Hume’s required medium

Instead of continuing my commentary of Hume’s Treatise of Human Nature,[1] I have decided to turn instead to his Enquiry concerning Human Understanding, beginning at section 4.

Due to the foreignness of Hume’s terminology to my own, I believe that if I were to write in-depth comments about his first fifteen paragraphs, I should then spend much time parsing his words, only to then find that his meaning, if interpreted with due charity, is something quite plain and undeniable, and at any rate irrelevant to my project. So I skip to the question at the end of ¶16, which I find curious enough to answer, although, at any rate, the answer was implicit in what I said before.[2]

In the context of our inferring, from some new object’s looking like bread, that it will nourish us, Hume asks:

These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know in fact, that it always is inferred. But if you insist, that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connexion between these propositions is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert, that it really exists, and is the origin of all our conclusions concerning matter of fact.

OK. Since he asked, I will produce the reasoning. But first, since I quoted from Hume – even for such a short passage – I must make some clarifications to dispel difficulties with his wording:

• First, of course, what I will produce is not the way in which everyone always derives one proposition from the other, but the way in which it may be done validly, which might happen much less often than invalidly.

• Second, I have no pretension that the reasoning between these two propositions “is the origin of all our conclusions concerning matter of fact” – I have no idea why Hume thought that it should be.

• Third, I think that, obviously, no “object” of experience is “attended with” any “effect” always and everywhere, but rather, that it is attended with that effect in a range of contexts. Hume himself must have known this, since he made such a big deal (in ¶2) about it not being logically necessary “that the sun will rise tomorrow” – even the least sceptical philosopher must admit that it will only rise if there are no impediments in place, and we all only differ about how certain we are that there will be no such impediments tomorrow. I want to make this more explicit, so I will add amendments about the context of the observation to both propositions.

Alright, so, the reasoning goes more or less like this:

• Proposition 1. (First Premise) I have found that such an object in such a context has always been attended with such an effect.

• Clarification 1: By “such an object”, I mean a collection of appearances which are precisely such as allow me to understand a certain form.

• Clarification 2: By “such a context”, I mean a different collection of appearances, by which I understand different forms.

• Proposition 2. (Second Premise – Medium) The forms which I understand through these appearances, when I perceive such an object in such a context, are all such as to which I can ascribe the motions which produce the effect.

• Clarification 3: By “forms”, I mean the objects of understanding, as defined in my metaphysics. The relevant fact about them here is, that the same conjunctions of forms are always connected with the same motions, which fact is called final causality.

• Proposition 3. (Conclusion) I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects in similar contexts.

• Clarification 4: By “similar objects”, I mean objects through whose appearances I can understand the same form that I can understand through this object’s appearances, insofar as I can ascribe their motions to it.

• Clarification 5: By “similar contexts”, I mean contexts through whose appearances I can understand the same forms that I can understand through this context’s appearances, insofar as I can ascribe their motions to them.

This could probably be restated more directly, but this will have to do. The way I have chosen to lay it out has the advantage of giving Hume’s (modified) propositions at the beginning and end, with the medium being in the middle, as the name would suggest that it should be.

While ¶17 implies that Hume is passing from this question into a more “positive” argument, he is really just repeating the question in different ways. “May I not clearly and distinctly conceive, that a body, falling from the clouds, and which, in all other respects, resembles snow, has yet the taste of salt or feeling of fire?” You can certainly imagine it; you may be able to conceive of it; you probably have no reason to expect it. If, through the appearance of those other respects, you would be able to perfectly understand the form of snow, then it follows that the taste and feeling do not belong to the nature of snow as you understand it, and that in such a situation, you would have simply found a unique type of snow – one that must have been, intelligibly, brought about by its particular context.

Hume is right in saying, in ¶19, that all, or almost all, propositions about experience are only probable judgments; but this is not because it is impossible to deduce effects from causes. It is rather because we usually do not take care to ascertain the true nature of what appears to us. We do not try to get apodictic knowledge that a car is a car before we get in it; it is sufficient to us that it probably is a car, and that we have no reason to expect otherwise. But we are certain that, if it is a car, then it has an engine, and the power of spinning its wheels in certain conditions, and whatever else we ascribe to the nature of a car.

