Four-Dimensionalism to the Rescue?

Let us return to that impressive product of porcine ingenuity, Brick House.  Brick House, whose completion by the Wise Pig occurred on Friday, is composed entirely of the 10,000 Tuesday Bricks.  I grant that there is a sum, call it 'Brick Sum,' that is the classical mereological sum of the Tuesday Bricks.  Brick Sum is 'generated' -- if you care to put it that way -- by Unrestricted Composition, the classical axiom which states that "Whenever there are some things, then there exists a fusion [sum] of those things." (D. Lewis, Parts of Classes, p. 74)  I also grant that Brick Sum is unique by Uniqueness of Composition according to which "It never happens that the same things have two different fusions [sums]." (Ibid.)  But I deny Lewis' Composition as Identity.  Accordingly, Brick Sum cannot be identical to the Tuesday Bricks.   After all, it is one while they are many.

Now the question I am debating with commenter John is whether Brick House is identical to Brick Sum.  This ought not be confused with the question whether Brick House is identical to the Tuesday Bricks.  This second question has an easy negative answer inasmuch as the former is one while the latter are many.  Clearly, one thing cannot be many things.

The question, then, is whether Brick House is identical to Brick Sum.  Here is a reason to think that they are not identical.  Brick Sum exists regardless of the arrangement of its parts: they can be scattered throughout the land; they can be piled up in one place; they can be moving away from each other; they can be arranged to form a wall, or a corral, or a house, or whatever.  All of this without prejudice to the existence and the identity of Brick Sum.  Now suppose Hezbollah Wolf, a 'porcicide' bomber, enters Brick House and blows it and himself up at time t on Friday evening. At time t* later than t, Brick Sum still exists while Brick House does not.  This shows that they cannot be identical; for if they were identical, then the destruction of Brick House would be the destruction of Brick Sum. 

This argument, however, rests on an assumption, namely, that Brick Sum exists both at t and at t*.   This won't be true if Four Dimensionalism is true.  If bricks and houses are occurrents rather than continuants, if they are composed of temporal parts, then we cannot say, strictly and philosophically, that Brick Sum at t still exists at t*.  And if we cannot say this, then the above argument fails.

But all is not lost since there remains a modal consideration.  Brick House and Brick Sum both exist at time t in the actual world.  But there are plenty of possible worlds in which, at t, the latter exists but not the former.  Thus it might have been the case at t that the bricks were arranged corral-wise rather than house-wise.  So Brick Sum has a property that Brick House lacks, namely, the modal property of being such that its parts could have been arranged in non-house-wise fashion.  Therefore, by the Indiscernibility of Identicals, Brick House is not identical to Brick Sum.

So even if the historical discernibility argument fails on Four Dimensionalism, the modal discernibility argument seems to work even assuming Four Dimensionalism.

Please note that my thesis is not that Brick House is a sum that violates Uniqueness of Composition, but that Brick House is not a classical mereological sum.    If Brick House were a sum, then it would be Brick Sum.  But I have just argued that it cannot be Brick Sum.  So it cannot identified with any classical sum.  It is a whole of parts all right, but an unmereological whole.  What does that mean?  It means that it is a whole that cannot be adequately understood using only the resources of classical mereology.

 

Comments

[William]

Following on from my comment here http://maverickphilosopher.typepad.com/maverick_philosopher/2010/09/van-inwagen-on-arbitrary-undetached-parts.html?cid=6a010535ce1cf6970c0134873a03a9970c#comment-6a010535ce1cf6970c0134873a03a9970c

and reading 'Brick Sum' as meaning 'these bricks'. And assume that the house the pigs used to live in ('that house') was composed of these bricks, which are now scattered in the field. Then both of the following sentences are true.

(*) That house was composed of these bricks
(**) That house is no longer composed of these bricks.

Or in your language, Brick House was identical with BriskSum, but is no longer identical. Indeed, Brick House no longer exists. So what's the problem? Why are you assuming that "A was identical with B" implies "A is identical with B"?

(I hope this makes sense - recently I have had great difficulty in making myself intelligible. Apologies).

[William]

Actually you do give an argument here

>>They [Brick sum and Brick House] cannot be identical; for if they were identical, then the destruction of Brick House would be the destruction of Brick Sum.

