Locke’s Essay: Book IV

John Locke Essay Concerning Human Understanding, Final Edition, 1699 (Original 1690).

Book IV: The Reality of Knowledge

Locke points out some implications of Book III. The key point is to distinguish between, for example, the idea of a tree and ideas about how an idea of a tree might relate to any supposed external reality. (When we reason about a map, we can’t just assume that the territory will be constrained by our conclusions, any more than we can expect a SATNAV to behave ‘intelligently’ in unusual circumstances.)


1. Our Knowledge conversant about our Ideas only.

2. Knowledge is the Perception of the Agreement or Disagreement of two Ideas.

3. This Agreement or Disagreement may be any of four sorts.

But to understand a little more distinctly wherein this agreement or disagreement consists, I think we may reduce it all to these four sorts:



1. Of the degrees, or differences in clearness, of our Knowledge: I. Intuitive

All our knowledge consisting, as I have said, in the view the mind has of its own ideas, which is the utmost light and greatest certainty we, with our faculties, and in our way of knowledge, are capable of, it may not be amiss to consider a little the degrees of its evidence. 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 INTUITIVE KNOWLEDGE. For in this the mind is at no pains of proving or examining, but perceives the truth as the eye doth light, only by being directed towards it. Thus the mind perceives that WHITE is not BLACK, that a CIRCLE is not a TRIANGLE, that THREE are more than TWO and equal to ONE AND TWO. Such kinds of truths the mind perceives at the first sight of the ideas together, by bare intuition; without the intervention of any other idea: and this kind of knowledge is the clearest and most certain that human frailty is capable of. This part of knowledge is irresistible, and, like bright sunshine, forces itself immediately to be perceived, as soon as ever the mind turns its view that way; and leaves no room for hesitation, doubt, or examination, but the mind is presently filled with the clear light of it. IT IS ON THIS INTUITION THAT DEPENDS ALL THE CERTAINTY AND EVIDENCE OF ALL OUR KNOWLEDGE; which certainty every one finds to be so great, that he cannot imagine, and therefore not require a greater: for a man cannot conceive himself capable of a greater certainty than to know that any idea in his mind is such as he perceives it to be; and that two ideas, wherein he perceives a difference, are different and not precisely the same. He that demands a greater certainty than this, demands he knows not what, and shows only that he has a mind to be a sceptic, without being able to be so. Certainty depends so wholly on this intuition, that, in the next degree of knowledge which I call demonstrative, this intuition is necessary in all the connexions of the intermediate ideas, without which we cannot attain knowledge and certainty.

II. 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. The reason why the mind cannot always perceive presently the agreement or disagreement of two ideas, is, because those ideas, concerning whose agreement or disagreement the inquiry is made, cannot by the mind be so put together as to show it. 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 OF OTHER IDEAS, (one or more, as it happens) to discover the agreement or disagreement which it searches; and this is that which we call REASONING. Thus, the mind being willing to know the agreement or disagreement in bigness between the three angles of a triangle and two right ones, cannot by an immediate view and comparing them do it: because the three angles of a triangle cannot be brought at once, and be compared with any other one, or two, angles; and so of this the mind has no immediate, no intuitive knowledge. In this case the mind is fain to find out some other angles, to which the three angles of a triangle have an equality; and, finding those equal to two right ones, comes to know their equality to two right ones.

3. Demonstration depends on clearly perceived proofs.

Those intervening ideas, which serve to show the agreement of any two others, are called PROOFS; and where the agreement and disagreement is by this means plainly and clearly perceived, it is called DEMONSTRATION; it being SHOWN to the understanding, and the mind made to see that it is so. A quickness in the mind to find out these intermediate ideas, (that shall discover the agreement or disagreement of any other,) and to apply them right, is, I suppose, that which is called SAGACITY.

9. Demonstration not limited to ideas of mathematical Quantity.

[It has been generally taken for granted, that mathematics alone are capable of demonstrative certainty: but to have such an agreement or disagreement as may intuitively be perceived, being, as I imagine, not the privilege of the ideas of number, extension, and figure alone, it may possibly be the want of due method and application in us, and not of sufficient evidence in things, that demonstration has been thought to have so little to do in other parts of knowledge, and been scarce so much as aimed at by any but mathematicians.] For whatever ideas we have wherein the mind can perceive the immediate agreement or disagreement that is between them, there the mind is capable of intuitive knowledge; and where it can perceive the agreement or disagreement of any two ideas, by an intuitive perception of the agreement or disagreement they have with any intermediate ideas, there the mind is capable of demonstration: which is not limited to ideas of extension, figure, number, and their modes.

My dictionary characterises mathematics as ‘an abstract science’, in which case using mathematical demonstrations to set the standard may not seem all that ambitious.

