The first premise expressed at 180 ("given that it is not made of ice it is necessarily not made of ice") is a priori. — Metaphysician Undercover

$P \supset \Box P$

is invalid. It is certainly not as it stands a priori.

The whole point of the argument is that ☐P in the case of the lectern is known a posteriori.

Edited: See . 'In other words, if P is the statement that the lectern is not made of ice, one knows by a priori philosophical analysis, some conditional of the form "if P, then necessarily P".'

Formal logic and its various notions of ‘truth’ depends for its sense on faith in intrinsicality. — Joshs

I don't think so.

It's more as if logic were embedded in a conditional... 'if you would talk in a coherent way, then you must follow these rules..."

Check out Gillian Russell's logical pluralism. Your argument might apply to logical monism, but that's not the only possibility.

Again, my take on the Kripke article is that this is a way of applying his formal method to natural languages, a way of approaching modality that avoids many issues, allowing us to talk in a coherent fashion.

One does not have to avoid contradiction, but since folk who do not avoid contradiction can say anything, their conversation is tedious, tending towards the tendentious.

So I'd prefer to talk to those who seek coherence.

From those first few paragraphs, do we now agree that, that Hesperus is Phosphorus is an a posteriori observation?

We know post hoc and a priori, as mere inference, water under a certain set of conditions will always boil at 100C. — Mww

I know water boils at 100℃ at normal pressure, as a result of experiments done at high school and reassurance from various authorities.

I don't know it a priori, nor by mere inference.

So I'm not following you at all here.

Length is fine, but you lost me early on.

,

$(x)(y) [(x=y) \supset (Fx \supset Fy)$

is not Leibniz's Law. That'd be something like

$UF(Fx \equiv Fy) \supset (x=y)$

Not the same. I don't see that the argument (1-4) uses Leibniz's Law. (1) is the other way around, with the identify on the left of the hook.

A quick note that we need to keep clear when Kripke is talking about an identity that is established by a proper name and one that is established by a description, theory or predicate.

An identity established by a proper name is generally a rigid designator. Cicero is the very same individual in every possible world. Of course, he may not have been named Cicero, and someone else may have been named Cicero in his place, but keep in mind that these are modal facts about Cicero.

Demonstratives may act as rigid designators: this lectern may have been in the other room, but may not have been made of ice - since it is made of wood, if we suppose that it might have been made of ice, we would better say that this lectern might have been replaced by another, made of ice.

An identity established by a description is generally not a rigid designator. Hence the rejection of the description theory of proper names; a proper name is a rigid designator, hence it cannot be the very same as a definite description which is not a rigid designator.

So back to Identity, bottom of p. 180.

It's clear from the examples given that statements of the form x=y can be discovered empirically, and hence at least some are not discovered a priori.

The alternative is that, as a result of some other considerations about necessity, some may suppose that all statements of the form x=y are necessary, and hence a priori (Is this @Mww's view?); and perhaps that only a very small number of expressions actually count as proper names (here I take Kripke to be referring to Russell's theory of descriptions, and hence perhaps @RussellA's view).

Krike's key argument here is that if one separates a priori/a posteriori on the one hand, from necessary/contingent on the other, one is not obligated to even enter into such discussions (top of p.181)

He goes on to again (indirectly) make use of the weaponised question - who is the sentence about? "Tully might not have been called "Cicero'" is a sentence about Tully; "Nixon might not have written the letter" is a sentence about Nixon. If names are rigid designators, there can be no question about identities being necessary.

But it doesn't follow that the identity is a priori.

Thanks to the mods for keeping the thread on topic.

is not Leibniz's Law. — Banno

(2) is Leibniz's law: A = A.

First published Wed Jul 31, 1996; substantive revision Sun Aug 15, 2010
The Identity of Indiscernibles is a principle of analytic ontology first explicitly formulated by Wilhelm Gottfried Leibniz in his Discourse on Metaphysics, Section 9 (Loemker 1969: 308). It states that no two distinct things exactly resemble each other. This is often referred to as ‘Leibniz’s Law’ and is typically understood to mean that no two objects have exactly the same properties...

The Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y. — SEP

A=A is the Principle of Identity.

this lectern may have been in the other room, but may not have been made of ice - since it is made of wood, if we suppose that it might have been made of ice, we would better say that this lectern might have been replaced by another, made of ice. — Banno

Could it have been made of a different kind of wood? Or of the same kind of wood from a different tree? Or different planks from the same tree?

