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Thursday, January 17, 2019

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This is a good post. Yes, sticking together the subject expression 'a' (Frege: object word) and the predicate expression 'F' (Frege: concept word) gives us our proposition.

But this detracts from the main problem, which is that in Aristotelian two-term logic we can always distinguish between wide and narrow scope negation. Abelard calls the former 'extinctive', because it extinguishes everything affirmed by the affirmative proposition, the latter 'separative', because it preserves the existence of the subject-thing (re permananente), but denies the predicate. Thus

Separative: 'Socrates is not white', 'some man is not white'.
Extinctive: 'It is not the case that Socrates is white', 'no man is white'.

The extinctive of the singular proposition includes the case where there is no subject-thing, i.e. no such thing as Socrates.

But for Fregean logic, while the Aristotelian distinction applies to quantified propositions, it collapses in the case of singular propositions.

Fa v ~Fa -> Ex x = a

My problem is that I see no difference between wide and narrow negation with respect to singular propositions.

>>My problem is that I see no difference between wide and narrow negation with respect to singular propositions.

Then necessarily Socrates exists. Then necessarily God exists - which brings us back to the ontological argument which prompted this discussion.

If wide scope negation includes every possibility whatever in which the affirmative is false, and if none of those possibilities includes the state where name fails to have a bearer, then necessarily there is a bearer.

The copula is the third element of all propositions. There is a subject, a predicate, and a mediating copula. It is the difference between "the red ball" and "the ball is red." As pointed out, the majority of languages don't have a be verb.
WIth communication in actu, "the essential office of the copula is to express a relation of a general term or terms [predicate] to the universe [Subject]. The universe must be well known and mutually known […] between speaker and hearer, between the [speaker’s] mind as appealing to its own further consideration and the [hearer’s] mind as so appealed to, or there can be no communication, or “common ground,” at all. The universe is, thus, not a mere concept, but is the most real of experiences” (CP 3.621

Ostrich, I can't make any sense of your claim about Fregean logic.

Fx v ~Fx means different things depending on context because x can be
1. A name, in which case the named thing is assumed to exist,
2. An existentially bound variable, in which case x is explicitly claimed to exist,
3. A universally bound variable, in which case x may not exist,
4. Unbound, in which case the clause does not even represent a proposition.

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