But once you put that in the correct logical form, in the past tense, you get

Brick house was destroyed, Brick sum was not destroyed

which is not a contradiction, even though Brick House was identical in the past with Brick sum. For (as the medieval philosophers knew) the principle of substitution does not work for statements in the past tense. For example

Socrates was pale (yesterday morning) and Socrates was not pale (yesterday afternoon, after a nice day on the beach at Piraeus, sunbathing with Xanthippe).

[Bill Vallicella]

William,

You are not reading me with any care at all, and I suspect you don't know anything about mereology. I have made it quite clear that 'Brick Sum' is a name for a particular classical mereological sum. Therefore, 'Brick Sum' does NOT mean 'these bricks.' The latter expression is a plural referring device while 'Brick Sum' is a singular term.

How can you fail to grasp what I have so clearly explained over several posts?

[William]

>>I suspect you don't know anything about mereology

I haven't the faintest idea, correct. I was trying interpret these bizarre statements in a way that made sense in ordinary English. The point is, how is there any problem at all when we get back to the ordinary world?

(*) That house was these bricks
(**) That house is no longer these bricks.

Where's the problem? Are you saying there is a problem about the invented-by-philosophers term 'mereological sum'? Well fine. Who cares? Ordinary language can take care of itself.

[William]

>>How can you fail to grasp what I have so clearly explained over several posts?

You have not been very clear at all.

[William]

>>If bricks and houses are occurrents rather than continuants

I mean, what exactly are you talking about here?

[John]

What Bill is discussing is a very common distinction in ontology. Compare the following: objects and events. At least on the face of it, objects and events are very different kinds of thing, and belong to distinct ontological categories. Objects are continuants, because they exist at more than one time, and their persistence through time is generally considered to be a matter of ENDURING; think of them as three-dimensional objects that sort of "move" (metaphorically, of course) through time. Events, on the other hand, don't seem to be like this at all. They seem to exist only at a single time; if they do exist at more than one time, then generally speaking their persistence from one time to the next is explained by appeal to the notion of a temporal part. As such, events and occurrents are typically thought to PERDURE through time. Just as, to exist at any point in space p, it suffices for an object to have a part located at p, the idea is that for an event to exist at a time t, it suffices for that event to have a temporal part located at t.

So when Bill discusses the idea that bricks and houses might be occurrents rather than continuants, part of what he is discussing is the idea that objects, as we ordinarily think of them, might turn out to be more like events. That is, they don't ENDURE, but PERDURE, because they have temporal parts. Someone like Ted Sider, for instance, argues that objects are four-dimensional entities, having both spatial and temporal parts, that perdure through time. Sider, then, is someone who thinks of bricks and houses as occurrents rather than continuants. By contrast, someone like Peter van Inwagen holds that ordinary objects (insofar as they exist at all, on his view) are continuants; they are three-dimensional entities that last through time.

It seems unfair to accuse Bill of being unclear when he invokes a fairly straightforward distinction which is relatively common in the literature.

[John]

Apologies for posting twice, but I also wanted to discuss something else about William's post. You ask what is the trouble with asserting each of the following:

(*) That house was these bricks.
(**) That house is no longer these bricks.

The trouble is that it violates a fairly straightforward feature of logic, namely, the necessity of identity. In modal logic, I believe the following is a theorem:

(1) If a=b, then it is necessarily the case that a=b.

Temporal (or tense) logic is a kind of modal logic, and has its own variant on that theorem:

(2) If a=b, then at all times, a=b.

Some have expressed their doubts about these theorems. Andres Gallois has an entire book on (2), entitled "Occasions of Identity", and Sider spends a good portion of his "Four-Dimensionalism" discussing (and ultimately rejecting) the view. But to suggest that it's simply obvious that two things can be identical at one time, and not identical at another, betrays a lack of familiarity with the relevant literature.

[William]

>>The trouble is that it violates a fairly straightforward feature of logic

Why is it a fairly straightforward feature of logic? The fact that some fairly elementary and commonly accepted statements seem to violate this feature suggest that it is not straightforward. I accept it is an assumption of formal logic, naturally, but I wasn't thinking about formal logic.

[William]

>>Some have expressed their doubts about these theorems.

Which suggests, again, that it is not straightforward.

[John]

That the feature of logic in question is straightforward does not entail that it is uncontroversial. To be straightforward is to be clear and precise, not to be beyond reproach.

