Wittgenstein on colour A Dissertation for the Special Degree in Philosophy BY Ian Jordan April 1990 Introduction The problem of Colour incompatibly lead to the collapse of two of the main supports of the TLP viz. the truth functional theory of complex propositions and the independence of Elementary propositions.Also Wittgensteins failure'to fulfill the implicit construal of TLP 6.3751,Plus his belief that no anticipated logical analysis would fulfill it,was responsible for the advance from the bipolar logic of the TLP to the language games of the philosophical Investigations'. In summary,this problem caused Wittgenstein both to extend his notion of the nature of Logic and to modify his ideas concerning the nature of a philosophical problem. The first part of this study will consist of a discussion of three of wittgensteins works viz. Tractatus logico- philosophicus(TLP); Some Remarks on Logical Form(SROLF) and the Philosophical Remarks(PR). In the second section of this study the 'Remarks on colour(ROC) will be examined and it is here where we shall leave Wittgenstein and examine the contemporary debate on colour incompatibility. The Tractatus Logico-philosphicus ------------ ~-------------------- First things First-first we must examine the basic concepts of the TLP,which can be summed up as follows.To states of affairs which are concatenations of simple objects there correspond elementary propositions which assert the existence of states of affairs elementary propositions are concatenations of names for simple objects(TLP 421-4221).A complete description of the world can be given by making a list of all elementary propositions and marking which are true and which are false-true elementary 2 propositions will record all the positive facts whilst those which are false will likewise correspond to all negative facts- the totality of such facts is the world(TLP 2.06,1.1) All Propositions With sense are truth functions of elementary propositions.Kenny(F1) asserts that it is natural to regard this as meaning that all propositions can be constructed out of elementary propositions plus logical constants as 'p . q is constructed out of This is misleading as it suggests that the logical operations add something noL pk@sent in the elementary proposition.The way a truth function of elementary propositions is by an operation(TLP 5.3).Following Wittgenstein(TLP 4.44) all operations producing truth functions out of elementary propositions can be regarded as modifications of that propositions truth table (TLP 5.234). The possible forms of elementary propositions depend on the possible combinations of objects,determined by an application of logic.To attempt to give an a priori list of elementary propositions leads to nonsense(TLP 5.5571),they cannot be ordered in a formal list like molecular propositions.A fully analysed proposition will be an enormously long truth-function Of elementary propositions,every possible elementary proposition will occur in the truth function,and every name in the language. constituted by a well formed arrangement of names which refer to non-composite objects (TLP 4.22).Objects which are coneatenated in an atomic fact are described by an isomorphic elementary Proposition,whose logical independence of other elementary propositions mirrors the logical independence of atomic facts.The 3 specific forms of the elementary Propositions is something for l@t;@i- ki-'Lzs(;uvery. i'.ruln Ls aelermined by a process of laying each elementary proposition against reality like a yard- stick(TLP2.1511-2.15121).The elementary propositions are truth functionally combined which leaves only a 'True? or False' as a nn@@il-IC value.Non-elementary Propositions are truth-functional compounds concatenated together by topic-neutral logical connective those meaning is given by truth tables(TLP4.31- 6.372).All inferences result from the principle of Tautology. Consider the following two propositions.The first (labelled 'R') is 'This patch is red at place one at time one', the second (which is labelled 'B') is 'This patch is blue at place one at time one '.The colour exclusion problem is introduced at TLP 6.3751,with the intention of illustrating the concept that all necessity is logical necessity. The impossibility of the presence of two colours spatially and temporally simultaneous is not a synthetic a priori truth but a logical one.The claim that R . B is contradictory implies in the TLP system that the two conjuncts are not elementary propositions and that red and blue are not names of non-composites-This is due to TLP 4.211,which asserts that a conjunction of elementary propositions cannot be contradictory The plan of action which is implicit in TLP 6.3751 on one interpretation eg.Hacker 1972(F2) would be to show that R when fully analysed into its logical constituents,it's truth would entail that R is not blue.In the S.R.O.L.F Wittgenstein asserts whilst returning to this problem(ie TLP),that he could explain this contradiction by saying that the colour red contains all 4 shades of red and no shades of blue-the colour blue conversely contains all degrees of blue and none of red. In Hintikka and Hintikka(F3) there is found an interesting discussion of the TLP and the problem of colour exclusion.Hintikka and Hintikka argues that the tractaterian objects are in fact Russellian objects of acquaintance(ie.sense data)(although Malcolm 1986 disagrees(F4)),although in Wittgensteins case all complex objects of acquaintance are eliminated as independent primitives-all there forms are built out of the forms of simple objects. However,it is often thought that a phenomenological interpretation of the TLP is made impossible by colour incompatibility(also by any similar prima facie dependence between simple phenomenological predicates).Accordingly 'red' and 'blue' cannot refer to non-composite objects,for the two elementary propositions R and B would not be independent since they are mutually exclusive.As this contradicts TLP 2.062 the conclusion is reached that phenomenological predicates cannot represent Tractarian objects-An argument of this type is found in Anscombe (1971 pages 25-29).Hintikka asserts that the problem which is posed by colour incompatibility is solvable,and that arguments of the same general type as Anscombes depend on an important presupposition which Wittgenstein does not accept. It is assumed by the Anscombe type arguments that if red and blue are objects,we must know what their logical type must be.The objection assumes,in effect,not only that the natural language Propositions 'R' and 'B' are incompatible but that that they are 5 subject predicate propositions as well-which are represented in llile correct notation as 'R(a) . B(a)'.The problem lies in the fact that the incompatibly is not logical in the sense of being shown by the notation which is used-the incompatibly does not reduce to a truth functional contradiction.A contradiction for Wittgenstein (TLP 4.46) is a precisely defined notion of truth- function theory,which lends a razor -- ..@j asse,.Lcion that colour incompatibilities can be though of as such contradictions- this is shown by TLP 6.3751.TLP 6.3751 is a corollary which concerns the status of colour attributions-they are not of the subject predicate form. Much of the force of Anscombes argument is therefore lost,due to its dependence on her attribution to her opponents of an assumption concerning the logical form of colour assumptions. With regards to alternative assumptions the situation is of course quite different.We may think that the general concept of colour is to be represented in language by a function,which maps points in visual space into a colour space.So the logical forms of R and B would be c(a)=r and c(a)=b,where'r' and 'are the two separate objects which are red and blue respectively. The logical incompatibility of the two colour ascriptions then be reflected by the fact that the colours red and blue are represented by different names.If so,the two propositions are logically incompatible after all.The incompatibility is shown by there logical representation in the logical notation ie. a function cannot have two different values for the same argument because of its logical form-due to its logical type.Wittgenstein in TLP 2.0131 asserts that attributions of different perceptual 6 qualities are single-valued and thus are represented logically speaking by genuine functions. Wittgensteins thought that he could Solve the problem of colour A ilj -nme way as spatial concepts(TLP 2.0251,2.171).It is Possible,so Wittgenstein thought,to devise a notation which reflects the necessary inter- relations of colour .