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[The following is summary, up to the end where I reproduce this section in full. My commentary is in brackets.]
David Hume
A Treatise of Human Nature
Book I: Of the Understanding
Part I: Of Ideas, their Origin, Composition, Connexion, Abstraction, etc.
David Hume
A Treatise of Human Nature
Book I: Of the Understanding
Section V: Of Relations:
§32
There are two senses to the term “Relation:”
1) the quality connecting two ideas in the imagination in such a way that one idea naturally introduces the other [in the manner explained previously.]
2) the particular circumstance that allows us to compare two arbitrarily combined ideas in the imagination.
Common language uses the first sense, “and it is only in philosophy, that we extend it to mean any particular subject of comparison, without a connecting principle.”
Thus distance will be allowed by philosophers to be a true relation, because we acquire an idea of it by the comparing of objects: But 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.
§33
Hume will now enumerate the seven sorts of circumstances that allow us to compare objects.
§34
1) Resemblance:
All relations must have some degree of resemblance, because in order to compare things they must first resemble each other. Yet, not every resemblance produces an association or connection of ideas. For example, when objects share a quality that is common to many other objects, our imaginations no longer are able to fix on any single object.
§35
2) Identity:
The relation of identity holds strictly for constant and unchanging objects. It is the most universal relation, because it is common to all beings with duration.
§36
3) Space and Time:
The relations of space and time are the sources of countless comparisons, such as distant, contiguous, above, below, before, after, and so on. Next to identity it is the next most universal and comprehensive relation.
§37
4) Quantity or Number
Objects which may be quantified or counted may be compared in terms of their numerical value.
§38
5) Degrees [Intensities] of Quality
When two objects share a common quality, they possess that quality in different degrees.
Thus of two objects, which are both heavy, the one may be either of greater, or less weight than the other. Two colours, that are of the same kind, may yet be of different shades, and in that respect admit of comparison.
[see entry on Oresme's Quantitative Intensities of Qualities.]
§39
6) Contrariety
It might seem that we cannot have contrariety as a relation, because all relations must have some degree of resemblance. But even relations of contrariety involve resemblance. For example, there is one definitive relation of contrariety: existence and non-existence. Here both ideas resemble each other insofar as they both imply some object, even though non-existence "excludes the object from all times and places, in which it is supposed not to exist."
§40
7) Cause and Effect:
The other objects that we find to be contrary are objects of experience, such as fire & water, and heat & cold. What we experience are the contrariety of their causes and effects. This is the "natural" relation of ideas. Later Hume will explain the resemblance involved in causal relations.
§41
Difference
Difference is more of a negation of relation, rather than a positive relation or real thing. There are two kinds of differences:
a) Difference in Number
b) Difference in Kind
[Directory of other entries in this series.]
[The following is the original text that is above summarized.]
SECT. V. OF RELATIONS.
The word RELATION is commonly used in two senses considerably different from each other. Either for that quality, by which two ideas are connected together in the imagination, and the one naturally introduces the other, after the manner above-explained: or for that particular circumstance, in which, even upon the arbitrary union of two ideas in the fancy, we may think proper to compare them. In common language the former is always the sense, in which we use the word, relation; and it is only in philosophy, that we extend it to mean any particular subject of comparison, without a connecting principle. Thus distance will be allowed by philosophers to be a true relation, because we acquire an idea of it by the comparing of objects: But 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.
It may perhaps be esteemed an endless task to enumerate all those qualities, which make objects admit of comparison, and by which the ideas of philosophical relation are produced. But if we diligently consider them, we shall find that without difficulty they may be comprised under seven general heads, which may be considered as the sources of all philosophical relation.
(1) The first is RESEMBLANCE: And this is a relation, without which no philosophical relation can exist; since no objects will admit of comparison, but what have some degree of resemblance. But though resemblance be necessary to all philosophical relation, it does not follow, that it always produces a connexion or association of ideas. When a quality becomes very general, and is common to a great many individuals, it leads not the mind directly to any one of them; but by presenting at once too great a choice, does thereby prevent the imagination from fixing on any single object.
(2) IDENTITY may be esteemed a second species of relation. This relation I here consider as applied in its strictest sense to constant and unchangeable objects; without examining the nature and foundation of personal identity, which shall find its place afterwards. Of all relations the most universal is that of identity, being common to every being whose existence has any duration.
(3) After identity the most universal and comprehensive relations are those of SPACE and TIME, which are the sources of an infinite number of comparisons, such as distant, contiguous, above, below, before, after, etc.
(4) All those objects, which admit of QUANTITY, or NUMBER, may be compared in that particular; which is another very fertile source of relation.
(5) When any two objects possess the same QUALITY in common, the DEGREES, in which they possess it, form a fifth species of relation. Thus of two objects, which are both heavy, the one may be either of greater, or less weight than the other. Two colours, that are of the same kind, may yet be of different shades, and in that respect admit of comparison.
(6) The relation of CONTRARIETY may at first sight be regarded as an exception to the rule, THAT NO RELATION OF ANY KIND CAN SUBSIST WITHOUT SOME DEGREE OF RESEMBLANCE. But let us consider, that no two ideas are in themselves contrary, except those of existence and non-existence, which are plainly resembling, as implying both of them an idea of the object; though the latter excludes the object from all times and places, in which it is supposed not to exist.
(7) All other objects, such as fire and water, heat and cold, are only found to be contrary from experience, and from the contrariety of their causes or effects; which relation of cause and effect is a seventh philosophical relation, as well as a natural one. The resemblance implied in this relation, shall be explained afterwards.
It might naturally be expected, that I should join DIFFERENCE to the other relations. But that I consider rather as a negation of relation, than as anything real or positive. Difference is of two kinds as opposed either to identity or resemblance. The first is called a difference of number; the other of KIND.
From: Hume, David. A Treatise of Human Nature. Ed. L.A Selby-Bigge. Oxford: Clarendon Press, 1979. Text available online at: http://ebooks.adelaide.edu.au/h/hume/david/h92t/
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