- S is the principle1 that “Two things cannot completely occupy the same place / volume / sub-volume at the same time”.
- Apparent exceptions that are fairly easy to explain2 include:-
- Proper Parts: My forearm only partly3 occupies the volume occupied by my body. The apparent exception “doesn’t count”.
- Sponges: The point is to “mingle” two things – in this case a sponge and a body of water – and then to recover them both afterwards. The things have to persist, or we can’t say they are two things4 in the same pace at the same time. Wiggins also considers (nomologically counterfactual) mingling as the atomic and subatomic level5. This “doesn’t count” either.
- Wiggins thinks he can resolve but one of the “difficult” questions arising from all this, but S is still inadequately formulated.
- The “is” of Constitution: Wiggins considers a tree6 (T) and its constituent matter (W). T and W occupy the same place at the same time, but are non-identical – because of Leibniz’s Law and the fact that they have different persistence conditions.
- W survives T’s decomposition into cellulose molecules, while T does not.
- T survives the loss of some of the constituent cells of W, in the course of organic change, while W does not.
- Wiggins thinks it’d be a “trick” to define an aggregate W1 with persistence7 conditions exactly the same as the tree’s. A trick because all you’ve done is define a tree.
- Wiggins spells this out: we have “contrived” an identity between stuff (W) and substance (T) by introducing a concept foreign to things falling under the “stuff” category – namely organisation.
- Wiggins has a footnote saying that more can be said about identity and the mereological treatment of aggregates – and refers us to "Wiggins (David) - Identity & Spatio-temporal Continuity", pp. 11-13, 67-8, 728.
- Wiggins has an excellent footnote9 illustrating – for artefacts – the difference between the stuff and the artefact from which the stuff is made. He proves, by transitivity, that the artefact cannot be identical to its stuff – in this case sweater, wool and socks – since the sweater is not identical to the socks, neither can be identical to the wool from which – at different times – they were made. The stuff (wool) must pre-exist the fabrication of the artefact, but the artefact cannot pre-exist its fabrication.
- However, he goes on to argue that none of this implies that T is something over and above W. His definition of over and above is open to objection10, in that he wants it to mean merely that there are no (material) parts of T that are not in W, or as he says, W fully exhausts11 the matter of T.
- Wiggins’s understanding of constitution12 includes:-
- The “is” of material constitution is not the “is” of identity.
- “x is constituted of y” is equivalent to:-
… “x is made of y”, or
… “x consists of y”, or
… “x is wholly composed of y”, or
… “x is merely y”, or
… “x merely consists of y”.
- Wiggins notes that if T = W is a consequence of materialism, then Wiggins is not a materialist13, as he denies this equation.
- Wiggins claims that his denial that T=W only puts an uninteresting14 obstacle in the way of reducing botany to organic chemistry.
- Wiggins leaves T & W with the remark that what he’s shown is similar to a philosophical commonplace of assigning objects to different logical types. He prefers his approach, however, because it makes a smaller claims (he says) for two reasons:-
- 1. It allows for a clear statement of the connection between objects and their constituting stuff, and
- 2. The Leibnizian principle for the predicative “is” (as opposed to the constitutive “is”) is highly intelligible15
If and only if A is an f (or is phi) then A is identical with an f (or with one of the phi-things); and if and only if A is one of the f's (or phi-things) then it must share all its properties with that f (or phi-thing).
- There is more to be said on the topic of “ranges of significance” – we’re referred to Russell’s simple or ramified Theory of Types16.
- The lesson from T & W is that we need to reformulate principle S as S*, namely
S*: No two things of the same kind can occupy the same volume at exactly the same time
- Wiggins’s gloss on kind is “… satisfy (the same) sortal or substance concept”.
- He thinks there are at least three reasons for thinking this a necessary truth:-
- 1. Space can be mapped only by its occupants.
- "Wiggins (David) & Woods (Michael J.) - Symposium: The Individuation of Things and Places"
- Wiggins closes with an application of principle S* to the problem of Tib and Tibbles. He attributes the puzzle to William of Sherwood, via Geach17
- … to be completed.
Footnote 1: It is something of an open question whether S is a physical or metaphysical question. Wiggins subsequently considers counterfactual physical circumstances which would allow indefinitely fine commingling of two distinct things, but this still leaves him thinking there’s a problem to solve. So, he thinks there’s an a priori metaphysical issue at stake.