- concepts,and thus to show how the appropriate structures(forms) are built into the objects we' are dealing with in colour attribution. That this is the general direction of Wittgensteins thought is shown by TLP 6-3751.Wittgensteins reference to'this contradiction' in TLP 6.3751 cannot mean colour incompatibility,but the more general problem of apparent incompatibly between the atomic proposition of an notation,which in physics can be attributions of a velocity or a location in space,to a point mass. The middle paragraph of TLP 6.3751 is a solvable analogue,according to Wittgenstein,to the problem from the field of Particle mechanics.Wittgenstein assumes that the incompatibly problem can be solved as in the example of particle mechanics,by @he simple expedient of a suitable kinematic notation.Wittgenstein claims that an analogous solution is possible in the case of colours-Wittgenstein,unfortunately,does not give any indication in the TLP of how this is done. However some indication of wittgensteins solution can be obtained from an entry in the notebooks 1914-1916 dated 16 August 1916(F5).Essentially the same point as in TLP 6.3751 is 7 apparently given as an explanation of colour inr-@-m-"atibly is presented as an object of comparison-this verifies Hintikka and Hintikka's ideas concerning the status of TLP 6.3751. Wittgenstein in the first paragraph of the notebook passage refers to the physical nature,however it is unclear that a nh-,7- -; -al analysis of colour is Wittgensteins aim eg. a reduction to electromagnetic radiation of a certain frequency.Given the nature of Wittgensteins later criticism,what he could mean is a phenomenological analysis which according to the later 'Remarks on colour' lies halfway between science and logic(ROC II.3)-this was rejected later-This is given further support according to Hintikka and hintikka that wittgensteins concern is the language of physics-Hintikka and Hintikka interpretation is given further support. if the gist of Wittgensteins treatment of colour incompatibility is an analogy between colour and space,why did wittgenstein not tell us that this was how he proposed to solve the problem?Why did he not tell us what the logical structure of colour concepts really is? According to Wittgenstein the answer is that it cannot be told a priori,by form Wittgensteins means something that a suitable logical notation can bring out.For instance,the difference between a one-place predicate and a two~place predicate is a difference in form-Such differences in form cannot be anticipated a priori TLP (5.55-5.5542,4.1274 (esp.clear 5.555). Hence the question of the correct form (representation of colour propositions)must be left to be gathered from our use of colour concepts(TLP 4.002,4.011).Hence He did not feel called upon to 8 explain it to us. Some Remarks on Logical Form --~ -------------------------- In the Remarks on Logic Form (S.R.L.F) Wittgensteins returns to the problem of col.oi,-- i-ncompatibility.First an important point has to be made-Wittgenstein himself was very dissatisfied with this paper to the point of publicly disownming it. In the S.R.O.L-F he explains that in the TLP he had felt that the contradiction R . B could be explained by how red contains all degrees of red and none of blue and vice-versa(F6).The S.R.O.L-F most important contribution is a destructive one-it exposes the incoherence of the Tractation solution.There he had wanted to treat statements of degree truth-functionally-as analyzable into logical products. To use Wittgensteins own example(F7),suppose we wish to reduce a statement of brightness(or any statement of degree) to its logical product.Thus 'Entity E has unit brightness b',would be expressed as E(b);and a composite statement E(2b) would be reducible to 'E(b) and E(b) and nothing else'.The problem here is a confusion between the logical connective 'and' with the additive 'and'.In a logical product 'E(b) . E(b)' is not 'E(b) plus E(b)';therefore 'E(b) E(b)' "equals" E(b) and not E(2b).'And nothing else' is likewise not an elementary assertion('...plus zero') but a general statement.Neither will r the alternative attempt succeed,of distinguishing between the units b' and b".Our original problem of exclusion and deduciblity clearly arises at this deeper level amongst the different units. According to Hacker(F8) there are two solutions.The first one 9 modif ies the syntax(ie.the rules which tell us in which connections a word gives sense) of the TLP or else the notion of simples as the correlates of logically proper names is to be abandoned as the foundations of language.In the S.R.O.L.F Wittgenstein opts for the rirsu alternative and thus hangs on to the concept of analysis and also of the concept of an ideal notation. This consists of two independent moves.First,numbers must enter into elementary propositions,in order that the irreducible propositions which attribute colour have the same logical multiplicity as the quality they attribute.The second move involves the modification of the rules for the logical connectives.This is due to the idea that the mutual exclusion of statements(note-not contradiction) of degree of quality could not be shown to be a consequence of the logical product of logically independent constituents of the analysans.So it might seem plausible to try to show that the conjunction of incompatibles is,in a certain sense,ill formed.What Wittgenstein is suggesting is that logical connectives are not topic neutral and that the semantic rules which are given in the TLP are incomplete.The meaning of the connectives will be given by truth tables which are specific to kinds of quality.The truth tables below are for the possession of degrees of quality at one spacial,temporal,location. So TLP (4.31)- p q p q T T T T F F F T F F F F 10 is rewritten in the S.R.O.L.F as- p I q I p ------------- q T I F F F T F F The top line of TLP 4.31 has to disaPpear,.. impossible c0m-bination.it it represents is in this disappearance which lies the exclusion rather than the contradiction.lf the contradiction did would have to be written thus- P I q I ------------- T T F T F F F T F F F F This is nonsense,as the top line would give the proposition a greater logical multiplicity than that of the actual Possibilities.A perfect notation will exclude such nonsensical constructions by definite rules of syntax.Such rules cannot be laid down until an ultimate analysis of the phenomenon in question.This,concludes Wittgenstein,has not Yet been done. The nature of this analysis is carried out by an inspection of :he phenomena which we want to describe,thus trying to understand -,here logical multiPlicity-In a certain sense this is an a ,Osteriori investigation~apparently Wittgenstein felt that he was ot under any obligation to explain the nature of a philosophical nvestigation which was simultaneously 'a posterior!? and ,ogical'(a priori). iittgenstein and the Vennia circle -------------------------~-------- i the Christmas of 1929 Wittgenstein returned to Vennia,where he t with M.Schlick and F.Waismann who were members of the Vennia Circle.Their Conversations were recorded by Waismann-it is to these we shall turn. Wittgenstein starts(F9) with a reference to TLP 2.15121 in which he makes the remark that a proposition is like a ruler which is laid against reality-only the outermost gradation marks touch the object which is to be measured. Wittgenstein now asserts that a system of propositions is laid against reality like a ruler-when a ruler is laid against a spatial object,all the graduating lines are against it simultaneously-The whole scale is laid against it.If an object reaches up to the tenth mark,I know it does not reach up to the eleventh. If I assert that point X in the visual field is green,then I know not merely that,but additionally,that it is not red,yellow,pink.I have laid the entire colour scale against it simultaneously-This is also the reason why point X cannot have several different colours simultaneously.For when I lay a system of propositions against reality,in each case only one state of affairs can exist-not several. At the time of writing the TLP,Wittgenstein thought that all inference was based on tautological form.He did not yet see that an inference can also have the form 'This man is 2 meters tall,therefore,he is not 3 meters tall'.This is connected with the concept that elementary propositions must be independent of one another,that you could not infer the nonexistence of one state of affairs from the existence of another. However if the present conception of a system of propositions is 12 -ect, it wi I I actual ly be the rule that from the existence Of one state of affairs the non-existence of all the other state of affnir.