Hume s Missing Shade of Blue as a Possible Key. to Certainty in Geometry

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1 Hume s Missing Shade of Blue as a Possible Key to Certainty in Geometry Brian S. Derickson PH 506: Epistemology 10 November 2015

2 David Hume s epistemology is a radical form of empiricism. It states that ideas are only valid as vehicles of knowledge if they are based in sensory experience. Thus, those ideas which do not lend themselves to being experienced with the senses, viz., the supersensible, the supernatural and even things as common as the self, are not considered knowledge. The relation between ideas and sense perception is a central part of this epistemology. One of the consequences of how Hume relates ideas and perception is that geometry is not considered an exact science. Yet, this particular part of Hume s theory is not without flaws. One important flaw, revealed in the problem of the missing shade of blue, will be addressed in this paper. It will be shown that a particular solution to this flaw will open up the possibility of geometry becoming an exact science in Hume s program. Ideas and Impressions If human knowledge is circumscribed by the boundaries of experience, then this experience must be qualified and quantified in such a way that is rational. Hume s habit for doing so was to base experience in sense perception. Sense perception is how information is obtained by the knower. But sense perception is not the only experience. Hume accounts for two modes of experiencing the real. All perceptions of the human mind, says Hume, resolve themselves into two distinct kinds. There is first the impression, which is the experience of the knower as he is impinged upon by the sensory world. The second, separated only by a degree of force and liveliness is the idea ), 1. 1 David Hume, A Treatise of Human Nature, ed. L. A. Selby-Bigge, M. A. (Oxford: Clarendon Press,

3 2 Central to Hume s empiricist epistemology is the fact that impressions and ideas are essentially the same, only differing by the intensity at which they are experienced. At the beginning of his Treatise on Human Nature, Hume establishes a general proposition, That all our simple ideas in their first appearance are deriv'd from simple impressions, which are correspondent to them, and which they exactly represent." 2 Later in the same work, Hume attacks the assertion of some philosophers and mathematicians that there are ideas which do not come from sensory perceptions but from some spiritual and refin d perceptions. 3 To the contrary, Hume insists that all our ideas are copy d from our impressions. 4 He says an idea is by its very nature weaker and fainter than an impression; but being in every other respect the same cannot imply any very great mystery. The mystery presumably being impressions from spiritual sources. Thus, all ideas are copies of impressions, but neither ideas nor impressions are all simple. As Hume says, simple perceptions or impressions and ideas are such as admit of no distinction nor separation. The complex are the contrary to these, and may be distinguished into parts. Tho' a particular colour, taste, and smell are qualities all united together in this apple, 'tis easy to perceive they are not the same, but are at least distinguishable from each other." 5 Humans are clearly capable of having ideas of something like red but also ideas of apple. But clearly apple is more complicated than red because contained within apple is red. As Robert Ackerman puts it, Ideas, in Hume's technical sense, are the result of the mind's analysis and combining of 2 Hume, Treatise, 4. 3 Ibid., Ibid. 5 Ibid., 2.

4 3 remembered impressions or parts thereof. 6 So an apple is a complex idea, one composed of several simple ideas. But the simple ideas, like red, are not composed of parts at all. Hume admits that some complex ideas entertained by humans do not have a corresponding impression. In the Treatise he gives the examples of The New Jerusalem and Paris. 7 The New Jerusalem, the city in Christian eschatology that will come down from Heaven to rest upon the earth, has never been seen by anyone on earth. Yet, it is a very real idea that subsists in many minds. Paris, though presently experienced by human sense organs, can never be recalled as it was actually experienced with a perfect count of the number of rats, each name of every street, etc. With complex ideas, there is not a direct correspondence between the impression and the idea. This is not the case with simple impressions. Simple impressions have a one-to-one correspondence with simple ideas. 8 This distinction has caused some Philosophers, such as William James and John Laird, to accuse Hume of contradiction. Farhand Zabeeh adds a helpful clarification to this deflect this accusation: What Hume wants to assert is not that ideas exactly resemble their impressions whenever we reflect upon ideas, but only that ideas exactly resemble impressions in their first appearance. Not that the recurring idea always represents all the qualities of its impression, but that only when there occurs an impression then there occurs an idea which exactly resembles it ), Robert Ackermann, Theories of Knowledge: A Critical Introduction (New York: McGraw-Hill Inc., 7 Hume, Treatise, 3. 8 Ibid. 9 Farhang Zabeeh, Hume: Precursor of Modern Empiricism (The Hague: Martinus Nijhoff, 1960), 70.

