Permissivism

Permissivism

Permissive views are those according to which there are wide swathes of highly visible extraordinary objects, right before our eyes.
Universalism is the permissivist thesis that composition is unrestricted: for any objects, there is a single object that is composed of those objects. What universalism does not tell us is whichkinds of objects there are. Whenever there are some atoms arranged turkeywise, universalism entails that there is some object that they compose. But it remains open to universalists (like the aforementioned non-nihilistic eliminativists) to deny that this composite is a turkey. However, assuming that there are such objects as turkeys, trout, and their front and back halves, universalism will entail that there are trout-turkeys, where a trout-turkey is a single object composed of the undetached front half of a trout and the undetached back half of a turkey. These are objects that have both fins and feathers and whose finned parts may be a good distance from their feathered parts.[7]
Diachronic universalism is the permissivist thesis that, for any times and any function from those times to sets of objects that exist at those times, there is an object that exists at just those times and has exactly those parts at those times. Roughly: there is an object corresponding to every filled region of spacetime. So, assuming that your kitchen table and living room table both exist, there also exists a klable—an object that’s entirely made up of your kitchen table every day from midnight till noon and is entirely made up of your living room table from noon till midnight. This is an object that, twice a day, instantly and imperceptibly shifts its location.[8]
The doctrine of plenitude is the permissivist thesis that, for every function from worlds to filled regions of spacetime, there is an object that exists at just those worlds and that occupies exactly those regions at those worlds (cf. Hawthorne 2006: 53). Put another way: if the empirical facts don’t directly rule out there being an object with a given modal property in a given location, then there is an object in that location with that modal property (cf. Eklund 2008: §4). When there is a red car parked in the garage, the empirical facts (e.g., that there is nothing blue there) do directly rule out there being an object in the exact location of the car that is necessarily blue. But they do not directly rule out there being an object there that is necessarily inside the garage: an incar. This is an extraordinary object which, as a matter of metaphysical necessity, cannot exist outside of a garage. As you begin to back out, the incar (if such a thing exists) shrinks and comes to be colocated with the part of the car that is still inside the garage. When you have finished pulling out, the incar has ceased to exist altogether.[9]
One further way of being a permissivist is by permitting a multitude of parts of ordinary objects that we do not naturally judge them to have. For instance, one might hold that, in addition to ordinary parts like arms and legs, you have extraordinary parts like leg complements, where your left-leg complement is an object made up of all of you except for your left leg. Together with some natural assumptions (e.g., about regions of space), leg complements and a legion of other extraordinary parts will be delivered by the doctrine of arbitrary undetached parts—or DAUP—the thesis that for any material object o, if r is the region of space occupied by o, and if r′ is an occupiable sub-region of r, then there exists a material object that exactly occupies r′ and which is part of o. (Roughly: for every region of space within the boundaries of a given a object, that object has a part that exactly fills that region.)[10]

2. Against Conservative Ontologies

2.1 Sorites Arguments

Sorites arguments proceed from a premise to the effect that minute differences cannot make a difference with respect to whether some property F (or kind K) is instantiated to the conclusion that nothing (or everything) is F (or a K). Here is a sorites argument for the elimination of stones:

(SR1)Every stone is composed of a finite number of atoms.
(SR2)It is impossible for something composed of fewer than two atoms to be a stone.
(SR3)For any number n, if it is impossible for an object composed of n atoms to be a stone, then it is impossible for an object composed of n+1 atoms to be a stone.
(SR4)So, there are no stones.

Premises SR2 and SR3 together entail that, for any finite number of atoms, nothing made up of that many atoms is a stone. But this, together with SR1, entails that there are no stones.[11]
Similar arguments may be given for the elimination of individual ordinary objects. One can construct a sorites series of contiguous bits of matter, running from a bit of matter, mk, at the peak of Kilimanjaro to a bit of matter, mp, in the surrounding plains. From the sorites premise that a bit of matter that’s n inches along the path from mp to mk is part of Kilimanjaro iff a bit of matter that’s n+1 inches along the path is part of Kilimanjaro (for any number n), together with the fact that mp is not part of Kilimanjaro, we reach the absurd conclusion that mk isn’t part of Kilimanjaro. So, by reductio, we may conclude that Kilimanjaro does not exist.[12]
Why accept SR3? Imagine a series of cases, beginning with a case involving a single atom and terminating with a case involving what would seem to be a paradigm stone, where each case differs from the preceding case only by the addition of a single atom. It seems highly implausible that there should be adjacent cases in any such series where there is a stone in one case but not in the other. Rejecting SR3 would look to commit one to just such a sharp cut-off.
But one can deny that SR3 is true without accepting that there is a sharp transition from stones to non-stones in such series, that is, without accepting that there is some specific object in the series that definitely is a stone and whose successor definitely is not a stone. For one may instead hold that there is a range of cases in which it is vague whether the object in question is a stone.[13]
Here is an illustration of how that sort of strategy might go. Let S be some object in the series that clearly seems to be a stone, let NS be an object that clearly seems to be a non-stone, and let BS be an object that seems to be a borderline case of being a stone. One might suggest that ‘stone’ is vague as a result of there being a range of candidate precise meanings (or “precisifications”) for the word ‘stone’,

(i)all of which apply to S,
(ii)none of which apply to NS,
(iii)some but not all of which apply to BS, and
(iv)none of which is definitely the meaning of ‘stone’.

