Book 1, Part 3, Sec 1-2: Knowledge, Probability, Cause, Effect

PART 3: KNOWLEDGE AND PROBABILITY

SECT. 1: KNOWLEDGE

• There are seven kinds of philosophical relation (Part 1, Sec. 5):
  1. Resemblance
  2. Identity
  3. Relations of time and place
  4. Proportion in quantity or number
  5. Degrees in any quality
  6. Contrariety
  7. Causation
• These relations are divided into two classes.
  • These classes:
    • depend entirely on the ideas which we compare together
    • may be changed without any change in the ideas.
• From the idea of a triangle, we discover the relation of equality its three angles bear to two right ones.
  • This relation is invariable as long as our idea remains the same.
• On the contrary, the relations of contiguity and distance between two objects may be changed merely by an alteration of their place, without any change on the objects themselves or on their ideas.
  • The place depends on 100 different accidents which cannot be foreseen by the mind.
  • It is the same case with identity and causation.
• Two objects, which perfectly resemble each other and appearing in the same place at different times, may be numerically different.
  • The power by which one object produces another is never discoverable merely from their idea.
  • It is evident that cause and effect are relations of which we receive information from experience, and not from any abstract reasoning or reflection.
• No single phenomenon can be accounted for from the qualities of the objects as they appear to us, without the help of our memory and experience.

• Therefore, only four of these seven relations can be the objects of knowledge and certainty:
  • Resemblance
  • Contrariety
  • Degrees in quality
  • Proportions in quantity or number.
• Three of these relations:
  • are discoverable at first sight
  • fall more properly under intuition than demonstration.
• When any objects resemble each other, the resemblance will at first strike the eye or rather the mind.
  • It seldom requires a second examination.
• The case is the same with contrariety and with the degrees of any quality.
  • Existence and non-existence:
    • destroy each other
    • are perfectly incompatible and contrary.
• It is impossible to judge exactly of the degrees of any quality, such as colour, taste, heat, cold, when the difference between them is very small.
  • But it is easy to decide that any of them is superior or inferior to another, when their difference is considerable.
  • This decision we always pronounce at first sight, without any enquiry or reasoning.

• We might:
  • proceed in the same way in fixing the proportions of amount
  • at one view observe a superiority or inferiority between any numbers or figures.
    • Especially where the difference is very big.
• We can only guess at equality or exactness from a single consideration.
  • Except in very short numbers, or very limited portions of extension which are comprehended in an instant, and where we perceive an impossibility of falling into any considerable error.
• In all other cases we must:
  • settle the proportions with some liberty, or
  • proceed in a more artificial manner.

• I have already observed that geometry or the art by which we fix the proportions of figures;
  • though it much excels both in universality and exactness, the loose judgments of the senses and imagination;
  • yet never attains a perfect precision and exactness.
• Its first principles are still drawn from the general appearance of the objects.
  • That appearance can never afford us any security, when we examine the minuteness of which nature is susceptible.
• Our ideas seem to give a perfect assurance that no two right lines can have a common segment.
  • But if we consider these ideas, we shall find that:
    • they always suppose a sensible inclination of the two lines
    • where the angle they form is extremely small, we have no standard of a I @ right line so precise as to assure us of the truth of this proposition.
• It is the same case with most of the primary decisions of the mathematics.

• Only the sciences of algebra and arithmetic can we:
  • carry on a chain of reasoning to any degree of intricacy
  • yet preserve a perfect exactness and certainty.
• We are have a precise standard to judge of the equality and proportion of numbers.
  • We determine their relations according as they correspond to that standard, without any possibility of error.
• When two numbers are so combined, as that the one has always an unite answering to every unite of the other, we pronounce them equal.
  • Geometry can never be a perfect and infallible science for want of such a standard of equality in extension.

• Geometry falls short of that perfect precision and certainty which are peculiar to arithmetic and algebra.
  • But it excels at the imperfect judgments of our senses and imagination.
• I impute geometry’s defect from its original and fundamental principles being derived merely from appearances.
  • This defect must always:
    • attend geometry
    • keep geometry from ever reaching a greater exactness in the comparison of objects or ideas, than what our eye or imagination alone is able to attain.
• I own that this defect so far attends it, as to keep it from ever aspiring to a full certainty:
  • But since these fundamental principles depend on the easiest and least deceitful appearances, they bestow on their consequences a degree of exactness, of which these consequences are singly incapable.
• It is impossible for the eye to determine the angles of a chiliagon [polygon with 1,000 sides] to be equal to 1,996 right angles or to make any conjecture that approaches this proportion.
  • But when it determines, that right lines cannot concur; that we cannot draw more than one right line between two given points.
  • its mistakes can never be of any consequence.
• This is the nature and use of geometry, to run us up to such appearances, as, by reason of their simplicity, cannot lead us into any considerable error.

