Unrevised draft accepted subject to revisions by Noûs, 1 October 2007. Substantially revised version: Noûs 43.2 (June 2009), 346-362 http://www3.interscience.wiley.com/journal/117997227/home

Phenomenal and objective size Definitions of phenomenal types (Nelson Goodman’s definition of qualia, Sydney Shoemaker’s phenomenal types, Austen Clark’s physicalist theory of qualia) imply that numerically distinct experiences can be type-identical in some sense. However, Goodman also argues that objects cannot be replicated in respect of continuous and densely ordered types. In that case, how can phenomenal types be defined for sizes, shapes and colours, which appear to be continuously ordered types? Concentrating on size, I will argue for the following points. (§2) We cannot deny the possibility of replication in respect of dense types, because this would imply that particulars have determinable sizes, shapes and colours. (§3) Phenomenal sizes and shapes are determinable types; objective, or super-determinate, sizes and shapes are unknowable. (§4) We can define and know, prior to verification, groupings of objective sizes for which indiscriminability is transitive. (§5) Phenomenal identity has to be defined on the basis of these transitive groupings, because finer-grained criteria lead to definition of objective identity. The quality space of phenomenal types consists of overlapping but not dense types, and this prevents a collapse of phenomenal types.

1. The problem: phenomenal types, matching, and replication For there to be phenomenal types, it has to be possible for numerically distinct experiences to be type-identical in some sense; and for some form of type-identity to be defended, an adequate response has to be found to the problem of non-transitive matching. Non-transitive matching can be illustrated as follows. It is possible to have three objects (x,y,z) such that the qualia (eg, the colour, size or shape experiences) caused by (x,y) match and the qualia caused by (y,z) match, while the qualia caused by (x,z) do not match. Opponents of sense-data theories, such as Armstrong, use this non-transitivity 1

of phenomenal matching to deny the existence of phenomenal types. One response to the failure of objects to pass the threewise matching test involves denying that the quale presented by y when it is compared to x, and the quale presented by it when it is compared to z, are identical (Jackson and Pinkerton, 1973); but this hardly strengthens the case for phenomenal types, and it weakens the case for a representationalist construal of them. A possible response to Armstrong involves denying that matching is nontransitive under ideal observation conditions (Schroer 2002). However, as Graff (2001) points out, a response to both problems (failure to pass the threewise matching test, and Armstrong’s objection to the existence of phenomenal types) is already provided by Goodman. The response involves defining phenomenal identity on criteria stricter than pairwise indiscriminability. Thus, according to Goodman, the qualia presented by two objects are identical not if the objects are indiscriminable, but if and only if they match the same sets of objects: (x,y) systematically match if and only if for any object z, z matches either both (x,y) or neither of (x,y). Goodman’s distinction between phenomenal matching and phenomenal identity is taken up by Austen Clark when he admits that there are phenomenal differences below the threshold of sensible discrimination.

This (‘Goodman/Clark’) solution raises two related problems. The first has been described as follows by Graff: ‘if two things look the same, then the way they look is the same [...] [W]hen one denies this conditional it starts to look implausible that the way a thing looks can still be considered a phenomenal quality.’ The second problem is that elsewhere, Goodman holds a position which appears to contradict his position on qualia and matching: he argues (like Sellars, 1953) that objects cannot be replicated in respect of any densely ordered types they instantiate, and that objects can only be replicas in respect of discrete or disjoint types. (Goodman 1976 ch.4, sect.II)

A case can be made that Goodman’s two positions (on qualia and on replication) are compatible. On the criterion of identity for qualia given further up, for an object y to be a phenomenal replica of x – that is, a replica of x in respect of its qualia – it would have to be such that no object z matches only one of (x,y) in respect of the relevant qualia. Although pairwise matching between (x,y) can be established – I would have to produce

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an object y which is pairwise indiscriminable from x – systematic matching cannot, since we cannot know that there is no object which matches only one of (x,y). At best, we could define phenomenal identity between x and its aspiring replica y relative to a verifiable set or ‘clan’ of objects (Goodman 1977, 210), leaving open the possibility that there are counter-examples (objects matching only one of (x,y)) which show that x and y do not after all instantiate the same phenomenal types. The case, however, is not convincing. For if unknowability leads us to deny the metaphysical possibility of replication, then it should also lead us to deny the metaphysical possibility of phenomenal identity. (Alternatively: why not admit replication by relativizing it to clans of verifiable objects, since we can do this in the interests of defining qualitative identity?) In what follows I will argue that although objective sizes, shapes, and colours are densely ordered, their phenomenal counterparts overlap without forming dense types, and that this permits us to define a form of phenomenal type-identity for sizes, shapes and colours. Concerning objective types, I will show that replication is metaphysically possible but unknowable; concerning phenomenal types, I will argue that replication is not only possible, but knowable and practically feasible. Specifically, in §2, I will argue that Goodman’s denial of replication and type-identity in respect of continuously ordered types is ill-founded, and that objective replicas are possible, though unknowable. In §3, I will argue that determinate phenomenal sizes and shapes correspond to determinable objective sizes and shapes. In §4 I will show that groupings of objective sizes in which indiscriminability is transitive are definable and knowable prior to verification. In §5, I will argue that these transitive groupings are phenomenal size types, and that although determinate phenomenal types overlap, they are not densely or continuously ordered. Finally, in §6, I apply these theses to show that phenomenal replicas in respect of size can be produced and known.

