[hist-analytic] The Two Color Problem:Putnam/Aune

Baynesr at comcast.net Baynesr at comcast.net
Fri Jan 1 12:14:58 EST 2010




A. One problem with Putnam's approach is that because in order 
to "prove" his case that the nothing can be red and blue all 
over he introduces the right postulates to get what he wants. 
And since he CAN get those postulates, he argues that it 
follows that we can regard the proposition just as analytic 
as 'All ba chelors are unmarried." 


One aspect of this is that he must use postulates to get 
one of the RST properties of the equivalence relation, transitivity, 
and he uses something like exact resemblance to get the other 
properties, viz. reflexivity and symmetry. So the postulate has 
to be stuck in there and then the other superadded and voila (!) 
he gets the relation "right." Just consider how a relation can 
under one set of circumstances be transitive but under another 
not. Take the relation 'has exactly the same hammer as'. Ok, 
now since it is possible that even though x has the same hammer 
as y and y has the same hammer as z, nevertheless x does not 
have the same hammer as z. In other words x and z may have 
different hammers. The relation, then, is not transitive. But 
now suppose that there is only one hammer; then if x has the 
same hammer as y and y as z then x has the same hammer as z, 
so the relation IS transitive. The relation 'has the same hammer 
as' is nontransitive. But nontransitivity will not afford 
Putnam what he wants, an equivalence relation. 


B. Suppose a thing were allowed to be both red and blue all over. 

Would it be blue? Partly blue? Partly blue all over? Clearly, we are 

faced with more than logical or ontological problems, problems 

I don’t think can be met by stipulating a meaning postulate or 

 constructing a system of postulates with an objective in mind of 

ruling out some things and other things in. 


C. Putnam has simply made up a “word” meaning “exactly 

the same Color as” then endowed it by fiat with a meaning 

 that rules out the offending synthetic a priori. 


D. I do not discover that this is the same color as that the 

way I discover that Hesperus is Phosphorus. There is much 

here I cannot digress to examine. If I know both colors I 

know they are not the same; but this is not the case with 

Hesperus and Phosphorus. 


E. An object can’t have two surfaces; what does this have to 

do with being two colors “all over.” The argument against 

synthetic a priori with respect to colors may depend on 

admitting it in the case of surfaces. 


F. I will address Bruce’s argument; the one he sent to the 

 list separately. I don’t think it does the job, but it does deserve 

careful attention. More soon. 


G. Sometimes it seems to me that Bruce thinks you can 

solve certain problems, the ones under discussion having 

 to do with defining, etc. “determinate colors” by simply 

going to the paint store and asking to view a color wheel. 

This sounds cynical, but it sure looks that way to me. I 

invite Bruce to reflect on a couple of quotes from Wittgenstein 

which I would introduce in opposition to his view as I see it. 


“Let us imagine that someone were to paint something 

from nature and in its natural colors. Every bit of the surface 

of such a painting has a different color. What color? How do I 

determine its name? Should we, e.g. use the name under which 

 the pigment applied to it is sold? But mightn’t such a pigment 

look completely different in its special surrounding than on the 

palette? (Remarks on Colour, para 68) 


“People might have the concept of intermediate colours or 

mixed colours even if they never produced colours by mixing 

(in whatever sense). Their language-games might only have to 

do with looking for or selecting already existing intermediary or 

blended colours.” (op. cit. para 8). 


“If I say a piece of paper is white and then place snow next to 

 it and it then appears grey, in normal surroundings and for 

ordinary purposes I would call it white and not light grey. I could 

be that I’d use a different and, in a certain sense, more refined 

concept of white in, say, the laboratory, (where I sometimes also 

use a more refined concept of ‘precise’ determination of time.” ( 

op. cit. para 160) 


“Couldn’t there be people who understand our way of speaking 

when we say that orange is reddish-yellow and who were inclined 

 to say this in cases in which orange occurs in an actual transition 

from red to yellow? And for such people there might very well be 

a reddish green. 


Therefore, they couldn’t “analyse blends of colours” nor could they 

learn our use of X-ish.” (op. cit. para 129). 


These quotes are pertinent to my disagreement with Bruce. I hope to 

elaborate, but for now I just want to post this stuff in such a way that will 

get the ba ll rolling again. 




