Really? Bemused, not amused. That is, puzzled, confused. Is that arrogance?

The bit about "I think" being ambiguous.

You know you don't have enough electricity for them.

I quite agree. I'm somewhat bemused that he is being taken seriously.

The F-word has little use, as can bee seen in this thread. But Trump does fit Paxton's list.

That'll do for now.

There is no such thing as a “Public Weal” — NOS4A2

Well, not any more, over where you are.

Fair.

Note that Banno's whole logical horizon is bound up with the bare particulars of predicate logic, so I'm not sure it is possible to easily convey an alternative semantics to someone who who has never been exposed to an alternative paradigm. — Leontiskos

More about me. Cool.

Cool. I take the pub Test to imply that you can't suggest anything that you can't explain in two sentences to a drunk.

Ok. I thought you had earlier expressed a preference for common sense. Happy to move on.

Quine's thesis is not merely skeptical, that we "cannot be certain." It's that there is no reference going on. That's a big difference. — Count Timothy von Icarus

Well, I don't agree. Rather, for Quine, reference does work, but holistically, not in individual cases.

But in any case, we can be quite certain. Said in a room where there is but one rabbit, the English phrase "the rabbit in this room," refers to the one rabbit. If someone intends to refer to a rake instead, they have misspoken (hence, the distinction of intended reference/intentions is important). Reference can be ambiguous and indeterminate, and it can be more or less so. — Count Timothy von Icarus

I doubt Quine would disagree. The context is so limited that it is relatively easy to see the whole. Of course, "certain" here is about confidence, a psychological rather than a logical state.

I think qualia cause more problems than they solve.

Does that make sense? — Arcane Sandwich

Well, yes, but I don't think it the best way that this stuff could be said. When I say that Truman exists because someone is Truman, I'm not refering to Truman's form, but to Truman. It's easier to work with individuals.

How does your idea fit with what in Australia is called the "pub test"? The common sense comparison you made elsewhere? Isn't "Truman exists" about Truman, rather than the-form-of-Truman?

If you want to talk about nothing, I'll not object. But I'll probably not join you, either.

Cheers. For my part I think I have a better understanding of extensionality as a result of this conversation, so thanks for your help, too.

I find that counter-intuitive. The flat piece of clay that I'm looking at is clearly not a human-shaped statue, so how could it still be Athena? — Arcane Sandwich

Well, then ~(Athena = Piece).

I see your solution as rejecting this, since for you there is no individual Athena or Piece, but only descriptions of them - predicates. You seem to be going back to the solution suggested by Russell and Quine. How that would work with modality would remain to be seen.

Let's leave it for now.

I never made the promise that my proposed solution actually works. It might be nonsense. I'm aware of that possibility. — Arcane Sandwich

Sure. Hopefully you see my objections as they are intended, as helping you think through the consequences of your idea. I'm enjoying this.

If you want to talk about empty domains, go ahead.

I guess I'm not seeing the problem you want to solve, or perhaps i think it was solved by Kripke.

The reasons that Quine had for dropping individual constants and proper names were pretty much smashed by Possible World Semantics, along with the description theory of proper names.

but only one of them survived: Piece — Arcane Sandwich

But since Athena = Piece, Athena survived, too.

See how you have to drop extensionality? That is, you can't maintain that Athena = Piece and still say only one of them survived.

Is it a necessary presumption? — Arcane Sandwich

Well, if not then A statement like ∀xP(x) would trivially be true, because there are no x to contradict it. And ¬∃x P(x) would be equivalent to ∀x ¬P(x). So you can do a sort of first order logic with empty sets, which is more or less what free logic is.

Doesn't matter, for this is a point in which I'm willing to part ways with Bunge. — Arcane Sandwich

Ok. It might be a path to madness, but on your head be it.

Athena can't survive flattening. — Arcane Sandwich

Then aren't you dealing with non-extensional contexts? For my money, the answer to "what was flattened?" is "Athena" as much as "Piece", since Athena = Piece. One can drop that, but at the cost of even more "alien language".

For what could be more obvious then that we do refer to things with our words and mean things by them? — Count Timothy von Icarus

Sure we do. When you try to understand what it is that someone is referring to in using a name, how confident can you be that you have it right? Or, a better question, how confident do you need to be in order to get on with the conversation?

