Here's the formal argument from the first pages. — Banno

$(1)\,(x)(y) [(x=y) \supset (Fx \supset Fy]$

Seems it would be worthwhile going over some of the "oddball symbology".

(x) is just "for all x".

(x=y) says that x and y are the same thing; they are co-referential. If you need more information, check out this Stanford Introduction to Logic page.

The hook is just material implication.

The F is capitalised, as opposed to a propositional variable, f. I take this as marking it as available for broader substations, like the substitution of (2) into (1) that gives (3)... yep, hope you noticed that. Kripke took out the F and replaced it with ☐(x=x), and with ☐(x=y), since they are the same thing...

(4) derives from of (3) by removing the ☐(x=x), since it is always true, since it is a logical law.

……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? — Banno

It is now, after the discovery of it. That water boils at 100C is known a priori only by those after having immediate experience, re: those that test for it, or mediate experience, re: those that learn of the test for it. It’s irrelevant that water always had a specific boiling point, as long as no one knew what it was.

“…. Mathematics and physics are the two theoretical sciences which have to determine their objects à priori. The former is purely à priori, the latter is partially so, but is also dependent on other sources of cognition….”

With respect to the theoretical science of the boiling point of water, the aspect partially a priori, to “determine their objects a priori” is to think how to find out the boiling point of water, to ask oneself, when does water boil, how do I find out, and herein “dependent on other sources of cognition” refers to the observation, hence the phenomenon, that water does in fact behave in a certain way given certain conditions. Somebody, somewhere sometime saw water boiling and wondered how hot it had to be to act like that, all a priori, even if under empirical conditions.

As I mentioned, this is one of the things in Kripke I took exception to, in that he said the astronomers that figured out P and H were “one and the same” couldn’t have done it by means of “a priori ratiocination”, when in fact, it was the only way they could have done it. No different than finding out water boils at 100C.

Seems it would be worthwhile going over some of the "oddball symbology". — Banno

Cool. Interesting. Thanks.
————

Question: why drop out the part known to be true?

Say there is a law. To remove something that makes it a law, is it legitimate to still call it a law?

If there is a certain undeniable truth already given, and it is deleted….dropped out…..how does that not go to great length to falsify the product of whatever formally contained it?

The whole thing begins with…..for any two objects x and y, if x has these properties and y has these same properties, then x is the same as y. Sounds rather obvious, at first, and just the words themselves are sufficient to call it a true statement, insofar as these words, taken by themselves, don’t contradict themselves.

This must be why Kripke dropped out the F, insofar as it is impossible for every property F to belong to both x and y simultaneously such that x = y. If it were possible, then x =x is false, but it is already an established necessary truth that x = x and cannot be both true and false.

I think one needs be no more than a low-level logician to understand that dropping out both a logical necessary truth and an empirical impossibility, are both required in order to sustain the ideas behind the article.

So….ok, two questions….can the article still have any meaning if those two dropped-out conditions are left in?
————

quote="Banno;767932"]Those diamonds and boxes and other oddball symbology serve us well in avoiding such misunderstandings.[/quote]

….or creating them?

Thanks for the clarification for is and =‘s.

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. — Metaphysician Undercover

Well, one consequence is that, that x=y may be discovered empirically - examples are given - but has necessary implications. While this may seem obvious now, it is contrary to both Kant and Quine, fir different reasons. The notion that an empirical fact implies a necessary truth is one of the novelties of this paper. — Banno

The next step, then, says that there is nothing contained in the conception of P that does not belong to the conception of H, therefore, P and H are the same thing, or, that P is H is a necessarily true statement. We don’t need the experience those conceptions represent, only that all of them are thought to co-exist equally in one object. — Mww

Kripke wrote: "To state finally what I think, as opposed to what seems to be the case, or what others think, I think that in both cases, the case of names and the case of the theoretical identifications, the identity statements are necessary and not contingent."

