Chapter 6
Coarse-Grained Vision and New Kinds of Phenomenal Character
1
Berkeley on Abstract Ideas
Berkeley characterises Locke’s view about abstract ideas as follows:
‘So likewise the mind, by leaving out of the particular colours perceived by sense that which distinguishes them one from another, and retaining only that which is common to all, makes an idea of colour in abstract which is neither red, nor blue, not white, nor any other determinate colour.’ (Berkeley, 1975, p67). Berkeley’s view is that he can form ideas of particular colours, but not an idea of colour in general:
‘Whether others, have this wonderful faculty of abstracting their ideas, they best can tell: for myself, I dare be confident I have it not… But…whatever hand or eye I imagine, it must have some particular shape and colour. Likewise the idea of a man that I frame to myself must be either of a white, or a black, or a tawny, a straight, or a crooked, a tall, or a low, or a middle-sized man. (Berkeley, 1975, p68). In his introduction to Berkeley’s Philosophical Writings, David Armstrong disagrees with Berkeley:
‘It is perfectly possible… to have a mental image of a piece of crimson cloth of no particular shade of crimson.’ (Berkeley, 1965, p28). In this chapter I try to make precise intuitions of the kind that Armstrong has, and which Berkeley doesn’t have, and I try to make some progress towards evaluating them (thanks to Ciara Fairley for pointing out the similarity between the issues I discuss in this chapter and Berkeley’s views).
2
Some Initial Definitions
Visual Experience:
Necessarily, for all objects x and y, and all properties F, x has a visual experience of y as F iff y phenomenally looks F to x.
Phenomenal Character:
Necessarily, for all visual experiences e1 and e2, what it’s like to have e1 is the same as what it’s like to have e2 iff e1 and e2 have the same kinds of phenomenal character.
There are different kinds of phenomenal character that a visual experience may have. At the least a visual experience has colour phenomenal character and location phenomenal character. We will say that the kinds of phenomenal character that visual experiences have are all kinds of visual phenomenal character.
The correspondence principle identifies a relation that holds between certain kinds of phenomenal character and certain properties that objects phenomenally look to have.
The Correspondence Principle:
(1) For all colour properties F, if it is possible that there are two objects, x and y, such that x phenomenally looks F to y, then there is a kind of colour phenomenal character K such that: (i) Necessarily, for all objects w and z, if w phenomenally looks F to z, then z’s visual experience of w has K. (ii) For all kinds of colour phenomenal character L, if L is not K, and if, necessarily, for all w and z, if w phenomenally looks F to z, then z’s visual experience of w has L, then K is more specific than L.
(2) For all location properties F, if it is possible that there are two objects, x and y, such that x phenomenally looks F to y, then there is a kind of location phenomenal character K such that: (i) Necessarily, for all objects w and z, if w phenomenally looks F to z, then z’s visual experience of w has K. (ii) For all kinds of location phenomenal character L, if L is not K, and if, necessarily, for all w and z, if w phenomenally looks F to z, then z’s visual experience of w has L, then K is more specific than L.
‘Specificity’: (i) (ii)
For all kinds of phenomenal character K and L, K is more specific than L iff: Necessarily, for all visual experiences e, if e has K, then e has L. It is not the case that, necessarily, for all experiences e, if e has L, then e has K.
When there is, for example, a colour property F and a kind of colour phenomenal character K which meet condition (1) of the correspondence principle, I will say that K corresponds to F. Similarly when there is a location property F and a kind of location phenomenal character K which meets condition (2) of the correspondence principle, I will say that K corresponds to F.
The correspondence principle states that, for every colour and location property that an object can phenomenally look to have, there are unique kinds of phenomenal character that correspond to those properties.
If an object can phenomenally look red21, then the correspondence principle entails that there is a unique kind of phenomenal character that corresponds to being red21. We shall call this kind of phenomenal character red21-phenomenal character. In general, for all F, if there is a unique kind of phenomenal character that corresponds to being F, then that kind of phenomenal character will be called F-phenomenal character.
3
The Colour Phenomenal Character Problem
Suppose that one is looking at two patches, patch1 and patch2. Patch1 phenomenally looks red1 to one, and patch2 phenomenally looks red2 to one. One can discriminate red1 from red2.
Suppose now that a dog is looking at patch1 and patch2, and the dog is unable to discriminate the colour that patch1 phenomenally looks to it from the colour that patch2 phenomenally looks to it. What might the colour phenomenal character of the dog’s visual experience be?
Let us introduce some terms.
S:
The set of all the kinds of colour phenomenal character that one’s visual experiences ever have.
S+:
S together with all the kinds of phenomenal character that are between the members of S.
S-:
The set containing all the kinds of colour phenomenal character from red1-phenomenal character to red2-phenomenal character inclusive.
Assuming that one’s visual experiences do have red1-phenomenal character and red2phenomenal character, S- is a subset of S+.
The description of S+ appeals to the notion of betweenness. Intuitively, some colours are between other colours. For instance, it seems intuitive that red21 is between red20 and red22. It is
also intuitive that some kinds of colour phenomenal character are between other kinds of colour phenomenal character. For instance, it is intuitive that red21-phenomenal character is between red20-phenomenal character and red22-phenomenal character.
One might be tempted by the following principle.
The Betweenness Principle:
For all properties F, G and H, if there are kinds of phenomenal character that correspond to being F, being G and being H respectively, namely F-phenomenal character, G-phenomenal character and H-phenomenal character respectively, then F-phenomenal character is between Gphenomenal character and H-phenomenal character iff being F is between being G and being H.
However, I will not rely on the betweenness principle. Later in this chapter I will discuss a view on which the colour properties that objects phenomenally look to us to have are disjunctions of properties. On this view, supposing that an object can phenomenally look red2 to us, being red2 is a disjunction of other properties. It is not clear whether there is an intuitive sense in which one disjunction of properties may be between two others. Nevertheless, even if being red1, being red2 and being red3 are disjunctive properties, say, it seems intuitive that there are betweenness relations between the kinds of phenomenal character that correspond to these properties. The intuition that there are such betweenness relations between these kinds of
phenomenal character is independent of the intuition that there are betweenness relations between the kinds of properties these kinds of phenomenal character correspond to.
Later in this chapter I will define the relation of x being in between y and z in terms of certain similarity relations. At this stage, however, I will rely on an intuitive understanding of which kinds of phenomenal character are between which.
We can now formulate two hypotheses about the kinds of colour phenomenal character that the dog’s visual experience has.
The Common Colour Phenomenal Character View: The only kinds of colour phenomenal character that the dog’s visual experience has are members of S+.
The New Colour Phenomenal Character View: The dog’s visual experience has a kind of colour phenomenal character, red*-phenomenal character, which is such that: (i) it is not a member of S+.
(ii)
it is more similar to any member of S- than it is to any member of S+ that is not a member of S-.
There is an intuition, I think, that the new colour phenomenal character view is worth exploring, and this chapter will be devoted to exploring this view.
4
Pointy and Gunky Colour Phenomenal Character
In this section I apply the notions of gunk and pointiness to colour phenomenal character. I will argue that the new colour phenomenal character is plausible only if colour phenomenal character is pointy.
I shall first apply the notions of gunk and pointiness to physical space.
Gunky space:
Space is gunky iff every part of space has a proper part.
Pointy space:
Space is pointy iff not every part of space has a proper part.
To understand the application of these notions to colour phenomenal character, we need to understand the notion of a range of colour phenomenal character. Consider figure 1.
Figure 1
Figure 1 phenomenally looks to have a range of colour, and, correspondingly, one’s visual experience of figure 1 has a range of colour phenomenal character.
According to one view, the pointy view of colour phenomenal character, the range of colour phenomenal character that one’s visual experience of figure 1 has is composed of kinds of colour phenomenal character that are not ranges, but which are homogeneous. A homogeneous kind of colour phenomenal character is a kind of colour phenomenal character that is not a range of colour phenomenal character.