2. Objective replication and determinateness Before examining the relations of identity and resemblance for phenomenal sizes and shapes, I will try to elucidate the nature of the objective sizes and shapes that phenomenal

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types group together on the basis of phenomenal similarity. I will argue that replication in respect of dense types is metaphysically possible, and that denying the possibility would amount to claiming that particulars cannot have determinate sizes and shapes. In doing so (and in defining the relations between objective and phenomenal sizes and shapes in subsequent sections), I will assume a continuist concept of space, since it is continuous orderings which are thought of as preventing type-definition and identity.1

On a continuist conception of space, for any two points that do not coincide, there is a region of space between them comprised of points. To apply this to the simple case of two-dimensional shapes, imagine that two outline drawings A and B with different sizes but identical shapes and orientations are superposed concentrically on a sheet of paper, so that further outlines (with identical shapes and orientations) can exist in the space between their outlines. Any outline C between A and B will be numerically distinct from both A and B, allowing, on the same principle, an outline drawing D between A and C, and so on. Each numerically distinct drawing on the sheet of paper will be an instance of a shape type; and just as any two such distinct particular outlines will allow further outlines between them, for any two given size types there will be a third type between them.

Now, if we attempt to apply to particular shapes some epistemic criterion of typeappurtenance, we will run into a difficulty pointed out by Goodman, and named by him ‘non-finite differentiation’: any particular shape will be such that its appurtenance to no more than one type is ‘logically and mathematically’ impossible to establish. (Goodman 1976: 134–137) I will return to this problem in §§ 3 and 4, but the point I wish to make in this section concerns objective, not phenomenal (or otherwise epistemic) types. Epistemic criteria, whether phenomenal or not, based as they are on encoding, and being

1

On the alternative conception, space is discrete. A tentative defense of such a concept of space is

presented in Le Poidevin 2004. Le Poidevin argues that a discrete concept of space may have the merit of accounting for spatial relations, as long as those relations are construed as supervenient on nonneighbouring discrete points. He rejects the position that distances are cumulations of ‘space atoms’ on the grounds that we cannot give a definition of the size of space atoms.

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subject to discrimination thresholds and memorization capacities, will be unable to reproduce the objective ordering of densely ordered objective shape and size types. If, for instance, there are phenomenal size types, then these can only be coarser, and vague, groupings of finer objective shape types. Non-finite differentiation does indeed imply that we cannot define dense epistemic types which reproduce the dense ordering of objective sizes and shapes. But it does not imply that we cannot define dense objective size and shape types. Thus, two numerically distinct shapes on different sheets of paper may be qualitatively identical in respect of size and shape, independently of whether this can ever be known. Numerically distinct lines with identical shape and size would be represented in an ordering of shapes and sizes by a single line, so there can be no vagueness in the ordering about the extent of the shape- and size-types they belong to. So lack of finite differentiation in the ordering of types does not entail that shape and size replicas are objectively impossible, and it is possible for objects to be identical in respect of size and shape.

From the preceding claim—that it is possible for there to be identical objects in respect of shape and size—I will now attempt to extract a further claim, namely, that there are super-determinate shape and size properties (shape and size properties which cannot be further determined).2 Looser conceptions of replication and identity, defined as the sharing of determinable shape and size properties (which is at work in phenomenal indiscriminability) would not entail acceptance of super-determinate shapes and sizes. But the conception described above denies that there are types grouping more than one line in the property space, and therefore defines types as grouping lines that are distinct only in the numerical sense. Thus, the relation between the size types and shape types on one hand, and on the other the sizes and shapes of particulars, is not a determinabledeterminate relation: it is a relation between an undeterminable property and its instantiations. The situation with respect to super-determinate shape and size properties can be summarized thus: (1) there are infinite shape and size types in the property-space,

2

On the concepts of determination dimension, property space and super-determinateness, and on the determination relation in general, see Funkhouser 2006.

