Sec 7: Abstract Ideas

• A very material question has been asked whether abstract or general ideas are conceived by the mind in a general or particular way.
• Dr. Berkeley, a great philosopher, has asserted that all general ideas are nothing but particular ones annexed to a certain term, which:
  • gives them a more extensive signification
  • makes them recall other individuals similar to them.
• I see this as one of the greatest and most valuable discoveries recently made in the republic of letters.
  • I shall confirm it by some arguments to put it beyond all doubt and controversy.

• In forming most of our general ideas:
  • we abstract from it every particular degree of quantity and quality
  • an object continues to be regarded as part of its species despite small alterations in its extension, duration and other properties.
• This is a dilemma that answers the nature of those abstract ideas.
• The abstract idea of a man represents men of all sizes and all qualities.
  • This can only be done by representing:
    1. All possible sizes and all possible qualities at once, or
       • This is absurd as it would imply an infinite capacity in the mind.
    2. No particular one at all.
       • This is the common representation for our abstract ideas, representing no particular degree of quantity or quality.
       • But this is wrong.
       • I shall show this error:
         • by proving that it is utterly impossible to conceive any quantity or quality without forming a precise notion of its degrees, and
         • by showing that even if the mind’s capacity is not infinite, we can at once form a notion of all possible degrees of quantity and quality that may serve all the purposes of reflection and conversation, however imperfect.

• This first proposition is: the mind cannot form any notion of quantity or quality without forming a precise notion of degrees of each.
• We may prove this by three arguments:

1. Objects that are different are distinguishable.
   • Objects that are distinguishable are separable by the thought and imagination.

• These propositions are equally true in the inverse.
  • Objects that are separable are also distinguishable.
  • Objects that are distinguishable are also different.
• For how can we:
  • separate what is not distinguishable, or
  • distinguish what is not different?
• To know whether abstraction implies a separation, we only need to:
  • consider it in this view, and
  • examine whether all the circumstances which we abstract from in our general ideas, is distinguishable and different from the ideas which we retain as their essential parts.
• But at first sight:
  • a line’s precise length is not different nor distinguishable from the line itself, and
  • the precise degree of any quality is not different nor distinguishable from the quality.
• Therefore, these ideas admit no more of separation than they do of distinction and difference.
• • Consequently, they are conjoined with each other in the conception.
  • The general idea of a line appears in the mind with a precise degree of quantity and quality, despite all our abstractions and refinements.
    • However, it may be made to represent others which have different degrees of quantity and quality.

2. It is contested that no object can appear to the senses.
   • In other words, no impression can become present to the mind without being determined in its degrees of quantity and quality.
   • The confusion, in which impressions are sometimes involved, proceeds only from their faintness and unsteadiness.
     • It does not come from any capacity in the mind to receive any impression.
       • In its real existence, any impression has no particular degree nor proportion.
   • That is a contradiction in terms.
     • It implies that it is possible for the same thing to be and not to be.

• Since all ideas are derived from impressions and are nothing but copies and representations of them, whatever is true of the one must be acknowledged concerning the other.
  • Impressions and ideas differ only in their strength and vivacity.
  • This conclusion is not founded on any particular degree of vivacity.
  • Therefore, it cannot be affected by any variation in that particular.
  • An idea is a weaker impression.
  • As a strong impression must necessarily have a determinate quantity and quality, the case must be the same with its copy or representative.

3. A general principle in philosophy is that:
   • everything in nature is individual
   • it is absurd to suppose that a triangle can have no precise proportion of sides and angles.

• If this is absurd in fact and reality, it must also be absurd in idea.
  • Since no clear and distinct idea which we can form is absurd and impossible.
• But forming the idea of an object and forming an idea is simply the same thing.
  • The reference of the idea to an object is an extraneous denomination.
    • It bears no mark or character in itself.
• It is impossible to form an idea of an object that has quantity and quality but has no precise degree of either.
  • It follows that there is an equal impossibility of forming an idea that is unlimited in quantity and quality.
  • Abstract ideas are therefore in themselves individual, however they may become general in their representation.
  • The image in the mind is only that of a particular object.
    • Though the application of it in our reasoning is the same, as if it were universal.