@ dpsnrihp(i hv -1 -.I -.&. -j. kiLuuus.Lv-ions can be inferred. Schlick goes on to raise a series of questions(F10),one of which is whether phenomenological questions(following Husserl) are synthetic a priori-A question which Schlick later himself takes up(Fll),Iater C.Radford,L.Kenner,F.Ferre' and D.Pears take up this problem. On the Link between 'Some Remarks on Logical Form' and the ------------------------------------------------ ~--------- 'Philosophical Remarks'. ---------------- ~--- Wittgenstein was obviously dissatisfied with S.R.O.L.F and never specifically addressed any remarks to it,however there is a passage in the P.R(PR 84) the first sentence of which can be read has a criticism of the S.R.O.L.F in that the account given there was a misrepresentation of the situation.The second sentence of this passage criticizes the proposed solution of the S.R.O-L.F ie.an investigation of the phenomena themselves.The third sentence(with a little straining) could be taken as a hint of the bed rock which is lying in wait for the investigation, into the conventions of language.If Austins interpretation(F12) is correct,then mention of systems of propositions or prepositional space,along with the yard-stick metaphor,must be viewed as precursors of the language games of the Blue and Brown Books and also of the Investigations.If this is so,one can readily see the radical difference in the solutions of the colour exclusion problem in the S.R.O.L.F and the PR,and the importance for the later writing. 13 According to Austin(F13) the solution in PR has been treated almost as it is if an elaboration of the. S.R.O.L.F.However if the two are not essentially different then there is no reason to suppose that the PR solution is in fact no sounder than th.- PP one-we would be forced to conclude that as there is no additional solutions to be examined,Wittgensteins treatment of this problem was i-nadequate.@L.L' Li-icy were inadequate then perhaps he abandoned his Tracteration foundations prematurely.So it is important to see why the PR solution is adequate,whilst the S.R.O.L.F is not. Philosophical Remarks(Chapter VIII) --------------~-------------------- In the Philosophical Remarks Wittgenstein asserts(F14) that a proposition P which attributes a degree of quality to an object is either an elementary or a compound proposition(eg 'A is 5r'). If P is compound then it must be a conjunction of elementary propositions,each of which attributes a 'quality' of r to A,conjuctively implying A's possession of 5r-however this is not possible(PRs76) as the conjunction of five identical elementary propositions 'A is lr' will not imply P,only 'A is lr'.If P is analyzable into 'A is lr . A is 2r... A is 5r',we have to distinguish between the 'co-presence'(following Hacker 1972) of these degrees(what is meant by the 'co-presence' of these degrees).Will we not be led to claim that white is presence in every instance of black?(PRs77) Secondly 'A is 5r' is the very proposition we called upon to analyze.Thirdly,these various degrees mutually exclude other-they cannot be co-present. The suggested analysis of P is in terms of a conjunction of five 14 alleged constituent degrees of r.Also required,as in S.R.O.L.F,is ,All @uppiemenlary clause which specifies that this is all the qualities which are present.Wittgenstein now asserts that this is nonsense-the logical and' is a sign of conjunction and not One cannot analyze 'A is 3 meters long' into 'A is 2 meters lone and A is also one meter it makes no sense to speak of adding further degrees or r by conjunction,it makes no sense to lay down that no further r can be added (PRs76). If P is an elementary proposition then the sum of constituent degrees of r is internal to P.One could conceive them in terms of tractatation objects conjoined together like links in a chain(PRs80).Even so,'A is 5r' and 'A is 6r' must be logically related to each other,even though they are elementary 'A is nr' may mean only n' or 'also n'.It makes no difference from the point of view of saving the doctrine of elementary propositions.If it means only n' then any other degree or quality is logically excluded.lf it means 'also n' then every degree or quality less then n is logically implied.Wittgenstein concludes that elementary propositions are not logically independent(PRS80). There do seem to be non-truth functional logical relations(PRs76).Elementary propositions belong to systems of propositions such that although two elementary propositions from different systems or dimensions are logically independent,two such propositions from one and the same dimensions are not(PRs81). Wittgenstein still believes(as in S.R.O.L.F) that the 15 grammatical rules in the truth-functional notation are incomplete and must be adapted for different combinations of kinds of elementary propositions,however there is on logical/empirical analysis of the phenomena to complete these rules(PRs821. 'I'he proper simile for a proposition is a ruler with multiple gradations which is analogous to a system of propositions which are syntactically interrelated.We compare the whole ruler ie.the whole prepositional system of reality,and determing one single point upon it eg.'this is red'-simultaneously determines all other points upon it eg.'not green','not pink'(PRs82,PRs84). In the Tractarian conception of the elementary proposition there had been no determination of the value of a lco- ordinate',ie.a deterimate of a determinable,but Wittgenstein says that his remark that a coloured body lies in a colour space(TLP 2.0131) should have brought him to see this(PRs83). At PR(1) Wittgenstein stresses that the task of Philosophy is to give a description of the grammatical conventions which govern the determinate-determinable relations for different determinables-The chapter-headings of our philosophical grammar according to Wittgenstein(PRs3) will be fcolour','tone','number'.These terms like Tractratation formal concepts will not appear in the text-that red is a colour is shown by the fact that 'red' is a value of the variable colour(PRs3). Wittgenstein appears to have thought both that one could reduce all empirical predicates to determinates and that the TLP distinction between showing and saying could be preserved more or 16 less intact.He then became increasingly convinced that the discovery of the insolubility of the C01Our-exclusion problem and the corresponding non-independence of elementary propositions,necessitated the dismantling of most of the doctrines of the tractatus.Indeed Wittgenstein did not adhere for long to the view that one should bends one effort to the elucidation of prepositional systems which are conceived on the above pattern. The development in Wittgensteins thinking is undoubtedly an important stage in the transition from the TLP to the 'Investigations'.Wittgenstein's 'new' philosophy does not emerge in one swift movement,but evolved (in part at least) from Wittgensteins struggles with the unsolved problems from the TLP. The important change in the PR is that there is a move towards a view which contains a plurally of systems.Logical space is being decenteralized,a proposition is no longer thought of reaching through the whole of it.Each proposition belongs to a space(a system of propositions) not to the system.Wittgenstein is beginning to make the shift from the concept of one language which is unified by the essential nature of propositions,to the concept of an endless variety of diverse and autonomous language games-each of which embodies a form of life- Remarks on Colour A few introductory remarks ----------------------- According to McCinn(F15) Wittgenstein in the 'Remarks on colour'(ROC) is concerned with the 'internal relations' between colour which establishes a 'mathematics' of colour esp.relations 17 of kinship and contrast Of colour-variOUs examples of impossible colours are also discussed eg.reddish~green and (the example we shall later concentrate on) transparent white.According to McGinn colour incompatibility is not discussed in these temarks,a fact which McGinn finds surprising-as one might have thought it to be an important