When Hume says, later on in ¶19, that “all our experimental conclusions proceed upon the supposition, that the future will be conformable to the past”, I take him to be speaking rather obliquely about the fact of final causality, which I mentioned above in Clarification 3. The proof of this fact, as it was given in my metaphysics, is that it is a necessary condition of the fact that any apparent objects are understood at all. It may be consistently denied only by denying that apparent objects are understood, and therefore remaining at the Parmenidean theses about being and non-being; but such a conclusion would break the First Rule of Philosophy. So, a philosopher is compelled, qua philosopher, to accept the alternative.

In ¶20, Hume says:

Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them. It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event. Now where is that process of reasoning, which, from one instance, draws a conclusion, so different from that which it infers from a hundred instances, that are nowise different from that single one?

I suppose that we might not form this expectation from the first appearances of eggs because, at that point, we do not yet know the nature of eggs. But after we know it, then whenever we see what we understand to be an egg, in what we understand to be an appropriate context, then we know exactly what range of tastes to expect from it. Usually, that is rather too much investigation about a small meal, and we are satisfied with probability about all these understandings; and it really may take many experiments to find which inessential appearances are best relied upon for a probable judgment. (For instance, these.)

I see nothing of interest in the paragraphs 21 through 23, so I pass over them.

Notes

[1] Following a preambular post to my commentaries in general, I have written commentaries of sections 1.1.5 and 1.1.6 of Hume’s Treatise.

As explained in the preambular post, the purpose of my commentaries is to find a plan of topics around which to write my opinions about metaphysics. Not finding them useful for this purpose, I skipped the first four sections of the Treatise, as well as the first three sections of the Enquiry.

[2] While I tend to avoid repetition of my own doctrines – which avoidance is the very reason for this blog – I could not help being engaged by Hume’s question. Generally, I find it difficult to look at rhetorical questions without trying to think of answers for them. So I wrote this post partly as an exercise, and I find this reformulation of my opinions to be interesting enough to be posted. If I ever bring my opinions into more systematic form, though, I should find some way to avoid such repetitions.

David Hume’s tables

In the old days (one supposes) when the philosopher, labouring by lamp-light in his study, came to this point in his argument, he set down his pen, and looked around for an object in the real world to interrogate. Very commonly that object was the nearest one to hand: his writing-table. ‘Table,’ he said, ‘how do I know that you exist, and, if you do, how do I know that my concept, table, represents your real existence?’ The table would look back without blinking, and interrogate the philosopher in its turn. It was an exacting exchange, and according to which one was the victor in the confrontation, the philosopher would inscribe himself as idealist or a materialist. Or so one must suppose from the frequency with which tables appear.

— E.P. Thompson, The Poverty of Theory

I was much amused by the above quote, which was pointed out to me by a friend. This led me to take notice of the quotations which I shall give below. Together, they support the thesis that, if there really was such a fascination with tables among modern philosophers as E.P. Thompson described, then the works of David Hume must have been a major source for it.

0. Table of contents

1. A Treatise of Human Nature
2. An Abstract of a Book Lately Published
3. A Letter from a Gentleman to His Friend in Edinburgh
4. An Enquiry concerning Human Understanding
5. Other works
6. Appendices

1. A Treatise of Human Nature

In what follows, references will be given by book, part, section, and paragraph, with the paragraph number given separately, since some editions don’t give it. So §1.2.3, ¶4 will refer to Book 1, Part 2, Section 3, paragraph 4. All quotes under this section are from the Treatise, but I will also write “Treatise” into each reference to make it easier to scroll through.

