An Argument for Tropes
William S. Robinson Iowa State University May, 2006
For the sake of clarity, I have presented the following material in the form of an argument. However, I have no principle that assures me that I have considered all reasonable alternative possibilities. Thus, I am really posing a pair of questions: (1) Do the considerations advanced really rule out the alternatives to allowing tropes that I have considered? and (2) Are there better alternatives than tropes to the views I have rejected?
The background for this discussion is the fact that color has three dimensions, hue, saturation, and brightness. Saturation is not easy to explain with precision, and there is more than one definition of it. Here is C. L. Hardin, in Color for Philosophers (Hackett, 1988, p. 26): AColors with the same hue may differ in the strength of that hue; they may have very little hue and thus be close to gray, or they may be strongly hued. We shall say that these colors differ in saturation.@ Pastels are colors of low saturation. A quick way to appreciate difference of saturation would be to take a red crayon and rub it lightly a few times on rough white paper. The hue will be the same in the crayon and the resulting patch on the paper, but the patch will be more like a pastel than the crayon B i.e., will be less saturated than the crayon. Or go to a place about half way down the web page, http://www.ncsu.edu/scivis/lessons/colormodels/color_models2.html
where there are a number of squares of a red hue with different degrees of saturation.
Now for the argument.
In what I= ll refer to as the 'target situation' , there is a red spot, a, in which the hue is highly saturated, and another spot, b, of identical size, shape and hue, but lower saturation. I ask A What is the proper way to represent the target situation?@
1. There are just three possible ways of thinking of the target situation, (i) degree of saturation is a property of particulars, (ii) degree of saturation is a second-level property of the hue, or (iii) degree of saturation is a property of the hue-in-x, i.e., a property of a perfect particular, or trope B i.e., a property of the individual instance of the hue property that is found in a particular spot.
2. Degrees of saturation are not properties of particulars.
Reason: Let A R@ be a predicate standing for the particular red hue that is exemplified by a and by b. Then, it is a truth that Ra & Rb. Let us suppose that the spots in the target situation are circular and square, respectively. So, we can represent part of the world with A Ra & Ca@ and another part (so to speak) with A Rb & Sb@ . Let A H@ and A M@ be predicates for the (putative) properties of particulars highly saturated and medium saturated, respectively. Then alternative (i), as I am taking it, represents the target situation as A Ra & Ca & Ha & Rb & Sb & Mb@ . (I suppress, because irrelevant, the size property that a and b share, and also the spatial relation that relates them.)
But this seems inadequate, because there seems to be some sense in which the degree of saturation depends on hue. There is some way in which degree of saturation has to do with the hue property that it does not have to do with the shape property; and this difference in A having to do with@ is not reflected in the foregoing representation. So, alternative (i) is incapable of adequately representing an obvious fact.
3. Degrees of saturation are not second-level properties of the hue property.
Reason: In general, let A F(G)@ represent that the first level property G has the second level property F. Spot a has a highly saturated red, and on the present notation, this implies that (at least) Ra & H(R). Spot b has the same hue, R, but in a medium saturated version, i.e., Rb & M(R). But H and M are incompatible degrees, i.e., H(F) implies ~M(F). So, the present proposal (i.e., (ii) ) implies M(R) & ~M(R), which is a contradiction. Therefore, proposal (ii) is wrong.
4. By 1. and argument by elimination, degrees of saturation are properties of instances of hues (aka perfect particulars, or tropes). High saturation is a property of the red hue in a, and medium saturation is a property of the red hue in b. The hues are the same, and so cannot bear contradictory degrees of saturation, but the instances are different, so the contradiction in 3. is avoided.
In addition, view (iii) seems intuitive. A The red in a is highly saturated, the red in b less so@ seems a perfectly natural way for a naive person to describe the target situation.
5. There are tropes.
Reason: Conclusion 4. and the principle that if the target situation is real (which is evident), and degrees of saturation are properties of tropes, then there are tropes.
Note: The foregoing problem arose for me exclusively from thinking about the target situation as I described it. If that is the only case that raises the problem, that does nothing to reduce the problematic character of the problem. It is, however, an interesting question (raised by Laird Addis) whether there are other cases. At present, I have no principle for circumscribing the range of cases, but it seems possible to me that timbres might be properties of instances of pitches.
Comments on any aspect of this are welcome! My e-mail is email@example.com