case of the necessity with which he is concerned n interprets these necessary a priori truths as 'laws of appearance'-truths about how things can look.Wittgenstein even speaks of them as 'phenomenological' in character. According to Harrison(F16) the discussion of this 'mathematics' (or'logic') is paralleled to a discussion of certain questions about the relationship of thought and language to reality,which the existence of such a logic raises.According to Harrison one fulcrum of this discussion is that there is not two separate enterprises of describing 'the way the world is' and 'logical grammar' or 'the rules of our language',the first producing a list of empirical truths,the second analytical ones-but that the same sentence can express both a logical and an empirical claim depending upon the context of the language game in which we employ it(ROC Il).To understand colour-language is to play a large number of such games,all of which are subtly and with great complexity related to one another(ROC III302). According to Wittgenstein grasping a colour concept is intrinsically connected with the capacity to give a certain kind of performance-He argues (ROC III163) that a person who claims to see reddish-green would be in a position to produce a colour series which begins with red,ends with green,for us this would 18 also constitute a continuous transition between the two.We might find that at ,- point where we see a certain shade of brown,he sometimes sees brown and sometimes reddish-qreen-al@n can always visually discriminate between two chemical compounds by appeal to this distinction. What constitutes colour-blindness is the concept that one person (,. @ n1 ----- I @--- -$&e whilst another person cannot(ROCII112).According to Harrison we cannot separate an array of purely analytic moves which create lancjuage,from contingent matters of fact which make up the nature of reality.(ROC III 114-115). In ROC III86 Wittgenstein asks if we cannot imagine people with a different logic of colours from our own(this involves the ideas that we can describe it,immediately respond to any request to describe it,also that we know unambiguously what is demanded of is).The obvious difficulty is this-isn't it precisely the logic :)f colours which shows us what we are talking about ie.about -olour-if this logic was different,we would not be talking about ,olour. Harrison remarks(F17) that the concept of us being able to .ranscend our phenomenal situation in reality,is very enticing- et it offers the spurious enlightenment of reductive nalysis(its obverse is a radical epistemological skepticism). Perhaps if I redefine my colour concepts in psychologically easurable capacities and still be talking about colours-ie.what iglish terms like 'red' or 'green' pick out when I (or you) see coloured surface can be left out of the account in assessing 19 the meaning and the truth of statements concerning colour.At this point familiar doubts creep in (n--- yuu are seeing something I do not see,could either of us ever know?) One merit of Wittgensteins discussion is that it ties colour concepts to 'language-games',and 'language-games' to the 'logic of colours'-and that logic to the bare appearances-to what is seen-too closely for either reductivism or skepticism to get off the ground. Westphal on colour Westphal begins his account by asking why something 'can be transparent green but not transparent white?'(F18) He remarks that Wittgensteins answer is either unclear or that Wittgenstein does not give one(at least Westphal cannot find one in the ROC)(F19),Westphal hopes that his own answer is at least clear perhaps misguided)(F20).If Westphal's answer is right then science does have a bearing upon the logic of colour concepts and that the Wittgensteinian distinction between logic and science is false.At best it will mark a contrast between the domains of logic and the claims of a particular scientific theory and a particular mode of scientific theorizing. Westphal asserts that there is a crucial difference between white and other colours which allow transparency.White is typically a surface colour and not a film or a volume colour(colours are said to appear in surface,volume,film or aperture,illumination and illuminant modes). As with other impossible colours which are discussed in ROC(eg.reddish green,illuminious grey),Wittgenstein is not concerned with the non-existence of transparent white,but with 20 its r Dn("T ')I t t ;;z.- E t ------- f-hnf- z.7,n cannot desc@-4œbc(orp air-,L) something which is simultaneously white and clear,nor can we give a description of how such an object would or should look.We do not know what is demanded of us. It has been noted earlier by Mounce(in a Book review) that Wittgenstein wanted to replace the question why transparent white is inconceivable with the question'why we do not know' what the words 'transparent white' demanded of us.According to Westphal this is wrong-Wittgenstein does not state that this is his purpose nor does he actually ask the question-all he says that we do not know what these words demand of us.According to Westphal the unasked second question comprises Wittgensteins general form of the solution to this puzzle.The point is that there is nothing these words demanded of us-'we do not know what these words demand of us' is an Wittgensteinian way of saying that an incoherent demand is made.There failure is one in the logical sense of ROC I27- Wittgensteins method(as far as he has one)is to in various ways to imagine the thing of which it is true that 'one does not know what one should imagine here'-the knowledge of inconceivably emerges from these doomed efforts.So,'a smooth white surface can reflect things:but what then,if we made a mistake and that which appeared to be reflected in the surface was really behind it and seen through it?Would the surface then be white and transparent?Wittgensteins use of this type of reducto ad absurdum argument makes it difficult to piece together a solution to the 2 1 whiteness puzzle, if according to Wesphal there is one. The nearest which Wittgenstein comes to this is the rule of appearance(ROCI20 III173) in which he assets that something white behind a coloured transparent medium appears in the colour of the medium,somethina Di-acx appears black.According to this rule black on a white background would have to be seen through a 'White transparent medium',as through a colourless one.According to Wittgenstein this is not a proposition of physics,but a rule of spatial interpretation of our experience.Even thought Wittgenstein derives an absurd consequence from this rule,there is no formal contradiction.It would be nice to have one as it would explain why 'one does not know what one should imagine here' in following Wittgenstein speaking of transparent white-as without a formal contradiction we will not get to the problems core. In order to solve Wittgensteins puzzle we have to give an account about what whiteness and transparency are ie.we have to give a theory of whiteness and transparency.We have to do what empiricists have asserted that we cannot do viz.something which has the function of resolving the concepts into - simpler concepts.If this can be done,one need not accept the empiricists account of the needed method,the colours(at the very least transparent white) will have been shown not to be logically simple.An acceptable conception of white,according to Wesphal,will have to connect the concept simultaneously with the phenomenal property(colour) and the physical property,which is supposed in psychophysics merely to stand in a correlation to it. We need a conception of whiteness which will connect the colour with the unique or asymmetrical property(it is asymmetrical in 22 that no other colour has it) of necessary opacity which is - our explanadum.Opacity like transparency is a physical property of objects,substances,surfaces and so on.The conception must not allow the physical and the phenomenal Properties to part company.If this occurred the prospect of finding a necessity(logical or otherwise) is lost-it is this necessity which is the ma-Ln- element in Wittgensteins puzzle. Wesphal can offer such an conception(F21) and expresses hopes that it clarifies just what the genesis of the logical element in the proposition that nothing can 'be white and transparent' is- yet it is incomplete as more needs to be said concerning whiteness in connection with the physiology and psychology of @olour perception-although Westphal believes