A consequence of the pointy view is that, although one’s visual experience of figure 1 as a whole has a range of colour phenomenal character, there are parts of figure 1, perhaps very small parts, such that one’s visual experiences of those parts have homogeneous kinds of colour phenomenal character.
According to another view, the gunky view of colour phenomenal character, every kind of colour phenomenal character is a range of colour phenomenal character. On this view, there are no homogeneous kinds of colour phenomenal character; one’s visual experience of any part, no matter how small, of figure 1, has a range of colour phenomenal character. On this view, the range of colour phenomenal character that one’s visual experience of figure 1 has overall is composed only of sub-ranges of colour phenomenal character.
The definitions of these views are as follows.
Gunky colour phenomenal character:
Colour phenomenal character is gunky iff every kind of colour phenomenal character is a range of colour phenomenal character.
Pointy colour phenomenal character:
Colour phenomenal character is pointy iff not every kind of colour phenomenal character is a range of colour phenomenal character.
Homogeneous colour phenomenal character: A kind of colour phenomenal character is homogeneous iff it is not a range of colour phenomenal character.
Consider figure 2.
Figure 2
One might think that it is clear that colour phenomenal character is pointy. After all, it does not seem that one’s visual experience of figure 2 has a range of colour phenomenal
character. It seems that one’s visual experience of figure 2 has a homogeneous kind of colour phenomenal character.
A proponent of the gunky colour phenomenal character view will hold that this intuition is not decisive against it. They will hold that there are ranges of colour phenomenal character the beginnings and ends of which are so similar that one is not able to discriminate them. That is, one will not be able to tell, of these ranges of colour phenomenal character, that they are ranges of colour phenomenal character as opposed to homogeneous kinds of colour phenomenal character. Given that one cannot discriminate the beginnings from the ends of these ranges of colour phenomenal character, one is liable to take them, incorrectly, to be homogeneous kinds of colour phenomenal character.
A proponent of the gunky colour phenomenal character view will account for one’s visual experience of figure 2 firstly by positing a range of colour phenomenal character, say grey26-phenomenal character, the beginning and end of which one is not able to discriminate, and secondly by holding either that one’s visual experience of figure 2 as a whole has grey26-colour phenomenal character, or that one’s visual experience of parts of figure 2 have grey26phenomenal character.
On the first hypothesis, on which one’s visual experience of figure 2 as a whole has grey26-colour phenomenal character, one’s visual experience of the left half of figure 2 will have one half of the grey26-colour phenomenal character range, and one’s visual experience of the right half of figure 2 will have the other half of the grey26-phenomenal character range. On the
second hypothesis, one’s visual experiences of parts of figure 2 have grey26-phenomenal character. Thus, there may be particular sub-regions of figure 2 of some area, say, 1mm2, such that one’s visual experiences of these sub-regions each have grey26-phenomenal character. According to the gunky view, on either hypothesis we are liable to think that our visual experience has a homogeneous kind of colour phenomenal character even though it does not.
Suppose that colour phenomenal character is gunky. Then red*-phenomenal character, red1-phenomenal character and red2-phenomenal character are ranges of colour phenomenal character. What might red*-colour phenomenal character be? It could be the range from red1phenomenal character to red2-phenomenal character inclusive. However, this range is in S+. After all, red0-phenomenal character and red3-phenomenal character are both in S+, and intuitively the range from red1-phenomenal character to red2-phenomenal character is between red0-phenomenal character and red3-phenomenal character.
If red*-phenomenal character is not the range from red1-phenomenal character to red2phenomenal character, then it is hard to conceive what red*-phenomenal character could be.
Suppose that colour phenomenal character is pointy. Suppose furthermore that red*phenomenal character, red1-phenomenal character, and red2-phenomenal character are homogeneous kinds of colour phenomenal character. It seems easier to imagine that there is a red*-phenomenal character on these assumptions. It seems that when one first considers the new colour phenomenal character view, and considers it to be worth exploring, one has in mind the
view that the kinds of colour phenomenal character in question are homogeneous kinds of phenomenal character.
The distinction between gunky colour phenomenal character and pointy colour phenomenal character is fairly abstract, and one might wonder what the significance of it is for the issues discussed in this chapter. The aim of this section has been to show that the distinction is relevant to the issues discussed in this chapter. I have argued that the new colour phenomenal character view is plausible only if colour phenomenal character is pointy.
5
The Location Phenomenal Character Problem
I shall now argue that one can also draw a distinction between the common location phenomenal character view and the new location phenomenal character view. Suppose that one is looking at patch1 and patch2, and patch1 phenomenally looks to have position property l1, and patch2 phenomenally looks to have position property l2. One’s visual experience of patch1 has l1phenomenal character, and one’s visual experience of patch2 has l2-phenomenal character. Suppose that one can discriminate l1 from l2.
Suppose that the dog, looking at patch1 and patch2, cannot discriminate the position property that patch1 phenomenally looks to it to have from the position property that patch2 phenomenally looks to it to have. What kind of location phenomenal character might the dog’s visual experience have?
Let us introduce some terms:
LS:
The set of all the kinds of location phenomenal character that one’s visual experiences ever have.
LS+: LS together with all the kinds of location phenomenal character that are between the members of LS. LS-: The set of all the kinds of location phenomenal character between l1-phenomenal character and l2-phenomenal character.
We can now formulate two hypotheses:
The Common Location Phenomenal Character View: The only kinds of location phenomenal character that the dog’s visual experience has are members of LS+.
The New Location Phenomenal Character View: The dog’s visual experience has a kind of location phenomenal character, l*-phenomenal character, which is such that: (i) (ii) it is not a member of LS+. it is more similar to any member of LS- than it is to any member of LS+ that is not a member of LS-.
Let us apply the terms ‘gunky’ and ‘pointy’ to location phenomenal character. To understand the application of these terms to location phenomenal character, we need to understand the notion of a region of location phenomenal character. Consider again figure 2:
Figure 2
Different parts of figure 2 phenomenally look to have different position properties. One’s visual experience of figure 2 has a region of location phenomenal character.
According to one view, the pointy view of location phenomenal character, the region of location phenomenal character that one’s visual experience of figure 2 has is composed of kinds of location phenomenal character that are not regions of colour phenomenal character, but rather are points of location phenomenal character; a point of location phenomenal character is a kind of location phenomenal character that is not a region of location phenomenal character. This view is analogous to the view on which a region of physical space is composed of zerodimensional spatial points.
According to another view, the gunky view of location phenomenal character, the region of location phenomenal character that one’s visual experience of figure 2 has is composed only of sub-regions of location phenomenal character. This view is analogous to the view on which a region of physical space is composed only of sub-regions of space that are non-zero-dimensional.
Gunky location phenomenal character:
Location phenomenal character is gunky iff every kind of location phenomenal character is a region of location phenomenal character.
Pointy location phenomenal character:
Location phenomenal character is pointy iff not every kind of location phenomenal character is a region of location phenomenal character.
Point of location phenomenal character: A point of location phenomenal character is a kind of location phenomenal character that is not a region of location phenomenal character.
Suppose that location phenomenal character is gunky. Then l*-phenomenal character, l1phenomenal character and l2-phenomenal character are regions of location phenomenal character. On this assumption, what might l*-phenomenal character be? It could be the region consisting of l1-phenomenal character, l2-phenomenal character, and every kind of location phenomenal character in between l1-phenomenal character and l2-phenomenal character. However, it follows from our definition of LS+ that this region is in LS+. On the assumption that location phenomenal character is gunky, it is hard to conceive of what l*-phenomenal character might be.
Suppose that location phenomenal character is pointy. Suppose further that l*phenomenal character, l1-phenomenal character and l2-phenomenal character are points of location phenomenal character. It is not obvious that we can conceive of an l*-phenomenal character on these assumptions.
