Van Inwagen on the Ship of Theseus

Peter van Inwagen's Material Beings (Cornell UP, 1990) is a very strange book, but he is a brilliant man, so one can expect to learn something from it. A central claim is that artifacts such as tables and chairs and ships do not exist. One can appreciate  that if there are no ships then the ancient puzzle about identity known as the Ship of Theseus has a very quick (dis)solution. 

The Ship of Theseus is a puzzle about diachronic artifact identity. Here is one version. You have a ship, or a rowboat, or any object, composed entirely of wooden planks. You remove one of the planks and replace it with an aluminum plank of the same size. The wooden plank is placed in a warehouse. After this minor replacement, you have a ship and indeed numerically the same ship as the one you started with. It is not a numerically different ship. Now replace a second wooden plank with an aluminum plank, and place the second wooden plank in the warehouse. Again, the numerical identity of the original ship has been preserved. Continue the replacement process until all of the wooden planks have been replaced with aluminum planks. You now have a wholly aluminum ship that is presumably numerically identical to the original wholly wooden ship despite the fact that none of the original matter is to be found in the aluminum ship. After all, the aluminum ship 'grew out of' the original wooden ship by minor changes each of which is identity-preserving.

Now take the wooden planks from the warehouse and assemble them in the form of a ship and in such a way that the planks bear the same relations to one another as the planks in the original wooden ship bore to one another. You now have two ships, a wooden one and an aluminum one. The question is: which of these ships is identical to the original wooden one?

Suppose the two ships collide on the high seas, and suppose the captain of the original ship had taken a solemn vow to go down with his ship. Where does his duty lie? With the wooden ship or with the aluminum one? Is the original ship identical to the resultant aluminum ship? One will be tempted to say 'yes' since the aluminum ship 'grew out' of the original wooden ship by minor transformations each of which was identity-preserving. Or is the original ship identical to the wooden ship that resulted from the re-assembly of the wooden planks? After all, it consists of the original matter arranged in the original way. Since the resultant wooden and aluminum ships are numerically distinct, they cannot both be identical to the original ship.

Van Inwagen makes short work of the puzzle: "There are no ships, and hence there are no puzzles about the identities of ships." (128) One way van Inwagen supports this bizarre solution is by re-telling the story in language that does not make even apparent reference to ships. Here is his retelling:

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (128-129)

If I understand what van Inwagen is claiming here, it is that there is nothing in the standard telling of the story, a version of which I presented above, that is not captured in his re-telling. But since there is no mention of any ships in the re-telling, no puzzle about ship-identity can arise. Perhaps van Inwagen's point could be put by saying that the puzzle about identity is an 'artifact' of a certain way of talking that can be paraphased away. Instead of talking about ships, we can talk about shipwise arrangements of planks. The planks do not then compose a ship, he thinks, and so there is no whole of which they are proper parts, and consequently no question about how this whole maintains its diachronic identity under replacement of its parts.

What are we to say about van Inwagen's dissolution of the puzzle? What I find dubious is van Inwagen's claim that ". . . at no time do two or more of these planks compose anything, and no plank is a proper part of anything." (129) This strikes me as plainly false. If the First Planks are arranged shipwise, then there is a distinction beween the First Planks and their shipwise arrangement. The latter is the whole ship and the former are its proper parts. So how can van Inwagen claim that the planks do not compose a ship? Van Inwagen seems to think that if the planks were parts of a whole, and there were n planks, then the whole would be an n + 1 th entity. Rejecting this extreme, he goes to the other extreme: there is no whole of parts. If there were ships, they would be wholes of parts, but there are no artifactual wholes of parts, so there are no ships. The idea seems to be that when we build an artifact like a ship we are not causing something new to come into existence; we are merely re-arranging what already exists. If so, then although a ship's planks exist, the ship does not exist. Consider what van Inwagen says on p. 35:

If I bring two cubes into contact so that the face of one is conterminous with the face of the other, have I thereby brought into existence a solid that is twice as long as it is wide? Or have I merely rearranged the furniture of the earth without adding to it?