5 4 That Hume acknowledged this distinction seems to follow necessarily from his own mention of the New Jerusalem and Paris. Zabeeh, dealing with this problem and others, gives a succinct formulation of Hume s relation between ideas and impressions: (1) That ideas on their first appearance occur with their corresponding impressions. (2) That provided we are conscious of the appearance of strong impressions, ideas have all the properties of their impressions except that ideas are weaker than their impressions. (3) That ideas when they appear in the absence of their corresponding impressions may appear vague and obscure. 10 This leads to the problem of the missing shade of blue. The Missing Shade of Blue The problem of the missing shade of blue is, as John Morreall calls it, a solid counterexample to Hume s theory what Morreall calls Hume s Copy Thesis. 11 This problem is introduced by Hume in the Enquiry in his section on the origin of ideas. In the section, Hume is attempting to prove that all ideas have their origins only in impressions. After making two arguments, Hume stops and offers a counterexample to his proofs. He wonders whether some person who has enjoyed their sight for thirty years, yet had never been acquainted with one particular shade of blue would be able to produce this shade of blue from his imagination. The thought experiment imagines that all the shades of blue are placed before this person, save for the one that he has never seen. Hume assumes that the person actually can imagine that shade of blue and that there are few but will be of opinion that he can That is, Hume expects everyone to believe the man s imagination can provide the missing shade of blue. 10 Zabeeh, John Morreall, Hume's Missing Shade of Blue, Philosophy and Phenomenological Research 42.3, (1982): David Hume, An Enquiry Concerning Human Understanding, ed. Tom L. Beauchamp (Oxford: Oxford University Press, 1999),

6 5 Though some philosophers believe this is not a real problem for Hume 13, Morreall, insists otherwise. Morreall points out that Hume disregarded the counterexample because there were so few examples of it. In Hume s own words [the problem of the missing shade of blue] may serve as a proof, that the simple ideas are not always, in every instance, derived from the correspondent impressions; though this instance is so singular, that it is scarcely worth our observing, and does not merit, that for it alone we should alter our general maxim. 14 Yet Morreall goes to great pains to show that similar problems exist with all the senses. 15 According to Morreall, if this problem is allowed to stand, Hume s maxim would be watered down, his Copy Thesis would become merely a rule of thumb, and his program of empiricism would suffer great harm. 16 In short, if one idea can be explained without a corresponding impression, they all can. Morreal sees the counterexamples to the thesis as reveal[ing] a feature of human imagination which Hume overlooked. 17 The overlooked feature is a certain freedom in human imagination. 18 He explains that, when attempting to supply the missing shade of blue, the person does not check his memory for that missing shade; rather, what happens is [we] familiarize ourselves with the degree to which one shade is lighter than the next in the series presented. We might say that we derive a pattern or rule for the gradations Tom L. Beauchamp gives an alternate explanation in the Introduction to Hume, Enquiry Hume, Enquiry, Morreall, Ibid., Ibid., Ibid.

7 6 Once we are familiar with the increment of gradation between given shades, we can produce in our minds an image of the shade missing from the series. 19 This freedom in our imagination, says Morreall, means that Hume s Copy Thesis must be given up. 20 However, he does not believe that Hume s entire system of empiricism must be abandoned. This is because the imagination is limited in what it can supply. It cannot supply a new hue, or some new quality which has not been experienced. It can only supply a new degree of some quality... with which we are already familiar. 21 If Morreall s thesis is true, it may not be confined to simple ideas like shades of blue. The Problem of Geometry Though it might seem shocking to the ancient philosopher, Hume denies that all mathematics admits of certainty. Instead, only algebra and arithmetic are sciences, in which we can carry on a chain of reasoning to any degree of intricacy, and yet preserve a perfect exactness and certainty. 22 Geometry is specifically excluded from this list. Hume s rejection of geometry as a perfect science has two foundations. First, Hume says [geometry s] first principles are still drawn from the general appearance of the objects; and that appearance can never afford us any security, when we examine the prodigious minuteness of which nature is susceptible. 23 That is, whatever two lines one might see, they can never be seen 19 Morreall, Ibid., Ibid, Hume, Treatise, Ibid., 71.