Thus, unlike the case of colour phenomenal character, the assumption that location phenomenal character is pointy does not seem to make the new location phenomenal character view more plausible.
5.1
The Apparent Asymmetry Between The Colour and Location Phenomenal
Character Problems
There are various reactions that we might have to the apparent asymmetry between the colour phenomenal character problem and the location phenomenal character problem.
One might argue that, if there are homogeneous kinds of colour phenomenal character, then we can imagine such kinds of colour phenomenal character. By contrast, if there are points of location phenomenal character, we cannot imagine points of location phenomenal character, and this explains why we cannot imagine l*-phenomenal character as a location phenomenal character point. According to this argument, if we could imagine points of location phenomenal character, then we could imagine l*-phenomenal character as a point of location phenomenal character.
A second reaction is that one doubts how plausible the new colour phenomenal character view is, on the assumption that colour phenomenal character is pointy. I will discuss this view below.
Thirdly, one might accept the asymmetry between the colour phenomenal character problem and the location phenomenal character problem. That is, one accepts that the new colour phenomenal character view is plausible on the assumption that colour phenomenal character is pointy, and that the location phenomenal character view is not plausible on the assumption that location phenomenal character is pointy.
If one was to develop the second reaction, one would try to explain away the intuition that the new colour phenomenal character view is plausible. One might appeal to the jumbled-up colour hypothesis. The terms used in the formulation of this hypothesis will be explained below.
The Jumbled-Up Colour Hypothesis:
When we conceive of red*-phenomenal character, we are conceiving of an region of location phenomenal character which is occupied by a jumbled-up collection of different kinds of colour phenomenal character, such as red1-phenomenal character, red56-phenomenal character, and so on.
In order to explain the jumbled-up colour hypothesis, we need to introduce the notion of a kind of colour phenomenal character occupying a kind of location phenomenal character, and we
need to define what it is for a kind of location phenomenal character to be occupied by a jumbled-up collection of kinds of colour phenomenal character.
I will start by introducing the notion of a kind of colour phenomenal character occupying a kind of location phenomenal character.
Suppose that, at t1, the following facts obtain:
t1
(i) (ii) (iii)
A particular cup, A, phenomenally looks red1 to one. The background to A phenomenally looks white to one. A phenomenally looks to have location l1 to one.
Between t1 and t2, A moves so that, at t2, the following facts obtain:
t2
(iv) (v) (vi)
A phenomenally looks red1 to one. The background to A phenomenally looks white to one. A phenomenally looks to have location l2 to one.
Certainly one’s visual experience at t1 has a different kind of phenomenal character from one’s visual experience at t2. However, both one’s visual experience at t1 and one’s visual experience at t2 have red1-phenomenal character. Furthermore, both one’s visual experience at t1 and one’s visual experience at t2 have l1-phenomenal character and l2-phenomenal character. After all, consider the part of the background that one sees at t1, and that A moves into and occludes at t2. One’s visual experience, at t1, of this part of the background has l2-phenomenal character. And one’s visual experience, at t2, of the part of the background that, at t1, A occluded has l1-phenomenal character.
Hence, it is not possible to describe exhaustively the phenomenal character of a visual experience by specifying simply the kind of colour phenomenal character and the kind of location phenomenal character that the visual experience has. One needs to introduce a relation of occupation between kinds of colour phenomenal character and kinds of location phenomenal character. The difference between t1 and t2 is that, at t1, the red1-phenomenal character of one’s visual experience occupies the l1-phenomenal character of one’s visual experience, and at t2, the red1-phenomenal character of one’s visual experience occupies the l2-phenomenal character of one’s visual experience.
The example we have just considered is a motivation for the occupation principle:
The Occupation Principle: Kinds of colour phenomenal character occupy kinds of location phenomenal character.
We will define ‘jumbled-up’ as follows:
‘Jumbled-Up’:
For all regions of location phenomenal character I, I is occupied by a jumbled-up collection of kinds of colour phenomenal character iff there are distinct sub-regions of I, I1, I2, I3, and there are distinct kinds of colour phenomenal character, C1, C2, C3, such that:
(1) I2 is between I1 and I3 (2) C2 is not between C1 and C3 (3) C1 occupies I1 (4) C2 occupies I2 (5) C3 occupies I3.
According to the jumbled-up colour hypothesis, when we take ourselves to conceive red*-phenomenal character, in fact we are conceiving a region of location phenomenal character that is occupied by a jumbled-up collection of kinds of colour phenomenal character. For instance, we may be conceiving of a region of location phenomenal character I, which has subintervals I1, I2 and I3, and which is such that: I2 is between I1 and I3; I1 is occupied by red57phenomenal character; I2 is occupied by red12-phenomenal character, and I3 is occupied by red36phenomenal character. This situation is represented in figure 3:
Figure 3
Red57-phenomenal character I1
Red12-phenomenal character I2
Red36-phenomenal character I3
A proponent of the jumbled-up colour hypothesis is likely to hold that, when we take ourselves to conceive of red*-phenomenal character, we are conceiving of a region of location phenomenal character whose sub-regions are occupied by very many different kinds of colour phenomenal character, as opposed to the three kinds in figure 3.
In this chapter I wish to explore the new colour phenomenal character view, so I will not be pursuing the jumbled-up colour hypothesis further.
Above it seemed that the assumption that location phenomenal character is pointy did not seem to make it any easier to conceive of l*-phenomenal character. The first reaction was that, despite this, l*-phenomenal character does exist. The second reaction was that we should abandon the idea that red*-phenomenal character exists. The third reaction was that we should acknowledge that red*-phenomenal character exists, but deny that l*-phenomenal character exists.
In what follows I will remain neutral between the first reaction and the third reaction. I will devote the rest of this chapter to exploring the new colour phenomenal character view on the assumption that colour phenomenal character is pointy.
6
Responses To The Colour Phenomenal Character Problem
6.1
The Being Red* Principle
If the new colour phenomenal character view is correct, then, when the dog looks at patch1 and patch2, its visual experience of both patches has red*-phenomenal character. In what follows I will assume the following principle:
The Being Red* Principle:
There is a unique property of being red* which red*phenomenal character corresponds to.
In the rest of this chapter I will explore what relationship holds between being red* and being red1 and being red2. The aim is to find a relationship between being red* and being red1 and being red2 that might explain the relationship that red*-phenomenal character bears to red1phenomenal character and red2-phenomenal character.
According to the asymmetric entailment view, being red* is entailed by either of red1 or red2, but does not entail either of red1 or red2. According to the disjunctive view, being red* is a disjunction of being red1 and being red2. According to the similarity view, being red* bears a special relation of one-many similarity to being red1 and being red2. These are the main views that I will discuss. However, before I discuss them, I will discuss a fourth view, the identity view.
6.2
The Identity View
The Identity View:
Being red* is identical with being red1 and with being red2.
I discuss the identity view because it follows from the following two principles, one of which we have argued for, and one of which many find plausible.
Necessary Colour Scepticism:
Necessarily, objects do not have the colour properties that they phenomenally look to have.
Necessary Coextension View:
For all objects x and properties F and G, if, necessarily, x is F iff x is G, then being F is identical to being G.
According to necessary colour scepticism, being red*, being red1 and being red2 are necessarily coextensive. According to the necessary coextension view, necessarily coextensive properties are identical.
The identity view, the being red* principle and the correspondence principle together entail that the new colour phenomenal character view is false. The identity view and the being red* principle together entail that red*-phenomenal character and red1-phenomenal character correspond to the same property. The correspondence principle entails that, for every property F that an object can phenomenally look to have, there is a unique kind of phenomenal character that corresponds to being F. It follows that, if red*-phenomenal character and red1-phenomenal
character correspond to the same property, then red*-phenomenal character is identical with red1-phenomenal character. This claim is inconsistent with the new colour phenomenal character view.