Footnote 2: What’s the compulsion to believe S? Worries often have to do with language (how would our counting work – or else various epistemological claims; these are Olson’s worries about persons and animals occupying the same place at the same time), but the worries ought to run deeper than this.
Footnote 3: The conundrums of Dion / Theon and Tib / Tibbles are relevant here.
Footnote 4: Is there an issue caused by the supposed possibility of intermittent existence?
Footnote 5: Something like the case of miscible fluids would only take us to the molecular level – but at least that’s further than sponges.
Footnote 6: A change from “the statue and the clay” (See Goliath and Lump1 in "Gibbard (Allan) - Contingent Identity", etc.) – and better, since artefacts might be a special case where human concerns and arbitrariness muddy the waters.
Footnote 7: I’d thought of aggregates having less strict persistence conditions than those demanded by mereological essentialism – a heap that has lost a grain is still the same heap – but Wiggins picks up on this. That said, his “take” is an extreme one for the sake of argument, but you could define persistence conditions for aggregates that didn’t mirror those of organic objects, and that were, therefore, less contrived.
Footnote 8: Footnote 9:
- There are obvious connections to the Ship of Thesesus paradox (Click here for Note) here: we could repair the sweater over time, and save the replaced threads, and make socks out of them.
- This is interesting – there’s no temptation to paradox in this case (as socks can’t be identical to a sweater) – but if we made the threads into another sweater, the paradox would return.
- This, I think, shows that the stuff returns to the universal pool of stuff, and carries no memory of its previous form with it.
- Yet we’re still left with disassembled and reassembled watches, bicycles etc. Yet they aren’t disassembled into stuff, but into parts, which retain part of the form of the artefact.
- So, the question is whether the material that makes ships and sweaters are parts or stuff. It would seem that pieces of wool have no relevant form, while planks of wood do – or might. Some planks will be interchangeable, while others are specific to function. Watch and bicycle parts, however, are very specific to place and function.
- I think the disagreement is only semantic. It’s common sense that “the whole is more than the sum of its parts”, but Wiggins doesn’t want to deny this. He’s simply speaking mereologically.
- The parts of the whole either support one another (as in the proverb) or else have form or structure.
- This structure may explain the suggestion that the heap of sand in my garden has different persistence conditions to a mere aggregate (which – one presumes – has mereologically essentialist persistence conditions – as does a set).
Footnote 13: I find this paragraph very difficult to construe. I repeat it here for reference:-
- I’m uncomfortable about this. If (counterfactually) we had immaterial souls, then we would – according to normal parlance – be something “over and above” the matter that constitutes our bodies, yet the matter under consideration (that of our bodies) would be “exhausted” – no more is needed.
- Also, Wiggins takes it that T is “nothing over and above” W if T is constituted of W and nothing else. Yet, form is very important. Are diamonds “nothing over and above” the carbon atoms that constitute them? Would Wiggins say “yes”?
If it is a materialistic thesis that T = W, then my denial that T = W is a form of denial of materialism. It is interesting how very uninteresting an obstacle these Leibnizian difficulties-real though they are-put in the way of the reduction of botany and all its primitive terms to organic chemistry or to physics. (If it does not follow from T # W that trees are something over and above their matter, how much the less can it follow that they are immanent or transcendent or supervenient or immaterial beings. This is obviously absurd for trees. A Leibnizian disproof of strict identity could never be enough to show something so intriguing or obscure.) I should expect there to be equally valid, and from the point of view of ontology almost equally unexciting, difficulties in the reduction of persons to flesh and bones ("Wiggins (David) - Identity & Spatio-temporal Continuity", p. 57), in psychophysical event-materialism, and in the materialisms which one might formulate in other categories (such as the Aristotelian categories property and state or the categories situation and fact). Over and above is one question, identity is another. But of course the only stuff there is is stuff. Footnote 14: What does he mean by this? That the obstacle is illusory?
Footnote 15: This seems to be a restatement of Leibniz’s Law in sortal terms.
Footnote 16: Presumably, this survives Russell’s failure to reduce mathematics to logic. Wiggins gives the following references:- Footnote 17: He thanks Geach for allowing him to use the material, but gives no reference. For some reason, he doesn’t mention the ancient Dion and Theon (Click here for Note), which is of exactly the same form as Tib and Tibbles.
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