[hist-analytic] Putnam and Aune on Color-incompatibilities

Bruce Aune aune at philos.umass.edu
Wed Nov 18 09:27:07 EST 2009


Largely because I wondered how Steve could have become so confused  
about what I said about the incompatibility of colors in my second  
chapter and why he insisted so strongly that I give him a definition  
rather than examples of what I meant by “determinate color,” I reread  
Hilary Putnam’s paper, “Reds, Greens, and Logical Analysis,” which  
Steve introduced into our discussion. I had looked the paper over when  
Steve Swartz reminded me of it, but I didn’t give it the careful read  
it deserved. I knew that Putnam’s argument was different from mine,  
but I thought we were defending the same basic thesis.  When I looked  
at the paper the other day, I realized that we weren’t defending the  
same thesis at all. Readers who followed my exchanges with Steve (if  
any readers actually did so) might be interested in some of the  
differences I found.



1.  Putnam’s wanted to show that “Nothing is red all over and green  
all over at the same time” is an analytic truth.  Not only did I not  
want to show this; I don’t even think it is an a priori truth. (I  
argued that a related assertion regarding yellow and green, which are  
equally generic colors, could in fact be false.) Also, I did not share  
Putnam’s conception of an analytic truth. I didn’t actually say, in my  
second chapter, what conception of analytic truth I accepted, but my  
discussion was structured in accordance with the definition I would  
defend in my third chapter. Putnam’s paper therefore contains an  
argument that is very different from the one I offered, and it arrives  
at a very different conclusion.



2.  Putnam was working with Frege’s conception of analyticity.  Putnam  
described it by saying “An analytic sentence is one that can be  
reduced to a theorem of formal logic by putting synonyms for  
synonyms.”  Because he accepted this conception, he had to show that  
his target sentence could be reduced to a logical truth by putting  
synonyms for synonyms. To do this he had to provide definitions giving  
synonyms for the predicates in his target sentence—specifically, for  
“red” and “green.” Since I was not working with this conception of  
analyticity, I had no need for such definitions. They were not  
pertinent to my task.



3.  The conception of analytic truth I accept is an extension (or  
development) of the definition Carnap used later in his career:  A  
statement is analytic true just when it is true by virtue of  
semantical rules. (This is a rough statement, of course; I discuss  
pertinent qualifications in my chapter 3 and in two appendices.)  Why  
don’t I accept the Fregean conception that Putnam accepts?  It is not  
that it isn’t good as far as it goes; it is that, like Kant’s  
conception, it doesn’t go far enough.  There are statements deserving  
the status of analytic truths that do not satisfy Kant’s conception or  
Frege’s conception.  Neither conception shows why logical truths are  
true, for instance (Frege’s simply assumes it), and neither accounts  
for the analytic character of certain assertions containing predicates  
that are only partially defined. As I explain in chapter 3, Carnap  
left Frege’s conception behind the early 1930’s, when he introduced  
the concept of a bilateral reduction sentence.



4.  Carnap regarded meaning postulates (he later preferred the  
description “A-postulates”) as special cases of semantical rules. For  
him, A-postulates are specifications of meaning, either complete or  
partial. If I propose to use a certain relation symbol, say “Rxy”, to  
represent an asymmetrical relation, I may indicate this by the A- 
postulate, “(x)(y)(Rxy --> ~ Ryx).”  This shows us that if the symbol  
“R” applies to a pair of objects <a,b>, it does not apply to the pair  
<b,a>.



5.  My proof that nothing can possess two determinate colors at the  
same place and time involved two A-postulates, which hold true for my  
talk about colors and, as I contend, for sophisticated English speech  
generally.  One is that determinate colors are distinct just when they  
are distinguishable and the other (RBJ made me realize this a distinct  
postulate) is that if anything possesses a determinate color C at a  
place and time, any determinate color it possesses there and then is C  
and only C.  This last postulate underlies our use of the definite  
article in such expressions as “the color of a (at p and t).” We use  
similar expressions (technically, functors) for a wide range of  
attributes that we attribute to familiar things:  the temperature of s  
(at t), the length in inches of x at t, the speed of x in miles per  
hour, and so on.



