Stanford - Vagueness
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What is it?
Stanford article on vagueness (less good than many of their others).
Where can it be found?
Sorensen, Roy, “Vagueness”, The Stanford Encyclopedia of Philosophy (Fall 2006 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2006/entries/vagueness/>.
Where does it fit in?
Williamson is going to use vagueness as a case study in Ch. 2 so I thought it’d be a good idea to get some background on it.
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Summary Description: - basically: a term is vague if it has borderline cases — distinction between relative (to a given means of determination) and absolute (Peirce: “intrinsically uncertain”) borderline cases — i.e. resists all attempts to find truth-value - compare with: - 1. ambiguity - (directly) having multiple meanings - 2. generality - covering several terms (e.g. ‘child’ to ‘boy’ and ‘girl’) — generality => vagueness (e.g. ‘prime number’) - precisifications of borderline cases not judged by truth-values, rather by simplicity, conservativeness, and fruitfulness - notion of truth involved in borderline cases as judgement-dependent (Wright & Shapiro) - borderline status implies a loss of warrant Philosophical Challenge (Sorites): - base: 1 day old human is a child - induction: if n day old is a child then n+1 day old is too - conclusion: 36,500 day old is a child Response: - deny induction step: — Boolos: because entails conditionals like “if 2 day old is child then 36,500 day old is a child” — but this then implies sharp threshold — epistemicists (Williamson) accept this and hold vagueness to be form of ignorance — also involves claim that much meaning is acquired passively - does classical logic apply to vague circumstances? — many-valued logic (up to that modelled on Reals between 0 and 1) — does not account for truth-value increase as a result of hedging — replacing one already overly precise tool with many, even more precise ones a bad idea? (no necessarily - series approximations) - supervaluationism (Fine, Lewis): no truth-value for borderline statements — compounds okay if same result no matter the precisification — hyperambiguity: many precise concepts with close resemblance — problem re: vague resists mixed interpretations whereas ambiguous does not — but convergence to classical logic only if interpretation is uniform — hence ~ many inference rules (contraposition, conditional, reductio) — Tarski’s disquotational truth convention in combination with the notion of truth at play here also seems to imply lack of truth-value gaps - contextualism: content of term shifts with context — in some sense then, a vague term is like an indexical — thus the conditional in the induction step is not valid — cannot have vague terms as literally indexical otherwise one would be able to stabilise reference — Raffman: context triggers gestalt shifts — Shapiro: discretion as a result of judgement-dependence — Graff: interpretation is relative to interests (pragmatic) All Vagueness Linguistic? - supervaluationism: we fill in meanings as we go along - fallacy of verbalism: attributing representational aspects to objects — link with plausibility of essentialism - mental imagery as vague, also view that language has arisen from human psychology and so language is merely an “intermediate bearer” of vagueness
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What do I think? - it’s interesting to see these sorts of ” I B E - Type” criteria being used in the context of precisification. I wonder if the connection is more than skin deep? (probably) - does denial of the induction step really imply that one must postulate some sort of sharp threshold?
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