Van Inwagen seems to be saying that when it comes to artifacts, there is only rearrangement, no 'addition to existence.' As a general thesis, this strikes me as false. A ship is more than its planks, and van Inwagen seems to concede as much with his talk of a shipwise arrangement of planks; but this shipwise arrangement brings something new into being, namely, a thing that has causal powers that its constituents do not have. For example, a boat made of metal planks properly arranged will float, while the planks themselves will not float.

Comments

[William]

I got as far as the claim that "artifacts such as tables and chairs and ships do not exist" and no further. What are these things, or kinds of things, that do not exist?

[Rob]

I keep returning to the relation between universal immaterial shipness and a particular material manifestation of a ship. Somewhere in the argument the two have got in a tangle ; they are used interchangeably. If planks can constitute a ship , then either they have an inherent form - a potential (Aristotle?) to be one when arranged in a certain way , or it is purely a universal mental thing with no real existence in the material world apart from a mind. But there must be a mind to dispose the planks shipwise : to talk of 'shipwise ' is to assume what is contested by Inwagen.

If I understand correctly , for Inwagen the captain took his solemn vow in a particular material structure . Yet, his oath is inconsistent or meaningless without the 'ship' part; we're talking about a captain here . What does the intentionality of his vow point to ?

Is his vow temporally bound to the particular ship as it existed at the specific time of his vow?

Confound it, this is too much !

[Bill Vallicella]

William,

I would have thought that you, as a nominalist, would have a little sympathy for van I's admittedly bizarre claim. You deny sets; he denies artifactual wholes.

[Bill Vallicella]

Rob,

It is too much. Perhaps a defender of van I will show up to explain it to us.

[Jeremy]

So what's the difference between a ship, and something 'arranged shipwise'? If I were to form a conception of something arranged shipwise in my mind (or see such an object), would it look like a ship? And if it did look like a ship, would I associate with it the things I would normally associate with a ship? Not being a philosopher, I don't understand how this answers the problem posed by the ship of Theseus (a problem I understand). Are there no ships because there are no essential natures? (e.g. specifically arranged collections of planks is only a ship because I conceive it as such?) That doesn't solve the practical problem...

[William]

>>I would have thought that you, as a nominalist, would have a little sympathy for van I's admittedly bizarre claim. You deny sets; he denies artifactual wholes.

You have to understand the nominalist claim. The nominalist (or at least my variety of nom) would not deny the existence of 'a dozen' for example. What he or she denies is the metaphysical interpretation of the grammatically singular a or one dozen.

For the same reason, the nom. would not want to deny the existence of 'a ship', any more than the existence of 'a dozen'. Does Inwagen actually deny the existence of ships or boats. If he does, there is proof against his claim. I sailed a boat last week, therefore boats exist.

[William]

>>So what's the difference between a ship, and something 'arranged shipwise'?

Quite. Perhaps Inwagen is denying the temporal identity of the things arranged shipwise. I can say that I sailed some things-arranged-boatwise last Wednesday, and that I sailed some things-arranged-boatwise last Wednesday the following today. But can I say that I sailed the same things-arranged-boatwise on the successive days, according to Inwagen? Presumably not (let's assume that the tiller fell off on Wednesday and was replaced with a new one the next day).

This contradicts common sense. I naturally might want to sail the same boat, and so might ask for the same one. Bill, does Inwagen address the practical common-sense aspects of this?

[Philoponus]

Bill,

What does Peter say about the obvious alternative that neither the aluminum boat nor the reconstruction from original parts is the same as the original ship? There is no puzzle or confusion over what has happened here, is there. In one case, we have produced an aluminum REPLICA of the original ship by piecewise replacement; in the other case, we have produced a RECONSTRUCTION of the original ship using all and only original parts. Is anyone sorely tempted to say replicas and reconstructions are “identical” to the original from which they derive? I don’t think so.