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(2) numerically distinct objects can be identical in respect of size or shape, in the superdeterminate sense of ‘identical’ (and not just in the sense of coming under a wider determinable). If we were to suppose that there are no such things as super-determinate sizes and that sizes are in principle always further determinable, we would be led to the conclusion that two numerically distinct lines necessarily also have different sizes. In that case, two lines could have the same shape and size only in the same sense as that in which a crimson and a scarlet object are both red.

The following objection could be raised against the claim that there are super-determinate shapes and sizes: “Numerically distinct objects could be identical in respect of size even without admitting super-determinate sizes. Assume there are not super-determinate sizes. With this assumption, two objects would be identical in respect of size if for any determinable size type the two objects either both share or both lack that type. It is simply the case that there is always a more fine-grained type that they also share.” This position could be called ‘weak objective identity’.

The reply is that there can be no weak objective identity because if two objects do not have identical size in the super-determinate sense, then they do not coincide in the ordering or property space of sizes, and if they do not coincide in the ordering, then there have to be sizes between them that they do not share. Suppose that there are no superdeterminate sizes, and that sizes S1 and S2 are identical in the weak sense.

(1) There are no super-determinate sizes. (2) Sizes S1 and S2 are identical in the weak sense. (3) (1) Sizes S1 and S2 do not coincide in the property-space. (4) (3) Size types S1 and S2 are separated by a region r in the property-space. (5) (1) Size types S1 and S2 are groupings of more highly determinate size types. (6) (4,5) S1 and S2 do not group the same more highly determinate size types. (7) (6) There are size types in r that S1 and S2 do not share. (8) (7) S1 and S2 are not identical sizes in the weak sense.

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Before considering some objections to the argument, it will help to illustrate the situation that weak objective identity attempts to describe. Imagine that there are no superdeterminate lengths, and that two matches appear to be the same length. Suppose that we can employ ever more powerful means of discrimination, and have infinite such means at our disposal, but that no matter how far we go, we can find no difference in length between the matches. Weak objective identity consists in imagining that such a situation can go on ad infinitum. The increasingly powerful means of discrimination are definitions of increasingly determinate length-types. My argument says that if the lengths are not super-determinately identical, they cannot coincide in the property-space, and therefore cannot be groupings of the same sets of more highly determinate lengths; in other words, we will in principle be able to reach a level of determinateness beyond which the matches will no longer share the same length-types. If, on the other hand, as a matter of principle, no carving up of the property-space of lengths, however fine, can define the matches as having different sizes, then this has to be because the matches have super-determinately identical lengths, since the alternative case has been excluded.

Now to potential weaknesses in the argument. First, in order to avoid the conclusion in (7), could the defender of weak objective identity not deny (3)? My reply is that if (3) is denied, the idea that S1 and S2 are determinables cannot be maintained. According to the concept of weak identity, all sizes are determinable, and as such they are regions of the property space which group other regions (finer-grained determinables), and so on ad infinitum. The negation of (3) says that regions S1 and S2 coincide; but if S1 and S2 coincide in a property space comprised of points, then they are super-determinately identical.

A follow-up to the preceding objection could be made on the following grounds: since I continue to maintain that the property space is comprised of points, does my argument not contain a petitio principii in favour of super-determinate sizes (which are delimited in the property-space by points as opposed to vague regions)? A petitio principii in favour of super-determinate identity would indeed lurk behind (3) if super-determinate identity was required by the concept of a property space comprised of points. But it is not

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required, because even if there were only determinable sizes, we could still map those sizes onto a continuous property space comprised of points—as in fact we have to do for determinable sizes anyway, even when we additionally admit super-determinates. The only thing we could not do is claim that the sizes of two particulars, when those sizes are not super-determinate, coincide in the property space. If this is correct, then numerically distinct objects cannot be identical (objectively, as opposed to phenomenally) in respect of size unless we admit super-determinate, or nondeterminable, sizes. Either we have to accept that objects are replicable in respect of the dense types they instantiate and accept super-determinate properties, or we have to deny replication and assert that particulars are determinable. In what follows I will choose the former: admit the objective replicability of densely ordered properties, as well as that there are super-determinate sizes, shapes and colours. This also allows us to uphold a useful distinction: if we admitted a definition of identity as the sharing of determinables, then, since ‘determinable identity’ is really only resemblance and not identity, there would be no difference between objective identity and objective resemblance.