• This application of ideas beyond their nature proceeds from our collecting all their possible degrees of quantity and quality in such an imperfect manner for the purposes of life.
  • This is my second proposition.
• When we find a resemblance [Footnote 2] among several objects that often occur to us, we apply the same name to all of them, whatever:
  • differences we may observe in their quantity and quality
  • other differences may appear among them
• After we have acquired this custom, the hearing of that name:
  • revives the idea of one of these objects, and
  • makes the imagination conceive it with all its particular circumstances and proportions.
• But the same word is also frequently applied to other individuals that are different from that idea immediately present to the mind.
  • The word is unable to revive the idea of all these individuals, but only touches the soul and revives that acquired custom.
• They are not really and in fact present to the mind, but only in power.
  • We do not draw them all out distinctly in the imagination.
  • Instead, we keep ourselves ready to survey any of them, depending on our present design or necessity.
• The word raises up an individual idea, along with a certain custom.
  • That custom produces any other individual one, for which we may have occasion.
• But the production of all the ideas, to which the name may be applied, is in most eases impossible.
  • We abridge that work by a more partial consideration.
  • We find but few inconveniences arising in our reasoning from that abridgment.

Footnote 2.

• Even different simple ideas may have a similarity or resemblance to each other.
  • It is unnecessary that the point or circumstance of resemblance should be distinct or separable from that in which they differ.
• Blue and green are different simple ideas, but are more resembling than blue and scarlet.
  • Though their perfect simplicity excludes all possibility of separation or distinction.
• It is the same case with particular sounds, and tastes and smells.
  • These admit of infinite resemblances on the general appearance and comparison, without having any common circumstance the same.
• This is certain even from the very abstract term ‘simple idea’.
  • They comprehend all simple ideas under them.
  • These resemble each other in their simplicity.
  • Yet from their very nature, which excludes all composition, this circumstance in which they resemble, is not distinguishable nor separable from the rest.
• It is the same case with all the degrees in any quality.
  • They are all resembling, yet the quality in any individual, is not distinct from the degree.

• This is one of the most extraordinary circumstances in the present affair, that after the mind has produced an individual idea on which we reason, the attendant custom:
  • is revived by the general or abstract term
  • readily suggests any other individual, if by chance we form any reasoning that does not agree with it.
• If we mention ‘triangle’ and form the idea of an equilateral triangle to correspond to it, and assert that its three angles are equal to each other, the other angles of a scalenum and isosceles triangles, which we overlooked at first, immediately:
  • crowd in on us
  • make us perceive the falsehood of this proposition
    • Even if it were true with relation to the equilateral triangle.

• If the mind does not always suggest these ideas, it proceeds from some imperfection in its faculties.
  • This imperfection is often the source of false reasoning and sophistry.
  • This is principally the case with abstruse and compounded ideas.
  • On other occasions:
    • the custom is more entire
    • we seldom run into such errors.

• The custom is not so entire.
  • The very same idea may be:
    • annexed to several different words
    • employed in different reasonings without any danger of mistake.
• Thus, the idea of an equilateral triangle with a perpendicular inch serves us in talking of:
  • a figure
  • a rectilinear figure
  • a regular figure
  • a triangle, and
  • an equilateral triangle.
• In this case, all these terms are attended with the same idea.
  • But as these terms are applied to an awareness of ideas, they:
    • excite their particular habits
    • keep the mind ready to observe that no conclusion is formed contrary to any ideas under them.

• Before those habits have become perfect, the mind might not be content with forming the idea of only one individual.
  • It may run over several to make itself comprehend:
    • its own meaning.
    • our awareness of that collection, which it intends to express by the general term.
• To define the word ‘figure’, we may:
  • revolve in our mind the ideas of circles, squares, parallelograms, triangles of different sizes and proportions
  • not rest on one image or idea.
• We form the idea of individuals whenever we use any general term.
  • We seldom or never can exhaust these individuals.
  • Those which remain are only represented by means of that habit, by which we recall them, whenever any present occasion requires it.
• This then is the nature of our abstract ideas and general terms.
  • In this way, we account for the foregoing paradox, that some ideas are particular in their nature, but general in their representation.
• A particular idea becomes general by being annexed to a general term.
  • This general term:
    • has a relation to many other particular ideas, from a customary conjunction
    • readily recalls those ideas in the imagination.

• The only difficulty is the that custom which so readily:
  • recalls every particular idea we may have occasion for
  • is excited by any word or sound we commonly annex to it.
• I think the most proper method of giving a satisfactory explanation of this act of the mind is by producing:
  • other instances analogous to it, and
  • other principles which facilitate its operation.
• To explain the ultimate causes of our mental actions is impossible.
  • It is sufficient to give any satisfactory account of them from experience and analogy.