A=A is the Principle of Identity. — Banno

Oh. I thought that was Leibniz's law.

How would this case differ from the "ice" example? He chose "it is not made of ice" for it's dramatic effect and yet to minimise other commitments:

Let us just take the weaker statement that it is not made of ice. That will establish it as strongly as we need it, perhaps as dramatically. — top p.179

Ah. So can we agree, @RussellA that the argument (1-4) uses identity but not Leibniz's law?

Kripke calls (1) the law of the substitutivity of identity.

Didn't Kripke mention Leibniz's law? Although I've thought A=A was Leibniz's law since I read a book about him. Don't know how I got that confused.

Yes,

It would seem that Leibniz law and the law (1) should not only hold in the universally quantified form, but also in the form "if a = b and Fa, then Fb", wherever 'a' and 'b' stand in place of names and 'F' stands in place of a predicate expressing a genuine
property of the object: ( a = b• F a ) > F b — p. 167

I take him here to be saying that the argument (1-4) applies when a and b are proper names and F a property.

take him here to be saying that the argument (1-4) applies when a and b are proper names and F a property. — Banno

Yes, you're right.

Thanks.

At its initial inception, and the ground of all others, A = A is one of Aristotle’s three logical laws of rational thought, this particular one found in “Prior Analytics”, 2, 22, 68. Whatever Leibniz or any others did with it, follows from that.

For what it’s worth….

So the slightest variation in constitution (?), any counterfactual at all, would bot be "this lectern"?

Length is fine, but you lost me early on. — Banno

Yeah, I feel ya, bruh. When I see “∀F(Fx ↔ Fy) → x=y.” my eyes just sorta glaze over, mind goes blank, reason goes…..say what????

P⊃□PP⊃◻P

is invalid. It is certainly not a priori.

It seems you have not understood the argument, the whole point of which is that P⊃☐P in the case of the lectern is known a posteriori. — Banno

Like I explained, there are two premises stated by Kripke, #1 "given that it is not made of ice it is necessarily not made of ice", and #2, through "empirical investigation" we know it is not made of ice. From these two premises he makes his conclusion that it is known a posteriori "that it is necessary that the table not be made of ice". Premise #1 is a priori, and premise #2 is "given" through empirical observation, therefore a posterior.

#1 is stated as a premise, not as a conclusion, so whether or not it is valid is not in question. We might investigate its soundness though. It is derived from the law of identity, that a thing is what it is, and cannot not be what it is. It is an a priori principle based in intuition, and it is not meant to be a valid conclusion From this Kripke derives the necessity required for the first premise "given that it is not made of ice it is necessarily not made of ice".

And from that necessity stated in that first premise, the a priori premise, he derives the necessity of the conclusion ""that it is necessary that the table not be made of ice". His mistake is that he characterizes this as an a posteriori principle, when the necessity stated in the conclusion is derived from the a priori premise, rather than from the a posteriori premise.

It's clear from the examples given that statements of the form x=y can be discovered empirically, and hence at least some are not discovered a priori. — Banno

This is incorrect, and is the result of Kripke's mistaken conclusion that the "necessity" of identity is a posteriori. That's wrong, as described above. The necessity of such statements is derived from the law of identity, that a thing is necessarily the same as itself, and cannot be other than itself, which is a priori, and not discovered empirically. Premise #2 above, that the thing is what it is named to be (wood and not ice), is a posteriori. But there is no necessity in that premise. Therefore the necessity of statements like "x=y" cannot be accounted for by empirical discovery. Empirical discovery does not provide the required necessity, which is only provided by the a priori principle of identity.

It seems to me that the use of the word necessary is redundant between objects, in that what does "if two objects have all the same properties, they are in fact necessarily one and the same" add to "if two objects have all the same properties, they are in fact one and the same"

Necessity between an object and its properties - between a lectern and its property wood
As regards the lectern, necessity is being used between an object and its properties, where he writes "So we have to say that though we cannot know a priori whether this table was made of ice or not, given that it is not made of ice, it is necessarily not made of ice. — RussellA

Read my last two posts. That the lectern is made of wood, and not made of ice is given empirically. But the empirical observations do not provide the necessity required to say that it is necessary that the lectern is made of wood and not of ice. The necessity is derived from the a priori law of identity, which implies that it is necessary that a thing is what it is, and not something else.