The notion of a mathematical demonstration has been considerably refined since Locke’s day. Thus demonstrations that Locke thought ‘as good as’ a mathematical one may now be considered not so reliable.

III. 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.


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.

Locke is sometimes taken to mean that however we divide our idea of totality into parts, there must be separate real ‘things’ that correspond to those parts. He doesn’t actually seem to argue this, though, so it might be better to think of a real totality that is comprehended as separate things but may not actually be so divided. (As in physics, chemistry and biology.)

5. Secondly, All Complex Ideas, except ideas of Substances, are their own archetypes.

Secondly, All our complex ideas, EXCEPT THOSE OF SUBSTANCES, being archetypes of the mind’s own making, not intended to be the copies of anything, nor referred to the existence of anything, as to their originals, cannot want any conformity necessary to real knowledge.

6. Hence the reality of Mathematical Knowledge

I doubt not but it will be easily granted, that the knowledge we have of mathematical truths is not only certain, but real knowledge; and not the bare empty vision of vain, insignificant chimeras of the brain: and yet, if we will consider, we shall find that it is only of our own ideas. The mathematician considers the truth and properties belonging to a rectangle or circle only as they are in idea in his own mind. For it is possible he never found either of them existing mathematically, i.e. precisely true, in his life. But yet the knowledge he has of any truths or properties belonging to a circle, or any other mathematical figure, are nevertheless true and certain, even of real things existing: because real things are no further concerned, nor intended to be meant by any such propositions, than as things really agree to those archetypes in his mind. Is it true of the IDEA of a triangle, that its three angles are equal to two right ones? It is true also of a triangle, wherever it REALLY EXISTS. Whatever other figure exists, that it is not exactly answerable to that idea of a triangle in his mind, is not at all concerned in that proposition. And therefore he is certain all his knowledge concerning such ideas is real knowledge: because, intending things no further than they agree with those his ideas, he is sure what he knows concerning those figures, when they have BARELY AN IDEAL EXISTENCE in his mind, will hold true of them also when they have A REAL EXISTANCE in matter: his consideration being barely of those figures, which are the same wherever or however they exist.

Berkeley criticises this exposition, as it could be interpreted as meaning that abstract reasoning can be ‘real’. Locke, who was not a mathematician, may have been trying to convey his interlocutor, Newton’s, views. Exactly what these ‘really’ were is unclear, but never mind.

18. Recapitulation.

Wherever we perceive the agreement or disagreement of any of our ideas, there is certain knowledge: and wherever we are sure those ideas agree with the reality of things, there is certain real knowledge. Of which agreement of our ideas with the reality of things, having here given the marks, I think, I have shown WHEREIN IT IS THAT CERTAINTY, REAL CERTAINTY, CONSISTS. Which, whatever it was to others, was, I confess, to me heretofore, one of those desiderata which I found great want of.

That is, while empirical knowledge is always liable to Cromwell’s rule, formal, idealised, knowledge need not be. For example, we can know a lot about triangles, but we can’t know for certain that any real thing actually corresponds or ‘is’ a triangle as we conceive it.


1. Maxims or Axioms are Self-evident Propositions.

THERE are a sort of propositions, which, under the name of MAXIMS and AXIOMS, have passed for principles of science: and because they are SELF-EVIDENT, have been supposed innate, without that anybody (that I know) ever went about to show the reason and foundation of their clearness or cogency. It may, however, be worth while to inquire into the reason of their evidence, and see whether it be peculiar to them alone; and also to examine how far they influence and govern our other knowledge.

20. Their Use dangerous where our Ideas are not determined

And as these maxims are of little use where we have determined ideas, so they are, as I have showed, of dangerous use where [our ideas are not determined; and where] we use words that are not annexed to determined ideas, but such as are of a loose and wandering signification, sometimes standing for one, and sometimes for another idea: from which follow mistake and error, which these maxims (brought as proofs to establish propositions, wherein the terms stand for undetermined ideas) do by their authority confirm and rivet.


1. Knowledge is not got from Maxims.

But from comparing clear and distinct Ideas.

7. The true Method of advancing Knowledge is by considering our abstract Ideas.

9. Our Knowledge of Substances is to be improved, not by contemplation of abstract ideas, but only by Experience.

EXPERIENCE HERE MUST TEACH ME WHAT REASON CANNOT: and it is by TRYING alone, that I can CERTAINLY KNOW, what other qualities co-exist with those of my complex idea, v.g. whether that yellow heavy, fusible body I call gold, be malleable, or no; which experience (which way ever it prove in that particular body I examine) makes me not certain, that it is so in all, or any other yellow, heavy, fusible bodies, but that which I have tried. … For example, I cannot be certain, from this complex idea, whether gold be fixed or no; because, as before, there is no NECESSARY connexion or inconsistence to be discovered betwixt a COMPLEX IDEA OF A BODY YELLOW, HEAVY, FUSIBLE, MALLEABLE; betwixt these, I say, and FIXEDNESS; so that I may certainly know, that in whatsoever body these are found, there fixedness is sure to be. Here, again, for assurance, I must apply myself to experience; as far as that reaches, I may have certain knowledge, but no further.