‘S is a stone’ is true because S falls under all of these precisifications of ‘stone’. ‘NS is a stone’ is false because NS doesn’t fall under any of them. And ‘BS is a stone’ is neither true nor false because BS falls under some but not all of the precisifications. And then SR3 itself turns out to be false: on every precisification of ‘stone’, there is some object in the series such that it but not its successor falls under that precisification. (This is sometimes known as a “supervaluationist” account.)
Defenders of sorites arguments often complain that this line of response still commits one tosome “sharp status transition”, for instance, a sharp transition from a case in which ‘there is a stone’ is true to a case in which it is neither true nor false.[14]

2.2 The Argument from Vagueness

It is natural to suppose that objects sometimes do, and other times do not, compose a further object. When a hammer head is firmly affixed to a handle, they compose something, namely, a hammer. When they’re on opposite ends of the room, they don’t compose anything. The following argument—commonly known as “the argument from vagueness”—purports to show that this natural assumption is mistaken.

(AV1)If some pluralities of objects compose something and others do not, then it is possible for there to be a sorites series for composition.
(AV2)Any such sorites series must contain either an exact cut-off or borderline cases of composition.
(AV3)There cannot be exact cut-offs in such sorites series.
(AV4)There cannot be borderline cases of composition.
(AV5)So, either every plurality of objects composes something or none do.

If the argument is sound then either universalism or nihilism must be correct, though which of them is correct would have to be decided on independent grounds.[15]
A sorites series for composition is a series of cases running from a case in which composition doesn’t occur to a case in which composition does occur, where adjacent cases are extremely similar in all of the respects that one would ordinarily take to be relevant to whether composition occurs (e.g., the spatial and causal relations among the objects in question). Understood in this way, AV1 should be unobjectionable. If it’s true that the handle and head compose something only once the hammer is assembled, then a moment-by-moment series of cases running from the beginning to the end of the assembly of the hammer would be just such a series. Premise AV2 looks trivial: any such series obviously must contain some transition from composition not occurring to composition occurring, and there either will or won’t be a determinate fact of the matter about where exactly that transition occurs in any given series.

AV3 is plausible as well. If composition occurs in one case but not in another, then surely there must be some explanation for why that is. In other words, the facts about composition are not “brute”. Yet the sorts of differences that one finds among adjacent cases in a sorites series for composition—for instance, that the handle and head are a fraction of a centimeter closer together in the one than in the other—can’t plausibly explain why composition occurs in one case but not in the other.[16]

Certain sorts of eliminativists are well positioned to resist AV3 without having to accept that compositional facts are brute. Suppose, for instance, that one accepts a view on which conscious beings are the only composite objects. Such eliminativists will deny that there is a sorites series for composition running from the beginning to the end of the assembly process, since they will deny that anything is composed of the handle and head (or that there are a handle and head) even at the end of the series. Every sorites series for composition, by their lights, will have to run from a case in which there is some number of conscious beings to a case in which there is some other number of conscious beings. And assuming that that there can’t be borderline cases of consciousness, every such series will contain a sharp cut-off with respect to the presence of the additional subject of consciousness. This, in turn, is poised to explain why composition occurs in the one case but not the other.[17]
Why, though, should anyone accept AV4? On the face of it, it seems just as clear that there can be borderline cases of composition (e.g., when the hammer head is just beginning to be affixed to the handle) as it is that there can be borderline cases of redness and baldness. This is not, however, “just another sorites,” to be blocked in whichever way one blocks the sorites arguments in §2.1. That’s because questions about when composition occurs look to be intimately bound up with questions about how many objects exist. This suggests the following line of argument in defense of AV4, no analogue of which is available for other sorts of sorites arguments.[18]

(AV6)If there can be borderline cases of composition, then it can be indeterminate how many objects exist.
(AV7)It cannot be indeterminate how many objects exist.
(AV4)So, there cannot be borderline cases of composition.

To see the motivation for AV6, notice that if the handle and head do compose something then there are three things: the handle, the head, and a hammer. If they don’t, then there are only two things: the handle and head. And if it is vague whether they do, then it will be vague whether there are two things or three. As for AV7, notice that one can specify how many objects there are using what would seem to be entirely precise vocabulary. For any finite number, one can produce a “numerical sentence” saying that there are exactly that many concrete objects. Here, for instance, is the numerical sentence for two: ‘∃x∃y(x≠y & Cx & Cy & ∀z(Cz→(x=z ∨ y=z)))’. (The restriction to concreta ensures that numerical sentences aren’t trivially false simply on account of there being infinitely many numbers, sets, and so forth.) And since these numerical sentences contain no vague vocabulary, it would seem to follow that it cannot be indeterminate how many objects there are.
AV6 can be resisted by denying that composition affects the number of objects in the way suggested. For instance, one might contend that even before the handle and head definitely come to compose something, there exists an object—a “proto-hammer”—located in the region that the two of them jointly occupy. The proto-hammer definitely exists, but it is a borderline case of composition: it is indeterminate whether the handle and head compose the proto-hammer or whether they instead compose nothing at all (in which case the proto-hammer has no parts).[19]
Alternatively, one might resist AV7 by pinning the vagueness on the quantifiers in the numerical sentence. After all, what seems to be vague is whether the handle and head are everything that there is and whether there is something other than the handle and head. But it is difficult to see how the quantifiers can be vague and, in particular, how their vagueness could be accounted for on the sort of standard, precisificational account of vagueness discussed in §2.1.[

Permissivism

Permissivism

2. Against Conservative Ontologies

2.1 Sorites Arguments

2.2 The Argument from Vagueness

Permissivism :: تعاليق

Permissivism