Hume against the abstract

Part One: that Abstract Ideas are Impossible

(In Three Arguments)


a.) Abstraction is separation

b.) By contraposition, the inseparable cannot be abstracted.

c.) But the impression or idea of line cannot be separated from its definite endpoints.

d.) But if anything could be abstracted, it would be an abstract quantity from a concrete one.

e.) So nothing can be abstracted.


a.) A merely faint and muddled idea that could be confused with its instances is not an abstract one

b.) But all ideas are merely faint impressions (from sec. 1-3)

c.) Therefore there are no abstract ideas.


a.) What is impossible to be understood by a clear and coherent idea in the mind is really impossible.

b.) Therefore, What is absurd for reality outside the mind is absurd for the reality within it.

c.) But abstract existence is impossible for reality outside the mind

d.) Therefore, abstract existence is impossible within the mind.

Part Two: What Supposedly Abstract Ideas Actually Are 

(Prologue with Four Explanations)


The putatively abstract idea is particular in its existence, but general in representation. By “general” we mean “we are accustomed to associate it with many”

So what is the basis of this “custom” that makes us associate some idea with many particulars? This is, for Hume, “the only difficulty that can remain on this subject”. His prologue to a proposed solution is fascinating:

The most proper method, in my opinion, of giving a satisfactory explication of this act of the mind, is by producing other instances, which are analogous to it, and other principles, which facilitate its operation. To explain the ultimate causes of our mental actions is impossible.

(Four Arguments)

a.) When things are hard to imagine, we invent symbol systems in order to make them more concrete. No one can visualize a chiliagon, but we can all understand a thousand-sided figure. The symbol is a remedy for the weakness of visualization.

b.) A single idea often sets off a cascade effect of evoking others, like a smell bringing back the idea of childhood, or a word that reminds us of a whole sentence, viz. “four-score” or “unalienable”.

c.) [I simply don’t get what description he is trying to give here, so I’ll just block-quote it]

Thirdly, I believe every one, who examines the situation of his mind in reasoning, will agree with me, that we do not annex distinct and compleat ideas to every term we make use of, and that in talking of government, church, negotiation, conquest, we seldom spread out in our minds all the simple ideas, of which these complex ones are compos’d. ’Tis however observable, that notwithstanding this imperfection we may avoid talking nonsense on these subjects, and may perceive any repugnance among the ideas, as well as if we had a full comprehension of them. Thus if instead of saying, that in war the weaker have always recourse to negotiation, we shou’d say, that they have always recourse to conquest, the custom, which we have acquir’d of attributing certain relations to ideas, still follows the words, and makes us immediately perceive the absurdity of that proposition; in the same manner as one particular idea may serve us in reasoning concerning other ideas, however different from it in several circumstances.

d.) Imagination is a prodigious genius at suggesting fit ideas for our use. It ranges freely over all concrete instances by a power, that we might never be able to explicate. But just because we can’t understand how this power works does not require us to say that it has recourse to something that has no concrete existence, any more than our failure to understand how a jet engine works requires us to say that it has parts with no concrete existence.


  1. May 2, 2015 at 11:26 am

    (c) is about cases in which we reason about a topic without actually pulling up any idea directly about that topic (just the sensible idea of the words, which have become associated with the particular ideas). So we can reason with words associated with particular ideas of a thing in just the same way we reason with the particular ideas themselves. (It’s partly necessary because abstract words are a reason to think that there are abstract ideas, which was recognized by Berkeley as well, and so there needs to be some way of dealing with abstract words without appeal to abstract ideas.)

    • May 2, 2015 at 6:02 pm

      Okay, so that is a step forward.

      Do you see him making a new argument about how AI’s arise? Maybe something like “We think we are abstracting because the words can be manipulated and combined just like the ideas can be”? Or is he merely responding to an unspoken objection like “we know there are abstract ideas because there are abstract words”? If this latter, I’m still a little puzzled about the argument.

      • May 3, 2015 at 6:45 am

        Berkeley does both, so either could possibly be in view; but I actually think that in context he is more focused on showing how one handles reasoning with abstract terms in the same way as one handles the other three things. That seems strongly suggested to me by the paragraph that introduces the three considerations (the prologue you note above), and the paragraph that concludes them: that it is part of the positive account that he is offering once we accept that abstract ideas are impossible.