that this can be lone,it is not necessary,all that is needed is the special case ihich is the physical part of the theory of whiteness. A white surface is one which reflects nearly all of the light ncident upon it.It is a surface with a reflectance of pproximately 80%(or higher) across the spectrum.If the arcentage of reflected light was much less then this,the result )uld be something other than white.The ratio of the @flectance,absorbance,and transmittance of a substance will vary )r different coloured lights across the spectrum,however in all ses the sum of the three is naturally the same. So,what would a transparent white surface be like? --ording to Westphal(F22) it would be a surface which first ansmits almost all incident light,this enables us to see what @s beyond it,second it would scatter back almost all of the 23 11.91AL dno transmits almost more.This is a straight doub'@e contradiction. We are told that every kind of statement must have its own kind of logic:then every kind of statement must have its own kind of contradiction.However in the proposed contradiction 'X is white and X is transparent' turns out to be an ordinary contradiction of the form 'P - -P'.Represented in the following truth table(F23),where W is the proposition that X is white,r that X has high diffuse reflectance,m that it has high transmission. W T W . T r m r.~M -r-m Cr.-m). (-r.m) ------------------------------- ---~------ T T F F F T F T F F F T F T F F F F F F This results suggests that there is no distinctive logic of @olour,only a logic which is applied to ordinary statements about --he distinctive facts and phenomena of colour. A white surface will always reflect most of the incident ight,it will not darken the light to any significant degree by bsorption,as reflection by surfaces will.A white object darkens o light in the sense that for any illumination,the incident lght is approximately the same in quantity and quality as the Affected light. So white,to use Wittgensteins phrase is always the lightest )lour in the tricolour(ROC III2) because the concept of a white )ject is the concept of something which does not significantly rken the light in the above sense. Whiteness is connected with the ratio of reflected and incident 24 light ie.with what the surface typically does to the light-The colours of objects are perceived in relation to the illumination- which regardless of colour is always treated by the eye as standard,the other colours are judged in relation to this. The reflectance of white objects is the same through changes in illumination,which results in what psychologists call colour constancy.A white surface scatters back all of any incident light.This is not true of a blue object which under blue illumination will do exactly what a white surface does.Provided we are aware of the illumination,differenation between the two objects is possible,even if there is no physical difference between them-as there relation to the illumination over the whole scene is different. If we are prevented from adapting to the illumination,we cannot tell the difference between the colour derived from the illumination and the colour which is a function of the chemistry of the object.We cannot tell the difference between a blue room filled with blue objects and illuminated by a white light and a white room with white objects which is illuminated by blue light,with the proviso that we must be looking in through a small window.This restriction is needed so we cannot tell in what characteristic(to each colour) way the objects in the room change the light. A white surface in blue light does not look blue- provided we are able to adapt to the colour of the illumination.It looks white and completely different from a blue surface which is illuminated with white light.This mistake is made by Ayer(F24),one empirical premise on which the argument from illusion(to sense-data) is based says that a white wall 25 biue wnen it is seen through blue spectacles-this is LO IOOR white. rvv'-'Ltl,gensteins crucial ?rule Of appearance@ is false,applying only in non-adaptive Situations-Accordingly it cannot explain the 0PaCity of Yjhite jbjec4-s or -Lily eise,Wittgensteins deduction fails.under the proposed conception several Wittgensteinian explananda fall into place vi---. 1) We learn why white is a surface colour and reverts to achromatic brightness in other modes.In order for anything to be white,it has to scatter back the required percentage of incident light.If it can do this,it is probably going to be sufficiently solid to count as a surface and present a literal barrier to the light- It becomes evident why a white object lying behind a coloured iediuin in an non-adaptive situation,or when the effective llumination is so strong adoption is impossible,should appear ith the colour of the medium.The white surface acts as an 3hromatic light shining through the coloured medium which Lnctions as a simple filter. ,ROC(I116) is confirmed-white does do away with darkness. Wittgenstein at ROC(III14) asserts that we do not speak of a itish cast on objects-This is interesting-we might notice,says stphal(F25),that the light at a particular time of day was lish(eg.the moon can appear blue)-but not that it was whitish the sense that it gave a whitish tinge to things.The :tinction here is between a light in the sense of a lamp and ht as the way of being lit.The former can be phenomenally 26 wh 1 t-,#n i 1 not.However it is white in a specialized sense-it is colourless, it allows thon Liiings Wittgenstein at ROC(IIII48) asserts that transparency could be compared with reflecting.Both transparency and reflecting can exist only in the depth of a visual image-The fact that white surfaces present a barrier to the light means that the dimension of depth needed for transparency cannot occur. All that has been asserted so far is quite independent of what light is.All that is required of such a theory is that we end up with the right properties of light eg-it illuminates,is reflected,makes shadows and so on.The spectral composition of the light reflected from a white surface is not relevant to the question of why it cannot be transparent.It is not even relevant to the question of whether the surface is white-The best logical level of explanation is determined by what is relevant to these questions.It determines ind is determined by what kind of thing('logical grammar Whiteness is-To know that emission of light waves is talking ,lace is not to know anything which is relevant to the opacity of hat surface-As mentioned previously blue and white obje can eflect light of exactly the same spectral composition-yet as @ere relation to the illumination is different,they are afferent colours. That is relevant to the solution of Wittgensteins puzzle is that iy light is reflected(like a mirror) by a white surface-In swer to the empiricists there is an important sense in that at we see is not complex-To say that high reflectance for all loured lights is complex in the sense of being composed of 27 anything is nonsense-Reflecting a high Proportion of the light is what the white object does to the light-this could not intelligibly be said to be composed of anything. our conception of white makes metallic surfaces and mirrors '@his can be prevented by making a distinction between specular reflection(where the image is preserved) and diffuse reflection Nothing which as been said so far shows absolutely that whiteness of a surface is the very same thing as its disposition to diffusely reflect a high proportion of the light.The theoretical definition(as asserted earlier) is not complete,it will not serve in a physicalist reduction from its phenomenological properties ie.its colour to light-emission of different wavelengths nor can it handle whiteness in contrast effects- The theory of the physical nature of whiteness as to be in accord with both the physiological and psychological theory of colour-something more subtle than saying contrast effects are a species of illusion needs to be said.However the definition is a true part of the story,it easily handles Wittgensteins a priori which Westphal(F26) supposes must be some kind of evidence as they are puzzles concerning the whiteness which we actually perceive.It is visible whiteness which is necessarily untransparent,visible whiteness which is a property of physical objects and surfaces.Thus the explanation of Wittgensteins puzzle is a physical one-but not in the low-level reduced sense of physicalism-It leads onto a