Terminology aside, are you asking me why the necessity of identity is a straightforward feature of logic? Presumably, because there is a fairly simple proof of it:

(1) a=b (Assumption for conditional proof)
(2) a=b -> (Fa -> Fb)
(3) Nec(a=a)
(4) a=b -> (Nec(a=a) -> Nec(a=b)) (Substitution Instance of (2))
(5) Nec(a=a) -> Nec(a=b) (Modus Ponens, 1&4)
(6) Nec(a=b) (Modus Ponens, 3&5)
(7) a=b -> Nec(a=b) (Conditional Proof, 1-6)

You say that you accept the necessity of identity as a matter of formal logic, but that you weren't thinking of formal logic. I gather from your remarks that you're worried about the apparent conflict between formal logic and ordinary language; since ordinary language doesn't abide by the necessity of identity, or the strictures of formal logic in general, so much the worse for logic-chopping analytic philosophers who use formal logic to understand what's going on in the world. Thus, you say, "ordinary language can take care of itself".

The trouble is that it can't. Our ordinary language commitments in any number of arenas are wildly inconsistent. Issues of material composition and constitution are just one example of the messiness of ordinary language. I would also mention the lottery paradox as a good example of a case in which our ordinary language fails to take care of itself. Part of the reason Quine's criterion of ontological commitment required that our best theory of the world be regimented in the language of first-order logic is that ordinary language is just too ambiguous to be of any help in understanding what the world is like.

Even if you're more optimistic about ordinary language, you say that you accept the necessity of identity as a matter of formal logic, but that you were only thinking of ordinary language. What then is the relationship between formal logic and ordinary language? It would seem, on your view, that there's at best a tenuous connection between the two. It's not at all clear how you can have two distinct sets of commitments, one as a matter of formal logic, and the other as a matter of ordinary language. You must think that the following two statements, one in formal logic, the other in ordinary language, are consistent:

(8) a=b -> Nec(a=b).
(9) An object a is contingently identical to another object b.

The conjunction of (8) and (9) looks like a contradiction to me.

[William]

@John:
>>To be straightforward is to be clear and precise, not to be beyond reproach.

To be straightforward is not the same thing as being clear and precise, nor is being beyond reproach quite the same thing as being insusceptible of doubt.

>>Presumably, because there is a fairly simple proof of it:

Step (4) of your proof is questionable. There are well-known counter-examples. E.g.

nec(4+5 = 9)
the number of planets = 9
nec(the number of planets = 4+5)

>>Our ordinary language commitments in any number of arenas are wildly inconsistent. Issues of material composition and constitution are just one example of the messiness of ordinary language.

This is something you need to show. I have argued that attempts at showing messiness and inconsistency result from poor 'translations' or interpretations of the ordinary language statements.

>>It's not at all clear how you can have two distinct sets of commitments, one as a matter of formal logic, and the other as a matter of ordinary language.

They are only the same commitment if we have translated them right. If the one is saying something completely different from the other, there is not necessarily inconsistency. One question is whether we can translate the grammatically singular terms as used in ordinary language ('the number of planets', 'this clenched hand') into the logically singular terms of formal logic.

By the way I have just looked at this paper http://philosophy.nd.edu/people/all/profiles/van-inwagen-peter/documents/TempSums8.doc by Inwagen, which Bill refers to in an earlier post. It is remarkably clear, and I agree with his conclusion (though his motivations I probably would not agree with). What I am not seeing is how the posts here engage with Inwagen's argument. I'm really lost. Part of the problem is the way the argument spreads itself across the different posts.

[John]

Regarding the meaning of "straightforward", I refer you to any number of dictionaries which make no mention whatsoever, in their definitions, of the word "controversial". To be straightforward IS to be clear, and precise, and lacking in ambiguity.

Step (4) of my proof isn't questionable because your "well-known counterexamples" are all widely known to fail. Take Quine's version of your "counterexample"

(1) Necessarily, 9>7.
(2) The number of planets = 9.
(3) Therefore, necessarily, the number of planets>7.

This counterexample is completely ambiguous as to whether or not the necessity in question is de re or de dicto. When read de dicto, it does fail. But it's highly questionable whether anybody ever meant it to be read de dicto in the first place. The counterexample should be read de re, in which case it is no counterexample at all. The issue in question turns on scope distinctions with the necessity operator. Here's how (1)-(3), read de re, looks:

(1*) 9 is such that it is necessarily-greater than 7.
(2*) 9=the number of planets.
(3*) Therefore, the number of planets is such that it is necessarily-greater than 7.

