Missing Shade of Blue
This essay is concerned with David Hume's empiricism. I will be taking a look at the 'missing shade of blue' thought experiment that he postulated in Book I of the Treatise of Human Nature. In expounding such an all encompassing theory of human knowledge, Hume concedes, by way of the thought experiment, that there are exceptions to his generalisation concerning the way humans derive knowledge. I shall analyse Hume's 'missing shade of blue' thought experiment in an attempt to develop an abstraction of the phenomenon it relates, which I will expand upon and utilise for my contention that the phenomenon can be accommodated within his empirical framework. I subsequently intend to provide some arguments as to why the idea of the missing shade is anything but innate and ultimately an empirical derivation hence it does not threaten the generality of his thesis. Prior to concluding, I also would like to briefly contemplate the verisimilitude of ideas such as that of the missing shade.
According to Hume, our mental contents contain both simple and complex ideas, both of which are derived from sensory impressions. "All our simple ideas in their first appearance are derived from simple impressions, which are correspondent to them, and which they exactly represent. [1] "Complex ideas, on the other hand, need not resemble impressions. We can imagine a winged horse, without having ever seen one, but the constituents of this complex idea are simple ideas [2] ,hence they also are derived from impressions. Hume soon goes on to raise an objection to his thesis that every idea is derived from a correspondent impression. He offers a counterexample in the 'missing shade of blue' thought experiment:
Suppose � a person to have enjoyed his sight for thirty years, and to have become perfectly well acquainted with colours of all kinds, excepting one particular shade of blue, for instance, which it never has been his fortune to meet with. Let all the different shades of that colour, except that single one, be plac'd before him, descending gradually from the deepest to the lightest; 'tis plain that, he will perceive a blank, where that shade is wanting, and will be sensible, that there is a greater distance in that place betwixt the contiguous colours, than in any other. Now I ask, whether 'tis possible for him, from his own imagination, to supple this deficiency, and raise up to himself the idea of that particular shade, tho' it had never been conveyed to him by the senses? I believe that there are few but will be of the opinion that he can; and this may serve as a proof, that the simple ideas are not always derived from the correspondent impressions; tho' the instance is so particular and singular, that 'tis scarce worth our observing, and does nor merit that for it alone, we should alter out general maxim [3] .
Hume's critics object that this affront to logic "either unwittingly destroys the generality of his thesis, which he needs given the uses to which he will put it, or else his dismissive attitude towards the counterexample reflects his disingenuous willingness to apply [his thesis] arbitrarily, while pretending that it really possesses the generality his uses of it require [4] .For example, according to Hume, "since every idea must be derived from an antecedent impression, it always makes sense to inquire into the origins of our ideas by asking from which impressions they are derived" [5] . If this process fails at any point, the idea in question lacks cognitive content. I maintain in defense of Hume's thesis that the idea of the 'missing shade of blue' is actually a particular type of idea, the formation of which ultimately depends on sensory impressions and empirical experience. Hence such an example is not an exception to his general maxim and can be subjected to Humean definition.
A resolution I propose to the problem raised by Hume is partly inspired by application of a similar principle to one he himself actually writes about in Book II of the Treatise:
Impressions and passions are susceptible of an entire union; and like colours, may be blended so perfectly together, that each of them may lose itself, and contribute only to vary that uniform impression, which arises from the whole. In these cases, two impressions or passions, both simples, blend to form a third [6]
Given that reference is made to colours in this example, it is plausible that simple ideas of blue shades and of white could be 'blended' to produce a third 'simplex' idea of the missing shade. I will now provide an analysis of Hume's thought experiment to investigate how an idea of the missing shade may be formed and what limitations are imposed upon the formation of such ideas; but firstly permit me to provide a brief explanation of the unsophisticated neologism 'simplex'.
It is clearly an amalgamation of the words simple and complex, chosen simply to represent the fact that an idea of the missing shade of blue possesses characteristics of both simple and complex ideas. Like a simple idea of the shade of blue it has the property of being an atomic sensory datum. Unlike a simple idea of the shade of blue, it was not directly derived from a visual sensory impression and therefore a unique quale of the shade was never experienced. Like a complex idea, its derivation ultimately requires two or more sensory impressions. Unlike a complex idea, in the sense that a unicorn or a golden mountain is a complex idea, it is not merely the conceptual compounding by conjunction of two or more simple ideas derived from distinct sensory impressions, but is rather the conceptual melding of distinct simple ideas derived from similar and related sensory impressions.
