The Limits of Knowledge

It now makes sense to turn to Locke’s official discussion of the limits of knowledge. Keep in mind that the two orders of classification Locke introduces (manners or degrees of knowledge and the objects known) cut across each other. I’ve chosen to frame the discussion in terms of the objects of knowledge: identity (known by intuition), relation (by demonstration), co-existence, and real existence (by sensation).

(From IV.i.1—Our Knowledge conversant about our Ideas only) Since the mind, in all its thoughts and reasonings, hath no other immediate object but its own ideas, which it alone does or can contemplate, it is evident that our knowledge is only conversant about them.

(From IV.i.2—Knowledge is the perception of the agreement or disagreement of two ideas) Knowledge then seems to me to be nothing but the perception of the connexion of and agreement, or disagreement and repugnancy of anyof our ideas. In this alone it consists. Where this perception is, there is knowledge, and where it is not, there, though we may fancy, guess, or believe, yet we always come short of knowledge. For when we know that white is not black, what do we else but perceive, that these two ideas do not agree? when we possess ourselves with the utmost security of the demonstration, that the three angles of a triangle are equal to two right ones, what do we more but perceive, that equality to two right ones does necessarily agree to, and is inseparable from, the three angles of a triangle?

(From IV.i.3—This Agreement or Disagreement may be any of four sorts) But to understand a little more distinctlywherein this agreement or disagreement consists, I think we may reduce it all to these four sorts: i. identity, or diversity. ii. relation. iii. co-existence, or necessary connexion. iv. real existence.

(From IV.i.4—First, of Identity, or Diversity in ideas) First, as to the first sort of agreement or disagreement, viz. identityor diversity. It is the first act of the mind, when it has any sentiments or ideas at all, to perceive its ideas; and so far as it perceives them, to know each what it is, and thereby also to perceive their difference, and that one is not another.

(From IV.i.5—Secondly, of abstract Relations between ideas) Secondly, the next sort of agreement or disagreement the mind perceives in any of its ideas may, I think, be called relative, and is nothing but the perception of the relationbetween any two ideas, of what kind soever, whether substances, modes, or any other. (From IV.i.6—Thirdly, of their necessary Co-existence in Substances) The third sort of agreement or disagreement to be found in our ideas, which the perception of the mind is employed about, is co-existence or non-co-existence in the same subject; and this belongs particularly to substances. Thus when we pronounce concerning gold, that it is fixed, our knowledge of this truth amounts to no more but this, that fixedness, or a power to remain in the fire unconsumed, is an idea that always accompanies and is joined with that particular sort of yellowness, weight, fusibility, malleableness, and solubility in aqua regia, which make our complex idea signified by the word ‘gold’.

(From IV.iii.9–Of their Co-existence, extends only a very little way) [A]s to the …agreement or disagreement of our ideas in co-existence, in this our knowledge is very short; though in this consists the greatest and most material part of our knowledge concerning substances. For our ideas of the species of substances being, as I have showed, nothing but certain collections of simple ideas united in one subject, and so co-existing together; e.g., our idea of flame is a body hot, luminous, and moving upward; of gold, a body heavy to a certain degree, yellow, malleable, and fusible: for these, or some such complex ideas as these, in men’s minds, do these two names of the different substances, flame and gold, stand for. When we would know anything further concerning these, or any other sort of substances, what do we inquire, but what other qualities or powers these substances have or have not? which is nothing else but to know what other simple ideas do, or do not co-exist with those that make up that complex idea?

(From IV.iii.10—Because the Connexion between simple Ideas in substances is for the most part unknown ) This, how weighty and considerable a part so ever of human science, is yet very narrow, and scarce any at all. The reason whereof is, that the simple ideas whereof our complex ideas of substances are made up are, for the most part, such as carry with them, in their own nature, no visible necessary connexion or inconsistency with any other simple ideas, whose co-existence with them we would inform ourselves about.