By the “two color problem” I mean the problem of determining 

the status of the proposition: “No two things can be the same 

color all over at the same time.” If we take the proposition 

synthetic, then we will either regard it as contingent or synthetic 

 a priori. Why shouldn’t we regard it as synthetic a posteriori? 

What is the argument that it is not. Now it would appear that this 

 is an issue for neither Aune nor Putnam, since both are prepared 

 to regard the above proposition as in some sense a priori. We 

 won’t discuss what sense, but we should take note that Putnam 

will speak of propositions which “feel” analytic. (p. 74). I think there 

 is something to this, but if there is we have to contend with a 

number of issues not discussed. 


One such issue is whether such “feelings” make a difference; 

perhaps not, but when we reflect on the above proposition it is 

 difficult to maintain that if there are such feelings, then while ‘A 

  ba chelor is an unmarried man’ may “feel” analytic, it sure doesn’t 

 sound as if ‘Nothing can be red and green all over at the same 

 time’ “feels” analytic in the same way. This is not a trivial point, 

 especially given the emphasis some philosophers have placed 

 on the idea of “epistemic counterparts” in dealing with the “feeling 

” or “appearance” of contingency with respect to propositions 

 that seem to be necessary, such as ‘Phosphorous is Hesperus’. 

 Without such “feelings” philosophy pro ba bly doesn’t come 

 into play; the rest may just be word games about common 

 sense discourse, games that resolve no puzzles, in particular 

puzzles that such “feelings” engender. So I think this is important. 





A number of philosophers have said that the problem of 

the synthetic a priori may not be very important. Sometimes 

these philosophers, then, go about the task of discussing 

the matter at great length. Is there a justification for this? Yes, 

 I think so. The “two color problem” brings this issue into play 

and how we deal with it tells a lot about our methods of analysis. 

There are at least four approaches to the two color problem. 


1. The method of formal language where constructing the 

 language is ba sed on an intuitive or scientific understanding 

of some pre-existing nature of the subject under examination. 


2. The method of formal language where constructing the 

 language is ba sed on pure construction; that is, where the 

 world is not understood as preexisting the construction but, 

 rather, is itself a notion to be constructed. 


3. The informal method dispensing with formal language all 



4. A mixed approach involving (1) and (3) or (2) and (3). 


There are other approaches but for the problem at hand these will suffice. 


Putnam adopts the first approach; it would appear that Aune 

subscribes to (4). Nelson Goodman is, perhaps, the best example 

of an advocate of (2). Of Goodman’s approach, Putnam once said this: 


“This brings me to perhaps my most important remark about 

Goodman’s philosophical methods and attitudes…by rejecting 

 the most fashionable problems of philosophy, he is totally free 

 of the “now philosophy is over” mood that haunts much of 

twentieth century philosophy. If there isn’t a ready made world, 

then let’s construct worlds, says Goodman. If there aren’t 

 objective standards, then let’s construct standards! Nothing 

 i s ready made, but everything is to be made.” (Forward to 

 _Fact, Fiction and Forecast_. Harvard, 1983, p. xv) 


Of particular interest is Putnam’s remark about the “now 

philosophy is over mood.” He doesn’t tell us what he means 

 but there is room for speculation. 




One thing that makes the “two color problem” important as 

well as interesting is not only that different methodologies 

are tested, but there has been a contest going on for some 

 time between epistemology and ontology, one that is 

clarified by attention to this issue. On the view I take, the 

“now philosophy is over” crowd to be mainly epistemologists 

who eschew metaphysics as it is both traditionally conceived 

as revealing the nature of the world, and as identifiable with 

ontology. I now offer a partisan comment on this conflict. 


During the 1920s the idea was still around that metaphysics 

 could provide some understanding of the logical structure 

 of the world and experience. The ascent of Tarskian 

semantics let to the overthrow of this point of view, at least 

in large measure. Epistemology felt the effect. No longer did 

epistemology trade in sense data; and no longer was the unity 

of consciousness, the nature of mental acts and questions 

related to the idealist tradition more generally the focus of 

 concern. Instead, there was a move towards “meta-epistemology”; 

 defining ‘knowledge’; induction, pro ba bility theory, 

confirmation theory, etc. These issues unrelated to 

traditional metaphysics supplanted the old regime. Philosophy 

was seen more in terms of mathematical considerations on 

pro ba bility, Bayesian analysis, and such notions as “reliable 

belief producing mechanism began to make it appear that 

science and mathematics not metaphysics was central. 