We have independent reason to reject the necessary coextension view, and therefore we have no reason to accept the identity view. Necessary colour scepticism and the necessary coextension view together entail that being red1 is identical with being green56. This claim entails the false conclusion that for all objects x and y, x phenomenally looks red1 to y iff x phenomenally looks green56 to y. If the argument that we gave in chapter 4 for necessary colour scepticism is sound, then we should give up the necessary coextension view.
6.3
The Asymmetric Entailment View
The asymmetric entailment view is as follows:
Asymmetric Entailment View: (i) Necessarily, for all x, if x is either red1 or red2, then x is red*. (ii) It is not the case that necessarily, if x is red*, then x is red1, and it is not the case that necessarily, if x is red*, then x is red2.
Necessary colour scepticism entails that (ii) is false. Necessary colour scepticism entails that, necessarily, if an object is red*, then it is red1.
One might argue that, if necessary colour scepticism is correct, then the new phenomenal character view is implausible in any case, and thus the question of what relationship might hold between red* and being red1 and being red2 does not arise. However, this seems incorrect. The independence intuition seems plausible:
The Independence Intuition:
It is epistemically possible that both necessary colour scepticism and the new colour phenomenal character view are true.
The independence intuition is that the issue of whether or not the new colour phenomenal character view is true is independent of the issue of whether or not objects could have had the colour properties that they phenomenally look to have. If the independence intuition is correct, then coming to believe necessary colour scepticism should not affect our credence in the new colour phenomenal character view.
The objection above to the asymmetric entailment view depended on necessary colour scepticism, which we defended in chapter 4. Necessary colour scepticism is certainly a controversial thesis, and many readers may prefer to give up necessary colour scepticism in order to defend the asymmetric entailment view. However, if the independence intuition is correct, then, even if necessary colour scepticism is false, it seems that we should reject the asymmetric
entailment view. According to the independence intuition, whether the new colour phenomenal character view is true is independent of whether necessary colour scepticism is true. According to the asymmetric entailment view, whether the new colour phenomenal character view is true is not independent of whether necessary colour scepticism is true. Therefore, if the independence intuition is correct, then the asymmetric entailment view makes the new colour phenomenal character view depend on the wrong kind of issue, namely whether or not necessary colour scepticism is true. This a reason to reject the asymmetric entailment view, and furthermore, it is a reason that is independent of whether or not necessary colour scepticism is in fact true.
One might argue that the relationship between being red* and being red1 and being red2 is being more coarse-grained than. I will be assuming that being F is more coarse-grained than being G iff being G entails being F, and being F does not entail being G. Hence, I am assuming that the relation of being more coarse-grained than is captured by the asymmetric entailment view. I called this chapter ‘Coarse-Grained Vision and New Kinds of Phenomenal Character’ not because I think that the phenomenon I discuss is correctly described in terms of the notion of coarseness of grain, but because I have noticed that this phenomenon is naturally thought of by many philosophers in terms of the notion of coarseness of grain.
6.4
The Disjunctive View
The disjunctive view is an attempt to develop the new colour phenomenal character view in the light of necessary colour scepticism.
The Disjunctive View:
Being red* is a disjunction of being red1 and being red2.
Necessary colour scepticism entails that being red1 or red2 is necessarily coextensive with being red1. However, having rejected the necessary coextension view, we are not under pressure to identify the disjunctive property of being red1 or red2 with being red1.
Later I will discuss the disjunctive view in more detail. I will briefly discuss a further view.
6.5
The Determinable View
The determinable view is as follows:
The Determinable View:
Being red* is a determinable of the properties being red1 and being red2.
According to one view, being F is a determinable of being G only if being G entails being F, and being F does not entail being G. On this view, the determinable view would entail the asymmetric entailment view, which we have argued is false.
According to another view, being F is a determinable of being G only if being F is a disjunction, one of whose disjuncts is being G. On this view, the determinable view entails the disjunctive view, which we shall consider below.
On another view, the relation of being a determinable of is primitive. This is a live option. However, before we consider taking it, it is worth exploring other responses to the colour phenomenal character problem. Before discussing the disjunctive view, I will discuss Dummett’s argument in ‘Wang’s Paradox’ (Dummett 1978).
7
Wang’s Paradox
There is some inclination to think that one of the arguments that Dummett develops in ‘Wang’s Paradox’ bears on the question whether the new colour phenomenal character view is correct (Dummett 1978). In this section I will argue that Dummett’s argument in fact addresses a different issue.
Dummett is considering an example in which one is looking at the minute-hand of a clock. He writes as follows:
‘For let us suppose that space and time are continua, and let us change the example so that the minute-hand now moves at a uniform rate. Let us further suppose that whether or not the minute-hand occupies discriminably different positions at different moments depends uniformly upon whether or not the angle made by the two positions of the minute-hand is greater than a certain minimum. It will then follow that, however gross our perception of the position of the minute-hand may be, there is a continuum of distinct phenomenal positions for
the minute-hand: for, for any two distinct physical positions of the minute-hand, even if they are not discriminably different, there will be a third physical position which is discriminably different from the one but not from the other.’ (Dummett, 1978, p266-267). Let us express Dummett’s argument as follows.
1.) For all objects x and y, there is a distance D such that whether or not a given subject S can discriminate x’s position from y’s position depends uniformly on whether or not x is more than D from y. 2.) For all objects x and y, if x and y are in distinct positions, then there is an object z such that z is D from y and z is more than D from x. 3.) For all objects x and y, if x and y are in distinct positions, then there is an object z such that S can discriminate x’s position from z’s position and S cannot discriminate y’s position from z’s position. 4.) For all objects x and y, if x and y are in distinct positions, then if x and y phenomenally look to S to have position properties, then the position properties that x and y phenomenally look to have are distinct.
This argument has a very striking conclusion: that however small a distance that an object moves between t1 and t2, the position property that the object phenomenally looks to have at t1 is different from the position property that the object phenomenally looks to have at t2.
There is an analogue of Dummett’s argument for colour properties. 1.)* is as plausible as 1.):
1.)* For all objects x and y, there is a determinable property N and a distance D between the determinates of N such that whether or not a given subject S can discriminate the colour x phenomenally looks from the colour y phenomenally looks depends uniformly on whether or not x’s determinate of N is more than D from y’s determinate of N.
N might be the property of reflecting some wavelength of light, and the distance between the determinates of this determinable will be the difference between wavelengths of light. A parallel argument to the one above will show that however small the difference between x’s determinate of N and y’s determinate of N, the colour properties that x and y will phenomenally look to have are distinct.
Since we are discussing the new colour phenomenal character view in this chapter, I will discuss the analogue of Dummett’s argument for colour properties. If this analogue of Dummett’s argument is sound, then there can be arbitrarily small differences between the colour properties that objects phenomenally look to us to have. A small extension to the argument would establish that there can be arbitrarily small differences between the kinds of colour phenomenal character that two visual experiences of a given subject have.
One might think that this latter consequence counts against the new colour phenomenal character view. However, I shall argue that the new colour phenomenal character view is consistent with this consequence.
Suppose that the disjunctive view is correct, and that patch1 phenomenally looks red1 or red2 to the dog. Consider the property of being red1` or red2`, where red1` is arbitrarily similar to red1, and red2` is arbitrarily similar to red2`. It may be that some third patch, patch3, phenomenally looks red1` or red2` to the dog. If patch3 phenomenally looks red1` or red2` to the dog, then it seems plausible that the dog’s visual experience of patch3 would have a kind of colour phenomenal character that is distinct from, but arbitrarily similar to, red*-phenomenal character.
This example shows that there is no inconsistency between the new kinds of colour phenomenal character that the new colour phenomenal character view postulates, and arbitrarily small differences between those new kinds of colour phenomenal character. That is, the existence of arbitrarily small differences between kinds of colour phenomenal character does not support the common colour phenomenal character view over the new colour phenomenal character view. Therefore Dummett’s argument in ‘Wang’s Paradox’ does not bear on the question whether or not the new colour phenomenal character view is correct.