1. When we mention any big number, such as 1,000, the mind generally has no adequate idea of it.
   • It can only produce such an idea through its idea of decimals, under which the number is comprehended.
   • However, this imperfection in our ideas is never felt in our reasonings.
   • It seems to be an instance parallel to the present reasoning of universal ideas.
2. We have several instances of habits, which may be revived by a single word.
   1. A person who has memorized a discourse can remember it through that single word.
3. We do not annex distinct and complete ideas to every term we use.
   1. In talking of government, church, negotiation, conquest, we seldom spread out in our minds all the simple ideas which make up these complex ideas.
   2. Despite this imperfection, we may avoid talking nonsense on these subjects.
   3. We may perceive any repugnance among the ideas, as well as if we had a fall comprehension of them.
   4. Thus, instead of saying the weaker in war have always recourse to negotiation, we should say that they have always recourse to conquest.
      1. Our custom of attributing certain relations to ideas:
         1. still follows the words, and
         2. makes us immediately perceive that proposition’s absurdity in the same way as one idea may serve us in reasoning on other ideas, however different in several circumstances.
4. The individuals are collected together and placed under a general term which resembles each other.
   • This relation must:
     • facilitate their entrance in the imagination, and
     • make them be suggested more readily.

• If we consider the thought’s common progress in reflection or conversation, we shall find great reason to be satisfied in this.
• The imagination’s readiness is most admirable.
  • This readiness:
    • suggests its ideas, and
    • presents those ideas the moment they become necessary or useful.
• The fancy runs from one end of the universe to the other in collecting those ideas belonging to any subject.
  • One would think that:
    • the whole intellectual world of ideas was at once subjected to our view, and
    • we did nothing but pick out ideas which were most proper for our purpose.
• However, only the ideas collected by a kind of magical faculty in the soul may be present.
  • This faculty is always most perfect in the greatest geniuses.
  • It is what we call a genius.
  • It is inexplicable by the utmost efforts of human understanding.

• These four reflections may help remove difficulties to the hypothesis I have proposed on abstract ideas.
  • This is so contrary to the prevailing hypothesis in philosophy.
• To tell the truth, I place my chief confidence in my proposition on the impossibility of general ideas, according to the common method of explaining them.
  • We must certainly seek some new system on this head.
  • There is none beside what I have proposed.
• If ideas are particular in their nature and finite in their number at the same time, only by custom can they:
  • become general in their representation, and
  • contain an infinite number of other ideas under them.

• I shall use the same principles to explain that distinction of reason which is:
  • so much talked of,
  • so little understood in the schools.
• Of this kind is the distinction between:
  • figure and the body figured, and
  • motion and the body moved.
• The difficulty of explaining this distinction arises from the above principle, that all different ideas are separable.
  • It follows that if the figure is different from the body, their ideas must be separable and distinguishable.
  • If they are not different, their ideas cannot be separable nor distinguishable.
• What then is meant by a distinction of reason, since it implies neither a difference nor separation.

• To remove this difficulty, we must have recourse to the foregoing explanation of abstract ideas.
• The mind would never distinguish a figure from the body figured, as being indistinguishable, different, nor separable, if it did not observe that there might be many different resemblances and relations, even in this simplicity.
  • When a globe of white marble is presented, we receive only the impression of a white colour disposed in a certain form.
    • We are unable to separate and distinguish the colour from the form.
  • But if we observe a black marble globe and a white marble cube afterwards and compare them with the white marble globe, we find two separate resemblances in what before seemed, and really is, perfectly inseparable.
    • After a little more practice of this kind, we begin to distinguish the figure from the colour by a distinction of reason.
    • We consider the figure and colour together, since they are in effect the same and undistinguishable.
    • But we still view them in different aspects, according to the resemblances they are susceptible of.
• When we would consider only the figure of the globe of white marble, we form in reality an idea of the figure and colour.
  • But we tacitly carry our eye to its resemblance with the black marble globe.
  • In the same way, when we consider its colour only, we turn our view to its resemblance with the white marble cube.
• Through this, we accompany our ideas with a kind of reflection which custom renders us insensible of.
  • A person who wants us to consider a white marble globe without thinking of its colour, wants an impossibility.
  • His meaning is that we should consider the shape and colour together, but still keep the resemblance to:
    • the black marble globe, or
    • any other globe of whatever colour or substance.

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