If "Hesperus" is "Phosphorus", then "Hesperus" is of necessity "Phosphorus", but Hesperus is not necessarily Phosphorus

I will use the practice that "Hesperus" is a name in language and either refers to or is described by its properties such as "bright", "visible", "ringless". Hesperus is an object in the world and is its set of properties bright, visible, ringless.

My belief is that Hesperus has no existence over and above its set of properties, in that, if all the properties were removed, then there would be no object, as argued by FH Bradley.

There are two identity statements to consider, "Hesperus is Phosphorus" and Hesperus is Phosphorus.

Analytic propositions
The statement "bachelors are unmarried" is an analytic proposition that is true solely by virtue of its meaning. As it is true by definition, its truth is a priori. As Kripke argues that this lectern made of wood is necessarily made of wood, a bachelor is necessarily unmarried. The meaning of words is determined by social institutions, and are codified either in dictionaries or similar or in daily use, as Wittgenstein proposed.

Empirical Observations
John and Mary observe an object first in position A and then later in position B. John believes the body moves smoothly from A to B. Mary believes the body moves in a series of jumps from A to B. It is empirically impossible to determine who is correct, as we can only infer what happens between A and B, from Hume's constant conjunction.

Axioms
If John is in the majority opinion within his society, the social institutions may codify the concept that well-behaved objects move smoothly between two points as an axiom, as the axiom of "spatio-temporal continuity". Axioms are regarded as being established, accepted or self-evidently true, as with Newton's Laws of Motion. However, it is in the nature of axioms that the axiom of "spatio-temporal continuity" may or may not be true, in the sense of corresponding with facts in the world.

In fact, if an object was observed to jump through space-time, by definition it wouldn't be a "well-behaved object". As the axiom of spatio-temporal continuity is true independent of any empirical observation, it is an analytic proposition, its truth is a priori, and well-behaved objects by definition necessarily pass smoothly through space-time.

"Phosphorus" is necessarily "Hesperus"
Phosphorus and Hesperus are objects. Phosphorus is observed as an object in the east, is named "Phosphorus". and Hesperus as an object in the west, is named "Hesperus". From the axiom of spatio-temporal continuity, and under the assumption that "Phosphorus" and "Hesperus" are well-behaved objects, moving smoothly from the east to the west, it may be concluded that "Phosphorus" and "Hesperus" is the same object, the same Planet. Note that "Phosphorus" exists in language, not in the world. For convenience this single object may be named "Venus"

If when observing the sky, what was thought to be "Hesperus" was observed not to be moving smoothly, then by definition it couldn't be "Hesperus" but must be another object.

Two possible identity statements
As the identity statement "Hesperus" is "Phosphorus is based on the assumption that both "Hesperus" and "Phosphorus" are well-behaved objects, and as well-behaved objects necessarily follow the axiom of spatio-temporal continuity, then the identity statement "Hesperus is Phosphorus" is necessarily true.

However, as it is impossible to empirically determine that when an object in the world has moved from one position to another that there have been no jumps, it cannot be proved that Hesperus is Phosphorus, meaning that the identity statement Hesperus is Phosphorus is not necessarily true.

I suppose I must stop now. All the very best to everyone in the New Year, whichever part of the world you are in. :smile:

Seems to me that much of this is addressed in the next part of the article. Leet's muddle on, but make sure we come back to this.

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

I searched through the essay and could not find any examples which deal with just what criteria we could possibly have for deciding whether it should be thought of as the same lectern in counterfactual scenarios. The way I see it, since nothing is separable for everything else, the identity of an object is its entire history up the present and none of that could be changed without losing its identity.

why drop out the part known to be true? — Mww

Because implication is transitive:
If A⊃[B⊃C] and B is a theorem, or true, then A⊃C.