Suppose as you say both replica and reconstruction sail and sink, and a question of insurance arises. The original ship had insurance, so which boat inherits it? I think the answer is likely to be neither. Most insurance policies void coverage if substantial modifications have occurred. So the all-aluminum ship is excluded. Disassembly and reconstruction is also probably going to be taken as exclusionary on the same grounds. Suppose the owners of the reconstruction reject this decision and sue the insurance company, claiming it is the “same” ship. Then it is becomes a court case and a jury gets to DECIDE if for legal purposes the reconstruction should be considered the same ship. This is important because it shows that the “identity” of original & reconstruction is not a matter of fact but of decision. It is the “same” ship for practical purposes like insurance if the jury decides it is, otherwise it is not. The decision could be made either way. Before the decision it is an open question, though most people, I think, would be inclined to see no identities.

Claims like “there are no ships or houses” seem to want a Moorean common sense response. We can’t doubt that there are ships or houses. Our world is full of them. I am looking at several right now. We just might discover that houses have some truly bizarre properties (like being haunted!), but haunted houses are still houses. Any view that claims that there are no houses or ships must be seriously wrong, but perhaps wrong in an interesting way. I don’t see the interesting mistake here.

[William]

@Philoponous

Agree, and see my comments on the more recent post above, re post office (letter sent to the same address) and declarations to the Inland Revenue (lived at the same address for 19 years). Sometimes we have to give a Moorean response. Are there such things as boats? Yes - proof: I sailed one last week.

[Erik]

What is the consequence of saying that in fact, Ship_1, the original ship, ceases to exist after replacing the plank? That for any object, the loss of a piece of it (in this case a plank of wood) constitutes a new object, very similar but not numerically identical.

Dr. V: A very fascinating discussion, I look forward to seeing how it develops.

[William]

>>What is the consequence of saying that in fact, Ship_1, the original ship, ceases to exist after replacing the plank? That for any object, the loss of a piece of it (in this case a plank of wood) constitutes a new object, very similar but not numerically identical.

The problem is that when I say 'I lived in the same house for 19 years' you are expressing numerical identity. It's not like there is this refined concept of identity that only philosophers and metaphysicians use, and a less refined one for everyday use.

[Bill Vallicella]

William,

There is an analogy between your denial and van I's denial. You don't deny the twelve eggs that make up a dozen; you deny that there is some one single thing -- a mathematical set -- that has the twelve eggs as members and is distinct from the 12 eggs. Van I does not deny the 1000 blocks that make up a house; he denies (if I understand him) that there is some one single thing in addition to the 1000 blocks.

Despite the analogy, there is a difference. The denial of a house or boat is subject to a Moorean rebuttal: 'I sailed a boat on Wednesday; ergo, a boat exists (or existed on Wednesday).' The denial of a set of 12 eggs is not subject to a Moorean rebuttal: 'I ate a dozen eggs on Sunday; ergo a set of 12 eggs existed on Sunday.' The latter is an invalid argument.

[Bill Vallicella]

William,

These two questions ought to be distinguished:

Q1 Is there such a thing as strict numerical identity of an artifact, e.g., a boat, over time? And if so, what does it consist in? The Theseus puzzle is meant to point up the difficulties involved in diachronic artifact identity.

Q2 Are there artifacts?

Van I. returns a negative answer to (Q2) and so (Q1) lapses. Thus he undercuts a presupposition of the Theseus puzzle.

[Bill Vallicella]

William brought up common sense. Does the denial of the existence of artifacts conflict with common sense? That depends on what common sense is. Van I says the following about common sense (Material Beings, p. 103): ". . . I do not think that there is any such thing as the body of doctrine that philosophers call common sense. There is common sense: Common sense tells us to taste our food before we salt it and to cut the cards. It does not tell us that there are chairs."

I should write a separate post on how van I. replies to the Moorean rebuttal to his denial of artifacts.

