Hume's Metaphysical Musicians

Hume's Metaphysical Musicians E. W. Van Steenburgh Having argued to the possible existence ofmathematical points, Hume concedes that checking for their actual existence is difficult because of the minuteness. He writes: the points, which enter into the composition of any line or surface, whether perceiv'd by the sight or touch, are so minute and soconfoundedwith eachother, that'tis utterly impossible for the mind to compute their number.1 He concludesthat theirminutenessrenderspoints uselessforpurposes ofmeasurement. "We are sensible, that the addition or removal ofone of these minute parts, is not discernible either in the appearance or measuring" (T 48). This objection to his points leads Hume to view measuring, not in terms ofpoints, but asjuxtaposition ofobjects one to another or to a common measure, correcting apparent equality by art and instruments. And, he argues, correcting comes to an end when one runs out of art and instruments, although correcting, once set in motion, may go on at the level offancying after art and instruments have announced an end to it. This holds true not only for equality of quantities but of qualities as well. A musician finding his ear become every day more delicate, and correcting himself by reflection and attention, proceeds with the same act ofthe mind, even when the subject failshim, and entertains a notion ofa compleat tierce or octave, without being able to tell whence he derives his standard. (T 48-49) The metaphysical musician, according to Hume, is unable "to tell whence he derives his standard." This objection by Hume looks like it ismissingthe mark. The metaphysical musician could tell from whence he derives his standard. It is derived from sensible appearances. It is derived from the undifferentiated case which, to ears subsequently more discriminating, turns out to be two different notes, not one. The source ofthe standard is specified. What, then, does Hume mean when he states that metaphysical musicians cannot tell us from whence they derive their standard? An apparent standard, if it functions as a standard, has objects forits terms. For the standard is neither equality Volume XVIII Number 2 151 E. W. VAN STEENBURGH itself, whatever that might mean, nor an object; rather, the standard is "being equal to this object," whatever the object might be—in this case a musical note. In other words, an unspecified standard—a standard that is neither this nor that—is not a standard. It becomes a standardifand only ifit is specified for some object. The question now shifts to the object without which no standard is specified. It could be actual. It could be imaginary. Either way, it is an object. Yet, the metaphysical musicians rules that no object satisfies the standard. The outcome is contradiction. If you don't specify the standard, you don't have a standard; and ifyou do, you contradict the ruling that no object satisfies the standard. Hume does not explicitly allege contradiction. However, the other sideofthecontradictioncoin is an unspecifiedstandard. AndthisHume does allege. Hume sometimes does speak as ifan imagined musical note—the object in this case—is itselfa note. He speaks this way out ofdeference to his general theory of ideas as copies of impressions. However, the claim to contradiction, to incomprehensibility, does not depend on Hume's special doctrine of ideas copying impressions. For when we imagine objects, the objects we imagine, if we are consistent, are possible objects. So what we are saying, ifwe say that we can imagine equal objects is this: equal objects are impossible. Either, then, the metaphysical musician's imaginary correction, the imaginary trek toward absolute equahty, is incomprehensible because there is no standard—no objects—by which "correction"makes sense; orelse there is such a standard—object equality is possible—and the general rule that object equality is impossible is contradicted. Suppose we downgrade the a priori necessary rule to a contingent generalization about ordinary objects. Now it is not impossible, only unlikely, that one will find equal actual objects. Given a candidate for prototypicality, one imagines that one is mistaken, that the objects one thinks are equal are not, after all, equal, and soon. Here the only equal objects are always possible objects, never actual ones. One simply refuses to use...