Addendum on Vagueness, Bivalence, and Science

Ilkka Pättiniemi

For this week’s installment I will tie up some loose ends from my post on vagueness, as there is always more to say. 

Thing the first: bivalence and realism.
It seems clear that scientific realism requires bivalence, but does bivalence (or the demand for bivalence) imply (a demand for) realism? Simply put: no. The instrumentalist and the pragmatist will wish for bivalence in her science as much as the realist. After all, classical logic and easy (enough) mathematisability are of pragmatic value in building theories. And indeed the solution Quine (1981) and I are offering is based on (potentially mutually exclusive, more on this later) stipulations made for pragmatic purposes. This seems to go against the spirit of realism, as for the (scientific) realist, the scientific theories reflect the world, not our interests. 

Thing the second: do cut-off points converge? Is there a correct definition?
Here’s a challenge from (say) the epistemicist (like Timothy Williamson from my last installment): “It is true that we might start our enquiry by making arbitrary precisifications. But the fact that we can refine our precisifications and make progress in our enquiries shows that there indeed is a correct dividing line, a correct definition!” Gosh darnit! They got me! Or did they? Recall, that for Quine, and for me, the precisifications were made based on our interests. We wish to do geography, and therefore we state that mountains are delineated thus and so. It might turn out that our interests are better served by another delineation, and so we change our precisifications. But a seismologist might have quite different interests in delineating mountains, so she will act accordingly. And there is no (pre-empirical) reason to think that these two precisifications converge. Maybe they do, maybe they don’t. But that will not – should not – have any bearing on whether geography and seismology are sciences in good standing. The same goes for biology. Differing definitions of ‘gene’ (say as a functional hereditary unit or a piece of DNA) need not converge. They might but it is not clear that the world forced this upon us. Perhaps molecular geneticists just persuaded their opponents to take up their interests and thus their definitions. So, it does not seem at all clear that our willingness to change our precisification and to accept new, better definitions coupled with epistemic progress is enough to justify the claim that there is a correct cut-off point or definition. The burden lies squarely at the realist’s feet.  

Thus endeth the sermon.


Quine, Willard Van Orman (1981). What Price Bivalence?, in Theories and Things, Cambridge MA: Harvard University Press, 31–37.

Published by Ilkka Pättiniemi

A Helsinki based philosopher and bassist. An idiot.

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