In (1*)-(3*), the necessity in question attaches to the predicate "is greater than" to form a new predicate, "is necessarily-greater than". And the number of planets has that property just as much as 9 does. Why? Because the actual number of planets is 9, as (2*) tells us, and it is true of 9 that it is necessarily-greater than 7. For an extraordinarily brief and clear presentation, see Sider's "Reductive Theories of Modality". (To ensure clarity on this point, note that my entire proof of the necessity of identity employs de re modality.)

You go on to say that you have argued that "attempts at showing messiness and inconsistency result from poor 'translations' or interpretations of the ordinary language statements." Here are two ordinary language statements that you employ:

(*) That house was these bricks.
(**) That house is no longer these bricks.

Here are some slightly informal translations:

(***) At some time t1, such that t1 is before the present, that house is identical to these bricks.
(****) At some time t2, such that t2 is the present, that house is not identical to these bricks.

One can very easily put (***) and (****) into more rigorously formal notation. The point is this: those translations are about as simple and clear as can be. The burden is on you to explain why they are "poor" translations, since it seems that they would be accepted by just about anybody who knows how to translate from ordinary language to formal logic. And then, of course, it is clear that the conjunction of (***) and (****) conflicts with the necessity of identity in temporal logic, which says:

(T) If at some time t3, a=b, then for all times t, a=b.

To lay it out, given that (***) says there is a time t1 such that that house is identical to these bricks, it follows from (T) that at all times t, that house is identical to these bricks. But that is just what (****) goes on to deny. Again, what YOU need to show is that something is wrong with the translations I've provided. Absent any such argument, it is clear that our ordinary language commitments conflict with our best logic. So, our ordinary language commitments cannot all be maintained. Some have to be given up.

You go on to ask "whether we can translate the grammatically singular terms as used in ordinary language...into the logically singular terms of formal logic", the answer is obviously "Yes". What reason could there be for denying that we can do so? Definite descriptions are singular terms. If you want to doubt this, you should probably have some actual counterexamples.

Finally, the posts here do not directly engage with PVI's argument. I have been defending some of Bill's remarks and "assumptions" from you, on Bill's behalf, because I have found your attacks wanting.

Getting back to the original issue, the point is that Bill's argument that Brick House is not identical to Brick Sum cannot be refuted by appealing to four-dimensionalism (hence the discussion of continuants vs. occurrents).

[Bill Vallicella]

John,

There is no need to apologize for posting repeatedly; you are the kind of person I want as a commenter since you obviously know what you are talking about and have been making helpful comments.

Thanks for explaining the continuant/occurrent distinction.

Consider the difference between a rainstorm and a man caught out in a rainstorm. The storm, let us say, starts at noon and lasts one hour. Intuitively, it is a process or event or occurrence which has temporal phases or temporal parts. As such, it is not wholly present at each moment at which it exists. Intuitively, and by contrast, a man is a substance, and substances do not have temporal parts: a substance is whiolly present at each moment at which it exists.

We can say that both storm and man persist, but their modes of persistence are different. As John remarked (drawing on D Lewis), processes perdure while substances endure.

Now given that some entities (storms, symphonies, etc) have temporal parts, some philosophers have gotten it into their heads that what we ordinarily think of as substances (and thus as continuants lacking temporal parts) are really occurrents composed diachronically of temporal parts. If you opt for this sort of ontology then you are a 4-dimensionalist, time being the 4th dimension.

[Bill Vallicella]

John,

Your proof above is valid, and William's objection to it is mistaken. I agree with what you say about de dicto/de re.

[Bill Vallicella]

John,

It seems obvious to me that if a = b, then Nec(a = b). But if it is necessarily the case that p, then it is true at all times that p. Right? So we can validly infer from the Necessity of Identity the temporal corollary that, if a = b, then for any t, a = b.

So, if there is a time at which Brick House = Brick Sum, then at every time at which both exist, they are identical. But obviously there is a time (late Friday) when Brick House does not exist (having been blown up) but Brick Sum does, whence it follows that Brick House and Brick Sum never were identical.

What is puzzling is why William cannot see the force of this argument.

If the 4-D dude pipes up, then I shift over to the modal discernibility argument. I don't even have to refute 4-D-ism.

[William]

John: >>Step (4) of my proof isn't questionable because your "well-known counterexamples" are all widely known to fail.

What is questionable is whether (4) is a good translation of ordinary language statements involving identity and necessity.