8
The Disjunctive View Discussed
In this section I explore the disjunctive view. To begin with, I consider two arguments that objects do not phenomenally look to have disjunctive properties.
One might argue that objects do not phenomenally look to have disjunctive properties on the grounds that, when, for some object A and some properties F and G, we say (1), what we mean is (2).
(1) A phenomenally looks F or G (2) Either A phenomenally looks F or A phenomenally looks G.
According to this argument, an object never phenomenally looks F or G, where ‘F or G’ is within the scope of ‘phenomenally looks’.
It may be the case that whenever we say that an object phenomenally looks F or G, what we mean is that either the object phenomenally looks F or it phenomenally looks G. But it does not follow from this that objects do not phenomenally look to have disjunctive properties.
It may be the case that whenever we say that some object phenomenally looks my favourite colour, what we mean is that the colour that the object phenomenally looks is my favourite colour. But this fact by itself does not show that objects do not phenomenally look my favourite colour, where ‘my favourite colour’ is within the scope of the ‘phenomenally looks’. More argument would be required to show that objects cannot phenomenally look to have the property of being my favourite colour.
Some have argued that there is a conflict between the claim that the properties that objects phenomenally look to have vary gradually and the claim that objects phenomenally look
to have disjunctive properties. According to this argument, disjunctive properties do not vary gradually.
It is not clear why one might think that disjunctive properties cannot vary gradually. In the section above on Wang’s paradox, it seemed plausible that disjunctive properties could vary gradually.
8.1
Phenomenal Character
The disjunctive view was offered as an explanation of the new colour phenomenal character view. The proposal was that the explanation of the dog’s visual experience of patch1 having red*-phenomenal character was that patch1 phenomenally looks red1 or red2 to the dog. In this section I consider whether the disjunctive view is an adequate explanation of the dog’s visual experience of patch1 having red*-phenomenal character.
If patch1 phenomenally looks red1 or red2 to the dog, then the colour phenomenal character of the dog’s visual experience may be either compositional or non-compositional. Compositional phenomenal character is defined as follows.
Phenomenal Compositionality:
For all x and y, x’s visual experience of y has a compositional phenomenal character iff for all properties F, if F is either a property, or a constituent of a property,
that y phenomenally looks to x to have, then x’s visual experience has F-phenomenal character.
I mean the notion of a constituent of a property as follows: being F is a constituent of the properties being F or G, being F and G, being not F, being F if G, and so on.
If patch1 phenomenally looks red1 or red2 to the dog, and if the dog’s visual experience of patch1 has compositional phenomenal character, then the dog’s visual experience of patch1 will have both red1-phenomenal character and red2-phenomenal character.
Suppose that patch1 is the only object one sees, and that every facing part of it phenomenally looks red1 to one. One’s visual experience of patch1 will have red1-phenomenal character. Intuitively, red1-phenomenal character will be the only kind of colour phenomenal character that one’s visual experience has. That one’s visual experience has red1-phenomenal character seems to exhaust what it is like colour-wise for one to have the experience. In such circumstances, it does not seem that one’s visual experience could also have red2-phenomenal character.
Suppose that patch1 is the only object that the dog sees, and that every part of patch1 facing the dog phenomenally looks red1 or red2 to the dog. The combination of the disjunctive view and the commitment to phenomenal compositionality entails that the dog’s visual experience of patch1 has both red1-phenomenal character and red2-phenomenal character. It
seems that we have good reason to reject the combination of the disjunctive view and the commitment to phenomenal compositionality.
A defender of the disjunctive view is likely to argue that, when patch1 phenomenally looks red1 or red2 to the dog, then the dog’s visual experience of patch1 has non-compositional phenomenal character. Let us define the non-compositional view as follows:
The Non-Compositional View:
Necessarily, for all objects x and y, and all properties F and G, if x phenomenally looks F or G to y, then y’s visual experience of x has non-compositional phenomenal character.
Non-compositional phenomenal character is phenomenal character that is not compositional. There is a question as to what might explain the non-compositional view. After all, phenomenal compositionality seems to hold when the property that an object phenomenally looks to have is a conjunctive property. That is, the principle of conjunction compositionality seems very plausible.
Conjunction Compositionality:
Necessarily, for all objects x and y, and properties F and G, if x phenomenally looks F and G to y, then y’s visual experience of x has F-phenomenal character and Gphenomenal character.
For instance, if an object x phenomenally looks red1 and at position l1 to y, then it is intuitive that y’s visual experience of x has both red1-phenomenal character and l1-phenomenal character.
One could explain the non-compositional view by arguing for the following principle:
The Neutrality Principle:
Necessarily, for all objects x and y, and all properties F and G, if one of the properties that x phenomenally looks to y to have is neutral between being F and being G, then y’s visual experience has non-compositional phenomenal character.
One definition of neutrality is the following:
The Entailment View of Neutrality:
For all properties F, G and H, being F is neutral between being G and being H iff for all objects x, (i) (ii) necessarily, if x is either G or H, then x is F; it is not the case that, necessarily, if x is F, then x is G; (iii) it is not the case that necessarily, if x is F, then x is H.
Since the properties in question are colour properties, and since the disjunctive view is intended to be consistent with necessary colour scepticism, I assume that a proponent of the
neutrality principle would not accept the entailment view of neutrality. I assume that they will take it to be a primitive fact that the disjunctive property of being F or G is neutral between being F and being G. Thus the property of being either such that 2 + 2 = 5 or such that 2 + 2 = 6 will count as neutral between the property of being such that 2 + 2 = 5 and the property of being such that 2 + 2 = 6.
It seems that the following principle is plausible:
The Disjunction Principle: Necessarily, for all properties F and G, if an object can phenomenally look F or G, then
(i)
there are properties H and I such that an object can phenomenally look H and I.
(ii) (iii) (iv)
an object can phenomenally look not F an object can phenomenally look not both not F and not G an object can phenomenally look F if G.
The argument for the disjunction principle is that, for all F and G, if it is possible for an object phenomenally to look F or G, then it would be ad hoc to deny any of (i) to (iv) above. If an object can phenomenally look F or G, and some of (i) to (iv) above are false, then some special reason for this would have to be given.
For instance, a proponent of the view that, for some F and G, objects can phenomenally look F or G, may appeal to ordinary language in support of their view. A proponent of this view might hold that we say such sentences as ‘he looks either courageous or foolish to me’. However, we also say such sentences as ‘she looks tall and brown-haired to me’, ‘she looks not interested’ and ‘the policy looks fine if there are no objections from the backbenchers’. It also seems that there will be some context in which one might say, for some x and for some F and G, that x looks not both not F and not G. Thus, if ordinary language is intended to support the view that, for some F and G, objects can phenomenally look F or G, then it seems that proponents of the view should endorse (i) to (iv) above too.
I will now argue that the combination of the neutrality principle and the disjunction principle has two counter-intuitive consequences. My arguments will employ assumptions such as that, for some x and some F and G, x phenomenally looks not F, and F if G, and not both not F and not G. I do not take a stand on whether these assumptions are true. My claim is that these assumptions follow from the disjunctive view, and thus it is legitimate to make them when assessing the disjunctive view.
8.1.1 Multiple Kinds of Colour Phenomenal Character like Red*-phenomenal character
A large part of the motivation for the non-compositional view is that we do have some idea of a kind of colour phenomenal character like red*-phenomenal character. That is, we do have an idea of a kind of colour phenomenal character that satisfies the conditions in the new colour phenomenal character view, which is, recall, as follows:
The New Colour Phenomenal Character View: The dog’s visual experience has a kind of colour phenomenal character, red*-phenomenal character, which is such that: (i) (ii) it is not a member of S+. it is more similar to any member of S- than it is to any member of S+ that is not a member of S-.
