The point is that anyone who takes an interest in the Sorites paradox is going to do so not because life calls for a theory of vagueness but for reasons that are completely internal to a certain way of proceeding in the practice of philosophy. Despite its ancient history, however, the reasons people worry about the Sorites are not as deeply entrenched as philosophy students these days may be led to believe. It may surprise those who find the Sorites and other problems and paradoxes of vagueness unavoidable to learn that we find no discussions of these issues throughout most of the history of Western philosophy, from Aristotle until the early twentieth century. (I will not speculate about the reasons for this absence but will point out only that it indicates that the problem of vagueness did not exercise humankind for at least two of it’s 2.5 millennia existence.)
Williamson’s agenda in his Mars paper renders unsurprising the revelation that what revivified the problem was the development of predicate logic, which allows you to cast the following argument in formally valid terms (and in various forms of those terms):Premise: One grain of sand does not a heap make.
Premise: If x grains of sand do not a heap make, then x + 1
grains do not a heap make.
Conclusion: Therefore, 100,000 grains of sand do not a heap make.The conclusion here seems obviously false. But where does the argument go wrong? The first premise seems indubitable. But if we reject the second premise, then we are committed to the implausible claim that there is some precise x such that x – 1 is not a heap but x, x + 1, x + 2...x + n are. A nonphilosopher might find this problem to be of a certain intellectual interest. But for a contemporary philosopher of language, it constitutes a threat. The reason is that the contemporary philosopher of language is interested in coming up with a formal theory—that is, one that works with predicates with precise extensions—that explains how natural languages do what they do. Because there are lots and lots of vague predicates in language, the Sorites looms everywhere. So if we can’t solve the Sorites, then the theorizing enterprise appears to be threatened.
The early logicians—Bertrand Russell in particular—did not feel this threat because they had more modest aspirations than do contemporary philosophers of language. Frege and Russell had no interest in generating a formal semantic theory of natural language. Their goal was to use logic to develop an ideal language. In his 1923 paper “Vagueness,” Russell says,In an accurate language, meaning would be a one-one relation; no word would have two meanings, and no two words would have the same meaning. In actual languages, as we have seen, meaning is one-many. (It happens often that two words have the same meaning, but this is easily avoided, and can be assumed not to happen without injuring the argument.) That is to say, there is not only one object that a word means, and not only one possible fact that will verify a proposition. The fact that meaning is a one-many relation is the precise statement of the fact that all language is more or less vague.
For Frege and Russell, then, the Sorites problem was a nonissue. Of course (thought they) expressions of natural language are vague. But if you aspire to use logic to come up with a general theory of natural language, then the Sorites will loom large for you.
This brief discussion of the Sorites suggests that for contemporary philosophers of language the interest in the vagueness problem is a function of a deeper interest in the project of using formal logic to generate a general theory of natural language (and not a function, that means, of various particular real-world interests in the history of Mars, the age of consent, hirsuteness, and so on). But now the impatient person that Williamson has in mind has reason to ask why he or she ought to find this project interesting. Nancy Bauer (2015) "What is to Be Done With Austin?" in How to do Things With Pornography, pp. 111-112.
The quoted passage is the end of chapter 6 of Bauer's lucid, adult, and all-round excellent book, which has a surprising amount of meta-philosophical meat. I know it's par for the course in feminist writings, but I did not expect it in a book with 'pornography' in its title (my bad).
In order to avoid confusion, Bauer does not deny that in "real-life" vagueness is often very important. What she denies is that a generic treatment of the sort that Williamson advocates will be salient in "real-life." Williamson here stands in for those who pursue philosophy as a theoretical, scientistic enterprise--those that "attempt to describe and explain phenomena systematically in internally consistent way that mandates or predicts what should will happen in relevant future cases." (106) And Bauer takes on Williamson's exemplary question whether "Mars always [was] either dry or not dry?" (108)
In his paper, Williamson calls this the 'original question.' And indeed Williamson treats it as a proto-philosophical question, and he stipulates that "a philosophical account of vagueness that did not tell us how to answer the original question would thereby be incomplete." And he later informs us that people "under the influence of the later Wittgenstein" are his targets. So, it's not wholly surprising that Bauer (who might be said to be shaped by later Wittgenstein in some sense) responds.