[Bill Vallicella]

Philoponus,

Van Inwagen is taking a radical line on the Theseus puzzle by denying one of its presuppositions, namely, that there are things like ships. (He maintains that every physical thing is either a living organism or a simple. p. 98)

You seem to be saying that there is no fact of the matter as to whether or not the car you are driving today is the same as the one you were driving five years ago. Van I would say to you that even that solution to the puzzle lapses if there are no cars.

This brings us to the Moorean rebuttal which van I discusses on pp. 100 ff. But to go into this requires a separate post.

Perhaps you should respond to William above who seems to think that there is a fact of the matter as to whether or not he is living in the same house for the past 19 years.

[William]

>>William brought up common sense. Does the denial of the existence of artifacts conflict with common sense? That depends on what common sense is. Van I says the following about common sense (Material Beings, p. 103): ". . . I do not think that there is any such thing as the body of doctrine that philosophers call common sense. There is common sense: Common sense tells us to taste our food before we salt it and to cut the cards. It does not tell us that there are chairs."

"There is nothing so crazy that some philosopher has not said it" ( was that Cicero? Descartes?)

I am wondering what it is that tells us there are chairs. Is it common sense? Or is it a set of procedures? Would it include the sort of considerations Van Inwagen is talking about? For instance, if the Inland Revenue ask me if I own any properties such as houses or flats, could I use van I's arguments to justify 'no'.

On a related note, the tax authorities in Greece are clamping down on yacht owners

http://www.ft.com/cms/s/0/28d3afd4-adff-11df-bb55-00144feabdc0.html

Could these owners legitimately deny they own any yachts, per Inwagen. Interesting

[William]

Bill, regarding your distinction between the existence question and the identity question: obviously they are different, but they are connected. The identity problem leads to the existence problem as follows. If there were no puzzle about the continued identity of a house or a boat, we could simply define our way out of the problem by defining 'house' or 'boat' as collective nouns applying to bricks, and planks respectively. Thus there could be a 'house of bricks' or a 'boat of planks' in the same way there is a 'pair of bricks' or a 'dozen [of] planks'. The collective noun is simple a grammatically singular term for a number of things that it is a collective of, just as a dozen eggs is simply the 12 eggs making up the dozen. But for that to work, the identity of the collective is determined by the identity of the individual components. If I remove one egg from the dozen and replace it with another, it is no longer the same dozen, because they are no longer the same eggs.

It is not the case with houses and boats. If there is such a thing as a house, it must be something whose identity remains even though the things of which it is composed do not remain. If I remove one brick and replace it with another, we still want to say that the bricks are part of the same house. Van I proposes, as I understand him, that there is nothing - either a single thing or collective - which remains the same through such a change. Thus there are no such things as houses, boats …. Thus the rejection of identity leads to the rejection of existence.

I wonder if he would reject such composites as herds of cows or flocks of birds. Suppose I have a herd of 20 cows in field A, and I replace one cow with a new one, and put the replaced cow in another field B. I repeat with another of the original cows, until there are now two sets of cows: the ones in field A, which are a replacement of the original herd, and the ones in field B, which is composed of all the original herd. Which herd is the same as the original herd? If we use the rule that a herd retains its identity over any individual replacement, and if identity is transitive (i.e. A=B and B=C implies A=C) then the herd in field A is the same herd as we started with. If we use the rule that it is the identity of the cows that matters, then it is the herd in field B. Neither answer seems satisfactory. Would Van I accordingly deny the existence of herds, flocks? Would he reject the existence of families? Which is a separate question, of course: our criterion for the identity of a family is different from the criterion of identity for simple collectives such as pairs, dozens, and from that of groups such as herds. I can't randomly remove someone from my family and replace them with another, without breaking the identity.

Thought: is there a causal solution the difficulty? I can clearly say that the same family has lived in this house for 300 years - even though the original inhabitants are long dead. And there are clear causal conditions that must be satisfied in order that this be true (genes, for example). Is there a similar approach we can take to houses, boats?