functionalist perspective,where 28 sensations are functions of the activity of perceptual systems. If the theoretical definition Of whiteness car-, ,,, capiain th(-, necessary truths that it generates,Westphal(F27) cannot see that anything could.Wittgensteins successors of 'grammar' ie.the Imathematics Of colour' and the 'logic Of colour concepts' are a pretty poor bet.Yet,it must be said that using these concepts Wittgenstein asked some of the most suggestive and interesting questions which can be asked,not just about transparent white,but about colour as a whole. Criticisms of 'White" ---------------------- According to McGlnn(F28) in his book 'The subjective view' the Wittgensteinian 'laws of appearance' raises questions paralleled by those raised by McGinn concerning colour incompatibility. The case of transparent white is explained as the impossibility that a surface could look both both white and transparent to a perceiver(F29).This could be challenged by a split brain case-a surface could be made to appear white in one eye,white in another-the Perceived effect being transparent white(F30). To McGlnn(F31) the obvious answer is that this shows 'that we cannot associate a unitary perceptual subject with a split brain- the proposition that surface X cannot look transparent white imposes a necessary condition of what it is to have a single Visual field. The question reducibility arises(as in the case of ncompatibility) in Wittgensteins examples.McGinn asks if it is ossible to give an explanation of the necessary character of hese truths in non-phenomenological terms(F32)-Exactly analogous )sections apply as in the previous example Which McGinn uses of 29 the incompatibility between secondary qualities viz.concerning whether the tinitv and sD(-c-ifity of the original proposition can be captured;whether its status epistemically is still n -------spending necessity at a physical levpl still exists(F33). According to the objectivist(eg.Westphal) it is impossible as a surface to be transparent is to transmit all incident light,to be white is to reflect all incident light. Transparent white is impossible as a surface cannot interact in both these ways simultaneously.McGinn(F34) then uses a variation of the inverted spectrum type of argument-consider a Martian who when we see green he sees white.This means that just as we are able to imagine a transparent green(eg.a'quality street'toffee paper),our martian friend should be able to imagine transparent white just as easily.This example contradicts the acknowledged necessity of the non-existence of transparent white surfaces. McCinn(F35) believes that this shows that the impossibility of transparent white cannot be explained in this objective way:the content of the impossibility is just that nothing could look transparent and white-the Martian would agree with us about this impossibility. Wittgenstein is now brought into play (ref.ROC III252 [I16),though there are connections between laws of appearance and )hysical laws,the former cannot be explained in the .atter.According to McGinn(36) the proper explanation is that in -,he process of becoming a (self?)conscious perceiver you learn to :onform to a system of phenomenological laws which govern how hings seem-these laws arise from the nature or perceptual 30 c-xperienc,- LO spell Out a consequence of the subjectivists views concerning secondary qualities,as the laws which are applicable to secondary qualities are subjective in origin,if those qualities are themselves subjectively constituted. narain s and Sanford's criticism of McGinn ------------ ------------------- According to Hardin(F37) the objective analysis which is presented to us is deficient although this can be reminded within an objective framework.It is clear that the Martian example does not have any force against objectivism and will not support his conclusion. White according to Hardin involves another surface property viz.diffuse reflectiveness-it alone as this property.McGinn's account is correct in that high unselective reflectivence is not the whole story.His account concerning the Martian is misguided as it requires a change of appearance similar to a change of @ue,except that the achromatic colours are slotted amongst the iues.it is at this point that McGinn's account becomes incoherent lue to the structural difference difference(and mutual ncompatibly) between achromatic and chromatic familles.The chromatic colours have to be slotted in as a family as there nly variation is in lightness.We can only assert that where we 3e green,the Martian sees achromatically.When he sees the .ghtest grey when we humans see the lightest green,the object incerned will be transparent.Will our Martian see a White ansparency? The transparency at which we are looking will,due a physical fact which is independent of the psychological istitution of the perceiver,be spectrally selective and will 31 necessary darken some colnlt-- is see,,-, Liiuugnr, it. What our Martian friend will see is an achromatic transparency,on certain frequencies of light significantly less light than is original source.If our Martian then sees the object as transparent and coloured he will see it as grey.Achromatic perception of our Martian is considered next- our Martian will see them as a specific colour,just as long as a certain amount of light is diffused.If an object reflects all the light without diffusion and has no perceivable surface character of its own,he will regard it as being clear-The problem of the nonexistence of the transparent specific colour then arises.Colour sensations have been dumped and there is no need to appeal to a system of phenomenological regulations. Sanfords Criticism ------------------- The impossibly of a single surface both reflecting and transmitting most of the incident light does nothing to show that a object cannot be transparent white,as the reflecting/transmitting surfaces are distinct(F38). Consider a sheet of glass with opposite surfaces A and B(see liagram overleaf).Surface A diffusely reflects light whilst -urface B transmits most of its light through surface A.How this Transparent white surface looks depends on the different levels f illumination between the two sides.One could see through from he darker to the brighter side. According to Westphal 80% of light as to be reflected in order )r a surface to be white,the other 20% must either be absorbed transmitted.As Sanford(39) concludes arguments showing the 32 impossible of a object being transparent white should be considered with caution,as there objects which are white and transparent.Hardins 'truths' that transparent glass never whitens light,so that objects perce@-,.,--@- 4+- - . look whiter and tl,-,at mirrors also never whiten light are contingent-there is nothing physical or phenomenological impossible about white mirrors and transparent white. Hardin asserts(F4 0) that white objects are diffusing reflectors- first an object can be white without any reflector-white light bulbs,white stars(also Wittgenstein ROC III226).Transparent white objects combine some properties of light emission with ordinary mirrors and properties found in transparency. One of Wittgensteins assumptions in ROC is that any glass not visual analogue of a loud hailer,a device which amplifiers light~ it provides light of the same frequency but with a higher intensity ie.dim objects look brighter,bright objects(to an extent)look brighter. Ordinary stained glass windows colour light by selective absorption-light of a number of frequencies is absorbed more than other frequency.Coloured 'loud-hailer' windows would colour light by selective amplification,where the intensity of some frequency of light is increased more than others.When viewed through normal red coloured glass an green object looks less green and darker.When viewed through an transparent red 'loud-hailer' window An green object will look less green and brighter.In both these cases the green looks more achromatic and not redder. A transparent white 'loud-hailer' window would make everything 33 -Ljitcr,something not already chromatic would look more achromatic.Everything will look )righter,everything will not look whiter for instance the dark rreys,greens,blues will all look less dark but are not shifted !lose enough to white,to look white.If it is Possible for omething of a certain colour to look whiter,it can look white ecause it is viewed through a transparent white 'loud-hailer' indow. Westphal and Wittgenstein on White' --------------- ccording