But it is worth noting that nothing Bauer says turns on (I am still quoting Williamson) "a premature and slightly facile pessimism" about the possibility of a formal semantics as such. Bauer might well grant, for the sake of argument, that a complete formal semantics of natural language is possible and worth developing. Her point, if I understand it, is two-fold: (i) drawing on Austin, she argues that such a formal semantics always leaves something out in the manner of language use (and while this is partially captured by pragmatics it is not wholly so captured). And (ii) the Williamson justification of formal semantics on offer is blatantly inadequate: that we really don't need to formal semantics to answer the original question. For, according to Williamson in order to answer that original question we must develop logical or metalogical theories (or, to use Williamson again, "complex, technical, metarepresentational theories").
In my view Bauer is right to criticize Williamson's claim that formal semantics is necessary to answer the original question. And she is also right to criticize his "contempt" for those that disagree with him. (108) He does not make a good faith effort to meet the concerns of those influenced by later Wittgenstein (note that this does not involve me--I have always been unmoved!) And I think a lot of folk who admire him for good reasons tend to offer equally bad arguments in the vicinity of this area (treating metaphilosophical critics of Williamson as if they are continental philosophers). And she is right to criticize the idea that somehow philosophy could be justified when it can offer formal semantics as a gift or exemplar to non-philosophers. On Bauer's views cases of vagueness are resolved in "real life" not by generic theoretical improvements, but are "invariably specific" (109) and often relatively arbitrary (110); thinking "about vagueness in general gets us nowhere." (109) However, I don't think Bauer needs these particular claims in this extreme form (not to mention that she is helping herself to "real life" without much argument). She could easily concede without undermining her argument that in some scientific or technical areas, the formal semantics of vague predicates may be very useful or could with minor adjustments be tailor-made to be very useful. (These areas may not count as sufficiently 'real-life' for her.)
Now, I have to admit I was a bit surprised by her claim that the Sorites paradox was (ahh) a dormant philosophical puzzle for very long stretches of philosophical history. In her excellent entry in the Stanford Encyclopedia of Philosophy, Diana Raffman places the revival of interest slightly earlier than Bauer does: "the paradox attracted little subsequent interest until the late 19th century. Marxist philosophers in the neo-Hegelian tradition, like Plekhanov (1908 [1937: 114]), cited the paradox as evidence of the failure of “customary” logic and the utility of the ‘logic of contradiction’." Even so, Raffman, too, notes the dormancy.
But it does not follow that phenomena that instantiate a Sorites paradox are not common in the history of philosophy. This is, in fact, in accord with Bauer's insight that problems of vagueness are not treated as generic problems of vagueness or a general Sorites paradox. So, I have argued in print that some elements in Hume's description of the missing shade of blue actually turn on a Sorites style paradox, and one can find other places in the history of philosophy and science where Sorites paradoxes are lurking but without them being treated as a general paradox. In my own case, I learned about the structure of Sorites paradox from Poincare (writing in late 19th century) before I ever took a class in metaphysics or sementics.
More important, one can agree with Bauer that something goes badly off the rails in Williamson's defense, while still granting (as I would, but she not) that (i) Martian history buffs could be made to see and find interesting that the original question is an instantiation of a general philosophical problem (108); (ii) that formal semantics is worth doing for intrinsic philosophical reasons; and (iii) that not all generic theories are equally bad. That is to say, while I think Bauer is right to think that certain kind of philosophical theories are being oversold with poor justification, it is not true that generic theories don't have a fruitful place in bringing philosophy into contact with all kinds of areas of special application.
As regular readers know (recall here; here; here), I am a fan of a species of generic theories, synthetic philosophy, by which I mean a style of philosophy that brings together insights, knowledge, and arguments from the special sciences with the aim to offer a coherent account of complex systems and connect these to a wider culture, policy, or other philosophical projects (or both). Now the generic theories of synthetic philosophy (I have used as examples game theory, information theory, Darwinianism, actor-network theory, etc. ) are developed within and in conversation with special sciences and need not be topic neutral in a general way. Yet, these generic theories are not just useful in the special sciences, but often can be made action guiding in non-trivial ways. In fact, given Bauer's feminist desire to transform the world (xi, 11 (etc.), she should not wish to throw out such generic theories. But I have gone on long enough, TBC.
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