>>To ensure clarity on this point, note that my entire proof of the necessity of identity employs de re modality.

Obviously.

>>it's highly questionable whether anybody ever meant it to be read de dicto in the first place.

Is it? Here's another example: the president of the united states was George Bush. Now (in 2010) the president of the united states is not George Bush. Do you agree with that statement? In which case it cannot be read de re.

>>The burden is on you to explain why they are "poor" translations, since it seems that they would be accepted by just about anybody who knows how to translate from ordinary language to formal logic.

I'm sure they would. The question is whether the formal logical 'translation' correctly renders what we actually mean. The formal logical translation means that it is impossible that the president of the united states was George Bush but the president of the united states is not now George Bush. Since it is clearly not impossible, I question the translation.

[Bill]>>if there is a time at which Brick House = Brick Sum, then at every time at which both exist, they are identical. But obviously there is a time (late Friday) when Brick House does not exist (having been blown up) but Brick Sum does, whence it follows that Brick House and Brick Sum never were identical.

Then what about this argument: "If there is a time at which Kennedy was the president of the US, then at every time at which both exist, they are identical. But obviously there is a time when Kennedy ceased to exist (having been assassinated), but the president of the US still existed (Kennedy was replaced by Johnson), whence it follows that Kennedy and the president of the US never were identical" ?

>>What is puzzling is why William cannot see the force of this argument.

The argument is valid. But one of your assumptions is incorrect. From the undoubted fact that Kennedy *was* identical with the President of the US, it doesn't follow that Kennedy *is* identical with the President of the US. You will object that the people (Kennedy, Johnson) are different. I agree, but that's not the point. Why can't 'Brick House' be identical with different 'Brick Sums' in the way that 'the president of the US' is identical with different people?

Or perhaps you will object that in

(*) Kennedy *was* identical with the President of the US, but Kennedy *is not* identical with the President of the US.

the two tokens of 'the President of the US' denote different persons. I reply: it denotes identically the same *office*. By analogy, can a house be related to its bricks by way of an 'identity' like the identity between a president and the person who currently holds that office? Thus the bricks can change, just as the person who holds the office changes. But the house, or the office, remains the same.

>>I don't even have to refute 4-D-ism.

4-D-ism is completely unintelligible to me, so I agree with you there.

>>Now given that some entities (storms, symphonies, etc) have temporal parts, some philosophers have gotten it into their heads that what we ordinarily think of as substances (and thus as continuants lacking temporal parts) are really occurrents composed diachronically of temporal parts. If you opt for this sort of ontology then you are a 4-dimensionalist, time being the 4th dimension.

I don’t understand what a 'temporal part' is. How can an 'occurrent', which I thought could only exist for a brief period of time, be composed of such parts? Surely it is the 'substance' that, according to the 4-D-ist, be composed of the temporal occurrents? Apologies if I misunderstand.

[William]

@John. There is a wider topic raised by your argument: as it is obtrusive on Bill to discuss here, I move it to here.

http://ocham.blogspot.com/2010/09/anybody-who-knows.html

If you want to comment, you are very welcome. Otherwise not.

[John]

@ William: I cannot comment on your post because I do not have a google account, and you do not permit anonymous comments. That said, your argument once again betrays a frightening lack of familiarity with any of the relevant literature. Here is your "counter-example" to the necessity of identity (in the temporal case):

(*) If it was the case that the president of the US was identical with John F. Kennedy then it is the case the president of the US is identical with John F. Kennedy

Obviously, (*) is false, so you conclude that the necessity of identity is false. The trouble with your "counter-example" is that it employs both definite descriptions and proper names. If you had read your Kripke, you'd know that only proper names are rigid designators, and that the necessity of identity holds only between terms that are rigid designators. Your "counter-example" is thus a blatant straw-man.

Now, of course, part of why Kripke drew the aforementioned distinction between rigid and non-rigid designators was so that he could object to a descriptivist theory of names. One response on the part of the descriptivist is to point out that some descriptions DO rigidly designate (i.e. "the even prime" designates 2 at all possible worlds), and that any definite description can be rigidified in the following way:

(Modal) Rigidify "the president of the United States" as "the ACTUAL president of the United States"

You'll notice that, if you rigidify descriptions in this way, that counter-examples to the necessity of identity fail. Consider a modal case:

(**) If Ben Franklin is the inventor of bi-focals, then necessarily, Ben Franklin is the inventor of bi-focals.