3. Phenomenal types as objective determinables These metaphysical points concerning the possibility of objective identity and replication, if true, stand independently of what can be known, be it phenomenally or by some other form of encoding. For objective identity and replication to have any known applications (such as the knowledge that two objects are identical in respect of size or shape), there would have to be a system capable of discriminating shapes and sizes superdeterminately. I will argue that it is impossible for any discrimination system to discriminate super-determinate shape and size properties. Once this is shown, we can begin to have a clearer idea of phenomenal types as groupings of experiences and mental contents which represent objective sizes and shapes.

For an encoding system to discriminate super-determinate shapes and sizes, it would have to keep super-determinate shapes and sizes disjoint. For two super-determinate lengths to

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be disjoint, a region would have to separate points. Suppose that a region r separates point a from point b. The system will recognize points as not being b (for example, towards the middle of r). But there will be no point it can recognize as being b, for there will be points sufficiently close to b for the system not to be able to discriminate them from b.

The fact that no encoding system can discriminate super-determinate sizes means that phenomenal sizes can only be determinable sizes. Phenomenal sizes also stand in a determination relation to objective sizes: they are determined by the objective size properties of perceived objects. In one sense, this is trivially and analytically true, since super-determinate sizes have to determine some determinable sizes. In another sense, this determination relation appears to ground a form of empirical knowledge, because it also applies to the relata of perceptual causation, ie, the process by which an objective size property causes a representational content to the effect that the object comes under a certain determinable.

So far, in describing phenomenal size types as groupings of regions in property spaces, we have given no indication of their mental status and structure. They are not the qualitative ingredient of phenomenal experience caused by objective size-properties, namely, visual field occlusion or occupation. First, visual field occlusion is not a determinable magnitude but a determinate one: it is regressive to ask whether I know the extent of my sense-datum, rather as it makes little sense to ask if I know what subjective colour my colour-sensation is. Secondly, phenomenal sizes are determinable sizes attributed to objects, and we do not attribute qualia to objects – qualia play a role in determining which content we have, they do not constitute content. This point, as well as another key point about phenomenal sizes, is brought out well in Shoemaker’s account of phenomenal character: ‘the properties that enter into [...] representational content, and in that way (i.e., by being represented) fix [...] phenomenal character, are not themselves features of our experiences – are not themselves qualia.’ (Shoemaker 1994, 296) Represented size – the size I represent an object as having, on the strength of perceptual discrimination – has this status: a determinate, objective size property S1 fixes (through

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discrimination, which is implemented by the machinery of encoding) phenomenal character P, which includes content to the effect that x has determinable size S. Thus described, phenomenal sizes can be part of a representationalist construal of phenomenal contents.

Stephen Yablo (1992) has put forward the idea that certain mental states and their realizers may stand in determination relations. The idea has been criticized by Eric Funkhouser (2006) on the valid grounds that mental states and their realizers have different determination dimensions. But it has not been shown that no mental state can stand in a determination relation to its realizers. Given that phenomenal sizes qua phenomenal contents have such a close resemblance to the objective sizes that cause them, it is tempting to use them in order to ask whether Yablo’s thesis may not be valid in certain cases. Trying this out involves speculatively stretching the concept of a realizer state; but the hypothesis could run as follows: if objective size was part of an extended system comprising a visual apparatus, a perceived object and a perceptual medium, which jointly realized a perception-dependent phenomenal experience, then the objective size of the object would both determine and realize phenomenal content.

Even with the allowances made, phenomenal sizes do not seem to confirm Yablo’s hypothesis. S1 is the objective size of x and causes mental state P, which includes content to the effect that x has determinable size S. For S1 to both realize and determine S, the phenomenal content would have to be S. But the phenomenal content is not S, it just represents S. Nevertheless, this helps clear a peristent ambiguity in the concept of phenomenal size (which has no equivalent in that of colour, though it may in that of shape). An expression such as ‘the phenomenal width of the doorframe’ can be construed as referring to the side of a rectangle occupying a portion of my visual field, as well as to a size determined by all objective sizes phenomenally indistinguishable from the objective width of the doorframe. The first is realized (arguably, in some sense) by the objective width of the doorframe, but not the second; the second is a phenomenal width determinable by the objective width, but the first is not a determinable width at all.