• I shall propose a second observation concerning our demonstrative reasonings, which is suggested by the same subject of the mathematics.
• Mathematicians pretends that those ideas, which are their objects, are of so refined and spiritual a nature, that they:
  • do not fall under the conception of the fancy
  • must be comprehended by a pure and intellectual view, of which the superior faculties of the soul are alone capable.
• The same notion:
  • runs through most parts of philosophy
  • is principally used to:
    • explain our abstract ideas
    • show how we can form an idea of a triangle, for instance, which shall:
      • neither be an isoceles nor scalenum
      • nor be confined to any particular length and proportion of sides.
• It is easy to see why philosophers are so fond of this notion of some spiritual and refined perceptions.
  • Since by that means, they:
    • cover many of their absurdities
    • may refuse to submit to the decisions of clear ideas, by appealing to such as are obscure and uncertain.
• To destroy this artifice, we only need to reflect on that principle so often insisted on, that all our ideas are copied from our impressions.
  • From this, we may conclude that the ideas copied from our impressions:
    • must be of the same nature
    • can never contain anything so dark and intricate, but from our fault.
• An idea is by its very nature weaker and fainter than an impression.
• But since it is the same in every other respect, it cannot imply a great mystery.
  • If its weakness renders it obscure, it is our business to remedy that defect as much as possible by keeping the idea steady and precise.
  • Until we have done so, it is in vain to pretend to reasoning and philosophy.

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SECT. 2: PROBABILITY AND THE IDEA OF CAUSE AND EFFECT

• Those four relations are the foundation of science.
• The other three relations do not depend on the idea.
  • They may be absent or present even while the idea remains the same.
• These three relations are:
  • identity
  • the situations in time and place
  • causation.

• All kinds of reasoning consist in a comparison and discovery of those constant or inconstant relations, which two or more objects bear to each other.
• We may make this comparison when:
  • the objects are present to the senses
  • neither objects are present, or
  • only one object is present.
• When both the objects are present to the senses, along with the relation, we call this perception rather than reasoning.
  • There is no exercise of the thought in this case, or any action.
  • There is a mere passive admission of the impressions through the organs of sensation.
• According to this way of thinking, we should not receive as reasoning any of the observations we may make concerning:
  • identity
  • the relations of time and place.
• Since, in none of them, the mind can go beyond what is immediately present to the senses to discover the real existence or the relations of objects.
• Only causation produces such a connection, as to give us assurance from the existence or action of one object, that it was followed or preceded by any other existence or action.
  • nor can the other two relations be ever made use of in reasoning, except so far as they affect or are affected by it.
• There is nothing in any objects to persuade us that they are always remote or always contiguous.
• and when from experience and observation we discover, that their relation in this particular is invariable, we always conclude there is some secret cause which separates or unites them.
• The same reasoning extends to identity.
  • We readily:
    • suppose an object may continue individually the same, though several times absent from and present to the senses.
    • ascribe to an object an identity, despite the interruption of the perception, whenever we conclude that if we had kept our eye or hand constantly on it, it would have conveyed an invariable and uninterrupted perception.
• But this conclusion beyond the impressions of our senses can be founded only on the connection of cause and effect.
  • We cannot otherwise have any security that the object is not changed upon us, no matter how much the new object may resemble the object which was formerly present to the senses.
• Whenever we discover such a perfect resemblance, we consider whether:
  • it is common in that species of objects
  • possibly or probably any cause could operate in producing the change and resemblance;
  • and according as we determine concerning these causes and effects, we form our judgment concerning the identity of the object.

• It appears that of those three relations, which do not depend on the mere ideas, the only one, that can be traced beyond our senses and informs us of existences and objects, which we do not see or feel, is causation.
• Therefore, we shall try to explain this relation fully, before we leave the subject of the understanding.

• To begin regularly, we must:
  • consider the idea of causation
  • see its origin.
• It is impossible to:
  • reason justly, without understanding perfectly the idea about which we reason
  • understand any idea, without:
    • tracing it up to its origin
    • examining that primary impression from which it arises.
• The examination of the impression bestows a clearness on the idea.
  • The examination of the idea bestows a like clearness on all our reasoning.

• Let us cast our eye on any two objects, which we call cause and effect.
  • Let us turn them on all sides to find that impression which produces an idea of such consequence.
• At first sight, I perceive that I must not search for it in any of the particular qualities of the objects.
  • Since whichever of these qualities I pitch on, I find some object that is not possessed of it, and yet falls under the denomination of cause or effect.
• There is nothing existent, externally or internally, which is not a cause or an effect.
  • Though it is plain there no single quality universally:
    • belongs to all beings
    • gives them a title to that denomination.