to P.Gilbert(F41) Westphal's answer in his paper is the rong sort of answer to Wittgenstein question (ROC I19).As noted reviously,Westphals conception makes metallic surfaces and irrors white-prevented,according to Westphal,by the additional ;sertion that white surfaces produce diffuse as opposed to Fractional reflection.What Westphal fails to appreciate is why would be a bad thing to call mirrors white-for if we can call mirror white we can call a window white as the fact that .ndows transmit whilst mirrors reflect most light is not a impelling reason against such labeling.The only reason against .ch labeling would be any difference in the way they looked.Yet e windows and mirrors do have there similarities in the way ey look~eg.surfaces of mirrors nearly always look ansparent.Mirrors are not called white as they look ansparent-not white.Westphal has no account of why something nnot look both white and transparent. he high degree of reflectiveness of white surfaces cannot .DIain the opaqucity of white surfaces,as it cannot explain why 34 white surfaces look opaque.opacity could only be explained by reference to some Property,the Possession of which ruled out the possibility of that surface being transparent.Yet high reflectivness is a property which white surfaces do share witn some things which do look transparent-viz.mirrors.We could,following Westphal,add diffuse reflectivness and thus obtain a propert., Might explain its opacity.According to Cilbert(F42),the difficulty with this is that it would be no longer whites unique colour le.its high reflectiveness(alia Westphal),but rather some property which is sometimes shared by other transparent colours.Why White is always diffusely reflective(hence opaque) is not explained by Westphal. Westphal fails to account for the fact that white,in colouring anything,necessarily renders that object opaque.What we want to know is not why raising its reflectiveness makes a surface 3ctually opaque,but why a way of doing this that involves ,olouring has this effect which is visually apparent. Westphal could come to some sort of explanation of the Opaqueness of white as follows-A surface which reflec(ts all ncident light has to reflect all the colours of which that ight is composed.If it is diffusely reflective it has to appear D be some colour,and some colour other than those of surfaces iich do not reflect all colours-That colour is white.It is due the fact that it is diffusely reflective that it looks opaque id has colour-due to its opaqueness it has colour.A transparent rface could not be coloured white as it does not have the high ffuse reflectiveness required to look white.Such an explanation es not answer Wittgensteins questioners part of this question 35 requires not only why something can neither be both whit, transparent,but why this is not even imaginable.Possibly,this could be shown by proving that the theory of light transmission and reflection which provides the explanation is embodied in our ordinary talk of colour-This Westphal has failed to show. Wittgensteins question is an request for an elucidation of the logical grammar oic Pi:opusicions which attributes whiteness of transparency to things.What needs to be explained is why our use of these notions rules out(not by contradiction but by exclusion(see S.R.O.L.F)) there conjoin attribution-Such an explanation will be a priori. Gilbert(F43) raises two questions,first is such an explanation possible?If it is possible would the facts of logical grammar(on which such an explanation depends) additionally require an explanation in terms of the necessary physical properties of white or transparent things?Westphal believes that Wittgenstein cannot provide such an explanation,what we have to do is to give an explanation of grammar in terms of 'what-it-is-to-be~ whiteness'.An explanation which Wittgenstein would have rejected,as no non-grammatical property of colours can explain -,here grammatical features.According to Wittgenstein opacity is a Grammatical remark,not an empirical fact. What account does Wittgenstein offer of the impossibly of ransparent white? Red glass for instance can colour the scene ehind it and it preserves the contrasts.The reason for the possibly of transparent white is that to be transparent it Duld have to reveal contrasts,yet to be white it would have to 36 obliterate such contrasts.Yet this is still unsatisfactory-it is conceivable to have a thin 'white alassl which would preserve enough contrasts.Also an analogous explanation would serve for black glass,those properties are sign@lr-; @cantly different- Wittgensteins asserts that even thin white glass would,due to its being cloudy,obliterate forrn.Black glass on the other hand does not similarly distort things which are seen behind it.Uniform blackness would be incompatible with transparency as uniform whiteness,it is conceivable that a progressive darkening of colours by black glass with no loss of transparency.The analogous example of white-a progressive lightning by white' glass without loss of transparency is inconceivable.Wittgenstein never adequately explained this phenomenon-yet it is clear that it proceeds quite differently than Westphals enquiry. Westphals reply to Cilbert ----------~-------------- destphal makes the claim that Giberts criticism had been inticipated(F44).Westphal believes that the best explanation of shy objects looks a certain way(in one sense of looks) because it s that way but because the no-wavelength strategy of Westphals aper 'White' was to explain the look of the colour. Westphal due to believing what he labels 'Principle P' which 'ates that anything can look like virtually anything else under iitable,thinks that objects can look transparent white and gives @e example of an reflection of a white sheet of paper in a ndow. ccording to Wittgenstein ROC I43 a surface can look transparent ite but more needs to be explained-why it isn't.Wittgenstein is only directing his puzzle to the way it looks. 37 ROC I19 seems fairly straight forward-why can X be transparent green but not transparent white? Despite P Wesphal .,@,,ild join with Gilbert in saying that equating white with light of all wavelengths does not produce a solution to Wittgensteins puzzle-white light does not look like light of all wavelengths.1 could look like Quasimodo but I do not.Principle P is true,thought things do look like themselves most of the time. Also Electro~magnetic radiation at the surface of the object of XYZ wavelength does not look like anything more that what mean molecular kinetic energy does.As 'Electro-magnetic radiation of XYZ wavelength' contains three theoretical terms it cannot refer to the Phenomenal colour 'white'.Given principle P things can look like other things,the other things have to be of the right category.In not falling for criticism that white doesn't look like what it is said to be Wesphal distinguishes himself from the physicalism of Armstrong and Smart-Westphal in 'White' does say that white actually does look like the high diffuse reflecting of a surface-It manifestly does not have other colours as components,if it did it would look quite different as there is only one relevant sense of contain eg.orange contains red if it reddish however white is not reddish,greenish and so on.This was a sufficiently important concept for Goethe and Wittgenstein to erect a science and philosophy on this spot.Westphal concludes that there is nothing in this particular line of criticism which dill force him to recant what he said in 'White'. 38 :iberts rejoinder t-,o Westphal --------------------------- 1 0, TP A z of white than ilbert,as Westphal thinks that X can look transparent white an.-A, ses Wittgenstein ROC I43 as an example.This shows than an xplanation of why it cannot be both transparen- eeded. 