I begin commenting Hume’s Treatise from §1.1.5, because I found the earlier sections less interesting. I will only cite it by section and paragraph number, not page numbers.
0. Contents
1. Terminological note2. Definition of relation (¶ 1–2)
4. Identity (¶ 4)
5. Space and time; quantity or number; degrees of quality (¶ 5, 6, 7)
6. Contrariety (¶ 8)
7. Cause and effect (¶ 9)
8. Difference (¶ 10)
1. Terminological note
In previous sections of the Treatise, Hume explains his theory of associations of ‘ideas’, which I do not cover here. He says that some associations are made voluntarily, and others are made by “a gentle force, which commonly prevails, and is the cause why, among other things, languages so nearly correspond to each other; nature in a manner pointing out to every one those simple ideas, which are most proper to be united in a complex one.” (§1.1.4, ¶1)
I shall refer to associations that are not made voluntarily as spontaneous. Hume calls them natural, which I must suppose is to be contrasted with artificial. But the will is also part of nature, and more importantly, I think that the term natural association may be ambiguous.
Most importantly, Hume calls them ideas, but says they are in the imagination. I admit of a faculty called the imagination, which is one of the internal senses; but its contents should not be called ideas, since ideas, properly so called, belong to the rational faculty. See, for instance, Poissy on the imagination and on ideas.
I shall assume that Hume is rightly interpreted as speaking about the contents of the imagination, which are properly termed images or phantasms. (I speak of images and phantasms interchangeably, and only use both words to avoid such cacophonous phrases as “images in the imagination”.)
To avoid confusion with Hume’s use of the word idea, I shall refer to ideas, as so called by Poissy, as concepts.
So, I shall only use the word “idea” in direct quotations of Hume, or when paraphrasing his statements. In my own voice, I shall keep images and concepts sharply distinct.
2. Definition of relation (¶ 1–2)
2.1. My definition
Often, to understand an object of experience, reference to a different object is made; this reference is what I shall call relation. To put this in more direct form, relation is a reference to another object which is used as a means to understand an object.
Since this is how I understand the term, I may speak of it as “the proper sense” or “the proper philosophical sense” in what follows, and this is not to be confused with either of the meanings Hume gives to the term.
2.2. Hume’s common meaning
Hume says the word relation has two meanings. The first is “that quality, by which two ideas are connected together in the imagination, and the one naturally introduces the other, after the manner above-explained”, i.e., the cause of the spontaneous association of two images in the imagination. Earlier, he had said that this cause can be either one of exactly three things, viz., resemblance, contiguity in time or place, and causation. Hume says that this first meaning is always the meaning of the word relation “in common language”.
Is it really? I think sometimes it is. In a conversation, I may say two things which someone might find to be unrelated to each other, or something which is unrelated to the topic at hand; in such a case, to explain the relation of the subjects it suffices to say why one reminded me of the other, i.e., the cause of the association of these thoughts in my imagination. I leave aside the question of whether Hume’s division of the causes of mental association is adequate.
In common language, though, now as in his time, relation often refers to family relations, as in the case of brothers or cousins, and I do not see how this is either one of his three causes of association. There are other common senses of the word besides, but I am not as certain that they were current then.
2.3. Hume’s philosophical meaning
The second meaning of relation, which Hume says is only used in philosophy, is “any particular subject of comparison, without a connecting principle.” I suppose “without a connecting principle” means that no cause of spontaneous mental association is required, since the philosophical sense of the word includes even the subjects of comparisons made “upon the arbitrary union of two ideas in the fancy”; in which arbitrary must be taken to mean voluntary, or free.
So, he gives the example of distance as a philosophical relation, since it is a possible subject of voluntary comparison, but cannot be brought under one of his three possible causes of spontaneous association. Accordingly, it is taken in common speech to be something opposed to relation – for “in a common way we say, that nothing can be more distant than such or such things from each other, nothing can have less relation; as if distance and relation were incompatible.” This really is a common way of speech, and if it is admitted that the philosophical sense of relation is foreign to common speech, it would appear to lend support to his division.
I think subjects of comparison, as broadly as Hume thinks of them, are not properly called relations, either commonly or philosophically, and I do not know of any other philosopher who used relation in this sense. Besides, I do not find that Hume’s seven ‘relations’ are all properly called subjects of comparison either. I think he was very confused. Nevertheless, they are interesting subjects to talk about, which is why I’m doing this commentary. If I knew of a more adequate division under which to treat of these things, I would use that division instead of commenting Hume.
3. Resemblance (¶ 3)
Hume speaks of resemblance between phantasms in the imagination, which is a simple bodily experience. Since it is infra-rational, it is not a relation in my sense, and it is not properly a subject of comparison either.
If we consider the senses in analogy to understanding, however, such that seeing is analogous to knowing, then resemblance will be analogous to the understanding of two things through the same universal concept; indeed, things that resemble each other tend usually to be capable of being understood through the same universal concept.
