Back

Hei-hoo! I'm back from "Sabbatical" when I renovated my new (old) appartment and blogged in Estonian at Tabernaakel. Now, back to singulars :).

First, I'll stick to the earlier conventions of + and - and drop some innovations, eg implicative context. Instead I'll introduce singulars using same symbols, i.e. angle brackets. E.g. speaking of simple terms we have [A] "Only A", (A) "Some A" and now we have also 〈A〉 "This A". Of complex terms we have [A+B] "Only A or B", [A-B] "Only A or non-B", [-A+B] "No A that is not B", [-A-B] "No A that is B", (A+B) "A that is B", (A-B) "A that is not B", (-A+B) "Non-A that is B" and (-A-B) "Non-A that is not B". Speaking of simple existence sentences we have [A] "Only A exists" (or "Everything is A"), (A) "Some A exists" (or "Something is A") and 〈A〉 "This A exists" (or "This is A").

In last message I stayed confused about treatment of singulars. Earlier I suggested that there is no problem with treating singulars like other terms, eg "Socrates is wise" as (S+W), even if this would be read as "Some Socrates is wise". This is awkward, even if we can benefit from being able to express "Only Socrates is wise" [S-W]. The awkwardness remains even if we introduce explicitly names by using quotes ('S'+W), reading it "Someone named 'Socrates' is wise". This is improvement, because we don't let name function directly as predicate any more, but it functions now indirectly the same way: "Someone of those named 'Socrates' is wise". And ['S'-W] would make explicit the flaw we might have not noticed in previous version: "Only someone of those named 'Socrates' is wise". It is not what is meant by "Socrates is wise", where we mean certain Socrates, namely the one we are speaking about (even if you don't know for sure which one I am speaking about). But now let's use specific context for this kind of reference "This Socrates is wise" (ie. the unique one we are talking about): 〈S+W〉. This context-marker has property of being auto-dual: -〈S+W〉=〈S-W〉 ie. "It is not the case, that (this) Socrates is wise"="Socrates is not wise".

It seems we are still able to refer to Socrates as the only wise one: [〈S〉-W].