6.  I could easily meet Steve’s often-repeated request for a  
definition of “determinate color”, but I didn’t want to introduce  
another word he would say he doesn’t understand. The definition I  
would want to give is, “A determinate color is any non-generic  
color.”  This definition uses the expression “generic color,” which is  
no more difficult than “generic property,” which is perfectly familiar  
to most analytic philosophers.* But for my purposes, no such  
definition is needed anyway. My meaning should be perfectly evident  
from the examples I cite.  Most of the words we use can’t be given  
explicit definitions.  Think of “sardonic,” “sarcastic,” “silly” or  
“stupid.”  I give long lists of such words at various places in my book.



7.  As I said on my last post, almost all of which Steve simply  
ignored in his last reply to me, Steve’s emphasis on the continuity  
(or denseness) of color is badly misplaced.  If color is supposed to  
be something we can perceive (as it is taken to be by philosophers  
worrying about color incompatibilities), there is no plausibility in  
the idea that it (or some relation on it) is dense in the way Steve  
said.  If two shades of red are very similar, very close to one  
another on a color chart, I may be able to recognize another shade as  
intermediate between those shades, but I can’t do this indefinitely: I  
will eventually encounter shades that are minimally different from one  
another: I will be unable to perceive any additional shade that  
separates them. My inability here will not be idiosyncratic; any other  
human being will share it. The continuity Steve imagines simply  
doesn’t exist in the domain of perceptible color.



Steve, holding fast to the continuity idea anyway, thinks that the  
existence of humanly imperceptible color differences (which he  
accepts) shows that there are no “discrete colors”.  As he puts it,  
“if it is always the case that between any two colors there is a  
third, and if the discrimination of individuals is limited, then there  
will be no discrete colors for these individuals.”  But if discrete  
colors are recognizable colors, this contention is absurd; it involves  
the logical howler I accused him of. From the fact (if it is a fact)  
that there are differences between shades of red that I cannot  
recognize, it hardly follows that I cannot distinguish any shades of  
red at all--dark shades from a light shades, or a shades of red from a  
shade of green. The analogy I drew between real numbers ordered by  
SMALLER THAN and shades of color ordered by the supposedly dense  
relation Steve seems to have in mind is, in fact, sound. In both cases  
we have a conditional assertion, “(x)(y)(xRy --> there is a z such  
that xRz & zRy),” and to infer from this that some minimal term z’  
possesses a special minimal value, we need a premise of the form “aRb”  
that we can know to be true. For this premise, the value of “a” and  
“b” need not be minimal at all.



Another point needs to be made in connection with the continuum of  
colors that Steve accepts. Suppose all shades of color can indeed be  
ordered (or are ordered) in some continuous way. What implication does  
this have for the shades I can see? Suppose I paint a room with a  
pearl gray latex paint. The room is well lighted.  As I look at a  
freshly painted wall, everything I see is pearl gray. Am I supposed to  
infer that the existence of infinitely many shades of many different  
colors proves that I do not see anything pearl gray or that the color  
I see is not “discrete”? I put “discrete” in quotes because it is a  
term that Steve introduced.  He insisted that I define it,** but it is  
not a term I used: it is his, and I am not sure what he means by it.  
Possibly he may believe it is just a stylistic variant of “determinate  
color,” which I did introduce.  But the property of being non-generic,  
which is all “determinate” connotes here, does not require  
discreteness in some sense.  Specificity or determinateness is  
perfectly compatible with Steve’s fancied continuum of color shades.



Bruce Aune



*If I were asked to explain what a generic property is to a student, I  
would begin with some examples.  Could anything be an animal, I would  
ask, without being some kind of animal—a dog, worm, or bird, for  
instance? Of course not.  Could something be a dog without beingsome  
kind of dog--an Airedale, a collie, or a mutt, for instance?  Could  
something be an Airedale without being one Airedale rather than another 
—without being a particular instance of the kind? Of course not. When  
I speak of a generic property, then, I am speaking of the sort of  
higher-order property that things possess only by virtue of possessing  
some lower-order property. Lowest-order or absolutely determinate  
properties are properties things possess without having to possess a  
property of any lower-order. Determinate colors can alternatively be  
described as color properties of the lowest order. There is nothing  
generic about them.



**In his last post he said, “All of this business about my ‘howlers’  
and lack of understanding etc would be unnecessary if Bruce would fill  
in the following blank as best he can: ‘Let us use 'discrete color' to  
refer to ....’” (Am I responsible for his arguments and claims about  
“the” color continuum?)
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