In
$(3)\,(x)(y) (x=y) \supset [ \Box (x=x) \supset \Box [(x=y)]$

(x)(y) (x=y) is A, ☐(x=x) is B, and ☐(x=y) is C. Hence

$\\ (4)\,(x)(y) [(x=y) \supset \Box [(x=y)]$

I find your puzzlement, puzzling.

My belief is that Hesperus has no existence over and above its set of properties, in that, if all the properties were removed, then there would be no object, as argued by FH Bradley. — RussellA

Good for you.

Kripke argues otherwise, and his argument is widely accepted, and this is a thread about his argument.

That is, the thread is about what Kripke believes, and not so much about what you believe.

I think that article indirectly addresses your argument, and finds it wanting. In particular, I think one might wield what I've called the weaponised question. That is, what is it that the sentence quoted above is about? It seems that it is about Hesperus. If one asks what it is that you are suggesting we remove the properties from, the answer is "Hesperus", and this is so even if the properties are removed.

That is, in Kripke's terms "Hesperus" is a rigid designator, while it's various properties may not be.

I searched through the essay and could not find any examples which deal with just what criteria we could possibly have for deciding whether it should be thought of as the same lectern in counterfactual scenarios. — Janus

That's a different point, and I agree, and I note that the lectern example is I think not repeated in Naming and Necessity.

We have the contingent "This lectern may have been in the other room", and we have the necessary "This lectern may not have been made of ice", and the question is, why is one contingent yet the other necessary?

I take the answer to be that the demonstrative "This lectern" is such that the lectern could have been in the other room but could not have been made of ice; that "this lectern" has the sense "This wooden lectern", giving us "This wooden lectern could have been in the other room" and "This wooden lectern could not have been made of ice".

But I wonder if the lack of clarity here is what led Kripke to drop the example.

The way I see it, since nothing is separable for everything else, the identity of an object is its entire history up the present and none of that could be changed without losing its identity. — Janus

Then I take it you are agreeing with Quine that modal utterances have no sense.

Fair enough. That kinda ends the discussion. Thanks for you contribution.

SO to the bottom of p. 181, where Kripke asks why folk suppose that we can't have a posteriori necessities, and offers two pictures that folk may be holding to that prevent their seeing the light...

The first is that folk mix two different ways of talking. This is the De re/de dicto stuff again, but as I said previously, putting it in those terms often doesn't seem to help. It's clear our words may have had different meanings, that for example we might have had "5" where 4 is, and found ourselves writing "2+2=5" and saying that it is true. That's certainly possible.

But as Kripke says, this is not what we want. Rather, given how we do indeed use the words, 2+2 could not be equal to 5. "We want to use the statement in our way and see if it could have been false".

Something along these lines might be what troubles when he suggests

That water boils at 100C is known a priori only by those after having immediate experience, — Mww

If we set "100℃" as another term for "the boiling point of water", if they equal the very same thing in the way 2+2 equals 4, then in any possible world, the boiling point of water would be 100℃. And since that's our definition, then Mww would be correct that the boiling point of water is, a priori, that is, from the nature of the very terms used, 100℃.

Then what Mww says would be understandable.

But what we did was to take the temperature at which water boils, and call that temperature 100℃. We set 100℃ as a rigid designation, so that it refers to the very same temperature, regardless of what temperature water boils at. We fix the referent of 100℃ by setting it to the temperature at which we find water boils; but once this is done, we can use it to refer to that very temperature even if water were to boil at a different temperature. We go past the boiling of the water and fix 100℃ to the temperature.

Similarly, we might fix "Tully" as the Roman orator who denounced Cataline, but once this is done, we might discover that Tully did not in fact denounce Cataline. In such a circumstance, we would be making a discovery about Tully. Once we fix the reference of "Tully" using "the Roman orator who denounced Cataline", we can refer to Tully without making use of that description.

But once we have this reference fixed, we then use the name 'Cicero' rigidly to designate the man who in fact we have identified by his authorship of these works. We do not use it to designate whoever would have written these works in place of Cicero, if someone else wrote them. — pp.183-4

Cheers, I'm surprised to find myself agreeing with Quine, but then I've never read much of his work. Perhaps I too hastily formed a bad opinion of it...