In Hume's example, the person is presented with a spectrum of blue that is gradually and consistently descending. The process of perceiving a blank and forming an idea of the missing shade of blue might be better understood by mathematical analogy. Consider the pattern of the descending blue spectrum to be correlative with a decreasing sequence of natural numbers. Each shade of blue corresponds to a natural number, the deepest shade corresponding to the greatest number. The difference in degree of hue between shades x and x+1 is the same as that between shadesx and x-1.
In this sequence the missing shade would correspond to the number 30, the shade of blue which is an increment darker corresponds to the number 31 and the shade which is an increment lighter corresponds to the number 29. For the idea of the missing shade to be formed, the person's visual discriminatory ability must initially perceive a gap, as the increment between 39 and 41 does not conform to the prevalent incremental pattern. By lightening the hue of the succeeding shade and deepening the hue of the preceding shade to a degree that corresponds with the difference between contiguous shades, a simplex idea of the missing shade is formed. This ability to mentally tint a shade can be performed because the person possesses a simple idea of white, simple ideas of succeeding and preceding shades of blue, and empirical experience that the mixing of white and a shade of blue lightens the shade or the mixing of two shades blue produces an intermediate shade. The notion I am attempting to relate is to an extent captured in the following passage:
We are not to think of our simple ideas of colors as an unorganized set of wholly distinct entities. The various hues are internally related to one another in degrees of resemblance. Hume also takes it for granted that these internal relations form the linear ordering of a spectrum: each hue occupies a determinate location within a color space composed of distinct (and presumably finitely many) hues. One such hue can be noticeably absent. Given these surroundings, the imagination is not faced with the insuperable task of producing a brute content ex nihilo [7] .
The formation of such simplex ideas requires simple ideas, therefore sensory impressions, to serve as 'admixtures'. As simple ideas are required for the purposes of comparison it is important that they bear contiguity and are consistent in their relation to one another.
Consider a version of the 'missing shade of blue' thought experiment where the person is presented with an incomplete blue spectrum that is incrementing inconsistently with the nth increment correlative to the nth decimal digit of pi.
The natural numbers which are not represented in this sequence correspond to missing shades of blue. Since the relation between preceding and succeeding shades of blue follows no apparent pattern, it would be considerably more difficult, if not impossible, for the person to accurately perceive of the number of blanks and their respective positions. If they perceive a blank in one of the numerically larger gaps, would it be possible for them to determine the degree to which the two bounding shades of the gap should be darkened or lightened to form simplex ideas of intermediate shades? In this pattern, there are only two contiguous shades, those corresponding to 5 and 6. Would it be possible for them to grasp this isolated contiguity and utilise it as a basis for successively darkening the lighter bounding shade of each gap? Consider if this isolated contiguity was absent. The new smallest interval between two shades could not be effectively used to fill in the odd gaps nor would the person have reason to perceive that there was a gap in the new smallest interval. The person needs to be presented with a favourable incomplete spectrum that is consistent in its ascension and at least contains a portion of contiguous ascension to serve as a basis from which they can interpolate missing intermediate shades in larger blanks.
Furthermore, in forming a simplex idea of a hue from simple ideas of other hues, not only must the simple ideas be contiguous and consistent in their relation, but there must also be sufficient qualitative empirical resemblance between them (and the simplex idea), for "where [impressions] resemble one another, the idea of one may suggest the idea of the other" [8] . Hume's 'missing shade of blue' example indicates that with internally related simple ideas presented in a linear ordering, a person is able to interpolate a simplex idea of a sensory impression that is absent from that pattern. But this ability is limited and although we possess some ability to recognise patterns in sequences of sensory data, I believe we possess no a priori knowledge that enables us to perceive of a blank in a spectrum solely on account of its mathematical properties. Nor do we possess innate knowledge of the phenomenon that there is something intrinsic about colour or our perception of it that by the combination of two particular colours the sensation of a third will be impressed upon our minds.
Imagine someone who has never experienced the sensation of blue is shown the entire electromagnetic spectrum corresponding to visible light, excepting that portion which corresponds to the colour blue. They are shown all the colours, ascending gradually from red to violet. Although there is a pattern to thisascension, it is uncertain whether the person would perceive a gap between green and violet. Despite a mathematical internal relation between the various colours, it is unlikely that the person would be able to deduce that there are colours available to them, namely green and violet, which can be mixed to form a composite blue. Even more unlikely would be an ability to mentally meld those colours and form a simplex idea of the colour blue. Only after empirical observation, for example the mixing of green and violet paint, can it be held with any certainty that upon mixing green and violet paint of proper proportions an awareness dawns that an unfamiliar sensation of blue can be impressed upon their minds by a mixture of already available sensory data.