In this section I argue that the disjunctive view, together with the neutrality principle, the disjunction principle and a further plausible principle together entail that there are multiple kinds of colour phenomenal character that satisfy conditions (i) and (ii). This is a counter-intuitive consequence, and is therefore a cost to accepting the disjunctive view.
According to DeMorgan’s law, being F or G is equivalent to not being both not F and not G. Thus, it seems that if being F or G is neutral between being F and being G, then not being both not F and not G is also neutral between being F and being G. The disjunction principle entails that, if an object can phenomenally look F or G, then an object can phenomenally look not both not F and not G. The neutrality principle entails that, if an object O phenomenally looks not both not F and not G to S, then S’s visual experience of O has non-compositional phenomenal character.
One might think that, if object O phenomenally looks F or G to S1, and O phenomenally looks not both not F and not G to S2, then the non-compositional phenomenal character of S1’s visual experience is the same as the non-compositional phenomenal character of S2’s visual experience. However, this possibility is ruled out by the following principle:
The Phenomenal Distinctness Principle: Necessarily, for all objects x, y and z, and for all distinct properties F and G, if x can phenomenally look F to z and y can phenomenally look G to z, then the phenomenal character that corresponds to being F is distinct from the phenomenal character that corresponds to being G.
One might wonder what the relationship is between the phenomenal distinctness principle and the correspondence principle. A consequence of the correspondence principle is that, for every property that an object can phenomenally look to have, there is a unique kind of phenomenal character that corresponds to that property. We could define the reverse correspondence principle as follows: for every kind of phenomenal character, there is a unique property that that kind of phenomenal character corresponds to. The reverse correspondence principle is similar to, though not equivalent to, the phenomenal distinctness principle. The phenomenal distinctness principle allows that there may be kinds of phenomenal character that correspond to no property that an object could phenomenally look to have, whereas the reverse correspondence principle does not allow this.
The argument for the phenomenal distinctness principle is that it holds for the standard properties that we think objects phenomenally look to have. For instance, if x phenomenally looks red1 to z, and y phenomenally looks red2 to z, then it is intuitive that the phenomenal character of z’s visual experience of x will differ from the phenomenal character of z’s visual experience of y.
One might argue that, given that, in section 6.2, we abandoned the necessary coextension view, and thus committed ourselves to a fine-grained way of individuating properties, the phenomenal distinctness principle is not plausible. This objection rests on the following principle:
The Anti-Phenomenal Distinctness Principle: Necessarily, for all objects x and y, and all properties F and G, if being F is necessarily coextensive with being G, and if x can phenomenally look F to y, and x can phenomenally look G to y, then the same kind of phenomenal character corresponds to being F and being G.
If object O1 phenomenally looks F or G to S, and object O2 phenomenally looks not both not F and not G to S, then the anti-phenomenal distinctness principle entails that the kind of phenomenal character that corresponds to being F or G is identical with the kind of phenomenal character that corresponds with being not both not F and not G.
However, necessary colour scepticism gives us a reason to reject the anti-phenomenal distinctness principle. Necessary colour scepticism entails that being red1 is necessarily coextensive with being green1. However, the kind of colour phenomenal character that corresponds to being red1 is distinct from the kind of colour phenomenal character that corresponds to being green1. Therefore, if necessary colour scepticism is true, one cannot object to the phenomenal distinctness principle by appealing to the anti-phenomenal distinctness principle.
The main premises of the first argument against the disjunctive view are as follows:
1.) By the disjunction principle, if an object can phenomenally look F or G, then an object can phenomenally look not both not F and not G. 2.) By the neutrality principle, a. if an object x phenomenally looks F or G to a subject S, then S’s visual experience of x has non-compositional phenomenal character. b. If an object x phenomenally looks not both not F and not G to S, then S’s visual experience of x has non-compositional phenomenal character. 3.) By the phenomenal distinctness principle, the phenomenal character that corresponds to being F or G is distinct from the phenomenal character that corresponds to being not both not F and not G.
Let us assume that the non-compositional phenomenal character that corresponds to the property of being red1 or red2 is red*-phenomenal character. Let us call the non-compositional phenomenal character that corresponds to the property of being not both not red1 and not red2 red**-phenomenal character.
Red*-phenomenal character was introduced as the kind of phenomenal character that satisfies conditions (i) and (ii) in the new colour phenomenal character view above. If red**phenomenal character exists, it seems plausible that it also satisfies (i) and (ii) in the new colour phenomenal character view. It is not clear what reason there would be for denying this claim.
This establishes that the disjunctive view is true only if there are at least two kinds of colour phenomenal character that satisfy conditions (i) and (ii) in the new colour phenomenal character view. Since we do not intuitively think that there are two such kinds of colour phenomenal character, this raises doubts about the adequacy of the disjunctive view in explaining the new colour phenomenal character view.
We can also establish that the disjunctive view is true only if there is a third kind of colour phenomenal character, red***-phenomenal character, which satisfies conditions (i) and (ii).
Being F or G is equivalent to being F if not G. Hence, if being F or G is neutral between being F and being G, then, intuitively, being F if not G is neutral between being F and being G. By the disjunction principle, an object can phenomenally look F or G only if an object can
phenomenally look F if not G. By an argument similar to 1.) to 3.) above we can establish that there is a kind of colour phenomenal character that corresponds to being F if not G that is a), distinct from red*-phenomenal character and red**-phenomenal character, and b), noncompositional. We can call this kind of phenomenal character red***-phenomenal character, and, if it exists, it seems plausible that it would satisfy conditions (i) and (ii) in the new colour phenomenal character view.
The fact that the disjunctive view is true only if there are at least three kinds of colour phenomenal character that satisfy conditions (i) and (ii) in the new colour phenomenal character view intuitively seems to be a cost of the disjunctive view.
8.1.2
Phenomenally Looking not F
Consider these two principles:
Conjunction Compositionality:
Necessarily, for all objects x and y, and properties F and G, if x phenomenally looks F and G to y, then y’s visual experience of x has F-phenomenal character and Gphenomenal character.
Negation Compositionality:
Necessarily, for all objects x and y, and all properties F, if x phenomenally looks not F to y, then y’s visual experience of x has F-phenomenal character.
Conjunction compositionality and negation compositionality together entail negated conjunction compositionality:
Negated Conjunction Compositionality:
Necessarily, for all objects x and y, and all properties F and G, if x phenomenally looks not both not F and not G to y, then y’s visual experience of x has both F-phenomenal character and Gphenomenal character.
If negated conjunction compositionality is true, then it is possible that an object x phenomenally looks not both not F and not G to some subject S, and for S’s visual experience of x to have compositional phenomenal character. This is not consistent with the neutrality principle, reproduced below, given that not being both not F and not G is neutral between being F and being G.
The Neutrality Principle:
Necessarily, for all objects x and y, and all properties F and G, if one of the properties that x phenomenally looks to y to have is neutral between being F and being G, then y’s visual experience has non-compositional phenomenal character.
The neutrality principle was offered as an explanation of the non-compositional view. Thus if it is false an alternative explanation of the non-compositional view is required.
Conjunction compositionality seems very plausible. It seems plausible that if an object x phenomenally looks red1 and at position l1 to subject S, then S’s visual experience of x has both red1-phenomenal character and l1-phenomenal character.
It seems more likely that a defender of the disjunctive view will reject negation compositionality. There is a minor cost to doing this. Recall the non-compositional view.
The Non-Compositional View:
Necessarily, for all objects x and y, and all properties F and G, if x phenomenally looks F or G to y, then y’s visual experience of x has non-compositional phenomenal character.
The non-compositional view did not strike us as implausible as we already had a pretheoretic idea of a non-compositional phenomenal character, namely red*-phenomenal character. Thus the non-compositional view fitted with our pretheoretic intuitions. However, in giving up negation compositionality, the disjunctive view is committed to holding that, when an object x phenomenally looks not red1 to a subject S, then S’s visual experience of x has noncompositional phenomenal character, which we can call not-red1-phenomenal character. There is no pretheoretic support for the existence of not-red1-phenomenal character, and indeed it is hard to conceive what it might be. The fact that the disjunctive view is committed to the existence of not-red1-phenomenal character is thus is a cost of the disjunctive view.