Ok. That the domain is not empty is a presumption for first order logic anyway, (a point that I suspect Leon has not appreciated). And I'm confident that Bunge's domain was not empty.

Seems to me the answer to the SEP article you pointed to was that

If Athena has different properties from Piece, then Athena ≠ Piece.

was wrong. The very same thing can have different properties. Kinda the point of modality.

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

Not following that. 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.

Except that f(x) says nothing, while ∃(x)fx says that something has the property f.

Definition 15.37 (Sentence). A formula φ is a sentence iff it contains no free
occurrences of variables.

So if we drop the distinction between free and bound variables, we no longer have any sentences. Or any formulae is a sentence.

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.


I gather its a work in progress, so no need to reply until you have it worked out.

Hmm.

From Open Logic, 15.8:

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?

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

Sure. And "Pegasus =" is also a predicate, not an equivalence.

So we have two ways of parsing "x is Pegasus". As an equivalence, x=p, which is a two-place prediction "=(pegasus, x)"; or as a single-placed predication, "=pegasus(x)".

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.

What I said should be read as a general critique of some forms of phenomenological method. In so far as Rödl is dependent on such a method his argument doesn't hold unless one is willing to insist that Pat is wrong in her account of her own metal life. Which is what Rödl appears to be insisting on in the section referred to by .

:up:

Syntax as pattern, semantics as what we do with the pattern?

Well, in "Pesasus=x", isn't x some particular x? And a free variable? So why isn't "P" much the same as "Pegasus=" in "Pegasus=x"

No, because x is a free variable. — Arcane Sandwich

I parse it strictly as "Some particular x" — Arcane Sandwich

I'm not sure how to reconcile these.

OK. I'm not seeing a reason for something so complex, but you might be able to make it work.

Px is to be read: is Pegasus. — Arcane Sandwich

So "P" is much the same as "Pegasus=" in "Pesasus=x"?

Yep. It's the simple observation that even if we disagree, we can often get on with the doing.

But Quine is saying that you can conceive of different meanings for the same verbal dispositions - that is the example. — Apustimelogist

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.

does ¬∀ have ontological import? — Arcane Sandwich

Well, yes. It hadn't occurred to me that folk might think otherwise. Ux(fx) is just fa ^ fb ^ fc... for every item in the domain. And ∃x(fx) is just fa v fb v fc...

There's a presumption that we are not dealing with an empty domain. I don't see that as a problem.


A seperate issue. That ∃!t is defined as ∃(x)(t=x) is a result of the need to maintain extensionality. The SEP article explains how. And extensionality is just the idea that we can swap one name for another that refers to the same thing, presumably becasue it is the thing we are talking about and not the name.

To say that ∃!t is to say that there is at least one thing in the Domain D - let's call that "x" - which is the very same as t. Which is to say that t exists.

We could move to non-extensional free logics, but I think we'd be overthinking it. And we would need to rework what it would mean to be consistent in such a logic; and tracking the semantics would be difficult. But go ahead, if you think it would help.

if 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

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 us

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.

Bunge seems to have been anticipating free logic.

If it is all syntax, what is semantics? And what of intent? There'd be a lot to fill out in explaining behaviour without making use of intent. Even if it is just a shorthand, that might make it useful enough to keep.

Why do people think a unique determination is a reasonable expectation? Quine talks about the consequences, not so much causes, of failure to perceive the indeterminacy. But it seems reasonable to blame this failure on the success of language in talking about real, physical relations. Its unreasonable effectiveness, if you will. — bongo fury

Interesting observation. So it is that becasue the word "gavagai" is so effective that folk have developed something like and expectation that it has a fixed referent?

I don't think you understood my post. It was about how Tobi's article pointed out that the capitalists might back Trump only so far as he is profitable. If he is unpredictable or if his policies are otherwise not conducive to profit, they will not back him.

'The word Fascism has now no meaning except in so far as it signifies "something not desirable"...' — Tom Storm

And yet it is worth a glance at Paxton's definition.

You find SEP unreliable? — Leontiskos

Not SEP, no.

See PM. Set it out, if it makes sense for you.

Forum Tips and Tricks - How to Quote

:up:

I'll leave you to it. I've found it best not to try to try to teach you logic.