Wednesday, January 30, 2008

No secret handshakes, II (BR's version)

ψ(ιx(φx)) ≔ ∃x(∀y(φy ↔ y = x) ∧ ψx).

(What means that? That's Russell's iota notation for definite descriptions (sort of the basis for any artificial language as well). It also means that whenever you assert something, you make an existence claim, and it means you usually are talking scheisse--any predications (such as the King of France is bald, or not bald) about non-existent entities are false)

So, an assertive sentence turns out to entail something like this in predicate form:

--There is an x such that x is Bubba the Sweatshop Boss (∃x(Bx))

--For every x that is Bubba the Sweatshop Boss and every y that is Bubba the Sweatshop Boss, x equals y (i.e. there is at most one Bubba the Sweatshop Boss, hopefully) (∀x(Bx → ∀y(By → y=x))) . That indicates uniqueness, a point which the greeks, classical mathematicians and even Frege had not quite grasped.

---Bubba the Sweatshop Boss is an Oppressor. (∀x(Bx → Ox)) (or, the Sweatshops of Bubba are Oppressive--An Oppressor would run an oppressive business, presumably)

So, one merely verifies that a Sweatshop X operated by Bubba does exist, and proves that X is indeed Oppressive, and calls the Better Bidness Bureau! QED.


J. L. Speranza said...

Good, J. And glad we are reviving this at the Grice club -- I should start a thread on Russell at that club. I liked your example, and you are right about the Greeks never having a clear idea about uniqueness. I may copy and paste from Grice in WoW on this -- he spends like 3 pages and a half on uniqueness ("Presupposition and conversational implicature" essay).

J said...

Thx. I probably should tie into themes from "On Denoting", but this is a start.

I am trying to locate some Gricean stuff--not much online (tho' the classic Grice/Strawson essay contra Quine on Two Dogmas is), so may have to purchase a text or something.

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