What had begun with the logical positivists as a critic of 

metaphysics became a critic of “philosophy” as traditionally 

understood. Epistemology was no longer, in other words, the 

“ontology of the knowing situation” as it had been for people 

 like Broad and the early Russell, to take two prominent 



Some of this was good, but not all. It is now made to 

appear, at least for some of us in the metaphysics camp 

 that if you want to know whether there are physical objects, 

 then “open your eyes stupid” is to be a significant part of 

 the new “epistemology.” And if you want to know what a 

 color is, just go to the paint store and they will be happy 

to show you a color chart; if you want to know the structure 

 of the world ask a physicist; as for essences, you can refute 

 them too; just find a three legged lion and you are all set! If 

 there is anything left we’ll just sweep in under the rug of 

“common sense.” Philosophy, then, has gone “casual,” 

 a occupation free from labor, a form of relaxation for the 

well to do with an inordinate sense of their own self importance. 

Now this is, admittedly, a very bias characterization. 


I bring it up because the “two color problem” on the 

 view I take is a metaphysical problem possessing many 

dimensions, each one a sort of handle one might take hold 

of in order in searching for the best grip. One reason 

 this is a metaphysical issue is the nature of color is very 

 much at issue, if I’m right. Putnam sees this, but it doesn’t 

appear to be very important to Aune; let me briefly 

elaborate one concern. 




A great deal of the “two color problem” depends on   

what we take colors to be, ontologically. If we take 

colors to be particulars we will get one solution (and 

it will be quick); if we take colors as objects, like physical 

objects, then the nature of identity statements is something 

 different from what it would be were we to regard colors 

as universals or mental entities. Let me supply a contrast 

that may be sufficiently illuminating to obviate any need for 

protracted discussion. Let us consider the identity 


Hesperus = Phosphorus 


How many times have we been told this was a significant 

discovery? Quite a few. We are told that it was significant 

 at least in part because it was truly informative. Why was 

it truly informative? Well, in the morning people would see 

one star and as the sun rose it disappeared and later they 

 saw another star. Later it was discovered that these two 

stars are identical. What happened was that two terms were 

*discovered* to be co-referential. This is what made the 

 identity “significant.” But not all contingent identities are 

 similarly significant, color providing a case in point. 

 Suppose that instead of pointing to a star in the morning and 

 one in the evening and later finding out that they are the same 

I point to a color in one room; then I go into the other room 

and point to a color and say that 


This color is exactly the same color as that 


Now what I would argue is that there is a sense in which this is 

no discovery at all. As long as I am talking about the color(s) 

and not the object which have the color(s) then one plausible 

 view is that the identity is contingent and a posteriori. 

 Alternatively, if we take this as a true identity it must be 

 a necessary truth. The first option is, itself, ambiguous. 

 If colors are tropes then if the identity holds it is necessary; 

 if colors are universals, then we are faced with problems of 

individuation of properties etc. Now we have three options 

 and if we add Putnam’s relevant sentence 


‘x is exactly the same color as y’ 


where ‘x’ and ‘y’ refer to objects, then we have 

 four possibilities where much depends on how 

 “exactly the same” and “being identical” are related. 

 If you are unconvinced of this sort of variation among 

identity sentences, that is whether there are different 

conditions for identity depending on the objects asserted 

to be identical, consider another problem, one which I think 

can be related to the “two color problem.” 


Suppose someone claims the following to be the case. 


No object can have two surfaces at the same time. 


Is this true? I think it is. Is it analytic? I don’t think so but, to use 

Putnam’s expression, it “feels” more analytic than 


No object can be red and green all over. 


Is there any justification for this intuition? Two objects may 

have the same color (unless they are tropes) but they cannot 

have the same surface. It seems to be the case that the very 

concept of a physical object precludes having more than one 

 surface, whereas it does not seem to me to be the case that 

 it is part of the very concept of a physical object that it can 

have both the color of that thing over there and this thing 

 here at the same time all over, which is a Putnamian way 

 of saying that nothing can have the same color all over at 

the same time. If an object can have two surfaces at the 

same time, then it is not absurd to suppose that an object 

can have two surfaces each with a different color. So, maybe, 

nothing’s being the same color all over at the same time 

depends on no object having more than one surface 

at the same time. But now what of 


No surface can have two shapes at the same time? 