So, the fact that the lectern is made of wood, and not made of ice, is supported by the empirical observations. But empirical observations do not make it necessary that the lectern is made of wood and not ice. The necessity, (that it is necessary that the lectern is wooden and not made of ice), is derived from the a priori law of identity, which states that a thing cannot be other than it is.

A = A is central to Leibniz's project, although I've dropped a lot of that in the bit bucket apparently.

So the slightest variation in constitution (?), any counterfactual at all, would bot be "this lectern"? — Janus

Well, no, since as you will have noted, he gives examples where this is not the case.

whether or not it is valid is not in question. — Metaphysician Undercover

Yeah it is.
You claimed:

The first premise expressed at 180 ("given that it is not made of ice it is necessarily not made of ice") is a priori. — Metaphysician Undercover

(my bolding)
It isn't. It is invalid, so it can't be a priori. If it is true, it is true a posteriori, as Kripke uses it.

It wasn't that that caused me to lose track, it was the bit were you appear to claim that, that water boils at 100℃ is known a priori.

I gather that you are thinking something like that 100℃ just is the boiling point of water, by definition?

I thin that's the sort of thing in the next part of the paper, so maybe tomorrow.

….some may suppose that all statements of the form x=y are necessary, and hence a priori (Is this Mww's view?) — Banno

Whole bunch of caveats before this is Mww’s view, first being, even assuming linguistic liberties in the original, no statement in itself is ever necessary in the domain of pure logic, to which the very idea of necessity solely belongs.

Second being, only x = x is necessarily true under any possible conditions, and that because the god Aristotle said so, and proved it in his way in his time.

Third, that x = x is necessarily true under any conditions because Aristotle said so, yet that truth is an a priori judgement, or cognition, is because the god Kant said so and proved it in his way in his time, as an extension of Aristotle’s law not addressed by him.

OK, so we got x = y. X is a dog, y is a mammal. It turns out it is necessarily true a dog is a mammal, even though a mammal is not necessarily a dog which an equality implies, so the formula holds in one direction but not in the other.

Staying with x = y, but this time x is a dog but y is a can of green beans. Here, it is absurd that a dog is a can of green beans. Why put rational trust in a logical construct that doesn’t hold under any conditions, which must include its own inversion? If it depends exclusively on what x and y are, such that x and y are somehow predetermined as connected to each other, how can a universal logical truth such as x = y be built on it?

And to cap it all off….that a series of square, diamond and oddball symbology will make it so, where a series of words won’t?

Way past my bedtime……

It isn't. It is invalid, so it can't be a priori. If it is true, it is true a posteriori, as Kripke uses it. — Banno

It is an a priori principle called "the law of identity". The law of identity implies that a thing is necessarily what it is, and not something else. It is used by Kripke in the first premise "If the table is not made of ice, it is necessarily not made of ice". That is an a priori principle. Whether it is true, false, valid, or invalid, is not what is at issue. What is relevant is that it is an a priori principle necessary for the conclusion produced "It is necessary that the table not be made of ice".

Notice he states "and this conclusion is known a posteriori, since one of the premises on which it is based is a posteriori". That mentioned a posteriori premise is what is derived from empirical investigation. It is stated as "The table is not made of ice". The other required premise, "if the table is not made of ice it is necessarily not made of ice", is a priori.

Therefore his claim, "this conclusion is known a posteriori" is not justified by his argument.

no statement in itself is ever necessary in the domain of pure logic, to which the very idea of necessity solely belongs. — Mww

Not even x=x?

x = x is necessarily true under any conditions — Mww

Hu?

OK, so we got x = y. X is a dog, y is a mammal. — Mww

Ah. That's a different "is". I found myself pointing this out the other day...

...folk have been using cognates of "S is F" without explaining what they are talking about. Is it that S=F (they are equal)? Or S ≡ F (they are materially equivalent)? Or just F(S) (predicating F to S)? or S∈F (S is an element of the set or class S), or none of these, or some combination, or something else? — Banno

Dogs are mammals is an example of F(S)-type "is". The "=" means that the thing on the left is the very same as the thing on the right. dog=mammal appears ill-formed.

Those diamonds and boxes and other oddball symbology serve us well in avoiding such misunderstandings.

"the law of identity"... is used by Kripke in the first premise — Metaphysician Undercover

$P \supset \Box P$
is not an instance of the law of identify.

I'll leave you to it, Meta. Not interested in playing your game.