The table before me is alone sufficient by its view to give me the idea of extension. This idea, then, is borrow’d from, and represents some impression, which this moment appears to the senses. But my senses convey to me only the impressions of colour’d points, dispos’d in a certain manner. If the eye is sensible of any thing farther, I desire it may be pointed out to me. But if it be impossible to shew any thing farther, we may conclude with certainty, that the idea of extension is nothing but a copy of these colour’d points, and of the manner of their appearance. (Treatise, §1.2.3, ¶4) 

When [the mind] considers the dye as no longer supported by the box, it can not without violence regard it as suspended in the air; but naturally places it on the table, and views it as turning up one of its sides. (Treatise, §1.3.11, ¶11)

To begin with the question concerning external existence, it may perhaps be said, that setting aside the metaphysical question of the identity of a thinking substance, our own body evidently belongs to us; and as several impressions appear exterior to the body, we suppose them also exterior to ourselves. The paper, on which I write at present, is beyond my hand. The table is beyond the paper. The walls of the chamber beyond the table. And in casting my eye towards the window, I perceive a great extent of fields and buildings beyond my chamber. From all this it may be infer’d, that no other faculty is requir’d, beside the senses, to convince us of the external existence of body. (Treatise, §1.4.2, ¶9)

My bed and table, my books and papers, present themselves in the same uniform manner, and change not upon account of any interruption in my seeing or perceiving them. (Treatise, §1.4.2, ¶18)

’Tis easy to observe, that tho’ bodies are felt by means of their solidity, yet the feeling is a quite different thing from the solidity; and that they have not the least resemblance to each other. A man, who has the palsey in one hand, has as perfect an idea of impenetrability, when he observes that hand to be supported by the table, as when he feels the same table with the other hand. (Treatise, §1.4.4, ¶13)

That table, which just now appears to me, is only a perception, and all its qualities are qualities of a perception. Now the most obvious of all its qualities is extension. The perception consists of parts. These parts are so situated, as to afford us the notion of distance and contiguity; of length, breadth, and thickness. The termination of these three dimensions is what we call figure. (Treatise, §1.4.5, ¶15)

It has been objected to the system of one simple substance in the universe, that this substance being the support or substratum of every thing, must at the very same instant be modify’d into forms, which are contrary and incompatible. The round and square figures are incompatible in the same substance at the same time. How then is it possible, that the same substance can at once be modify’d into that square table, and into this round one? I ask the same question concerning the impressions of these tables; and find that the answer is no more satisfactory in one case than in the other. (Treatise, §1.4.5, ¶25)

When I view this table and that chimney, nothing is present to me but particular perceptions, which are of a like nature with all the other perceptions. This is the doctrine of philosophers. But this table, which is present to me, and that chimney, may and do exist separately. This is the doctrine of the vulgar, and implies no contradiction. There is no contradiction, therefore, in extending the same doctrine to all the perceptions. (Treatise, appendix)

These other passages of the Treatise were not quoted because, while they also mention tables, the mention does not use tables as an example of a perception: §1.4.5, ¶11; §2.1.3, ¶5; §2.1.10, ¶2; §2.2.5, ¶17; §2.3.8, ¶3; §2.3.10, ¶8; §3.2.3, ¶10, note 75. Nevertheless, they show that tables were present to Hume’s mind.

2. An Abstract of a Book Lately Published

In the Abstract, Hume repeats his example of the two billiard balls from the Treatise, §1.3.14, ¶18; but this time he mentions the table that they are on:

Here is a billiard-ball lying on the table, and another ball moving towards it with rapidity. They strike; and the ball, which was formerly at rest, now acquires a motion. [...] I see a billiard-ball moving towards another. I cannot distinguish whether it moves upon its axis, or was struck so as to skim along the table. In the first case, I know it will not stop after the shock. In the second it may stop.

You may count the table as being implied whenever billiard balls are mentioned, if you wish; I have been counting only explicit tables.

3. A Letter from a Gentleman to His Friend in Edinburgh

Speaking of scepticism, Hume wrote this rhetorical question into the Letter:

If I be as much assured of these Principles, as that this Table at which I now write is before me; can any Thing further be desired by the most rigorous Antagonist?

4. An Enquiry concerning Human Understanding

As with the Treatise, I will cite the Enquiry by section and paragraph. I am just calling it Enquiry, since the Moral Enquiry is not as relevant here; see §5 of this blog post for that.

