The Selection Is Appendix 1 of Reference and Essence

Salmon Notes

The selection is Appendix 1 of Reference and Essence

Relevant principles:

(I) It is impossible for the same table x to be originally constructed from a hunk of matter y and in addition to be originally constructed from a distinct hunk of matter y'.

(IV) For any possible table x and any possible hunks of matter y and y' if it is possible for x to be originally constructed from hunk y while hunk y' does not overlap with hunk y, and it is also possible for a table to be constructed from hunk y', then it is also possible that table x be originally constructed from hunk y and in addition some table or other x' be originally constructed from hunk y'.

(V) If it is possible for a table x to be originally constructed from a hunk of matter y, then necessarily, any table originally constructed from hunk y is identical with x.

(V') If it is possible for a given table x to be originally constructed from a certain hunk of matter y according to a certain plan P, then necessarily, any table originally constructed from hunk y according to P is identical with x.

(V'') If it is possible for a table x to be the only table originally constructed from a certain hunk of matter y according to a certain plan P, then necessarily, any table that is the only table to be originally constructed from the same hunk y according to P is identical with x.

Salmon: Sometimes spatiotemporal continuity doesn't seem to suffice for persistence E.g., see case of Columbus' ship whose pieces are gradually replaced—the ship which is disassembled and put back together that is made of the original ship seems to be the original ship that left port. (NB One might think that a ship being made of the original parts of Columbus' ship is valuable even if strictly it isn't identical with the ship that left port. It is "close to identical", as it were.)

Sometimes spatiotemporal continuity is sufficient for identity: The case of a body whose cells are constantly replaced over time.

Chandler's claims with respect to W and W' (Figs 1 and 2 respectively) are a sort of closest continuer theory.

The hunks of matter that compose a and c in W are spatiotemporally continuous. This is what makes it the case that a and c are identical (226).

Salmon: Identity is necessary, pace Chandler. But constitution is not. So in Fig 3 (W'), hunk d' constitutes a at t3 (where hunk d'=hunk a'), and in W hunk c' constitutes a at t3 (where hunk b' doesn't overlap at all hunk c'). So you can accommodate the intuitions Chandler is after without claiming that a closet continuer theory is right. NB: That said, Salmon's "solution" here is strange—the same intuitions that lead one to say that identity can't be held hostage to outside factors would lead one to say that constitution (composition) can't be either.

Four Worlds Paradox:

Assume that objects could have come from a hunk of matter slightly different from the one they came from but couldn't have come from an entirely different hunk of matter.

So suppose a ship a is made of 100 planks of wood in a world W1. Suppose also that it could have come from 98 of the 100 planks it comes from in W1. Then suppose there is another world W2 in which a ship b comes from P1…, P97, P101, P102, and P103 (where P101, P102, and P103 are qualitatively identical with P98, P99, P100). We know a is distinct from b because there is not overlap of 98 planks between a and b.

Now, a and b could have come from collections of planks that overlap the planks that they come from in W1 and W2 (respectively) by 98 planks. So then consider a third world W3 in which the ship a comes from P1…P97, P98, P102, and P103. And finally consider a fourth world W4 in which b comes from P1…P97, P102, and P103. W3 and W4 have qualitatively identical yet distinct ships in them; we know that a in W3 is distinct from b in W4 because a in W1 is distinct from b in W2.

This seems to falsify (V''):

Also, it is puzzling that you can have qualitatively identical yet distinct ships, one might think. Indeed, W3 and W4 can be qualitatively identical yet with different ships—these ships differ only in their haecceities.

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A solution (pp. 232 ff)

Claim W3=W4 and go with counterpart theory. Then you really have three worlds here, W1, W2 and a third—call it Wc and call the ship in it 'c'. Wc makes it true that a could have come from P1…P98, P102, and P103 when we consider the ship in that world under the "a" counterpart relation. Wc makes it true that b could have come from P1…P98, P102, and P103 when the ship there is considered under the "b" counterpart relation. (See, e.g. Forbes' solution here:

http://www.jstor.org.libproxy.lib.csusb.edu/stable/pdfplus/4319699.pdf as well as Salmon's response here: http://www3.interscience.wiley.com.libproxy.lib.csusb.edu/cgi-bin/fulltext/120154303/PDFSTART .)

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Salmon's Solution:

Consider another world, W5 in which a is constructed exactly as b is in W2. W5 is possible relative to W3, but not relative to W1. It's impossible for a to come from planks 97% the same as those it actually comes from, but it is contingently impossible—it is possibly possible for a to come from planks 97% the same as those it comes from. And indeed, W4 is not possible relative to W1. What about (V'')? It is fine, because a world like W4, which would falsify it, aren't possibly—they are impossible, but contingently so.

Salmon argues that identity is not vague; here's a way of putting it:

Suppose it is, and that it is vague that a=b. So a has the property being vaguely identical with b. But b lacks that property. So contrary to the assumption, a is determinately distinct from b. So it's impossible that a be vaguely identical with b.

How does vagueness enter into things? Maybe by way of a vague accessibility relation (see pp. 247-248).

(V'') says W3 is not possible relative to W4 and conversely. It also will entail that W4 is not possible relative to W1. Why? W3 is possible relative to W1, so we know that in W1, necessarily anything that comes from P1-P98, P102, P103 is a. But then that would force a contradiction in W4; it would entail that the ship from P1-P98, P102, P103 there is a, but we're given that it's b. So W4 isn't possible relative to W1.

The same sort of reasoning gets you W3 not being possible relative to W2.

The overlap principle (if x comes from h but could come from h1, then h1 sufficiently overlaps h—here is it 97% of the planks) gets you W5 not being possible relative to W1, but possible relative to W3.

Some Forbes notes:

Forbes:

Chisholm's Paradox (though really it is Chandler's paradox): Set up a series of worlds W1 to Wn in which

a) any object x could have come from slightly different though not totally different matter from the matter it comes from

b) In W1 an object o comes from a hunk of matter h1

c) In W2 o comes from a hunk of matter h2 that sufficiently overlaps h1 such that o can come from h2

d) In W3 o comes from a hunk of matter h3 that sufficiently overlaps h2 such that o can come from h3

and so on until

d) In Wn o comes from a hunk of matter hn that doesn’t overlap h1 at all.

Salmon will say that Wn is not possible relative to Wn. Forbes claims that there is vagueness involved in the puzzle, and although identity can't be vague, whether or not an object is a counterpart can be vague. However, Salmon as well allows for this vagueness, though it's in the accessibility relation. So Salmon could allow for degrees of truth in the way Forbes does (pp. 175-179).

Compare to a sorites paradox:

(1) Anyone 3' tall is short.

(2) If anyone 3' tall is short, so is anyone 3.0001' tall.

If anyone 5'11 and 1/10000" is short, so is anyone 6' tall.

_________

Anyone 6' tall is short.

Chisholm's Paradox can be put this way:

It's possible for o to come from h.

If it's possible for o to come from h, it's possible for o to come from h1.

If it's possible for o to come from h1, it's possible for o to come from h2.

If it's possible for o to come from hn-1, it's possible for o to come from hn

________

It's possible for o to come from hn.

So, Forbes reasons, we should respond to both a sorites paradox and Chisholm's Paradox in the same way.

Salmon can do this, though, the vagueness in "short" is analogously located in "it is possible that."

Two objections to counterpart theory:

1) It involves superessentialism—if an object x exists only in one world, x has all its properties essentially.

2) It doesn't follow from the fact there could be something that is similar to me that has a property F that I could have been F.