In lieu of an abstract, here is a brief excerpt of the content:139. COULD AN IMPRESSION BE A PROCESS? Processes are of two main kinds, depending on whether the process has or lacks culmination. I am concerned with non-culminating processes, e.g., with a burning fuse sans explosion. This is reported as secondary by any good dictionary, derived from the head, or culminating, sense of 'process'. An ontological criterion for 'process' is as follows: something is absolutely unchanging, if it is unchanging (...) in every sense of the word. Those who hold that, e.g., a monotonous sound is absolutely unchanging hold that in an absolutely unchanging universe there is no reason why there should not be such a sound. Like any absolutely unchanging existent, a sound is caught, so to speak, in an instantaneous freeze on all change. Those who opt for process hold that change is, so to speak, of its essence. Hence, in an absolutely unchanging world, there could not be a process. The question I wish to raise is not whether there are processes, and certainly not whether Hume opts for processes. It is doubtful that Hume entertained the question of process. Indeed, that is the point. One of Hume's main commentators, R. W. Church, holds that Hume's perceptual atoms, defined by his dictum that distinguishability mutually entails separability, as well as their philosophical relations, are incompatible with the thesis that "experiences exist not in succession but in process." Church goes on to say that it is "difficult to see how... 'process' can have meaning for Hume. He plainly holds perceptions and their contents to be successive merely. I begin by considering Church's reason why Hume must reject processes, and then consider an additional reason drawn from Hume's account of time. Specifically, 140. divisibility òf time terminates in unchanging atoms. The essence of process is change. Hence, no temporal atom is a process. Neither reason, I argue, suffices for holding that impressions and processes are mutually exclusive. Hume holds that distinguishability mutually entails separability. Church holds that this dictum defines Hume's perceptual atomism. To highlight the atomism it is supposed to define, he rewords it, as follows: "Whatever is distinguishable is intrinsically self-identical and therefore self-contained." What does this rewording mean? According to Church, Hume, in the body of the Treatise, holds that resemblance is qualitative identity distributed, numerically, over many complexes. "On Hume's theory of abstract ideas, 'resemblance' is a verbal term referring (in virtue of habits of association) to any case of a qualitative 4 identity numerically distributed." Further, the qualitative identity in question is not relative to any difference from another quality, Bradley to the contrary notwithstanding. Difference, for Hume, is incompatible with relation and it is itself not a relation. It follows, according to Church, that Hume's absolute self-identity mutually entails self -containment. So much for Church's version of Hume's perceptual atomism. Is it incompatible with process, as Church claims? A trombone's slide illustrates non-culminating process with succession. Let us use it as a basis for an account. A trombone's slide is unbroken not only qua sound but qua pitch. Nevertheless, it incorporates pitch multiplicity. By "successive merely" does Church mean that the transition from pitch to pitch must be broken, contrary to what is heard, and, for this reason, Hume cannot account for the slide qua process? If so, he is mistaken. 141. Distinguishability mutually entails separability for Hume, but this does not mean that the transition from pitch to pitch cannot be experienced as a slide. In fact, it is easy to show that a trombone's slide conforms to Hume's dictum, by reason of the just noticeable difference and Hume's philosophical relation of contiguity in time. We are dealing with three notions: first, distinction, and, in particular, how pitches in the slide are distinguished. Second, separability, and, in particular, how separation corresponding to distinction is guaranteed by the fact of process. Third, slide, and, in particular how Hume's philosophical relation of temporal contiguity, coupled with the just noticeable difference, guarantees phenomenal slide. I take up these three notions in the order mentioned. The distinction between two pitches in the trombone's slide is... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:61. HUME'S GEOMETRIC "OBJECTS" Arithmetic and algebra allow of precision and certainty. The science of geometry is not likewise a perfect and infallible science. At any rate, this is Hume's teaching in the Treatise. When two numbers are so combin ' d, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and 'tis for want of such a standard (...) of equality in extension, that geometry can scarce be esteem'd a perfect and infallible science. 1 The ideas of, say, equality and right line shade into· inequality and curve. It must not be supposed, however, that the vagueness of these ideas renders all judgments uncertain and fallible. 'Tie evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies....Such judgments are not only common, but in many cases certain and infallible. (T47) Nevertheless, geometry is a fallible science because its essential ideas are vague. Vagueness, due to lack of boundaries between ideas, is in the ideas themselves. For this reason, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. (T49) (Yet, some forty pages earlier Hume argued at length that the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each [T18]) As far as the Treatise goes, geometry is the science of measurement and as such it must allow for error. Even if precise geometric standards could be had, they would not make the propositions of geometry certain. Thus, we might precisely define a right line by a rule of order of indivisible points. But geometry, construed as the science of measurement, would not be perfected. Nor, if it were (the standard), is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserv ' d. The original standard of a right line is in reality nothing but a certain general appearance. (T52) 62. In the Enquiries, Hume continues to hold that notions essential to geometry, for example, equality, right line, and so on, are sensibles. But they are no longer generic appearances. They are determinate. The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate... even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. 