8 7 to such minute detail as to know that they are perfectly parallel. Hume says that we have no standard of a right line so precise, as to assure us that the lines are actually parallel. This first reason for rejecting geometry can be addressed with Morreall s modification to Hume s epistemology. Given that one has seen two lines which incline towards each other at one extrema, and two lines that incline towards each other at the other extrema, the idea of parallel lines is analogous to the missing shade of blue. The difference between the first and second set of lines is one of a degree of a quality, namely angle, and not a new quality in itself. The imagination would then be able supply the missing angle, namely the one where the two lines do not intersect. However, this does not completely solve the problem of geometry. Hume s second reason for denying geometry is much more difficult to deal with. It is the denial that the mind has the ability to grasp concepts such as surfaces, lines and points at all. Hume s argument is essentially that these concepts imply an infinite regress. If a line is the terminus of a surface, and one attempts to imagine that last line in the surface, whatever one imagines can always be divided more. But ideas in Hume s program cannot be divided into parts. Thus, whatever one is able to imagine a line to be, it is never the actual, indivisible, infinitesimal thing that geometry demands a line must be. 24 It is not as clear that Morreall s fix is helpful here. It seems rather unlikely that the mind is capable of imagining infinitesimal variance in degrees of thickness, such that one s imagination can fill in the missing, infinitesimal thickness. However, there might be another way to solve the problem. This starts with the recognition that what every individual eye has ever seen is merely a surface. For any solid, opaque body, all light that is reflected from it to the observer s eye comes from the surface. When one sees a body, they are only seeing the surface 24 Hume, Treatise,

9 8 of that body. In another sense, what one actually sees, even if looking at the interiors of glowing translucent clouds, is that light that reaches the surface of the eye. However one looks at it, the eye only sees in two dimensions. But this means that the mind already knows the idea of a surface without resorting to talk of infinitesimals. With two eyes, the mind is able to comprehend depth. Hume may argue that depth perception would fall more properly under the province of intuition because it is discoverable at first sight. 25 However, to do so, Hume would have to reject that people can have ideas of bodies extended in space. If he is not willing to do so, then it is clear that people can have ideas and impressions of surfaces by closing one eye, and impressions and ideas of solids or bodies, by seeing with both eyes. The question becomes, is dimensionality a quality of an impression in a way similar to blueness? Remember that the missing shade of blue can be filled in because the mind can supply a new degree of an already known quality. If it is accepted that dimensionality is a quality already known, and the mind has a pattern of the degrees of gradation by seeing in two dimensions and in three, then it is conceivable that the mind can apply that pattern to supply the other degrees of gradation, viz., one dimensional lines and zero dimensional points. It is admittedly not obvious that dimensionality is a quality. Conclusion In conclusion, Hume s empiricist program, though robust, is not without flaws. To confine all knowledge to a combination of simple, indivisible sensory perceptions is to radically limit what can be considered knowledge. In doing so, Hume has likely contradicted himself. 25 Hume, Treatise, 70.

10 9 However, these flaws do allow for correction, and his empiricist program is not to be entirely disregarded. One correction, proposed by John Morreall for the problem of the missing shade of blue, seems fix a flaw in Hume s copy thesis. Interestingly, there is potential that his correction can be applied to mathematical notions. It would only apply if dimensionality could be considered a quality of an impression. If that is an acceptable position, then geometry can be seen, in a Humean system, as certain as arithmetic and algebra.

11 10 Bibliography Ackermann, Robert. Theories of Knowledge: A Critical Introduction. New York: McGraw-Hill Inc., Bonjour, Laurence. Epistemology: Classic Problems and Contemporary Responses. 2nd ed. Lanham, MD: Rowman & Littlefield Publishers, Inc., Hume, David. An Enquiry Concerning Human Understanding. Edited by Tom L. Beauchamp. Oxford: Oxford University Press, Hume, David. A Treatise of Human Nature. Edited by L. A. Selby-Bigge, M. A. Oxford: Clarendon Press, Morris, William Edward and Charlotte R. Brown. "David Hume", The Stanford Encyclopedia of Philosophy (Fall 2015 Edition). Edited by Edward N. Zalta. Accessed October, Morreall, John. Hume's Missing Shade of Blue. Philosophy and Phenomenological Research 42.3 (1982): Accessed November 9, Rickaby, Joseph, S. J. Free Will and Four English Philosophers. London: Burns and Oates, Zabeeh, Farhang. Hume: Precursor of Modern Empiricism. The Hague: Martinus Nijhoff, 1960.