4esphal as misunderstood the example,what Wittgenstein as )ticed in his own example that a white surface looks transparent ien it reflects things.Suppose a surface like this is in reality .ansparent,and not reflective.The reason according to ttgenstein why we do not call it white is because it is ansparent,and its looking transparent is incompatible with its oking white-which is opposite of what Westphal is trying to ove. estphals example of an transparent white object(a white sheet paper reflected in a window) is unfortunate.It is not insparent white as the reflected sheet of paper presents a ible aspect,where we can see it either as white(where we would oblivious to the colours of objects which were lying behind it part of the window) or as transparent(thus enabling us to ,ceive the colours of these objects).We cannot see it as insparent white any more we could see both aspects iultaneously. sphals principle P is incorrect.Objects which look white not look transparent white anymore than solid cubes look ultaneously hollow,thought at different times solid cubes can k hollow and vice versa.Westphal would be compelled to reply b in the case of white a surface could be visualized with both 39 contradictory properties-Gilbert(F46) asserts that the case against Westphal is not that transparent white cannot be Visualized as it is contradictory,but that no contradiction he adduces shows why transparent white cannot be visualized. It is possible to visualize a surface which does reflect most light and we could imagine being able to see through that surface LO the objects which are behind it as transmits most light(eg.a two way mirror) we would be imagining something which is contradictory-but not transparent white which goes against Westphals analysis-That the conjoint Possession of properties presented in the visual aspects of a thing involves a contradiction cannot explain why those double aspects cannot be simultaneously perceived. If a object looks a Particular way,it must be Possible for a person to have some conception of the way it would look-this applies to transparent white.Such a conception in only Possible,according to Westphal,ln the sense of it's description being logically contradictory as it unimaginable. When Wittgenstein at ROC I31 asks why we can't @imagine transparent white,is he seeking an explanation of the futily of the exercise? What Wittgenstein aims to show is why this this attempt collapses.Finding the reason for this will show why an Transparent white object is unimaginable. Westphals explanation of the looks of the colour could not do o.An explanation in terms of diffuse reflection fails to explain onceptions of bright,brilliant and dazzling-it fails to explain hese conceptual connections. 40 pilcations as if Westphal give us this concept,prior expectation of an objects looks would not be necessary in order to understand how it looks.If an object looks highly reflective because it looks white,its lonki-nl- &--.y'ily i reflective cannot explain its looking white.Also as the non- diffusely reflecting of a surface does not have any looks at all,the concept of white is not that of high diffuse reflectance.So WestPhal seems to have a loser of an conception on his hands. Conclusion I have tried to cover two related debates,that between McGinn and Harding and Sanford and that between Gilbert and Westphal.I want to draw attention to two conclusions reached,first that Transparent White is possible and that the conception of Transparent white reached by Westphal,due to its failure to explain various conceptions related to colour eg.glitter,is shown to be inadequate.It,perhaps,should be noted that more thinking is necessary on these concepts~there is a good deal of useful raw material on colour to be found on these concepts in ROC.IN addition to these two debates I tried to show how colour incompatibly influenced Wittgensteins philosophy.All in all I must conclude that more work is necessary,in what is a fascinating topic. 41 Footnotes (2) 'Insight and illusion',D.Hacker page (3) 'Investigating iiiiilikka and Hintikka page 121- 131 (4) 'Wittgenstein',N-Malcolm page 10 (5) 'Note-books' L.Wittgenstein Page 8le (6) 'Some remarks on Logical Form',L.Wittgenstein(Copi and Beard) Page 35 (7) it it page 35 (8) 'Insight and Illusion',D-Hacker page 88 (9) 'Wittgenstein and the vennia circle ',F.Waismann page 63 (10) page 65 (11) 'Is there factual a priori',M-Schlick(Readings in phil-analysis (newyork1949) (12) 'Wittgensteins solution to the color exclusion problem',J.Austin page 212 (13) it 9t page 207 (14) 'Philosophical Remarks',L.Wittgenstein page 108 (15) 'The Subjective view',C.McGinn page (16) Book review on the 'Remarks on colour',B.Harrison page 565 (17) tvtl 19 tilt page 566 (18) 'White',Westphal page 311 (19) 19 it page 311 (20) page 311 (21) page 316 (22) page 317 (23) Wesphal 'Colour:some philosophical problems from Wittgenstein' page 20 (24) 'The central questions of philosophy',A.J.Ayer page 74 (25) 'White',J.Westphal page 320 (26) page 327 (27) page 328 (28) 'The Subjective view',C.McGinn page35 (29) it it page35 (30) it it page35 (31) tit 99 11 page35 (32) qv page36 (33) page36 (34) page 36 (35) page36 (36) page36 (37)'A transparent case of subjectitivism',Hardin page 117 (38)'The possiblity of transparent white',D.Sanford page 213 (39) sanford page 213 (40) hardin page 119 (41) 'Westphal and Wittgenstein'P.Gilbert Page 399 (42) page 399 (43) tell lit? page 401 (44) 'Reply to Gilbert',J.Westphal page 603 (45) 'Rejoinder to Wesphal',P.Gilbert page 422 (46) fill ?Aft page 424 42 Works of Wittgenstein Bibliography ------------------ 'Tractatus Logico-philosophicus',L.Wittgenstein (trans.C.K.Ogden,published by Routledge and Kegan paul,1922,1981) (trans Pears and McGuinness 1961,1981 " n 11 n ) I 'PhiliosoDhical L.Wittgenstein (trans.R.Rhees,Blackwell,1975) 'Some Remarks on Logical Form',L.Wittgenstein,A.S.S.P Vol 9 1929 also Copi and Beard 'Essays on Wittgensteins Tractatus' (Blackwell,1966) 'Remarks on Go-'Luur i,.Wir-rgenstein,(Trans.L.McAlster and M.Schattle, Blackwell,1977) 'Note books 1914-1916',L.Wittgenstein,(Blackwell 1961) 'Zettel',L.Wittgenstein (Blackwell 1967) 'L.Wittgenstein and the vennia circle",F.Waismann,(Trans B.McGuinness, Blackwell,1967) Books on Wittgenstein -----------~----------- 'Wi ttgenstein', D. Pears, (Fontana, 1971, 1985) 'Wittgenstein',A.J.Ayer (Pelican 1895) 'Wittgenstein',R-J.Fogelin (Routledge and Kegan Paul 1987) 'Wittgenstein',N.Malcolm (BlackWell 1988) 'Wittgenstein',A.Kenny (Pelican 1973) 'The Subjective view',C.McGinn (Clarendon press 1983) 'An introduction to Wittgensteins Tractatus',G.Anscombe, (Hutchinson,1963) 'Principles of Lingustic Philosophy',F.Waismann,(Macmillan 1968) 'Insight and illusion',P.S.M.Hacker,(Oxford 1972) Articles on Wittgenstein ------------~------- 'Wittgensteins solutions to the color exclusion problem',J.A.Austin (Philosophy and phenomenological research 1980) Book review on 'Remarks on Colour' B.Harrison (Philosophy 1980) Book review on 'Remarks on colour',H.O.Mounce (Philosophical Quartly 1980) 43 'The PuzZle of Wittgensteins Phanomenologiel,H-Spiegelberg (American Philosophical Quartly 1968) 'The Logical independence of elementary propositions',D.Pears(In Iperspectives on the philosophy of Wittgenstein' ed.by I.Block, Blackwell,1981) 'Tractatus 6.3751),E.B.Allaire,(Analysis,1959) 'White',J.Westphal,(Mind,1986) 'Black',J.Westphal,(Mind,1989) 'Wittgensteins Philosophische Bemerkungen',N.Malcome(Philosph Review 1967) 'Reflections on white',P.Gilbert (Mind,1989) 'Reply to Gilbert',J.Wesphal,(Mind,1988) 'Westphal and Wittgenstein on White',P.Gilbert (Mind,1987) 'Colour:Some philosophical problems from Wittgenstein',J.Westphal (Blackwell 1987) Book review of Westphals 'Colour' P.Lewis (Philosophical Investigations 1988) Articles on Colour Incompatbibly -------------------------------- 'A new look at color' C.L.Hardin (Americian philosophical Quartly,1984) 'To color',J.A McCilvray (Synthese 1983) 'Colour concepts and colour experiences',C.Peacocke,(Synthese 1984) 'Colour incompatibility and language-games',F.Ferre,(Mind 1961) 'F-Ferre on colour incompatibility',R.Arbini,(Mind 1963) 'Red and Green all over again',P.Remnant,(Analysis 1961) 'Colours',F.N.Sibey,(P.A.S 1968) 'Incompatibilities of colours',D.Pears,('Logic and Language'2nd series ed.by A.Flew (Blackwell 1953) 'The incompatibility of colours',R.Swiggart (Mind 1963) 'Colour incompatibilities and analyticity',A.Sloman,(Analysis1967) 'Incompatibilites of colours',C-Radford,Mind 1968 44 of the red-green problem' C.Radford, (Analysis 1963) 'The triviality of the red-green problem',C.Kenner,(Analysis1965) 'Red and green all over again',J.Hilton,(Analysis 1961) 'Red,Green and absolute determinay',D.Sanford,Mind 1965 'The possibility of transparent white',D.Sanford,(Analysis 1986) 'A Transparent case for subjectivism',C.Hardin,(Analysis 1985) 'Philosophy and the incompatibility of colours',R.Dolby,(Analysis 1973-1974) Historical Background ------------ 'Theory of colours',J.W.Von Goethe,(MIT Press 1970) 'on vision ' A.Schopenhauer,untranslated as far as known.(Ref.in various books on author) 'I.Newton Trinety note-book',I.Newton,(C.U.P 1983) 45