[William]

Another thought (sorry for this - fertile day). Van Inwagen employs an interesting principle in the argument you quote half way down.

(*) If it is possible to describe any situation where we employ term X, in such a way that term X does not occur, then conclude that X's do not exist

Call this the Redundancy Principle. It is blatantly fallacious. For example, instead of saying 'There are a dozen eggs' I can always say 'there are 12 eggs'. Does that mean that dozens do not exist? Of course not. 'A dozen eggs' means the same as '12 eggs'. The Principle would need to be strengthened to the effect that the analysing statement (the one which does not use term X) has a different meaning to the analysed statement (the one which includes X). But then a legitimate objection would be: how do we know that the situation described without using X is the same situation as described in using it? Thus there are two possible objections to his argument, depending on whether we use the strengthened or the fallacious unstrengthened principle.

(Objection 1) The situation where planks exist in a 'shipwise arrangement' is identical to the situation where a ship exists. Thus Inwagen cannot conclude there are no ships.

(Objection 2) The situation where planks exist in a 'shipwise arrangement' is not identical to the situation where a ship exists. Thus Inwagen cannot claim "that there is nothing in the standard telling of the story … that is not captured in the re-telling." What is not captured (given the presumed difference in meaning between 'shipwise arrangements exist' and 'a ship exists') in the re-telling is the existence of a ship.

Hope that's clear - I am writing rather hastily. This is a standard and powerful objection to any reductionist account. Either the reductionist account means the same as what it replaces, in which case nothing has been reduced. Or it means something less - has less existential commitment - in which case it is not genuinely reductionist. If you claim that mind = matter, and so mind does not exist, you are clearly wrong, for matter exists. If by contrast you claim that mind is something beyond matter alone, the onus is on you to show that only matter exists. Using analysis as in the fallacious principle (*) above is not enough.

[Erik]

>>It is not the case with houses and boats. If there is such a thing as a house, it must be something whose identity remains even though the things of which it is composed do not remain.<<

I am not sure that this is quite right. I think that when we call a house/ship the same after replacing *only* one brink or plank, we are being very casual about the relationship between the brick and the plank and its whole the house and ship.

My original question was whether this part/whole relationship jeopardized the way in which we refer to objects, as picking out the same thing, not in terms of numerical identity, but as the object/thing to which we refer. I am inclined to think that when we refer to things like material objects (in this case artifacts) we are invoking a formal concept of the artifact, and also referring to the constitutive stuff of the artifact. In this sense, to say that there is a different object after removing a brink or plank of wood is to say something about the constitutive stuff "shaped shipwise or housewise". Alternately, when we say that it is the same boat or house, we are invoking the formal concept.

This does not address the larger questions raised in BV's original post, but it is I think a gesture towards an answer to the problem raised by the Ship of Theseus.

[Philoponus]

Bill,

If I may, I’d like to address this to William, as you suggest.

Perhaps we should talk about “common sanity” rather than common sense. I really don’t know what to say to someone who, sitting in a chair in my house, having driven over in his car, persists in claiming that chairs and houses and cars don’t exist. I’m afraid I suspect a real pathology rather than the more benign dysfunction called philosophy. Maybe I should walk him over to my psychiatrist and see if in his persists in spouting his delusions? In Arizona psychiatrists can sign an order for 30 days involuntary confinement & examination. I suspect that treatment rather than argument may be what is needed here.

I liked your point about the Inland Revenue. So if a philosopher denies houses exist, but files a tax return claiming mortgage payments for his “house”, we have someone denying and asserting that houses exist. Is this fraud or mental illness?

[William]

>>I am not sure that this is quite right. I think that when we call a house/ship the same after replacing *only* one brink or plank, we are being very casual about the relationship between the brick and the plank and its whole the house and ship.

OK but the question is whether it is true or false that the house is the same. It is true that I have lived in my house for 19 years. During that time, quite a few parts of the house have changed.

