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“Science constantly furnishes us with astonishing ideas about the nature of reality. Physics tells us that there may be an infinite number of universes, of which ours is just one, and that perhaps two particles in no physical contact with one another can somehow influence each other’s properties. From evolutionary biology we learn that birds are the only living descendents of dinosaurs. Geologists reveal that, as a result of the current trajectory of the Earth’s tectonic plates, Australia will eventually collide with Alaska. Contemporary educated people have grown used to the idea that, at least where the causal structure of the world uninfluenced by human agency is concerned, our stock of“commonsense” assumptions and principles is systematically unreliable as a guide to the facts. Our everyday scale of perceptions, along both its temporal and its spatial dimensions, is simply too pinched and unrepresentative to be trusted as a direct window onto wider truths, at least about physics, geology, astronomy, microbiology, and so on.”
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“[U]nderdetermination problems can't be made to go away by logic alone. They can only be mitigated by having plenty of data. Pragmatically, one should stop worrying that one's model is underdetermined at the point where it would take superogatory levels of ingenuity to find a competing one.”
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“Scientists, famously, use a lot of mathematics, at least in many disciplines (including both cognitive science and economics). Much of this is simply statistics, and derives from the importance of exact measurement. But that is not the whole story. Natural languages and the distinctions they draw are evolutionary products shaped by the interaction of cultural and genetic selection. They therefore encode, in deeply embedded and mutually reinforcing levels, distinctions important to folk theories—that is, the nonscientific social-cognitive structures that organize relationships important to special human purposes. Mathematical language is quite different, and this reflects differences between the nature of mathematical and of practical reasoning. Mathematical reasoning begins from sets of rigorously fixed procedural concepts, and these fixed points then have absolute authority, relative to special purposes in application, over what can and cannot be stated in the language. If we suspect there may be some particular structural fact but cannot figure out how to express it mathematically, this does not show that there is no such fact; but it implies that we must do some more work, either logical or empirical or both, before we can say that we are quite sure just what the putative structural fact is that we are trying to claim.”
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