What I am suggesting in the previous two examples is that we possess no innate sensory data 'templates', nor do we possess an ability to somehow utilise the internal relations of physical data within a spectrum and their mathematical properties to form an idea of how they would be impressed upon out minds; both of which might enable us to 'fill' a randomly incomplete or empirically dissimilar spectrum if presented with a substantial portion of it to rouse our relevant mental faculties.
In the Treatise Hume writes that "we cannot form to ourselves a just idea of the taste of a pineapple, without having actually tasted it" [9] . It is important to note that he does not entirely dismiss the possibility of forming an idea, only that it cannot be just [10] Why does he believe that we are unable form a just idea of the pineapple, yet is confident that one will be able to form to themselves a just idea of a missing shade of blue? Might I not just as easily say that we cannot form to ourselves a just idea of the colour of a particular shade of blue, without having actually seen it? Hume's example suggests that we can form a just idea of the shade, provided that it is intermediate between shades of blue of which we possess simple ideas. Similarly, should it not be possible for one to form an idea of the taste of pineapple by way of a description that it is intermediate between various previously tasted fruits for example. In an attempt to interpolate how pineapple tastes or what the hue of a missing shade of blue is, an idea of the former is more demanding and therefore less just because with respect to flavors, we have had little experience corresponding to the highly structured presentation of a color spectrum" [11] . Although we can employ our mental faculties to interpolate simplex ideas, they shall never possess the degree of vivacity that a corresponding simple idea would, for no matter how just a simplex idea may be unlike a simple idea its formation is not associated with a unique quale. If Hume's shade deprived individual were to be presented the incomplete blue spectrum in the form of paint, then by physically mixing, as opposed to mentally melding the various shades of blue, only then can they form a superior idea of the missing shade.
It has been established in this essay that Hume could have avoided a contradiction in his philosophical system by paying attention to the composite nature of colours and "had modified his principle so as to make it apply not to the origin but to the realisation of ideas" [12] . If Hume agrees that both white and blue can be impressions, therefore simple ideas, then one should be able to form an idea of the missing shade of blue by 'blending' these hues. The resultant idea possesses both aspects characteristic of simple ideas and aspects characteristic of complex ideas, hence have been termed 'simplex'. There is little reason to suppose why simplex ideas should be regarded as innate (in any absolute sense of the word); rather we possess inherent faculties that enable us, granted that we possess congruent sensory data and have had relevant empirical experience, to interpolate such ideas. If these requirements are not met, then there is little thought experiment substantiation to suggest that some innate assistance will enable us to deduce blanks and furthermore form an idea of them. For this reason it is plausible to maintain that simple ideas are ultimately empirical derivations. Given this, Hume's 'missing shade of blue' need not be considered a threat to his philosophical system and should stand subjected to distinctive elements of his empiricism such as his account of definition.
References
[1] David Hume, A Treatise of Human Nature, ( Penguin Books, 1985 [Originally Published 1739 and 1740]), p.52.
[2] Russell, Bertrand, A History of Western Philosophy, (, Simon & Schuster INC, [Originally Published 1945]) p. 661.
[3] Hume, Treatise of Human Nature, p.54.
[4] Stanford Encyclopedia of Philosophy entry on David Hume accessed at http://plato.stanford.edu/entries/hume/ on 2/9/02.
[5] Kembling, Garth, "Hume: Empiricist Naturalism", accessed at http://www.philosphypages.com/hy/4t.htm on 2/9/02.
[6] Hume, A Treatise of Human Nature, p.415.
[7] Fogelin, Robert J, "Hume and The Missing Shade of Blue" in Philosphy and Phenomenological Research, (1984), p.267.
[8] Mounce, H.O., Hume's Naturalism, (London: Routledge, 1999), p.26
[9] Hume, A Treatise of Human Nature, p. 53
[10] This was brought to my attention in Fogelin's article that I have made reference to.
[11] Fogelin, "Hume and The Missing Shade of Blue", p.268
[12] Ayer, A. J., Hume (Oxford University Press, 1980), p.32