In this section I have argued for two claims. Firstly, I argued that the disjunctive view is plausible only if the non-compositional view is correct. Secondly, I argued that there are some costs of accepting the non-compositional view.
9
The Similarity View
In the last few sections we have assumed the being red* principle, reproduced below, and we have been considering what relation might hold between being red* and being red1 and being red2.
The Being Red* Principle:
There is a unique property of being red* which red*phenomenal character corresponds to.
In this section I discuss the similarity view, which is as follows.
The Similarity View:
Being red* bears the relation of one-many similarity to being red1 and being red2.
The aim of this section is to define the relation of one-many similarity, and to explore the similarity view.
By appealing to similarity relations between being red*, being red2 and being red2, the similarity view mirrors the way in which new colour phenomenal character view explains the
relation between red*-phenomenal character, red1-phenomenal character and red2-phenomenal character.
The New Colour Phenomenal Character View: The dog’s visual experience has a kind of colour phenomenal character, red*-phenomenal character, which is such that: (i) (ii) it is not a member of S+. it is more similar to any member of S- than it is to any member of S+ that is not a member of S-.
The relevant sets are as follows:
S:
The set of all the kinds of colour phenomenal character that one’s visual experiences ever have.
S+: S-:
S together with all the kinds of phenomenal character that are between the members of S. The set containing all the kinds of colour phenomenal character from red1-phenomenal character to red2-phenomenal character inclusive.
The central idea in the new colour phenomenal character view is that red*-phenomenal character is not a member of S+, but that it is more similar to red1-phenomenal character, red2phenomenal character, and all the kinds of phenomenal character between red1-phenomenal
character and red2-phenomenal character, than it is to any other kind of colour phenomenal character in S+.
Just as red*-phenomenal character is introduced in terms of the similarity relations that it bears to red1-phenomenal character and to red2-phenomenal character, the similarity view explains the relation between being red* and being red1 and being red2 also in terms of a special kind of similarity relation, the one-many similarity relation.
9.1
The One-Many Similarity Relation
The one-many similarity relation is as follows:
1.)
x is one-many similar to y and z iff a. x is equally similar to y and to z. b. there is no w such that i. w is between y and z ii. x is more similar to w than it is to either of y or z. c. x is distinct from y and z.
The simplest way of defining ‘betweenness’ involves assuming that colour space, i.e. the set of colour properties, is a metric space. This assumption is as follows. I assume that, where x and y are colour properties, d(x,y) is the degree of dissimilarity between x and y.
The Metric Space Assumption:
For all colour properties x, y and z: (i) (ii) (iii) (iv) d(x,y) ≥ 0. d(x,y) = 0 iff x = y. d(x,y) = d(y,x). d(x,z) ≤ d(x,y) + d(y,z).
The metric space assumption holds that there are degrees of dissimilarity between colour properties that can be added together. If the metric assumption is correct, then we can define ‘betweenness’ as follows:
2.)
x is between y and z iff d(x,y) + d(x,z) = d(y,z).
‘x is equally similar to y and to z’ is defined as follows:
3.)
x is equally similar to y and to z iff d(x,y) = d(x,z).
‘x is more similar to y than to z’ is defined as follows:
4.)
x is more similar to y than to z iff d(x,y) < d(x,z).
A formal model of the one-many similarity relation is as follows. Consider a set containing three elements, a, b and c. Let us stipulate the following to be true:
(i) (ii) (iii)
d(a,b) = 1 d(a,c) = 1 d(b,c) = 0.5
In this model, a is one-many similar to b and c: (i) (ii) a is equally similar to b and to c. There is no x in between b and c which is such that a is more similar to x than it is to either of b and c. (iii) a is distinct from b and c.
The similarity view holds that being red* is one-many similar to being red1 and to being red2. Figure 4 below is a representation of a set of colour properties, where colour properties at a higher level are one-many similar to a set of colour properties at a lower level. Being red1 is onemany similar to being red1.1, being red1.2 and being red1.3. Figure 4 is an abstract representation of certain colour properties. Although we have represented these colour properties using lines, this should not be taken to imply anything about the metaphysical nature of the colour properties. In particular, the figure should not be taken to suggest that the colour properties are ranges of colour in the way that, according to the gunky view of colour phenomenal character, kinds of colour phenomenal character are ranges of colour phenomenal character.
Quite possibly there is a densely ordered set of colour properties between being red1.1 and being red1.3 to which being red1 is one-many similar. Being red1.3 is one-many similar to being
red1.31, being red1.32 and being red1.33. Being red1.1 and being red1.2 are also one-many similar to various colour properties, but these colour properties are not represented in figure 4.
Figure 4
Red1 Red1.1 Red1.2 Red1.3 Red1.31 Red1.32 Red1.33 Red1.331 Red1.332 Red1.333 Red1.3331 Red1.3332 Red1.3333 Red1.33331 Red1.33332
…….
9.2
The One-Many Similarity Relation Involving Non-colour Properties
It seems that the following principle is plausible:
Negation Invariance:
Necessarily, for all properties F, G and H, being F is more similar to being G than to being H iff being not F is more similar to being not G than to being not H.
Negation invariance entails that being red* is one-many similar to being red1 and being red2 iff being not red* is one-many similar to being not red1 and being not red2.
The similarity view was advanced as an explanation of the new colour phenomenal character view. Suppose that objects could phenomenally look to have properties such as being not red*, being not red1, and being not red2. It might be thought a consequence of that supposition that not-red*-phenomenal character bears a similar relationship to not-red1phenomenal character and not-red2-phenomenal character as red*-phenomenal character does to red1-phenomenal character and to red2-phenomenal character.
It is not clear that, given the supposition that objects can phenomenally look to have properties such as being not red*, that the above consequence of this supposition is a cost of the similarity view. Furthermore, it is not clear whether this supposition is indeed correct. Thus, without further argument, we should not take negation invariance to present a problem for the similarity view.
It seems that being red1 is one-many similar to having position l1 and having position l2 for the following reason:
(i) (ii)
being red1 is equally similar to having l1 and having l2; there is no w such that i. w is between having l1 and having l2 ii. being red1 is more similar to w than to either of having l1 or having l2.
(iii)
being red1 is distinct from having l1 and having l2.
That being red1 is one-many similar to being at l1 and being at l2 does not seem to be a cost of the similarity view. The similarity view holds only that being red* is one-many similar to being red1 and being red2, and that this fact explains why the new colour phenomenal character view is correct. This explanatory project does not seem to be jeopardized by the fact that being red1 is one-many similar to being at l1 and being at l2.
9.3
Vertical/Horizontal Relations
In this section I will argue for the following constraint on the relation of one-many similarity.
The Horizontal/Vertical Principle:
Necessarily, for all x, y and z, if x is one-many similar to y and z, then d(y,z) < 2d(x,y).
The proof of this principle is as follows. If x is one-many similar to y and z, then x is not between y and z. This follows from condition 1.)b of the definition of one-many similarity. Suppose that the following are true:
(i)
d(x,y) = 1
(ii)
d(x,z) = 1
(iii) d(y,z) = 2
It follows from (i)-(iii), together with the definition of betweenness above, that x is between y and z. Furthermore, it is not possible that (i), (ii) and (iv) be true:
(iv)
d(y,z) > 2
This establishes the horizontal/vertical principle. The principle above is called ‘the horizontal/vertical principle’ because when x is one-many similar to y and z, it can help to think of the similarity relations between y and z as horizontal relations, and the relations between x and y, and between x and z, as vertical relations. The horizontal/vertical principle imposes a constraint on the relation between horizontal similarity relations and vertical similarity relations.
