--- by JLS
-------- for the GC
ANDY WAS ASKING in 'Comments to "Truly Understood"", this blog:
How are the concepts to which the uppercase words refer actually represented?
I tried to post this below under that thread, but failed, so here it goes. And thanks again for the question (which I take as not just 'rhetorical'!)
α and β is what Grice uses, sometimes. And we should follow (his) suit (How do you follow a suit? I suppose it contains the bowtie because I won't follow a bowtie-less suit).
----
In all cases, what Peacocke and Grice mean are SENSE DATA. When I posted the thing, "On understanding the past tense" for example, indeed Peacocke's point is to refute Dummett (his tutor), on things like "The Queen of England WAS bald" (Queen Elizabeth I). For Dummett this is just as nonsensical as "The present king of France is bald" because (being an intuitionist) he thinks that we have no access to the past. Like Bradley, Russell, and myself in my best moments, we think that what we SENSE is ALWAYS present.
So, the cat is on the mat -- becomes
The α is β.
Or more formally,
(ιx)αx & ((y)(yα <-> xα) -> y = x) & βx.
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If we use 'β' to represent what Lakoff would have as SHAGGY (Grice, WoW:vi -- not quoting Lakoff, of course), we have Grice using the 'belonging' symbol in set-theory,
SHAGGY means 'the set of hairy-coated things'. There need be NO intenSion involved.
So if we want to say that
The dog that Jones calls "Fido" --- symblised by "alpha"
--- The dog that Jones owns -- symbolised by "alpha '"
--- 'shaggy' symbolised by "beta"
--- 'hairy-coated' symbolised by 'beta'"
we get to see what we may be meaning.
In no case is the necessity to go for uppercase letters, as Andy confides of never having seen the point of.
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