If I see a billiard-ball moving towards another, on a smooth table, I can easily conceive it to stop upon contact. (Enquiry, §5, ¶11)

It seems also evident, that, when men follow this blind and powerful instinct of nature, they always suppose the very images, presented by the senses, to be the external objects, and never entertain any suspicion, that the one are nothing but representations of the other. This very table, which we see white, and which we feel hard, is believed to exist, independent of our perception, and to be something external to our mind, which perceives it. Our presence bestows not being on it: Our absence does not annihilate it. It preserves its existence uniform and entire, independent of the situation of intelligent beings, who perceive or contemplate it.

But this universal and primary opinion of all men is soon destroyed by the slightest philosophy, which teaches us, that nothing can ever be present to the mind but an image or perception, and that the senses are only the inlets, through which these images are conveyed, without being able to produce any immediate intercourse between the mind and the object. The table, which we see, seems to diminish, as we remove farther from it: But the real table, which exists independent of us, suffers no alteration: It was, therefore, nothing but its image, which was present to the mind. These are the obvious dictates of reason; and no man, who reflects, ever doubted, that the existences, which we consider, when we say, this house and that tree, are nothing but perceptions in the mind, and fleeting copies or representations of other existences, which remain uniform and independent. (Enquiry, §12, ¶8–9)

5. Other works

David Hume also mentioned tables in other works, but it was not very relevant to the present subject. For completeness, though, and since this is very easy to do:

• True Account of the Behaviour and Conduct of Archibald Stewart, page 18
• An Enquiry concerning the Principles of Morals, §6, ¶11
• Dissertation on the Passions, §2, ¶31
• History of England, §2, ¶50; §3, ¶51; §5, ¶7; §8, ¶15; §9, ¶10, ¶56; §11, ¶33; §14, ¶35, 39; §16, ¶17; §17, ¶75; §20, ¶11; §21, ¶3, 10; §23, ¶8; §26, ¶37 and the note 23; §31, ¶71; §32, ¶27; §36, ¶30; §37, ¶25; §39, ¶39; §39, ¶86, note 186; §40, ¶4; §44, ¶55, note 98; Appendix 3, ¶60, ¶68; §47, ¶19; Appendix 4, ¶30; §51, ¶65; §52, ¶16, 17, 20, 22; §53, ¶15, 22; §54, ¶38, 44, 72, 87; §59, ¶57; §60, ¶26; §61, ¶62, 63; §62, ¶68; §64, ¶56; §70, ¶60; §71, ¶91.
• Essays: Of Tragedy, ¶4; Of Eloquence, ¶4; Of the Rise and Progress of the Arts and Sciences, ¶40, note 15; Of Polygamy and Divorces, ¶11; Of Simplicity and Refinement in Writing, ¶2; Of Commerce, ¶13; Of Refinement in the Arts, ¶1; Of Money, ¶21.

6. Appendices

Addition from 2023-10-08: One later philosopher who made notable mention of tables was Bertrand Russell, in Chapter 1 of his 1912 book The Problems of Philosophy. David Bostock’s 2012 book Russell’s Logical Atomism, p. 116, describes Russell as holding the “extreme view that I never perceive such things as tables.” [2025-10-12: See also the opening of the introduction to Arthur Eddington’s The Nature of the Physical World, 1928, where he compares his “ordinary table” to his “scientific table”.] [2025-04-26: See also Quine, Word and Object, 1960, which begins, “This familiar desk manifests its presence by resisting my pressures and by deflecting light to my eyes.” Quine doesn’t dwell on the desk, however.]

Addition from 2025-02-20: Tables come up a lot in the metaphysical debate on the existence and ontological status of “ordinary objects”, as this debate is called; see SEP, Ordinary Objects. The book Empty Ideas, by Peter Unger, which uses this debate as a case in point for a general critique of analytic philosophy, also makes extensive mention of tables.

Hume’s relations

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 note
2. Definition of relation (¶ 1–2)

2.1. My definition

2.2. Hume’s common meaning

2.3. Hume’s philosophical meaning

3. Resemblance (¶ 3)
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.