    • May 5, 2015 at 2:58 pm

      Let me see if I follow – ‘c’ may be roughly analogous to ‘a’, where ‘a’ accounts for abstract ideas by assimilation to symbolic codes.

      As the impossible impression of a chiliagon is encoded in the definition ‘thousand-sided polygon’ because we cannot actually visualize all its sides, complex ideas such as ‘nature’, ‘government’ etc. are encoded in customary definitions which omit some if not almost all of the concrete thing considered. This allows for their expression and manipulation, and non-absurdity-to-general usefulness if they can be made fleshy by ‘b’.

      Put another way, we make sense and use of a word like ‘nature’, eliding some particular fly speck, the same way we make sense of ‘chiliagon’, eliding the side segment EG-EH. And should the matter come to it where we actually encounter said fly speck, we perceive its nonrepugnance to ‘nature’ if it should cascade web of associations to the ‘abstract’ term, much as we might see EG-EH connected by EF-EG, EH-EI, etc., and recognize it by those associations as part of the large, closed figure we are looking at.

  2. Socrates said,

    May 3, 2015 at 1:30 pm

    Dear Mr. Chastek:

    How would you answer this question please:

    “There is suffering in the world – you recognise that.

    You, being catholic, believe that god is all powerful and all good – you recognise that.

    This question then is simple.

    Can your god achieve its goals (whatever they may be) without causing (directly or indirectly) any suffering?

    This is a yes or no question. Any other response than ‘yes’ or ‘no’ is not relevant.”

    Thank you.

    Christi pax.

    • May 3, 2015 at 4:24 pm


      (To include something non relevant, one of his goals was to save the world by his own suffering.)

  3. Socrates said,

    May 4, 2015 at 2:54 pm

    Dear Mr. Chastek:

    I have another question (I actually have a million but I wouldn’t flood you with them): how do you understand the hard sayings in the Old Testament, like the commands to break Babylonian children’s skulls, or to kill the women and children of other tribes?

    Thank you,

    Christi pax.

    • May 4, 2015 at 3:26 pm

      I don’t have an opinion on the Super Flumina psalm you reference, though I have spoken of the Amalekite genocide before. I think these genocides are regressions from the progress of Israel from Abraham to Moses. The true nature of Israel is to intercede with God for mercy – which was clear in the beginning but then lost in the time of the Judges. When God tells you some nation is to be wiped out, then the true Israel will to pray to God and offer him anything until he relents, not stupidly execute the command as though they had no wills of their own, or as though they had wills no different from the Gentiles.

      • Socrates said,

        May 4, 2015 at 10:06 pm

        Very fascinating! I never thought of it like that!

        So, in your view, God was slowly offering the choice between Justice and Mercy to Israelites, with little bit more each time. Abraham and Moses choose Mercy over Justice, but then Saul and the rest choose Justice over Mercy. Paul himself writes about this: how the Law, Justice, and power themselves don’t save, but Mercy, forgiveness, Grace, and Love do. Justice without Mercy leads to death, just as the Law without Grace leads to condemnation.

        This is not to say that Justice is bad, but that there is a hierarchy: Justice is greater than injustice, but Mercy is greater still.

        We could even go and say that Saul took Justice into his own hands, rather than allowing the Lord to enact Justice. Saul was trying to act like God instead of trusting in Him.

        The old Israel failed on interceding for Mercy, while the new Israel succeeded. This failure of the Jews also explains why many of them would reject Messiah. Abraham and Moses both, when the Strong Arm of God sought Justice, asked for Mercy instead. They didn’t necessarily get it, but they did interceded for it. Christ Himself sits at the Strong arm of God, interceding Mercy for all of us, perfecting and completing what was started by Abraham.

        Thank you. This explanation was the light which illuminated many other Truths 🙂

        Christi pax.

      • May 5, 2015 at 9:53 am

        God was slowly offering the choice between Justice and Mercy to Israelites, with little bit more each time.

        God is revealing himself to those who want him to be the the vindicator, the god of battles, etc. In Girardian terms, we want God to be the victim maker. This desire is inveterate and fundamental – just ask yourself what the typical Right-winger would say if God revealed himself promising to wipe out all the pro-aborts or sodomites or what the typical Left-winger would say to God’s promise to wipe out corporate exploiters or racists. This is, however, a lesser good, as anyone could see by imagining the world after God had wiped them all out. So what now? Would anything change? We’d just build the same system we had to begin with. We’d just get “the world” that the Gospel speaks of.

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