Hume is probably right in thinking that only close resemblances produce spontaneous associations of images. To be sure, though, I would like to see what more recent experimental psychologists have found on the subject.
4. Identity (¶ 4)
Identity, if understood absolutely, is not properly a relation or a subject of comparison, but a transcendental property of being, since everything is identical to itself.
Hume seems to have in mind an object’s capability of being understood to be the same thing before and after some change, though. This happens when the concept by which the object is understood remains the same; it may be called existential identity.
Understood as obtaining between the object before the change and the object after the change, this is not properly a relation, but it is a subject of comparison. To compare two objects in respect of their identity, though, is the same as to compare them in every other possible respect.
5. Space and time; quantity or number; degrees of quality (¶ 5, 6, 7)
These get a section together because Hume was right about calling them subjects of comparison, and they are also the sources of some relations in my own sense of the term. The way in which this happens is somewhat analogous in each case, as well.
Space and time seem to be the sources of some relations in the proper philosophical sense; specifically, the duration or size of one thing may be used as a means to understand the duration or size of another. Thus it was that Aristotle ranked “double”, “half” and “greater” within the category of relation, and gave no other examples of it.
Space and time are also correctly said by Hume to be “the sources of an infinite number of comparisons, such as distant, contiguous, above, below, before, after, &c.”
The numbers of elements in groups of things are also sources of proper relations, as when one number is understood by means of its being greater than, less than, or in some proportion to, another. And they are subjects of comparison as well.
Degrees of qualities are also, similarly, sources of proper relations, as well as subjects of comparison.
It must be noted that, although degrees of proper sensible (a.k.a. secondary) qualities may be ranked ordinally, that is, into more or less intensive, they may not be subject to arithmetical comparisons. There are not, properly, lights that are twice as bright as other lights, or sounds that are twice as loud as other sounds, or colors which correspond to the sum or average of other colors.
All alleged cases of such things are always produced by means of varying common sensible (a.k.a. primary) qualities in the causes that produce the proper sensible qualities. There are, accordingly, different methods of mixing colors, which would be absurd if mixing colors were truly a kind of arithmetical addition.
6. Contrariety (¶ 8)
Hume speaks of contrariety between phantasms in the imagination, which is a simple bodily experience. Since it is infra-rational, it is not a relation in my sense, and it is not properly a subject of comparison either.
Two things are contraries when they cannot be imagined existing in the same place at the same time: as with white and black, fast and slow, square and round.
If we consider the senses in analogy to understanding, such that seeing is analogous to knowing, then contrariety will be analogous to strict contradiction between concepts; indeed, contraries are often understood by contradictory concepts, but this does not always happen.
Contradictory concepts, of which one negates the other, cannot even be conceived of as existing in the same place at the same time; as with white and not-white, fast and not-fast, square and not-square.
Hume says “that no two ideas are in themselves contrary, except those of existence and non-existence”. Actually, we can have no image of “existence”, in general, in our imagination; but to imagine an object existing is just to imagine the object, and to imagine an object not existing is just to imagine something else, in which we then understand that the object does not exist.
Properly, there can be no negation in images, as there can be in concepts, and so, no two images are contradictory to each other, and there can only be a contrary opposition between them. There may be contradiction, however, between the concepts by which we understand the images.
So, many images are in themselves contrary to each other, but no images are contradictory to each other. Since Hume did not keep the relevant terms and faculties distinct enough, he was led to say that “no two ideas are in themselves contrary”, right in the same breath as he called contrariety a relation between ‘ideas’; leaving the reader to wonder why, if they are not contrary in themselves, any ‘ideas’ would be contrary at all. Certainly it is not mere convention which opposes them so.
7. Cause and effect (¶ 9)
Cause and effect is a relation in my sense of the term. In fact, all four kinds of causation are relations, although Hume only included the efficient kind; and they are the most important relations in my sense, being the only ones necessary to all understanding of sensible things.
They are a subject of comparison, insofar as we may compare two things by noting that they had different causes. But to mention that one is the effect of the other is only indirectly a comparison, inasmuch as we know that something cannot be the effect of itself, so that if one thing is the effect of another, the other must have a different cause, which is a difference.
8. Difference (¶ 10)
Hume is right to consider difference “rather as a negation of relation, than as any thing real or positive.”
And it is fair enough to divide difference into “two kinds, as opposed either to identity or resemblance.”
Hume is right to call the negation of identity a difference of number. But the negation of resemblance is not exactly the same as a difference of kind, though it tends to coexist with it.
A difference in kind exists when two images are understood by different concepts. This tends to coincide with the images lacking resemblance in the imagination, but does not always coincide with it, and is at any rate something distinct.
So, to give a proper name to the negation of resemblance, I shall call it a difference of appearance. Accordingly, the other two kinds of difference may be collectively called differences of reality.
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