(From IV.iii.25) If a great, nay, far the greatest part of the several ranks of bodies in the universe escape our notice by their remoteness, there are others that are no less concealed from us by their minuteness. These insensible corpuscles, being the active parts of matter, and the great instruments of nature, on which depend not only all their secondary qualities, but also most of their natural operations, our want of precise distinct ideas of their primary qualities keeps us in an incurable ignorance of what we desire to know about them.
I doubt not but if we could discover the figure, size, texture, and motion of the minute constituent parts of any two bodies, we should know without trial several of their operations one upon another; as we do now the properties of a square or a triangle. Did we know the mechanical affections of the particles of rhubarb, hemlock, opium, and a man, as a watchmaker does those of a watch, whereby it performs its operations; and of a file, which by rubbing on them will alter the figure of any of the wheels; we should be able to tell beforehand that rhubarb will purge, hemlock kill, and opium make a man sleep: as well as a watchmaker can, that a little piece of paper laid on the balance will keep the watch from going till it be removed; or that, some small part of it being rubbed by a file, the machine would quite lose its motion, and the watch go no more. The dissolving of silver in aqua fortis, and gold in aqua regia, and not viceversa, would be then perhaps no more difficult to know than it is to a smith to understand why the turning of one key will open a lock, and not the turning of another. But whilst we are destitute of senses acute enough to discover the minute particles of bodies, and to give us ideas of their mechanical affections, we must be content to be ignorant of their properties and ways of operation; nor can we be assured about them any further than some few trials we make are able to reach. But whether they will succeed again another time, we cannot be certain. This hinders our certain knowledge of universal truths concerning natural bodies: and our reason carries us herein very little beyond particular matter of fact.

(From IV.vi.9—No discoverable necessary connexion between nominal essence gold, and other simple ideas) As there is no discoverable connexion between fixedness and the colour, weight, and other simple ideas of that nominal essence of gold; so, if we make our complex idea of gold, a body yellow, fusable, ductile, weighty, and fixed, we shall be at the same uncertainty concerning solubility in aqua regia, and for the same reason. Since we can never, from consideration of the ideas themselves, with certainty affirm or deny of a body whose complex idea is made up of yellow, very weighty, ductile, fusible, and fixed, that it is soluble in aqua regia: and so on of the rest of its qualities. I would gladly meet with one general affirmation concerning any will, no doubt, be presently objected, is not this an universal proposition, “allgold is malleable”? to which I answer, it is a very complex idea the word ‘gold’ stands for. But then here is nothing affirmed of gold, but that that sound stands for an idea in which malleableness is contained: and such a sort of truth and certainty as this it is, to say a centaur is four-footed. But if malleableness make not a part of the specific essence the name of ‘gold’ stands for, it is plain, “all gold is malleable”, is not a certain proposition. Because, let the complex idea of gold be made up of whichsoever of its other qualities you please, malleableness will not appear to depend on that complex idea, nor follow from any simple one contained in it: the connexion that malleableness has (if it has any) with those other qualities being only by the intervention of the real constitution of its insensible parts; which, since we know not, it is impossible we should perceive that connexion, unless we could discover that which ties them together.

(From IV.i.7—Fourthly, of real Existence agreeing to any idea) The fourth and last sort is that of actual real existenceagreeing to any idea.

(From IV.ii.1—Of the degrees, or differences in clearness, of our Knowledge)

1. Intuitive: The different clearness of our knowledge seems to me to lie in the different way of perception the mind has of the agreement or disagreement of any of its ideas. For if we will reflect on our own ways of thinking, we will find, that sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other: and this I think we may call intuitiveknowledge.