2 In addition, geometry is no longer merely the science of measurement. The truths of Euclid, Hume holds, would remain truths even if there were no figures in nature. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. (EHU25) Professor Zabeeh, in his commentary on Hume, holds that Hume did not mean to imply that Euclid could dispense with the observation of figures. However, whenever possible Hume should be taken at his word: observation of figures is not a truth condition for propositions of geometry. A distinction must be drawn between discovery conditions and what Hume calls the "truth or evidence" of a geometric proposition. We may suppose that observation of figures is a discovery condition. But it is hardly a truth condition. The certainty, as opposed to the discovery, of geometric propositions does not depend on the existence in nature of any figure. I am mainly concerned, however, with Professor Zabeeh' s account of how, according to Hume, geometric propositions retain their certainty and evidence in the face of recalcitrant experience. Noting that Hume does not "fully explain," he gives the real reason for Hume's belief in the apodeictic certainty of mathematical truths. He appears to assume we never allow such truths to be controverted by empirical evidence. That is to say, if perchance we find, by measurement, that the sum of the angles of a Euclidean triangle 63. does not equal 180 degrees, either we say that we measured wrongly or we say that the triangle we have been measuring is not Euclidean.4 This formulation of Hume's reason avoids... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:61. HUME'S GEOMETRIC "OBJECTS" Arithmetic and algebra allow of precision and certainty. The science of geometry is not likewise a perfect and infallible science. At any rate, this is Hume's teaching in the Treatise. When two numbers are so combin ' d, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and 'tis for want of such a standard (...) of equality in extension, that geometry can scarce be esteem'd a perfect and infallible science. 1 The ideas of, say, equality and right line shade into· inequality and curve. It must not be supposed, however, that the vagueness of these ideas renders all judgments uncertain and fallible. 'Tie evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies....Such judgments are not only common, but in many cases certain and infallible. (T47) Nevertheless, geometry is a fallible science because its essential ideas are vague. Vagueness, due to lack of boundaries between ideas, is in the ideas themselves. For this reason, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. (T49) (Yet, some forty pages earlier Hume argued at length that the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each [T18]) As far as the Treatise goes, geometry is the science of measurement and as such it must allow for error. Even if precise geometric standards could be had, they would not make the propositions of geometry certain. Thus, we might precisely define a right line by a rule of order of indivisible points. But geometry, construed as the science of measurement, would not be perfected. Nor, if it were (the standard), is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserv ' d. The original standard of a right line is in reality nothing but a certain general appearance. (T52) 62. In the Enquiries, Hume continues to hold that notions essential to geometry, for example, equality, right line, and so on, are sensibles. But they are no longer generic appearances. They are determinate. The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate... even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. 2 In addition, geometry is no longer merely the science of measurement. The truths of Euclid, Hume holds, would remain truths even if there were no figures in nature. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. (EHU25) Professor Zabeeh, in his commentary on Hume, holds that Hume did not mean to imply that Euclid could dispense with the observation of figures. However, whenever possible Hume should be taken at his word: observation of figures is not a truth condition for propositions of geometry. A distinction must be drawn between discovery conditions and what Hume calls the "truth or evidence" of a geometric proposition. We may suppose that observation of figures is a discovery condition. But it is hardly a truth condition. The certainty, as opposed to the discovery, of geometric propositions does not depend on the existence in nature of any figure. I am mainly concerned, however, with Professor Zabeeh' s account of how, according to Hume, geometric propositions retain their certainty and evidence in the face of recalcitrant experience. Noting that Hume does not "fully explain," he gives the real reason for Hume's belief in the apodeictic certainty of mathematical truths. He appears to assume we never allow such truths to be controverted by empirical evidence. That is to say, if perchance we find, by measurement, that the sum of the angles of a Euclidean triangle 63. does not equal 180 degrees, either we say that we measured wrongly or we say that the triangle we have been measuring is not Euclidean.4 This formulation of Hume's reason avoids... (shrink)

In lieu of an abstract, here is a brief excerpt of the content: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... (shrink)