• The idea of causation then must be derived from some relation among objects
  • We must now try to discover that relation.
• Whatever objects are considered as causes or effects, are contiguous.
  • Nothing can operate in a time or place, which is ever so little removed from those of its existence.
• Distant objects may sometimes seem productive of each other.
• They are commonly linked by a chain of causes, contiguous among themselves and to the distant objects.
  • When in any particular instance, we cannot discover this connection, we still presume it to exist.
• We may therefore consider the relation of contiguity as essential to that of causation, until we can find a more proper occasion (Part 4, Sec. 5) to clear up this matter, by examining what objects are or are not susceptible of juxtaposition and conjunction.

• The second relation essential to causes and effects, is not so universally acknowledged.
  • But it is liable to some controversy.
• It is that of priority of time in the cause before the effect.
  • Some pretend that:
    • it is not absolutely necessary that a cause should precede its effect.
    • any object or action, in the very first moment of its existence, may:
      • exert its productive quality
      • give rise to another object or action, perfectly co-temporary with itself.
• But that experience in most instances seems to contradict this opinion.
  • We may establish the relation of priority by a kind of inference or reasoning.
• It is an established maxim in natural and moral philosophy, that an object which exists for any time in its full perfection without producing another, is not its sole cause.
  • It is assisted by some other principle which:
    • pushes it from its state of inactivity
    • makes it exert that energy which it secretly had.
• If any cause may be perfectly co-temporary with its effect, it is certain, according to this maxim, that they must all be so.
  • Since any one of them, which retards its operation for a single moment, exerts not itself at that very individual time when it might have operated and therefore is no proper cause.
• The consequence of this would be the:
  • destruction of that succession of causes which we observe in the world
  • utter annihilation of time.
• For if one cause were co-temporary with its effect, and this effect with its effect, and so on, it is plain that:
  • there would be no such thing as succession
  • all objects must be co-existent.

• It is good if this argument appears satisfactory.
  • If not, I beg the reader to allow me the same liberty of supposing it such.
  • For he shall find, that the affair is not important.

• After discovering the two relations of contiguity and succession to be essential to causes and effects, I find I:
  • am stopped short
  • can proceed no farther in considering any single instance of cause and effect.
• Motion in one body is regarded on impulse as the cause of motion in another.
• When we consider these objects with utmost attention, we find only that as the one body approaches the other, its motion precedes the motion of the other, but without any sensible interval.
  • It is in vain to rack ourselves with farther thought and reflection on this subject.
    • We can go no farther in considering this particular instance.

• Should any one leave this instance and pretend to define a cause by saying it is something productive of another, it is evident he would say nothing.
  • For what does he mean by production?
  • Can he give any definition of it, that will not be the same with that of causation?
• If he can, I desire it may be produced.
  • If he cannot, he here runs in a circle.
    • He gives a synonymous term instead of a definition.

• Shall we then rest contented with these two relations of contiguity and succession, as affording a complete idea of causation?
  • No.
• An object may be contiguous and prior to another, without being its cause.
  • There is a necessary connection to be taken into consideration.
  • That relation is much more important than any of the other two above-mentioned.

• Again, I turn the object on all sides to discover the nature of this necessary connection.
  • I find the impression, or impressions, from which its idea may be derived.
• When I cast my eye on the known Qualities of objects, I immediately discover that the relation of cause and effect does not depend on them.
  • I can find only their relations of contiguity and succession.
    • I have already regarded them as imperfect and unsatisfactory.
• Does this mean that I have an idea which is not preceded by any similar impression?
  • This would be too strong a proof of levity and inconstancy.
  • Since the contrary principle has been already so firmly established, as to admit of no farther doubt, at least until we have more fully examined the present difficulty.

• Some people who look for something, beat about all the neighbouring fields without any design, hoping their good fortune will guide them.
• Therefore, we must proceed like them.
• We need to:
  • leave the direct survey of this question about the nature of that necessary connection of cause and effect.
  • try to find some other questions which might afford a hint, that may clear up the present difficulty.
    • There are two of these questions.

1. Why is it necessary that everything should also have a cause?
2. Why should such causes have such effects?
   • What is the nature of:
     • that inference we draw from the one to the other?
     • the belief we repose in it?

• The ideas of cause and effect are derived from the impressions of reflection and from those of sensation.
  • For brevity, I mention only the latter as the origin of these ideas.
  • Though I want whatever I say of them to also extend to the former.
• Passions are connected with their objects and with one another, no less than external bodies are connected together.
  • The same relation of cause and effect, which belongs to one, must then be common to all of them.

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