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Perhaps as a final go at grasping the particular metaphysical relation between objective and phenomenal size, we could call size a ‘revelatory property’.3 Objective size properties cause phenomenal contents which reveal the nature of the properties that cause them by placing those properties within their objective ordering or property-space. The contrast between revelatory and non revelatory properties can be grasped if we compare sizes with colours. A colour-experience does not tell us what the property that causes it is like, and we have had to discover the nature of objective colour – its determination dimensions and the structure of the property-space – a posteriori. Phenomenal shape, although less revelatory than size, is nevertheless more informative on the nature of its objective causes than colour is: even when a phenomenally circular shape supervenes on a shape which is super-determinately and indiscriminably irregular, so that the two kinds of properties do not even share the same determination dimensions, at least both kinds of properties come under the determinable shape. Phenomenal shape may generally relate in this way to objective shape. If this is so, the fundamental differences between size, shape and colour can be brought out simply as follows: phenomenal sizes are determined by objective sizes, phenomenal shapes have different determination dimensions to objective shapes but are determinates of the same super-determinable shape, and phenomenal and objective colours are not determinates of any determinable. Yet, the determination relation remains indispensable for a definition of phenomenal shapes: phenomenal shape is determined by determinate shapes which are not yet super-determinate, so that relations between different levels of encoding can be analyzed as determination relations.

4. Phenomenal identity for sizes (I) A resemblance relation between objects which is not transitive does not amount to identity. If indiscriminability is such a form of resemblance, then indiscriminability does not amount to identity. But when we say that indiscriminability does not ensure identity, we are in effect asserting two propositions: (i) indiscriminability does not ensure objective identity, (ii) indiscriminability does not ensure phenomenal identity. The first

3

The expression is Peter Kail’s.

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thesis is already entailed by the fact that no encoding system can discriminate superdeterminate, objective types (§3). I will argue that the second thesis is false, and that indiscriminability does ensure phenomenal identity.4

My argument, which concentrates on phenomenal size, has two parts. First (§4), I will show that indiscriminability is transitive for groupings of objective sizes (and the sets of objects which instantiate those objective sizes), and that those groupings can be defined and known prior to any verification by matching. Secondly (§5), I will argue that any attempt to define phenomenal identity on criteria finer than indiscriminability (such as Goodman’s definition of qualia) leads to a definition of objective identity, and to the false conclusion that phenomenal types are densely ordered. Then I will maintain that transitive groupings, since they preserve type-identity, qualify as phenomenal size types.

Here is how we can define and know – prior to any verification by matching – groupings of objective sizes which are transitively indiscriminable. In the diagram below, Sh, Sj, Sk, Sn are different super-determinate lengths, (Sj, Sk) match, and (Sh, Sk), (Sj, Sn) are discriminable so that (Sj, Sk) fail the threewise matching test. The shaded area (grey and black) represents a continuously ordered region of objective length types which cannot be discriminated using pairwise matching. Because this shaded region is defined as a function of discrimination and encoding, we cannot know exactly which superdeterminate lengths it includes (§3), and therefore cannot define its exact extent in the objective property-space. However, within this region, we can define a second region of the property space, the black region r, which is disjoint from Sj and Sk , so that for any length S in r, Sj < S < Sk . Sh

Sj

Sk

Sn

———————|———|———|———|————> r

4

An introduction to this question is given in §1.

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Now we can formulate a non-trivial sufficient condition about the objective size an object has to have in order to have a given phenomenal size. (A trivial sufficient condition would be to say that an object has to have objective size S1, where S1 is a determinate size somewhere between and excluding Sj and Sk: the condition is trivial because it is impossible to know whether any object has objective size S1.) The condition is that if an object has any of the determinable sizes in disjoint region r of the objective propertyspace (ie, between, and excluding, Sj and Sk ), then it will have a certain phenomenal size S. All determinable sizes within r are regions, so there are encoding systems – not much finer than perception – which can discriminate such sizes, by picking out a region inside r. Note that to know that an object has a determinable size from within the disjoint region r, we do not have to be able to discriminate the super-determinates Sj and Sk themselves, which is not possible for any encoding system. We only have to be able discriminate sizes as not being Sj or Sk , and this is possible for discrimination systems. Since the objective sizes Sj and Sk are not pairwise discriminable – their objective difference does not pass the threshold of discrimination – any two objective sizes differing by less will not be discriminable either. The objective sizes in r are all such sizes. Region r is disjoint from the regions before Sj and after Sk (since it is separated from them by at least Sj and Sk), so there is no ambiguity about the type-appurtenance: all ambiguous cases have been placed in the regions before Sj and after Sk. Phenomenal encoding can record no difference between these sizes even by using threewise matching: if (x,y) instantiate objective sizes from r, then for all objects z which instantiate any objective size from r, Mz,x  Mz,y. Thus, by using a discrimination system finer than perception, we can define and know – prior to verification of particular objects by matching – sets of objective sizes for which phenomenal indiscriminability is transitive.