9.4
Weaker Starting Assumptions
We stated that the similarity view is as follows:
The Similarity View:
Being red* bears the relation of one-many similarity to being red1 and being red2.
We defined ‘one-many similarity as follows:
1.)
x is one-many similar to y and z iff a. x is equally similar to y and to z. b. there is no w such that i. w is between y and z ii. x is more similar to w than it is to either of y or z. c. x is distinct from y and z.
We made the metric space assumption, the assumption that colour space is a metric space, and defined ‘betweenness’ as follows:
2.)
x is between y and z iff d(x,y) + d(x,z) = d(y,z).
If colour space is not a metric space, then we would have to reject the similarity view. However, we could accept a view similar to the similarity view, namely the comparative similarity view:
The Comparative Similarity View:
Being red* is comparatively one-many similar to being red1 and being red2.
‘Comparative one-many similarity’ is defined in the same way as ‘one-many similarity’, except that ‘betweenness’ is replaced with ‘comparative betweenness’:
5.)
x is comparatively one-many similar to y and z iff a. x is equally similar to y and to z. b. there is no w such that: i. w is comparatively between y and z ii. x is more similar to w than it is to either of y or z. c. x is distinct from y and z.
‘Equal similarity’ and ‘comparative betweenness’ are defined in terms of the three-place similarity relation of x being more similar to y than to z:
6.) a. b. c.
x is comparatively between y and z iff y is more similar to x than it is to z. z is more similar to x than it is to y. There is no w such that either: i. w is as similar to y as x is to y, and w is more similar to z than x is to z. or ii. w is as similar to z as x is to z, and w is more similar to y than x is to y.
‘x is as similar to y as it is to z’ is defined as follows:
7.)
x is as similar to y as it is to z iff a. x is not more similar to y than it is to z.
b. x is not more similar to z than it is to y.
Hopefully 7.) is plausible and does not stand in need of much explanation. For instance, in figures 5 and 6, x is as similar to y as it is to z:
Figure 5
y
x
z
Figure 6
x
y
z
The reasoning behind conditions 6.)a and 6.)b is as follows. If we consider figure 5, it is clear that a constraint on x being between y and z is that z is closer to x than it is to y, and y is closer to x than it is to z.
The reasoning behind condition 6.)c is as follows. Consider the following case:
Figure 7 x y w z
In this case, conditions 6.)a and 6.)b are met, but in no intuitive sense of ‘between’ is x between y and z. What ensures that x is not comparatively between y and z is condition 6.)c. There is a w such that w is as similar to z as x is to z, but which is more similar to y than x is to y.
Betweenness, as defined by 2.), and comparative betweenness come apart in two ways. It follows from 2.) that for all x and y, x is between x and y. However, it follows from 6.) that, for all x and y, x is not between x and y. 6.)a blocks y from being identical with z, and 6.)b blocks y from being identical with x. This difference, however, between betweenness and comparative betweenness is small; it can be removed by adding a condition on betweenness, as defined by 2.), that x be distinct from y and z.
Betweenness and comparative betweenness come apart if colour space is metric and if it contains gaps. A gap in colour space is defined as follows:
8.)
There is a gap in colour space iff there are two colours x and y such that: a. d(x,y) > 0 b. there is no colour z such that: i. z is distinct from x and y. ii. z is between x and y.
Recall figure 7:
Figure 7 x y wz
Suppose that colour space is metric, and that w does not exist. This situation is represented in figure 8:
Figure 8 x y z
Conditions 6.)a and 6.)b are met. Furthermore, we may assume that there are enough gaps so that condition 6.)c is met. Therefore, although x is not between y and z, x will be comparatively between y and z.
This is a counter-intuitive instance of comparative betweenness: comparative betweenness applies when no intuitive notion of betweenness applies. One might take this to be a problem for our appeal to the notion of comparative betweenness. However, we appeal to comparative betweenness only on the assumption that colour space is not a metric space. If colour space is not a metric space, then there will be no gaps as we have defined them, and therefore problematic instances of comparative betweenness of the above kind will not arise. If
colour space is a metric space, then we will not appeal to comparative betweenness, as we will have no need for it, but rather to betweenness, as defined by 2.).
The horizontal/vertical principle, reproduced below, can still be defended even if colour space is not a metric space.
The Horizontal/Vertical Principle:
Necessarily, for all x, y and z, if x is one-many similar to y and z, then d(y,z) < 2d(x,y).
We will understand ‘d(y,z) < 2d(x,y)’ as ‘y is less than twice as dissimilar from z as x is from y’.
Before defining ‘x is less than twice as dissimilar from z as x is from y’, we will define ‘x is twice as dissimilar from y as z is from y’:
9.)
x is twice as dissimilar from y as z is from y iff there is a w such that a. w is as similar to y as z is to y. b. w is between x and y c. w is as similar to x as it is to y.
In figure 9, x is twice as dissimilar from y as z is from y:
Figure 9 x w y z
9.) explains why x is twice as dissimilar from y as z is from y. There is a w such that w is as similar to y as z is to y; w is between x and y; and w is as similar to x as it is to y.
‘x is less than twice as dissimilar from y as z is from y’ can be defined as follows:
10.)
x is less than twice as dissimilar from y as z is from y iff there is a w such that:
a. w is twice as dissimilar from y as z is from y. b. x is more similar to y than w is to y.
The proof of the horizontal/vertical principle, using only the notion of comparative similarity, is as follows.
1.)
Condition 5.)b in the definition of ‘comparative one-many similarity’ entails that if x is comparatively one-many similar to y and z, then x is not comparatively between y and z.
2.)
If x is equally similar to y and to z, and if y is not less than twice as dissimilar from z as x is from y and z, then x is comparatively between y and z.
Suppose that the following are true:
(i) x is equally similar to y and to z. (ii) y is twice as dissimilar from z as x is from y.
It follows from (i) and (ii) that x is comparatively between y and z. Recall the definition of ‘comparative betweenness’:
6.)
x is comparatively between y and z iff a. y is more similar to x than it is to z. b. z is more similar to x than it is to y. c. There is no w such that either: i. w is as similar to y as x is to y, and w is more similar to z than x is to z. or ii. w is as similar to z as x is to z, and w is more similar to y than x is to y.
It follows from (i) and (ii) that 6.)a and 6.)b are met. Furthermore, 6.)c is met. Take any w such that w is as similar to y as x is to y. Since y is twice as dissimilar from z as x is from y, it follows that w is not more similar to z than x is to z. The same applies to any w such that w is as similar to z as x is to z. And the same reasoning applies when we replace (ii) with (iii):
(iii) y is more than twice as dissimilar from z as x is from y.
This establishes the horizontal/vertical principle.
Initially we defined the ‘one-many similarity’ relation on the assumption that colour space is a metric space. The purpose of the last section has been to show that there is a notion of comparative betweenness, and, if colour space is not a metric space, then one can use the notion of comparative betweenness to define a relation similar to the one-many similarity relation, namely the comparative one-many similarity relation.
10
Conclusion
We started by considering the new colour phenomenal character view. It seemed that this view was plausible only if colour phenomenal character is pointy. We did not pursue the new location phenomenal character view, as it was not clear whether that view is plausible either on the assumption that location phenomenal character is gunky or on the assumption that location phenomenal character is pointy.
The bulk of the chapter was devoted to exploring the new colour phenomenal character view, and, in particular, to giving an account of the relationship between being red* and being red1 and being red2 that would explain the new colour phenomenal character view. We rejected the asymmetric entailment view, and discussed some costs of the disjunctive view. We did not discover any obvious problems with the similarity view, but we must acknowledge that the claim
that there is a colour property, being red*, which is one-many similar to being red1 and being red2, is speculative.
We have not reached a conclusion about which solution to the colour phenomenal character problem is correct. My aim has been to describe the problem, and to discuss some solutions to it.
