1 A VAGUE CONCEPT BALDNESS Borderline Clearly bald
1. A VAGUE CONCEPT: BALDNESS Borderline (Clearly) bald “Almost bald” (Clearly) not bald
2. BORDERLINE ITEMS: CLASH OF INTUITIONS Classical logic is correct E. g. Principle of Excluded Middle – either P or not P Borderline cases are “real” and violate classical logic For a border case: neither P nor not P One solution is to deny that borderline cases are real (all persons are in reality clear-cut bald or not bald). “Borderline-ness” is just an epistemic phenomenon
3. THE SORITES ARGUMENT FOR SHARP CUT-OFFS A. Peter with zero hairs is bald B: One hair does not change the justice with which we call someone bald. Or explicitly: B 0: If Peter with zero hairs is bald, then he is bald with 1 hair AND B 1: If Peter with 1 hair is bald, then he is bald with 2 hairs AND B 2: If Peter with 2 hairs is bald, then he is bald with 3 hairs AND … B 999: If Peter with 999 hairs is bald, then he is bald with 1. 000 hairs. C. Hence: Peter with 1 Mio hairs is bald. One of the Bis must be false. This means there is a sharp cut-off! But that is counterintuitive…
4. THREE FORMS OF IGNORANCE Example Characterization I can practically know if I make the necessary epistemic effort Weak My ignorance of the number of people in this room Strong A randomly printed and destroyed word that nobody has seen A (theoretical) epistemic position exists from which I could know Deep Sharp borders for vague predicates (according to the epistemic account) Necessarily and completely unknowable
5. EPISTEMIC VIEW: T. WILLIAMSON There are sharp cut-offs ! We cannot know sharp borders because such “knowledge” were unstable This is so because a “Principle of margin for error” holds in the border area: Had the meaning of “bald” been slightly different (and it could have easily been) a contrary judgment would have resulted. But we must judge in a stable way ! Problem: we cannot belief in any sharp cut-off value, we cannot belief that there are sharp cut-offs and want to know (ideally) what draws the sharp border
6. SUBJECTIVE EXTENSIONS extension of “bald” = the set of all people to which “bald” applies. PROPOSAL: Extensions are determined by the disposition to assert (or not) of a person From this it follows that extensions are: • • subjective – Each individual has its “own extensions” adaptive and hence change over time – E. g. concept acquisition of children, accept “expertise”, etc. context-sensitive – The surroundings, mood, etc. may bias my judgment sharply bordered – “ Button test”: Do you press the “decision (assertion) button” or not when confronted with a person and the question “Is this person bald? ”
7. BORDERLINE ITEMS DO NOT VIOLATE THE “EXCLUDED MIDDLE” Principle of Excluded Middle (PEM) Three possible outcomes of a subjective judgment BALD* Actively considered and judged Determined “by elimination” NOT BALD BORDER-BALD* NOT BALD*
8. CONCLUSIONS What we have gained: • Sorites paradox solved • Conservation of classical logic • Borderline cases exist (not an epistemic illusion) • Understanding that there are sharp borders • We still ignore the exact cut-offs, but not “deeply” (“no conceptual blind-spot”) – We cannot practically map out our dispositions to assert the applicability of a vague predicate but we can conceive of a theoretical method to do so Possible objections and problems: • Truth subjectivism and relativism ? • Infallibility ? • Etc.
- Slides: 8