5. Phenomenal identity for size (II) My purpose now is to show that these groupings (in the diagram, the black region r) of objective sizes, which preserve transitivity, are phenomenal size types. Such a claim would conflict with Goodman’s definition of qualia:

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Qu x  (x=y)  (z) (Mz,x  Mz,y) Under that definition, for x and y to present identical qualia, there has to be no object which matches only one of them (Goodman 1977, 210). The groupings defined in §4 do not meet this condition because we do not know that there is no such object anywhere; we only know that there is no object matching only one of (x,y) in a certain definable region of the property space.

First, note that Goodman’s definition has no knowable applications, and can therefore only be valid as a theoretical description of what must obtain if there is to be phenomenal identity. If we take ‘(z)’ in Goodman’s definition to mean ‘any object anywhere’, and not just in a pre-selected clan of objects, then indiscriminability cannot be known by using the kind of matching test described in the logical formula, since we cannot verify all objects in the relevant respect. On the other hand, if ‘(z)’ means ‘anywhere in a clan of verified objects’, then Goodman’s definition is false: it is possible that all the objects in a clan have sizes from within the transitive grouping r, corroborating the indiscriminability of (x,y), which nevertheless would be defeasible by objects with sizes from outside r.

This question of knowability aside, is the definition valid as a metaphysical definition of phenomenal identity? If so, the definition will work for pairs of objects which are so close (by human discrimination standards) in the objective property space, that any other objective size will be phenomenally indistinguishable either from both or from neither. So imagine an object y which is longer than an object x by a very small magnitude, α. Now, suppose an object z which differs from y by magnitude (k–α), where k is the smallest magnitude which can be recorded by our threshold of visual discrimination. During the threewise matching test, the cumulative difference between z and x ((k–α)+α) will be k, which passes the threshold of discrimination, so (x,y) will not pass the threewise matching test for z. Since what makes pairwise indiscriminable objects fail the threewise matching test is the cumulative difference (between x,y and y,z), the same will apply to any pair of objects, however small their objective difference: there will always be an actual or a possible object which prevents (x,y) from satisfying Goodman’s definition. The only cases which satisfy Goodman’s definition are those in which there is

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no objective difference at all between (x,y) – in other words, cases of super-determinate objective identity. So the definition collapses into a definition of objective types and identity, leaving no room for phenomenal types and identity.

The reason for this collapse is that we have admitted as phenomenal differences the indiscriminable objective differences between (x,y) and (y,z), which only amount to a phenomenal difference when they are cumulated. A similar distinction between phenomenal indiscriminability and phenomenal identity is adopted by Austen Clark when he says that that there are phenomenal differences below the threshold of sensible discrimination, or ‘a qualitative difference between the sensations engendered by indiscriminable things’.5 The difference could also be described as that between looking phenomenally identical and being phenomenally identical. It is based on the following principle: If

indiscriminable

objective

differences

pass

the

threshold

of

discrimination when they are cumulated, then those objective differences are phenomenal differences. If we accept this principle, lengths differing by a single Å have indiscriminable phenomenal differences, since sufficient cumulation of the objective difference would eventually pass the threshold of discrimination. The only indiscriminable objects which do not present such cumulable objective differences are indiscriminables which also happen to be super-determinately identical. But if only super-determinate identity counts as phenomenal identity, then the concept of phenomenal identity no longer has any

5

Clark writes: “Suppose we have a match between x and y, and y and z, but not between x and z. If the

sensation of y were qualitatively identical with that of x, then the indiscriminability of y and z would establish that x and z must also be indiscriminable. But x and z are discriminable. Hence the sensations engendered by x and y must be qualitatively distinct, although x and y are (pairwise) indiscriminable. For the sake of an abbreviation, such a difference will be called an 'indiscriminable qualitative difference': a qualitative difference between the sensations engendered by indiscriminable things. Qualitative differences exist below the thresholds of discriminability. Matching, or even indiscriminability, is too weak a relation to define qualitative identity; x and y must match, not only one another, but also the same sets of items z” (emphasis added).

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application for dense types (while the remaining, objective concept, has no knowable application). If we admit a concept of indiscriminable phenomenal difference, there will be no phenomenal identity.

What, then, does failure to pass the threewise matching test tell us about the resemblance relation obtaining between two objects which match pairwise? (If it does not tell us that the particulars x and y are phenomenally different, and that there are qualitative differences below the threshold of discriminability, as Clark and Goodman maintain?)