I'm surprised to find myself agreeing with Quine... — Janus

As am I, but then I think Kripke showed his view to be misguided. Seems to me that counterfactual sentences make sense. After all, you might not have agreed with Quine...

After all, you might not have agreed with Quine... — Banno

I'd say that if I do indeed agree with him right now, then it is not the case that I might not have agreed with him right now, because that would mean comprehensively changing the way I presently think. On the other hand I might not have agreed with him in the past, or I might not agree with him in the future, but neither of those possible scenarios would be counterfactuals, as far as I can tell.

...that would mean comprehensively changing the way I presently think. — Janus

And that's not something we might consider?

:wink:

And that's not something we might consider? — Banno

Well it is, but then it could not happen right now, as I currently think just the way I do; it would take time. But then as I say, if I later changed my standpoint, it would not be a counterfactual scenario, but a change in the factual.

But this seems to raise the question as to whether there are various possibilities as to how my life will unfold, and of course, from the epistemological and the logical points of view, there are. But are there really?

That, I would say, is unknowable; which seems to mean we are not entitled to an opinion on that question. I also think we have to acknowledge that the granting of alternative future possibilities is only relative to the limited context of what we know and what we can imagine.

We go past the boiling of the water and fix 100℃ to the temperature. — Banno

This is where Platonic idealism misleads us into nonsense. Temperature scales relate numbers to the physical world. That there are numerous different temperature scales based in different principles for making such a relationship demonstrates that this is the case. The idea that we "fix 100℃ to the temperature" implies that there is something independent from the scale and its relationship to the physical world, an independent "ideal" called "the temperature", which "100℃" actually refers to.

Clearly this is false because there is nothing independent of physical things designated to be 100℃ that we could point at and say this is what "100℃" refers to. So to say that there is a thing called "a temperature" which "100℃" refers to is just a creative fiction, produced to facilitate communication.

This is the reason why Platonic idealism misleads us so easily, because it is so effective at facilitating communication. For example, instead of having to demonstrate what the numeral "2" means in each instance of usage, we assume an independent ideal, "a number" as a named thing which that numeral refers to, and this makes the use of "2" much easier.

The assumption of real ideals, as real objects which exist independently of the context of actual usage of the symbols, presents an ontological problem. This problem truly exposes itself when we try to determine what type of existence these supposedly named things, ideals, actually have. That problem was well demonstrated by Plato.

If we set "100℃" as another term for "the boiling point of water", if they equal the very same thing in the way 2+2 equals 4, then in any possible world, the boiling point of water would be 100℃. And since that's our definition, then Mww would be correct that the boiling point of water is, a priori, that is, from the nature of the very terms used, 100℃. — Banno

So, this issue is not as simple as you make it out to be. As discussed in another thread, the boiling point of water is equally a function of pressure, as it is temperature. Therefore we cannot correctly claim that "in any possible world, the boiling point of water would be 100℃". This mode of speaking is just facilitated by your Platonic idealism, which assumes an independent object called "the temperature". This makes temperature an object rather than a property, which is a category mistake.

Then we still have the further ontological mistake made by Kripke, which is the proposition that an object designated by a "rigid designator" could be the same object in a multitude of possible worlds, despite having different properties. Kripke's work is just riddled with ontological mistakes, one after the other, and it is highly questionable as to what his intent actually was..

I find your puzzlement, puzzling. — Banno

My fault; I’m not up on the subtleties.

I mean….what’s the point in having identity, giving it absolute power as an irreducible necessity, then say it can have substitutivity attributable to it? Makes no friggin’ sense to me. From which follows, of course, x = y becomes a metaphysical abomination.

...giving it absolute power as an irreducible necessity, — Mww

It's just a way of talking.