>>Perhaps we should talk about “common sanity” rather than common sense. I really don’t know what to say to someone who, sitting in a chair in my house, having driven over in his car, persists in claiming that chairs and houses and cars don’t exist.

Precisely my difficulty.

[William]

>>My original question was whether this part/whole relationship jeopardized the way in which we refer to objects, as picking out the same thing, not in terms of numerical identity, but as the object/thing to which we refer.

That is precisely what numerical identity is: sameness of referent.

[William]

I have another aporetic pentad: one that I think is closer to the original Theseus argument.

A. An artifact remains numerically the same if one of its components is replaced, and the rest remain the same.

B. An artifact is numerically the same if all of its components are numerically the same.

C. Identity is transitive (if A=B and B=C, then A=C)

D. If artifact a and artifact b have numerically different components at the same time, a and b are numerically different.

E. Artifacts exist.

It is easy to prove that these are inconsistent. So at least one is false. And clearly A-D logically support Inwagen's conclusion. But are A-D true? Only D seems obvious. Clearly the ship made of the aluminium bits cannot be identical at the same time with the one reconstructed from the wooden bits. But we could question the others. Someone above has already questioned A: is my house the same house if I replace one of the bricks with a new one? Is B true? Why should the reconstructed ship, which has no continuity with the original assemblage, be considered identical? (I can think of an argument that it is, but will leave for now). Finally, is identity transitive? Is it really true that A=B and B=C implies A=C? (Probably, but I will leave the argument for now).

[William]

It's gone a bit quiet here? I have re-blogged the comments above as follows:

http://ocham.blogspot.com/2010/08/reduction-by-re-telling.html - on Inwagen's 're-telling' argument.

http://ocham.blogspot.com/2010/08/identity-in-replacement.html - on the aporetic proposition set mentioned above. This post also examines proposition A above in more detail. Is this bike, which has a new mudguard, the same as the bike which I took to the repair shop with an old, damaged mudguard, yesterday.

[David Brightly]

W,

Just thinking. Not sure about your (A). What if the artifact consists of two similar or near similar halves? I'm thinking of those old travel chests with a 'bottom' and a 'top' hinged together. Take two of these and interchange the tops. Is there a fact of the matter regarding identity of the chests? Likewise, two pairs of shoes of same style, size and colour, if a pair of shoes can be thought an artifact.

I have never understood 'numerical' identity. You have lived in the same house for 19 years but the house now is not the same as it was 19 years ago. This makes perfect sense. Are there two kinds of sameness here? Which, if either, is 'numerical' sameness?

[William]

>>Not sure about your (A). What if the artifact consists of two similar or near similar halves?

That is a difficulty, but if you make the replaced part small enough, surely we all agree that identity is preserved. Suppose a small corner gets rubbed off (or even a molecule). Then if we agree on the identity, and if we then agree on the transitivity of identity, we get the problem.

>>I have never understood 'numerical' identity. You have lived in the same house for 19 years but the house now is not the same as it was 19 years ago. This makes perfect sense. Are there two kinds of sameness here? Which, if either, is 'numerical' sameness?

I address that here http://ocham.blogspot.com/2010/08/identity-in-replacement.html . Numerical identity is mere sameness of referent, or sameness of subject and predicate. E.g. 'I moved into this house 19 years ago' involves the identity this house = the house I moved into 19 years ago. If that is true (and I promise you it is), then we have numerical sameness. If by contrast I say that this house has changed a bit since we moved into *it*, we have the assertion of qualitative difference or non-sameness. It also contains, note, the assertion of numerical identity - see the emphasised 'it'. We can't understand the reference of 'it' - the house we moved into 19 years ago - unless we understand the sameness of reference with 'this house'. So we are using numerical sameness (this house = it) to assert qualitative difference (it is now very different - we replaced the brickwork in the attic, e.g.).