Let us look more closely at what happens when two objects which match pairwise fail to pass the threewise matching test. Although we can infer that (x,y) are not identical from observation that M(x,y), M(y,z), and M(x,z), we do not, as a result of this inference, see that (x,y) are different, or have a qualitatively different size-experience of y.6 The only qualitatively new experience that we are certain of having during unsuccessful threewise matching tests, is the experience which is caused by the fact that the objective difference between x and z passes the threshold of discrimination (unlike the objective differences between (x,y) and (y,z)), and we perceive a difference in size between the two objects. We have two token experiences of y (one when it is compared to x, one when it is compared to z) which we have reason to consider qualitatively identical, since they are caused by the same objective size each time (that of y). However, both these token experiences of y come under two phenomenal size types, because they are in the overlap of two phenomenal types: the type that also includes the experience of x, and the type that also includes the experience of z. On this account, the second perception of y (when it is compared to z) does not cause a qualitatively new experience of y, nor is a new experience-type or phenomenal type generated in the process of threewise matching. If we could have new experience-types at 6

Jackson and Pinkerton (1973), seeking to avoid the threat to the identity of percepts which is implicit in

non-transitive colour-matching, appeal to perceptual relativity and maintain that the experience of y is different when y is compared to x and when y is compared to z. For the reasons pointed out in the next paragraph, the account presented here raises a problem for their proposal.

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this rate, the ordering of phenomenal types would be dense: there would be as many ways of looking phenomenally identical (without being phenomenally identical) as there are determinable objective sizes. Instead, the fact that we do not have a new size-experience of y means that phenomenal size types are not densely ordered (which does not imply that they are discrete either, because they can still overlap). In other words, although phenomenal size types are objectively determinable (group many objective size types), they are phenomenally determinate, that is, they cannot be determined by further phenomenal sizes. Indiscriminability could, precisely, be described as a negation of density: it is not the case that there is a third phenomenal type between any two phenomenal types, and the absence of further types is the inability to discriminate all remaining, finer-grained, objective differences. So the ordering of phenomenal sizes is not dense. If we say that sizes are densely ordered, either we are referring to objective sizes, or else we are using a form of shorthand to express the fact that phenomenal sizes, apart from grouping type-identical size experiences, also group the densely ordered objective causes of those experiences. What failures to pass the threewise matching test tell us then, by inference, is that certain phenomenal groupings of densely ordered objective types overlap. When we try to solve this problem by admitting finer-grained phenomenal types, we in effect fall into the trap of defining non-phenomenal types in order to capture differences that discrimination cannot capture; and in its systematic form, which is Goodman’s definition of qualia, this introduction of finer-grained types leads to a definition of objective types. The alternative presented here is to use the threewise matching test, not to in order to define phenomenal identity, but in order to define phenomenal groupings which do not overlap, and which therefore preserve type-identity. These are the groupings defined in §4. We cannot know exactly which objective sizes will make two indiscriminable objects fail threewise matching (in the diagram in §4, they are somewhere between, and excluding, Sh and the black region r, and the black region r and Sn). But we can know, without any ambiguity, a set of objective sizes, r, such that all objects instantiating them will be transitively indiscriminable. If we limit a definition of phenomenal size types to those regions, phenomenal identity will be transitive.

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The lack of density (despite the overlap or lack of disjointness) in the phenomenal ordering suffices to prevent a soritic collapse of phenomenal types into one another. Density makes it impossible even in principle for a discrimination system to establish types and type-appurtenance, unless a grouping principle based on criteria foreign to the densely ordered property is imposed on that ordering. The encoding capacities of an organism provide this principle: the distance required in the objective ordering for phenomenal difference is a function of those capacities. Once types are defined on this basis, they do not collapse because they are differentiated in an objective way, ie, as a function of encoding. Continuity means that under optimal observation conditions we can only – as a matter of biological necessity – make phenomenal judgments which are ‘out’ in the objective ordering by less than the threshold of discrimination. Thus, (for some possible organism if not humans) 0.75mm belongs to both the phenomenal type that covers 1mm and the type that covers 0.5, but belongs neither to the phenomenal type that covers 0.25 nor to the phenomenal type that covers 1.25. This much can be done with the phenomenal ordering ‘as it stands’, on a biological basis. Thus construed, phenomenal types can play the role required of them by representationalism. A given phenomenal size represents an infinite disjunction of objective sizes which is a subset of the larger infinity of sizes, and therefore excludes other objective sizes.

