does ¬∀ have ontological import? — Arcane Sandwich
Bunge's dichotomy looks to be much the same as that used in free logic, with conceptual existence taking the place of empty terms. I'm presuming that Bunge would suppose t=t to be true, even if t does not exist - Pegasus is Pegasus. So I'm understanding his idea as an interpretation of positive free logic. So yes we can drop the subscripts. But then "Pegasus does not exist" would be ~∃!(Pegasus); that is, ~∃x(x=Pegasus). This has the advantage of dropping the idea of treating proper names as pretend predicates - dropping parsing "Pegasus exists" as "Something pegasises". This directly gives usif I don't accept Bunge's dichotomy between conceptual existence and real existence, then there is no need for me to use subscripts... — Arcane Sandwich
And seems to me to be an improvement over Quine's idea of simply dropping proper nouns and individual constants.Bunge's approach also manages to accommodate the idea that proper nouns can be treated as individual constants. — Arcane Sandwich
It might be worth adding "... and get the same result". The same behaviours might be seen with very different interpretations - we get a rabbit stew even if "gavagai" means undetached rabbit leg.But Quine is saying that you can conceive of different meanings for the same verbal dispositions - that is the example. — Apustimelogist
Bunge's approach also manages to accommodate the idea that proper nouns can be treated as individual constants. — Arcane Sandwich
And seems to me to be an improvement over Quine's idea of simply dropping proper nouns and individual constants. — Banno
Yes, but if something is not linguistic then it does not constitute a reference of any kind, scrutable or inscrutable, no? Or rather, if we do not recognize something as a linguistic sign, then it cannot be inscrutable, for we would never say, "That non-reference is an inscrutable reference," or, "We will never figure out what that thing is referring to, namely that thing which we do not believe to be referring to anything."
In fact I want to say that in order to identify something as referential one must already have a foothold of one kind or another. Without such a foothold there is insufficient reason to posit a referential reality (i.e. an intentional sign). — Leontiskos
So "P" is much the same as "Pegasus=" in "Pesasus=x"?Px is to be read: is Pegasus. — Arcane Sandwich
Px is to be read: is Pegasus. — Arcane Sandwich
So "P" is much the same as "Pegasus=" in "Pesasus=x"? — Banno
No, because x is a free variable. — Arcane Sandwich
I parse it strictly as "Some particular x" — Arcane Sandwich
So I think the target is more various philosophical notions of reference rather than the whole ability to communicate. — Moliere
What I'd commit to is the idea that though reference is inscrutable we can still communicate. — Moliere
You don't need these extraneous interpretations for people to communicate or use words, and the idea that you can coherently assign divergent meanings is something like a reductio to the thought that verbal behavior, language and understanding is anything above the physical events responsible for word-use.
Well, in "Pesasus=x", isn't x some particular x? — Banno
Sure. And "Pegasus =" is also a predicate, not an equivalence.But I don't say "Pegasus=x", because the phrase "is Pegasus", in the case of Px, is not the "is" of identity, it is the "is" of predication. — Arcane Sandwich
But you said that these were not the same "becasue x is a free variable". I just wasn't able to follow that. Not a big point in the context. Leave it if you like. — Banno
Definition 15.33 (Free occurrences of a variable). The free occurrences of a vari-
able in a formula are defined inductively as follows:
1. φ is atomic: all variable occurrences in φ are free.
2. φ ≡¬ψ: the free variable occurrences of φ are exactly those of ψ.
3. φ ≡(ψ ∗χ): the free variable occurrences of φ are those in ψ together
with those in χ.
4. φ ≡∀x ψ: the free variable occurrences in φ are all of those in ψ except
for occurrences of x.
5. φ ≡∃x ψ: the free variable occurrences in φ are all of those in ψ except
for occurrences of x.
Definition 15.34 (Bound Variables). An occurrence of a variable in a formula φ
is bound if it is not free.
You can change that definition for your own purposes, if you like, but why? — Banno
Wouldn't that just mean that any non-constant was free, and so free variables would just be variables? That'd just be dropping the distinction between bound and free variables.it's better to define a free variable as any variable that is not identical to an individual constant. — Arcane Sandwich
Wouldn't that just mean that any non-constant was free, and so free variables would just be variables? That'd just be dropping the distinction between bound and free variables. — Banno
Definition 15.37 (Sentence). A formula φ is a sentence iff it contains no free
occurrences of variables.
Except that f(x) says nothing, while ∃(x)fx says that something has the property f. — Banno
There's a sort of synthetic operation here, in a formula like∃(x)fx. You're not saying "just one thing", you're saying two different things that only make sense when said together, but they're still two different declarations, even though neither can be declared independently of the other. — Arcane Sandwich
Unless you are saying that ∃(x)fx says there is at least one thing and one thing is f - ie, that the domain is not empty. That might make sense. — Banno
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