(From IV.ii.2)

1. Demonstrative: The next degree of knowledge is, where the mind perceives the agreement or disagreement of any ideas, but not immediately. Though wherever the mind perceives the agreement or disagreement of any of its ideas, there be certain knowledge; yet it does not always happen, that the mind sees that agreement or disagreement, which there is between them, even where it is discoverable; and in that case remains in ignorance, and at most gets no further than a probable conjecture. … In this case then, when the mind cannot so bring its ideas together as by their immediate comparison, and as it were juxta-position or application one to another, to perceive their agreement or disagreement, it is fain, by the intervention ofother ideas, (one or more, as it happens) to discover the agreement or disagreement which it searches; and this is that which we call reasoning. …

(From IV.ii.14)

1. Sensitive knowledge of the particular existence of finite beings without us. These two, viz. intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of these, with what assurance soever embraced, is but faith or opinion, but not knowledge, at least in all general truths. There is, indeed, another perception of the mind, employed about the particular existence of finite beingswithout us, which, going beyond bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, passes under the name of knowledge. There can be nothing more certain than that the idea we receive from an external object is in our minds: this is intuitive knowledge. But whether there be anything more than barely that idea in our minds; whether we can thence certainly infer the existence of anything without us, which corresponds to that idea, is that whereof some men think there may be a question made; because men may have such ideas in their minds, when no such thing exists, no such object affects their senses. But yet here I think we are provided with an evidence that puts us past doubting. For I ask any one, whether he be not invincibly conscious to himself of a different perception, when he looks on the sun by day, and thinks on it by night; when he actually tastes wormwood, or smells a rose, or only thinks on that savour or odour? We as plainly find the difference there is between any idea revived in our minds by our own memory, and actually coming into our minds by our senses, as we do between any two distinct ideas. If any one say, a dream may do the same thing, and all these ideas may be produced, in us without any external objects; he may please to dream that I make him this answer:

(From IV.iv.1—Objection: “Knowledge placed in our ideas may be all unreal or chimerical”) I doubt not but my reader, by this time, may be apt to think that I have been all this while only building a castle in the air; and be ready to say to me: To what purpose all this stir? knowledge, say you, is only the perception of the agreement or disagreement of our own ideas: but who knows what those ideas may be? Is there anything so extravagant as the imaginations of men’s brains? where is the head that has no chimeras in it? … If it be true, that all knowledge lies only in the perception of the agreement or disagreement of our own ideas, the visions of an enthusiast and the reasonings of a sober man will be equally certain.

(From IV.iv.2—Answer Not so, where Ideas agree with Things) To which I answer, That if our knowledge of our ideas terminate in them, and reach no further, where there is something further intended, our most serious thoughts will beof little more use than the reveries of a crazy brain. … But I hope, before I have done, to make it evident, that this way of certainty, by the knowledge of our own ideas, goes a little further than bare imagination: and I believe it will appear that all the certainty of general truths a man has lies in nothing else.

(From IV.iv.3—But what shall be the criterion of this agreement?) It is evident the mind knows not things immediately, but only by the intervention of the ideas it has of them. Our knowledge, therefore, is real only so far as there is a conformitybetween our ideas and the reality of things. But what shall be here the criterion? How shall the mind, when it perceives nothing but its own ideas, know that they agree with things themselves? this, though it seems not to want difficulty, yet, I think, there be two sorts of ideas that we may be assured agree with things.

(From IV.iv.4—As, first all simple ideas are really conformed to things) First, the first are simple ideas, which since the mind, as has been showed, can by no means make to itself, must necessarily be the product of things operating on the mind, in a natural way, and producing therein those perceptions which by the Wisdom and Will of our Maker they are ordained and adapted to. From whence it follows, that simple ideas are not fictions of our fancies, but the natural and regular productions of things without us, really operating upon us; and so carry with them all the conformity which is intended; or which our state requires: for they represent to us things under those appearances which they are fitted to produce in us: whereby we are enabled to distinguish the sorts of particular substances, to discern the states they are in, and so to take them for our necessities, and apply them to our uses. Thus the idea of whiteness, or bitterness, as it is in the mind, exactly answering that power which is in any body to produce it there, has all the real conformity it can or ought to have, with things without us. And this conformity between our simple ideas and the existence of things, is sufficient for real knowledge.