[William]

Perhaps I can make this point clearer: the notion of change itself requires the notion of numerical identity. That is, I can't even express the idea that this thing has changed, namely that *it* is now different from how *it* used to be, without invoking numerical identity, i.e. the sameness of reference for the first 'it', which refers to it as it is now, with the second 'it', which refers to the thing as it was before the change. Change involves non-sameness, clearly, otherwise it wouldn't be change. But it also involves a different kind of sameness, namely the sameness of reference, the same 'it'.

Without numerical identity, there could be no change. We would simply have an aggregate of elements existing at t1, an aggregate existing at t2, and so on. We could not express numerical sameness or difference of the aggregate or its elements, and so on. This is the idea that underpins nearly all of Aristotle's philosophy.

[David Brightly]

Hi W,

Well, I'm a bit concerned that the identity of some medium-sized dry good seems to be rather poorly defined, but for the time being let's agree that the objects under discussion have many small substitutable parts.

I think I follow your account of numerical identity and change. Numerical identity would seem then to be a presupposition of the sort of tensed predications by which we express change. Now I'm trying to understand your proof that (A)-(E) are inconsistent. The argument seems to take the form of defining some conditions in which we will say an object is an artifact and showing that these conditions cannot be fullfilled. You say things like 'Then suppose we replace one of its [artifact X's] components to give artifact X1'. I'm not sure I understand what kind of thing X1 is. It appears to be a temporal sub-part of X since it comes into existence when the first part of X is replaced, or perhaps the 'state' X is in after the replacement, but we don't normally own up to such things in everyday talk. X2 is then defined in terms of X1 as if X1 were a fully-fledged object. The object Y which comes into existence when the spare parts of X are reassembled is unproblematic, but what exactly are the X1, X2, etc?

[William]

>>I'm not sure I understand what kind of thing X1 is.

Understanding this is not logically necessary for the proof http://ocham.blogspot.com/2010/08/identity-in-replacement.html . Assumption A is that 'An artifact remains numerically the same if one of its components is replaced, and the rest remain the same.'. Thus if we replace one of the components of X with another, (A) says that the result is an artifact that is identical with X. E.g. let X be my house. Then (A) says that if I replace one of its components, say a brick, with another component (add to this the obvious assumption that the component is 'of the same sort', i.e. is a brick of the right size), we get an artefact X1 which is identical with X, i.e. is numerically the same as my house.

>>It appears to be a temporal sub-part of X since it comes into existence when the first part of X is replaced, or perhaps the 'state' X is in after the replacement, but we don't normally own up to such things in everyday talk.

I don't know what a 'temporal sub-part' is. Why do we need to know. Assumption A simply captures the intuition that if I replace any brick with another suitable one, my house remains the same house. This is a simple and basic idea.

>>X2 is then defined in terms of X1 as if X1 were a fully-fledged object.

Well the assumption is that X1 is an object (a house, say). Is a house a 'fully fledged object'. Depends what you mean by that.

>>The object Y which comes into existence when the spare parts of X are reassembled is unproblematic, but what exactly are the X1, X2, etc?

X1 is house. X2 is a house. X3 is a house. ... Xn is a house - Xn however is made of an entirely different set of bricks than X.

It's obvious from what you say here that my argument was utterly obscure and unclear. Sorry about that :(

[David Brightly]

Hi W, you say 'Xn is a house - Xn however is made of an entirely different set of bricks than X.' This is where we disagree. If X is an enduring but changing object then Xn is made of exactly the same bricks as X, but they are not the same bricks that X *used* to be made of.

[William]

>>Hi W, you say 'Xn is a house - Xn however is made of an entirely different set of bricks than X.' This is where we disagree. If X is an enduring but changing object then Xn is made of exactly the same bricks as X, but they are not the same bricks that X *used* to be made of.

Yes, and thank you for correcting me on that simple and elementary point. Given the identity Xn = X, Xn *is* made of the same bricks that X *is* made of, but not the same bricks that X *was* made of. Shows just how easy it is to be caught out by language on holiday.