Now it would almost seem that this is false for reasons we 

may touch on later; but for now the point is simply this: how 

we solve the two color problem, or address it, will tell us 

something about our ontology; if the claim that no object 

 can be red and green all over is analytic, like ‘all ba chelors 

 are unmarried’ then there is nothing informative in the 

assertion beyond the way we use our words. Both Aune 

and Putnam hold this to be an analytic and so just as trivial as 


Hesperus is Hesperus. 


I think this is a reduction of their position, precisely because I think 

it is informative in a way that such sentences as these are not. 


Now I don’t think Putnam shares Goodman’s form of “constructivism.” 

Putnam is “modeling” the world, so to speak in the medium of formal 

 l anguage; Goodman is creating worlds. If he admits to understanding 

what Putnam is saying, then he’ll pro ba bly have some view on the 

subject as to the sense in which he does or does not align himself 

 with this trend. The point of bringing this up is that it raises the important 

question of whether the two color problem has a solution; that 

 is, whether it is a problem or a mere figment of a problem; what 

 Schlick first called a “pseudo-problem.” (1920). 


Putnam maintains that to such questions that lead to such problems 

“there is never a final answer.” (Sumner and Woods p. 77) One 

can see the reasoning here in Goodman’s case. We create worlds; 

there is no “final world” so there can never be a final answer to any 

 questions that go beyond any one constructed world. For Putnam, 

 the case is less clear. However, here is what I think Putnam is 

suggesting: while there are no final answers, some answers are 

 better than others; that is, we may construct any one of a number 

of answers, but no answer is “right.” What he may mean is that there 

is a cost associated with any one of a number of answers and we 

have to decide what price to pay. Since philosophers vary on what 

is valuable etc. the price to pay varies; there being no “natural” price; 

we are in the realm of “exchange value” so to speak. So we have it 

that there may be a number of answers but no right answer. What 

is Aune’s view on this? 


Aune will sometimes rely on informal methods as central to 

solving a problem. Other times he seems to rely on formal 

 methods, such as introducing “meaning postulates,” 

something we will discuss shortly. Given this “mixed” 

approach – that is, “mixed” in a way that Putnam’s is 

not – with respect at least to the problem under investigation 

 there is not deciding whether for Aune there are in fact 

solutions to ANY philosophical problems. Clearly, he wouldn’t 

 propose them if he didn’t believe they were indeed solutions, 

but this does not exclude the possibility of other, equally good, 

solutions. It would be interesting to know his feelings on this matter. 



We have been talking about the a priori in the context of 

Bruce’s formulation of an empiricist theory of knowledge. 

I think it is important to see where we may disagree on the 

 importance of what I’ve been calling the “two color problem” 

 in arriving at some conclusion as to the viability of empiricism. 

 Some such views are more radical than others. 


Although we have been discussion judgments and 

 whether or not Kant has been refuted it is important t o 

 keep in mind that for Kant there is more to the issue 

 than judgments. For Kant not only are some judgments 

 a priori some concepts are a priori as well. The empiricist, 

traditionally, has held that there are no a priori concepts, but 

 there may be a priori judgments. This is possible as long 

as the judgments that are a priori are analytic. The reason 

 for this is that the empiricist wants to rule out knowledge of 

 necessary connection between worldly objects. He can 

have an a priori but only if it is analytic, that is, as long as its 

 truth (the judgment, that is) does not describe the world. 


In the case of the judgment that no thing can be two 

 colors all over at the same time, we have an interesting 

case. It is interesting because it seems to say something 

 about the world and yet it appears necessary. This is 

 just the sort of thing that will cause most empiricists to 

 recoil. So the empiricist must analyze the nature of 

 color etc. in such a way the judgment becomes analytic. 