We can also divide the objective property space into less determinate disjoint phenomenal types. Sometimes the disjoint types are cultural devices, such as the ideas one has of what an inch, a metre, or one’s own height amount to. Disjoint orderings can be illustrated with phenomenal colours (in a way which still applies if the colour spectrum is inverted): we have different experience types for vermillion and scarlet, which occupy discrete parts of the quality space, and arguably also for some intermediate hues Cj and Cn between vermillion and scarlet; but between these intermediate hues there are hues which belong to both phenomenal types Cj and Cn. Why does this not end up causing a collapse into each other of such types as we can discriminate, such as scarlet and vermillion, or even blue and yellow? Because scarlet and vermillion are disjoint, or separated by objective colours which belong to two determinate phenomenal types. For

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any values taken from disjoint regions r1 or r2 of the objective property space of colours, such that their distance in the objective ordering is greater than that between objective colours which are pairwise indiscriminable, objects are discriminable in a way that cannot be defeated by cumulating imperceptible objective differences. So if, by a series of indiscriminable transitions, I pass from vermillion to scarlet, I will still be able to classify the last pair of colours as scarlet instead of vermillion, because the ordering of phenomenal colour types is fixed on the basis of objectively definable discrimination differences.

6. An application An application of Goodman’s stricture on replication in respect of dense types is his denial that there can be perfect phenomenal forgeries of paintings. To hold that indiscriminable forgeries are still not replicas is in effect to hold that indiscriminability does not ensure phenomenal identity. The motivation behind this position can be reconstructed as follows. On Goodman’s theory, phenomenal type identity of objects x and y in respect of their dense properties could be known only by verifying that there is no object z that matches only one of x or y. So if I produce a copy y of x which matches x, I cannot know a priori that all objects will match both x and y, and therefore cannot know that x and y come under the same phenomenal type.

The definition of sufficient objective conditions for phenomenal identity shows that objects can be phenomenally replicated in respect of dense types, and that such replicas can be known to be replicas. The following suffices to guarantee replication of x in respect of its size. Produce an object w which is pairwise-indiscriminable from x. x has super-determinate size Sj and w has super-determinate size Sk . Then produce an object y with size S such that S {Sj ... Sk}, S Sj , SSk . This condition can be met practically, ie is not beyond the discrimination capacities of systems finer grained than perception, since it does not require discrimination of a super-determinate type, only discrimination of points or regions as being inside a region. The resulting indiscriminabilty is transitive for

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all objects meeting the same condition as y (having a size S such that S {Sj ... Sk}, SSj , SSk). Showing, on the same principle, that objects can be replicated phenomenally not just in respect of size but also in respect of shape and colour, is a more complicated matter, but in principle feasible. To define a sufficient condition for the phenomenal replication of shapes, we would need to define a region including the diverging, converging and overlapping lines of shapes which appear phenomenally to coincide (to be a single line in a property space). It is likely that we would have to use an encoding system at one remove from that used in defining phenomenally identical size types: an encoding which relates to the encoding for sizes in the way that the encoding for sizes relates to perception. But there is no logical obstacle to doing any of this: it is still a matter of establishing disjoint regions of an ordering by using a sufficiently fine-grained discrimination system.7

7

Nor does this require us to define a property space for shape in general, which may not be possible. On

this, see Funkhouser 2006.

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REFERENCES Clark, A. 1989. ‘The Particulate Instantiation of Homogeneous Pink’. Synthese 80(2) pp. 277-304. Clark A. 1985 ‘A Physicalist Theory of Qualia’ Monist 68 (4), pp. 491-506. Dokic, J. & Pacherie, E. 2001 ‘Shades and concepts’. Analysis 61: 193–201. Funkhouser, E. 2006. ‘The determinable-determinate relation’ Noûs 40. Goodman, N. 1977. The Structure of Appearance, 3rd edition, Dordrecht Reidel, Boston. Goodman, N. 1976. Languages of Art: An Approach to a Theory of Symbols. Indianapolis: Hackett. Graff, D. 2001. ‘Phenomenal Continua and the Sorites’, Mind, 110: 905-35. Jackson, F & Pinkerton, RJ (1973) ‘On an Argument against Sensory Items’ Mind, 82: 269-72. Le Poidevin, R. 2004. Space, supervenience and substantivalism. Analysis 64: 191–198. McDowell, J. 1996. Mind and world. Cambridge, Mass.: Harvard University Press. Peacocke, C. 1987. Depiction. Philosophical Review XCVI: 383–410. Sellars, W. 1953. ‘Classes as abstract Entities and the Russell Paradox’, Review of Metapyhsics 17(1) Shoemaker, S. 1994. ‘Self-Knowledge and “Inner Sense”: Lecture III: The Phenomenal Character of Experience’, Philosophy and Phenomenological Research 54(2), pp. 291314. Shoemaker, S. 1994. ‘Phenomenal character’. Noûs 28/1, pp21-38. Schroer, Robert (2002) ‘Matching Sensible Qualities: A Skeleton in the Closet for Representationalism’, Philosophical Studies 107.3: 259-273 Yablo, S. 1992. ‘Mental Causation’ Philosophical Review 101(2).

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