It isn't clear how Jacob Bronowski came to be delivering the Silliman lectures for 1967 at Yale University, but in doing so he delivered a marvellous and, apparently, criminally overlooked book which many of today's leading popular science writers might do well to read. Bronowski was by training an academic algebraic geometrist (I'm not sure that there is any other kind), but by inclination a polymath, working in a remarkably eclectic range of fields from operations research to biology to anthropology to poetry, and as he did so taking time to publish an acclaimed biography of William Blake and write and produce a well-received BBC anthropology series, The Ascent of Man.
The Silliman foundation at Yale is dedicated to "illustrating the presence and providence of God, as demonstrated in the natural and moral world", so it made an odd choice in selecting Bronowski, a non-religious scientist, to present its 1967 lectures, but the choice was an inspired one, for instead of banging on sanctimoniously about how only science and mathematics can bring us to a true understanding of the universe, Bronowski the polymath instead put these endeavours in their human, social and - literally - literal context.
Bronowski's view is that our sciences contantly evolve and that they are a function of our favoured modes of observation (primarily visual) and means of description (wholly linguistic - in the sense that we can only theorise what we can commit to some formal symbolic system or other). Not just pure mathematics but any science - or language, for that matter - is a closed symbolic system, and is subject to the formal limitations of such systems which have been explained by mathematicians (such as Goedel's undecidability), practical limitations, and epistemological limitations. Even ignoring the formal limitations, practically we never have anything like enough evidence to soundly make a "true" theory - that would involve all data in the universe. But curiously, even if we had this, the theory wouldn't tell us anything interesting anyway, since we'd be able to deduce all possible consequences as a matter of logic - the empirical theory wouldn't add anything, in the same way that repeatedly rolling dice won't tell you anything you couldn't work out anyway about probability theory). In a fascinating chapter entitled "knowledge as algorithm and as metaphor" Bronowski charts this inevitable trade-off between theoretical completeness and practical usefulness and makes the (quite unexpected, but undeniable) observation that the very very incompleteness of a theory is what gives it its power.
Curiously, Bronowski speaks in terms of thorough reductionism - he says "I believe that the world is totally connected: that is to say, that there are no events anywhere in the universe that are not tied to every other event in the universe" but in contrast to writers like Dawkins reaches a surprisingly pragmatist conclusion: since it is not just practically but *conceptually* impossible to gather all data in the universe (which is what you would need to truthfully explain any single one of these events) we should resign ourselves to an imperfect solution which we must always remember is contingent and subject to improvement or change. This argument, like Quine's as to the dogmas of empiricism, is arrived at from a purely traditional, analytic approach, and is relatively immune to charges of woolly postmodernism. But in every other way it resonates far more closely with anti-essentialists like Richard Rorty, Thomas Kuhn and Paul Feyerabend than it does with the latter day Dawkinses.
The final chapter strays off brief into political and moral matters, and suffers because of it: Bronowski makes an unconvincing attempt to rebut Hume's statement of the naturalistic fallacy that you can't convert an 'is' to an 'ought', and ends up saying (and immediately regretting) things like "once you know that there are two sexes, then certain behaviour becomes pointless". My guess is he wasn't talking about fishing. Leaving aside the quaint value-judgments this seems to imply, it also seems to have abandoned the idea, forcefully argued in the first five lectures, that these "truths" we know are contingent anyway and that behaviour which seems ridiculous from one perspective might have a perfectly sensible utility described from another: there's no priority of perspective, after all.
Nonetheless, these final comments aren't anything like enough to detract from the quality of this overall book, which I recommend warmly to all inquiring minds.