Thou shalt have no other gods before me?

This is where Platonic idealism misleads us into nonsense. — Metaphysician Undercover

Well, that made me laugh.

The reference of names is rarely or almost never fixed by means of description. — p. 185

And then

So, let us suppose that at least one half of prevailing views about naming is true, that the reference is fixed by descriptions. Even were that true, the name would not be synonymous with the description. but would be used to name an object which we pick out by the contingent fact that it satisfies a certain description. And so, even though we can imagine a case where the man who wrote these works would not have been the man who denounced Cataline, we should not say that that would be a case in which Cicero would not have been Tully. We should say that it is a case in which Cicero did not write these works, but rather that Cassius did. And the identity of Cicero and Tuly still holds.

This, very much contra Russell, Searle, and many, many others.

A description may be used to pick out some individual in order to give it a name. But thereafter, the name can be, and Kripke claims, is, used to pick out that individual without using the description. And again the argument is the weaponised question: What is the sentence about? Suppose that we use "the man who denounced Cataline" to pick out Tully. It make sense to then ask, who is the sentence "Tully might not have denounced Cataline" about? And it is clear that it is about Tully. That is, "Tully" refers to Tully, even in the counterfactual case that Tully did not denounce Cataline.

This was one of a number of arguments from around that period that pretty much put an end to the description theory of proper names.

Just to be clear, the idea of the "weaponised question" is my way of presenting Kripke's argument. It fits with my view that what is often most important in a philosopher's writings are the tools they provide that have a more general use. That is, perhaps the most valuable lesson in this article is to learn to ask critically, "What is the sentence about?"

A note on the use of "individual". Individuals are those things to which you might give a proper name. In particular, "individual" is not limited to persons.

It's the things to which, in a formal system, the individual variables a,b,c... refer.

I’m not even going to ask how you did that.

Must suck to have to stop and teach the preliminaries before you can get to what you want to talk about.

A description may be used to pick out some individual in order to give it a name. But thereafter, the name can be, and Kripke claims, is, used to pick out that individual without using the description. — Banno

This would only work for those who already know the individual being referred to by name. This requires context, which is established by description; so it seems rigid designation is always underpinned by implicit description, even in cases where no explicit description is required. The only way around that would be to have just one unique name for every individual, but that would be enormously cumbersome.

What happened to @Shawn?

Must suck to have to stop and teach the preliminaries before you can get to what you want to talk about. — Mww

Would it help you if I preceded every post with "I might be wrong, but..."?

For me, the all are.

This would only work for those who already know the individual being referred to by name. This requires context, which is established by description; so it seems rigid designation is always underpinned by implicit description, even in cases where no explicit description is required. — Janus

That was my Honours thesis. It's wrong.

Trouble is, as I think Donellan pointed out, we can use proper names correctly even when we do not have a suitable definite description.

Hence there need be no implied definite description. Proper names just refer.

So, you're saying that I can use a name correctly even if I don't know who or what it refers to?

I'm still here. Nothing really to add at the moment.

I'm more interested in consistency across possible worlds, as people get hung up on this.

Banno So, you're saying that I can use a name correctly even if I don't know who or what it refers to? — Janus

...we can use proper names correctly even when we do not have a suitable definite description. — Banno

Well, that made me laugh. — Banno

Maybe it's off topic for this thread, but how would you say that "100℃" refers to a thing called "the temperature" if not by invoking Platonism?

A description may be used to pick out some individual in order to give it a name. But thereafter, the name can be, and Kripke claims, is, used to pick out that individual without using the description. — Banno

In your interpretation of Kripke does the thing referred to with "100℃" qualify as an individual? If not, then how does "100℃" become a rigid designator for you, naming the very same thing in all possible worlds?

The problem obviously, is that "100℃" is a description, and only by Platonist ontology does this descriptive term refer to an object. Likewise, only by Platonist ontology can we say that the descriptive term "2" refers to a thing called a number.