 Putnam points out just as we might analyze ‘All ba chelors 

are unmarried” in such a way as to make it analytic, similarly 

 we want to analyze ‘No object can be two colors at the 

same time all over’ in such a way that it, too, comes out 

analytic. It is not important whether two colors cannot be had 

by one object at the same time all over. What is important is 

the status of this judgment. The empiricist may argue that it is 

analytic that this is analytic   or, alternatively, that is merely 

contingently true. Bruce and Putnam arrive at similar arguments, 

but there are crucial differences. Let’s begin with Putnam and 

 then go to Aune. 




We begin with the idea that logical truths, such as ‘Ba v ~Ba’, are 

analytic. But such truths are not the only ones considered to be 

analytic. Recall how it is, typically, shown that ‘All ba chelors are 

unmarried’ is analytic, although it is not a logical truth. What we 

do is show that it can be converted to a logical truth by way of 

definitions. We may consider what is required as definitions or 

as “meaning postulates.” There is a difference but let’s give the 

illustration and go from there. We begin with: 


1. All ba chelors are unmarried. 


We, then, introduce the meaning postulate or definition: 


2. ‘ ba chelor’ means ‘unmarried man’.’ 


From this the following logical truth is derived by substitution: 


3. All unmarried men are unmarried. 


Now something very similar is afoot in attempting to 

 argue that the sentence ‘Nothing is red all over and 

green all over at the same time’. What we need to do i n 

order to show this analytic is to derive a logical truth 

 from it along with definitions. In attempting to demonstrate 

 the analyticity of ‘Nothing is red all over and green all over 

 at the same time’, Putnam will engage the task of showing 

 that ‘Nothing is the same color as A and the same color as 

 B at the same time where A and B are not exactly the same 

 color. Mimicking the approach to the analyticity of (1) he will 

 introduce a couple of properties of the relation ‘exactly the 

same color as’. One property is that it is a stronger relation 

than ‘indistinguishable from’ since it entails this relation without 

being entailed by it. Later he will provide a definition (Sumner 

and Woods p. 79) which depends on this weaker relation. The 

other property which goes into defining ‘exactly the same color 

as’ is transitivity. So the claim will be that that original sentence, 

‘Nothing can be red all over and green all over’, can be shown 

to be analytic by being shown to be a logical truth once these 

 definitions are added to the language. 



There are three claims essential to Putnam’s paper that 

I want to focus our attention on. They are: 



  9) (x)(~Ex[A, B] -> . Ex[x, A] -> ~Ex[x, A} -> ~Ex[x, B]) 


10) (x)(~Ex[x, B] & (x)(~Ex[x, B]) 


11) ~Ex(A, B) 


Where ‘(x)(~Ex[x, y]’ reads “x is exactly the same color as y.” 

In connection with this relation Putnam lays down the first two of a 

number of postulates he will, eventually, require to make his point. These are: 


1.     It is an equivalence relation 

2.     ‘Ex’ implies ‘indistinguishable from’, not vice versa. 

(Summer and Woods p. 75) 


Logically, his point will be that from (9) the equivalence of (10) 

 and (11) follows. So it will turn out that, given, (9), if two things 

 have different colors (i.e., not exactly the same colors), then 

no thing has them both. But this will not give us what he wants, 

namely, analyticity of ‘Nothing can be two colors all over’ 

 (hereafter “S”). How, then, we do we get the analyticity 

and, thereby deny the rationalist factual necessities, such 

 as S? What he does is point out that (9) is equivalent to (12): 


12. (x)(Ex[x, A] ->. Ex[x, B] -> Ex[A, B]) 


He points out that (12) “expresses the transitivity” of “EX”’, 

 keeping in mind that transitivity is guaranteed by the postulates. 

In this way, he arrives, eventually, at the conclusion that S is 

 analytic. A couple of formal observations are in order. 


It it is important to notice that he can derive (10), but he can’t 

do it from (9) alone; he needs (11). (11) is not analytic. So (10) 

may not be analytic after all, IF you mean by ‘analytic’, in part 

at least, that analytical statements do not depend, essentially, 

on contingent facts. Suppose there is a way around this. There 

 is something I think is more interesting. Although (10) may 

be inferred from (9) and (11), as a matter of fact (9) follows 

 f rom (10)! If so, then, given (11), (9) and (10) are equivalent; 

and, since (9) is equivalent to a postulate, (10), and so S, will 

have (11), alone, as the single premise upon which the argument 

depends. (We don’t include postulates among the premises). 