Presumably, (**) appears to be a counter-example to the necessity of identity in just the same way as your (*) counter-example. But now rigidify the definite description in question:

(***) If Ben Franklin is the ACTUAL inventor of bi-focals, then necessarily, Ben Franklin is the ACTUAL inventor of bi-focals.

Notice that (***) is true. A similar move can be made in the temporal case, by rigidifying the descriptions in question to a particular time:

(Temporal) Rigidify "the president of the United States" as "the president of the United States at time t"

Once this is done, your counter-example fails:

(****) If it was the case that the president of the United States in 1963 was identical to John F. Kennedy, then it is the case that the president of the United States in 1963 is identical to John F. Kennedy.

Notice that, like (***), (****) is true.

My point is this: your "counter-example" is a straw-man in that it ignores whole swaths of important literature on the subject of naming and necessity (like, say, Kripke's book of the same title).

[Bill Vallicella]

>>>[Bill]>>if there is a time at which Brick House = Brick Sum, then at every time at which both exist, they are identical. But obviously there is a time (late Friday) when Brick House does not exist (having been blown up) but Brick Sum does, whence it follows that Brick House and Brick Sum never were identical.

Then what about this argument: "If there is a time at which Kennedy was the president of the US, then at every time at which both exist, they are identical. But obviously there is a time when Kennedy ceased to exist (having been assassinated), but the president of the US still existed (Kennedy was replaced by Johnson), whence it follows that Kennedy and the president of the US never were identical" ?<<<

John has already touched on the main point that names are not descriptions. 'Brick Sum' and 'Brick House' are both names (rigid designators). 'Kennedy' and 'the president of the US' are not both names: the latter is a definite description satisfied by different people at different times, and, at the same time, by different people at different possible worlds. Thus Obama now satisfies 'the president of the US' but McCain might have satisfied it now.

Your attempted refutation of my argument trades on a confusion of names and descriptions.

Exercise. Explain why the following argument is invalid:
1. Nec (George Orwell = Eric Blair)
2. George Orwell is the author of 1984. Ergo:
3. Nec (George Orwell is the author of 1984).

[Bill Vallicella]

William sez: >>Why can't 'Brick House' be identical with different 'Brick Sums' in the way that 'the president of the US' is identical with different people?<<

Again, you are missing the distinction between names and descriptions. 'Brick House' and 'Brick Sum' are names. The capitals indicate that. There have been many presidents of the US. But that is not to say that the president of the US is identical with different people. 'The president of the US' is not a name but a definite description.

'Obama is the president of the US' is not an identity sentence with the 'is' of identity flanked by proper names.

[William]

Bill:>>Again, you are missing the distinction between names and descriptions.

No, I'm perfectly aware of that distinction, indeed I noted it in a comment above. I said "One question is whether we can translate the grammatically singular terms as used in ordinary language ('the number of planets', 'this clenched hand') into the logically singular terms of formal logic."

If there is such a distinction, which you now seem to concede, it confirms my argument about the perils of translating ordinary language into formal logic.

Bill >>. 'Brick Sum' and 'Brick House' are both names (rigid designators).

If they are, then I concede your argument. But putting capitals on an expression doesn't make a logically proper name. I could write e.g. 'The President Of The United States'. Perhaps you intended to signify rigidity of reference. Then your argument is valid, yes, but kind of begs the question.

John: >>If you had read your Kripke, you'd know that only proper names are rigid designators

I read naming and Necessity before it was published in 1980 in the Davidson-Harman translation and studied it with Adam Morton http://en.wikipedia.org/wiki/Adam_Morton at Bristol in 1979, so I have a rough idea of what it is about. I haven't read Kripke for years; I now study medieval literature on the subject of modality and temporal reference, I haven't kept up to date with the more recent literature, e.g. Sider.

Obviously *logically singular terms* like 'a' and 'b' are rigid designators, indeed it should have been clear all along that I agree with that.

>>... and that the necessity of identity holds only between terms that are rigid designators. Your "counter-example" is thus a blatant straw-man.

I'm sorry, it is your argument that is a straw man :) I have been very specific that the placeholders in my argument stood in for any ***grammatically*** singular term. A definite description is a ***grammatically*** singular term, but not a ***logically*** singular term. I even said "One question is whether we can translate the ***grammatically*** singular terms as used in ordinary language ('the number of planets', 'this clenched hand') into the ***logically*** singular terms of formal logic." And you said earlier

>>You go on to ask "whether we can translate the grammatically singular terms as used in ordinary language...into the logically singular terms of formal logic", the answer is obviously "Yes". What reason could there be for denying that we can do so? Definite descriptions are singular terms. If you want to doubt this, you should probably have some actual counterexamples.

