once philosophers’ paradoxes are dissolved, the actual power of paradox to help our thinking and acting and our reconciliation to the peculiarities of our life-world, can start to be unleashed. Paradoxes often indicate an a poria in our thinking, a hovering, a nonsensical desire to say things that are uncotenable. But not always. If we get clearer about when they (/we)do, then we can start to get clearer about when they don’t, or needn’t.
Let me sketch briefly here my latest thoughts (since even the book went to press, six months ago) on what the book concerns and hopes to accomplish, by focussing in on a few of the key chapters.
In Chapter 1 of the book, I offer a radically revisionist take on ‘Logicism’, the view, often wrongly ascribed to the early Wittgenstein, that arithmetic can be derived from logic. I seek to defuse Russell’s paradox, by arguing that it doesn’t have to be seen as undermining Frege’s system, provided that one takes that system in a way different from the way that Frege himself inclined to taking it. I use Frege’s own arguments against Kerry to undermine the felt-necessity of that inclination.
Consider in this context the following wonderful passage from Wittgenstein’s Remarks on the foundations of mathematics:
“Is there such a thing…as the right logical calculus, only without the contradictions?
Could it be said, e.g., that while Russell’s Theory of Types avoids the contradiction, still Russell’s calculus is not THE universal logical calculus but perhaps an artificially restricted, mutilated one? Could it be said that the pure, universal logical calculus has yet to be found? //
…The formalization of logic did not work out satisfactorily. But what was the attempt
made for at all? (What was it useful for?) Did not this need, and the idea that it must be capable of satisfaction, arise from a lack of clarity in another place?
The question “what was it useful for?” was a quite essential question. For the calculus was not invented for some practical purpose, but in order ‘to give arithmetic a foundation’. But who says that arithmetic is logic, or what has to be done with logic to make it in some sense into a substructure for arithmetic? If we had e.g. been led to attempt this by aesthetic considerations, who says that it can succeed? (Who says that this English poem can be translated into German to our satisfaction?!) (Even if it is clear that there is in some sense a translation of any English sentence into German.)”
Chapter 2 brings up to date my thoughts on the paradoxes of time-travel, explored here on an earlier occasion: http://blog.talkingphilosophy.com/?p=3239; thanks to those who commented then, for strengthening my thinking on this topic.
Chapter 3 of the book, I take on the philosophical linguistics of Noam Chomsky. After first allowing certain of Chomsky’s insights into Wittgensteinian philosophy, and his appropriate scepticism as to human science – take for instance this lovely quote from him, which I have just discovered today: “As soon as questions of will or decision or reason or choice arise, human science is at a loss.” – I then criticise Chomsky on the grounds, roughly, that he doesn’t in my view adequately see the sense in which (as argued for instance in my THE NEW WITTGENSTEIN) there cannot be any such thing as having an external point of view on language.
Towards the end of the book, having addressed and defused various ‘philosophers paradoxes’, I look towards possible and actual ways in which paradoxes can be positively beneficial, and in which their continuing need not be conceived of by philosophers as something needing rectifying or eliminating. For example, consider the (itself somewhat paradoxical) category of ‘fictitious history’. This category is crucial to understanding what the latter Wittgenstein is quite often up to. Through offering us fictitious histories, Wittgenstein frees our minds from constriction by unwitting and/or dogmatic assumptions that imprison us. He offers us alternative possibilities (as the later Gordon Baker, in particular, stressed). Now think in this connection of what Nietzsche does in a book like The genealogy of morality (the subject, alongside Wittgenstein, of chapter 10 of my book). What is it that he does (especially in the second essay of the Genealogy) but offer a potentially-fictitious history of punishment and of morality? The point isn’t whether his account is true or not; the point is that something like it might be true; and that punctures our complacency in morality as we have inherited it. This then frees us up for the amazing and beautifully-paradoxical operation that Nietzsche undertakes in the third essay of the Genealogy: destroying ‘ascetic’ morality from within.
The last lines of the book should give you a flavour of my overall purpose in it:
“I hope this book might help play some role in the search for a truer intellectual freedom. An intellectual freedom genuinely at home in our thoroughly social and embodied nature. In our lives that are so empty of what philosophers typically call ‘paradoxes’ – and yet nonetheless, sometimes, so full of paradox.”
If readers of this blog get to read the book, I would love to know what they (you) think of it.