So now the burden is, largely, on the transitivity of ‘exactly the 

 same color as y’. I reject the transitivity and, therefore, reject 

the idea that ‘Ex’ is transitive. If I can sustain this claim, 

 Putnam is refuted. But can I? 


Bruce Aune’s approach will, critically, depend on the 

 notion of being a “determinate color’; Putnam’s approach 

will not. The reason, I think, is this: Putnam believes, as do 

 I, that there are no determinate colors. Putnam remarks 

 that “ …when we think of the color concepts, the most 

striking fact we observe is that they form a continuum.” 

(op. cit. p. 78). This will prove very important to Putnam’s 

 case. He will introduce a lot of postulates to accommodate 

 this fact. So many that I am inclined to include him among 

 the “American Postulate Theorists”! But setting this aside, 

consider why he might do this and, at one point, even admit 

 that people may suspect him of “smuggling” in some stuff. 

 One of the cleverest of his many clever proposals is related 

to this and brings into the picture views, originally, expressed 

by Henri Poincare. Poincare was a Kantian. He was loathe to 

admit to actual infinities. He was, therefore, adverse to the idea 

of a “continuum” in the sense of being a real structure. We 

construct it. The mathematical continuum on his view is 

derived from what he called the “physical continuum.” The 

 idea is both ingenious and believable, even if it is wrong. 

I’m not sure that it is. Here is what he said: 


“It has, for instance, been observed that a weight A of 10 

 grammes and a weight B of 11 grammes produced identical 

sensations, that the weight B could no longer be distinguished 

 from a weight C of 12 grammes, but that the weight A was 

 readily distinguished from the weight C. Thus the rough results 

of the experiments may be expressed bythe following relations: 

A=B, B=C, A<C, which may be regarded as the formula of the 

 physical continuum. But here is an intolerable disagreement 

with the law of contradiction, and the necessity of ba nishing 

this disagreement has compelled us to invent the mathematical 

 continuum.”_Science and Hypothesis_ Dover. P. 22. 



The main problem with Aune’s approach is he assumes 

that the colors of things are determinate. He, also, 

appears to accept the idea that colors, themselves, are 

 determinate. He offers no reason for believing either of 

these two assumptions. 


If there are determinate colors, then on any meaning I can 

attach to ‘determinate’, this will entail that the number of colors 

 is finite. I’m not so sure this is true, unless we resort to certain 

 limitations on the eye; but let’s leave eyes and light waves out 

of the picture, for now. 


Crucially, Aune’s proof depends on the transitivity of identity, 

but when it comes to colors as objects of visual awareness 

I don’t believe this. Suppose two things are the same color 

(I am looking at them). But there is a third thing that is identical 

in color to the second but not the first. Then it would appear 

 that I have at least three colors, although only two are 

 distinguishable. How often can I repeat this procedure? 

 No one can tell for sure, but in theory it looks like it could 

 go on forever. This sort of thing seems to be assumed by 

Putnam as we shall see. In other words, if Bruce admits to 

“determinate” colors, then by any definition I can see the 

number of colors must be finite. I see no reason to believe 

 this. In addition, this will prove irrelevant because there is 

 another problem with his account related to the alleged 

 transitivity of identity between colors. But before harping 

on that theme, let’s take a look at what his formal proof 

actually proves, for if I am right, using the same methods 

one can prove that it is impossible for one man to hold 

two hammers at the same time. 



Putnam says, 


“Consider the conditions under which we would say that 

 that two objects are exactly the same color. These do 

not always coincide with the conditions uner which we 

would say that they are indistinguishable, e.g., let A and B 

be indistinguiahable but supposre that C is indistinguishable from 

B but distinguishable from A. Then we would say that the color of 

 B is *between* that of A and that of C. In other words, that every 

 thing that is indistinguishable from A be indistinguishable 

 f rom B (and vice versa) is a necessary condition for A an B being 

exactly the same color.” (p. 79) 

Let's take a close look at this; more on Aune. Better yet, let's get off this topic 

and move on to the rest of Aune's book. Sorry for all the errors here. 


STeve Bayne
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://rbjones.com/pipermail/hist-analytic_rbjones.com/attachments/20100101/45cd77d8/attachment-0002.html>

More information about the hist-analytic mailing list