!!!!!!!!!!! I keep feeling this temptation to write in capital letters like the more deranged members of the internet community but shall continue to resist.

>>My point is this: your "counter-example" is a straw-man in that it ignores whole swaths of important literature on the subject of naming and necessity (like, say, Kripke's book of the same title).

A straw-man argument is one that fails to address the main point (or even concedes the main point - "grammatically singular terms may not be logically singular" - but presumes the opponent was arguing something else, perhaps even the opposite). An argument from authority is one that appeals to authority, e.g. "swathes of important literature".

Bill>>Explain why the following argument is invalid ...

It is invalid because grammatically singular terms are not always logically singular terms. As I have been saying all along (see way above).

[Bill Vallicella]

So now you concede the argument. It took you long enough.

[William]

Perfect! Reverse Straw Man. http://ocham.blogspot.com/2010/09/reverse-straw-man.html

But seriously, is there any way we can repair this? One way I have found useful to resolve the confusion is for one side to state what they think the other side is arguing. So here is what I think you and John have been arguing.

1. The argument of your initial post is that Brick House is not identical with Brick Sum, because of the "indiscernibility of identicals". Or rather the non-identity of discernibles. Brick Sum has the modal property of being such that its parts could have been arranged in non-house-wise fashion. Brick House does not have this, ergo they are not identical. Is that your argument?

2. This clearly involves the principle of indiscernibility of identicals, which is closely related to what John calls 'the necessity of Identity'. Yes?

3. Both John and you think I have been arguing against the "necessity of identity". Correct?

And here's what I have been arguing.

1. We must distinguish 'grammatically singular terms', which include terms which refer to an object under some description, from 'logically singular terms', which do not refer under a description. I did not define this distinction clearly enough from the start, so I plead guilty to using terms without a clear definition.

2. The principle of 'necessity of identity' does apply to logically singular terms.

3. The principle of 'necessity of identity' does not apply to terms which refer under a description, as the well-known counter-examples show. Hence it does not apply to all grammatically singular terms.

4. Thus 'If A was B, then A is B' is true - and fundamental - when 'A' and 'B' are logically singular terms. It may not be true when they are grammatically singular terms. Proof: 'the President of the US' and 'Kennedy' are grammatically singular. But 'Kennedy was the President of the US' is true, and 'Kennedy was the President of the US' is false. Ex vero nunquam sequitur falsum, consequentia non valet.

5. The validity of Bill's argument therefore depends on whether 'Brick House' and 'Brick Sum' refer under some description or not. It is not enough to argue that the capital letters, which signify proper names, also signify logically singular terms. For requires proof that a 'proper name', which is a grammatical/ordinary language concept, is always a logically singular term.

I don't believe we ever had a disagreement. Rather, there was an apparent disagreement which seems to have resulted in some acrimony. Does that resolve the disagreement? And does it dissolve any acrimony there might have been?

With every kind wish,

William

[John]

All of that seems admirably clear, William. Whether or not it resolves the disagreement, or simply casts it in a much clearer light, I'm not sure.

You're right that must distinguish grammatically singular terms from logically singular terms, and that the validity of Bill's argument depends on both "Brick House" and "Brick Sum" being treated as logically singular terms. For my part, I've been working under the assumption that they are logically singular terms. I don't know of any reason to treat them otherwise, but perhaps I just haven't thought hard enough about it. In support of my assumption, let me just say that Bill's naming of the objects in question seemed remarkably like the kinds of "baptisms" you read about in the literature on causal-historical theories of names. And names introduced in this manner are (or at least can be) rigid designators, i.e. logically singular terms. So that's where I'm coming from.

[Bill Vallicella]

Gentlemen:

When I said, right at the outset, "call it 'Brick Sum'," wasn't that sufficent to indicate that I was bestowing a proper name upon the sum?

Now if William is clear about the modal discernibility objections to identities such as Brick House = Brick Sum, then the next step is to examine the reasons why Varzi et al. are not persuaded by these objections.

The main point of the post was that the NONMODAL discernibility objections can be met by adopting four-dimensionalism, but this still leaves the modal objections.