  • That for Locke ‘experience’ is not passive.  It relies on active ‘trying’ and ‘application’.
  • Also, knowledge is just knowledge of what has been found by experience: If one extrapolates beyond experience (as in ‘induction’) one is going beyond what can be known.

Locke continues:

10. Experience may procure is Convenience, not Science.

I deny not but a man, accustomed to rational and regular experiments, shall be able to see further into the nature of bodies, and guess righter at their yet unknown properties, than one that is a stranger to them: but yet, as I have said, this is but judgment and opinion, not knowledge and certainty. This way of GETTING AND IMPROVING OUR KNOWLEDGE IN SUBSTANCES ONLY BY EXPERIENCE AND HISTORY, which is all that the weakness of our faculties in this state of mediocrity which we are in this world can attain to, makes me suspect that NATURAL PHILOSOPHY IS NOT CAPABLE IS BEING MADE A SCIENCE. We are able, I imagine, to reach very little general knowledge concerning the species of bodies, and their several properties. Experiments and historical observations we may have, from which we may draw advantages of ease and health, and thereby increase our stock of conveniences for this life; but beyond this I fear our talents reach not, nor are our faculties, as I guess, able to advance.

13. The true Use of Hypotheses.

Not that we may not, to explain any phenomena of nature, make use of any probable hypothesis whatsoever: hypotheses, if they are well made, are at least great helps to the memory, and often direct us to new discoveries. But my meaning is, that we should not take up any one too hastily (which the mind, that would always penetrate into the causes of things, and have principles to rest on, is very apt to do) till we have very well examined particulars, and made several experiments, in that thing which we would explain by our hypothesis, and see whether it will agree to them all; whether our principles will carry us quite through, and not be as inconsistent with one phenomenon of nature, as they seem to accommodate and explain another. And at least that we take care that the name of PRINCIPLES deceive us not, nor impose on us, by making us receive that for an unquestionable truth, which is really at best but a very doubtful conjecture; such as are most (I had almost said all) of the hypotheses in natural philosophy.

14. Clear and distinct Ideas with settled Names, and the finding of those intermediate ideas which show their Agreement or Disagreement, are the Ways to enlarge our Knowledge.

15. Mathematics an instance of this.

Chapter xv: Probability

This is not just about classical, numeric, probability. It is not even considered as a part of mathematics.

1.•Demonstration is showing the agreement or disagreement of two ideas by the intervention of one or more proofs,·theseparate links of·which have a constant, unchangeable,and visible connection with one another; and•probability is nothing but the appearance of such an agreement or disagreement, by the intervention of proofs whose connection isn’t perceived to be constant and unchangeable, but is or appears for the most part to be so, sufficiently to induce the mind to judge the proposition to be true or to be false.

2…. most of the propositions that we think with, reason with, use in discourse, and indeed act on,are ones of whose truth we can’t have undoubted knowledge. … But here there are degrees·of•confidence·from the very neighbourhood of certainty and demonstration right down to improbability and unlikelihood of truth, and downfurther to the brink of impossibility; and also degrees•ofassent from full assurance and confidence right down to conjecture, doubt, and distrust.

4.. . . .The grounds of probability are the two following. First, the conformity of something with our own knowledge, observation, and experience….

This may involve the dreaded ‘abstract reasoning’.

Chapter xvi: The degrees of assent

1.The grounds of probability laid down in the preceding chapter serve not only as the basis on which to decide whether to assent·to a proposition·but also as the measure of how strongly we should assent. Bear in mind, though, that whatever grounds of probability there maybe, they will operate on the truth-seeking mind only to the extent that they appear to it in its first judgment or its first look into the matter. … It suffices that they did once carefully and fairly sift the matter as far as they could, and that they have searched into everything that they can imagine might throw light on the question, and done their best to evaluate the evidence as a whole; and having thus once found on which side the probability appeared tot hem, after as full and exact an enquiry as they can make, they store the conclusion in their memories as a truth they have learned; and for the future they remain satisfied with the testimony of their memories that they have seen evidence for this opinion that entitles it to the degree of their assent that they are now giving to it.

3.I have to admit that men’s sticking to their past judgments and adhering firmly to conclusions formerly made often leads them to be obstinate in maintaining errors and mistakes. But their fault is not that they rely on their memories for what they previously judged well, but that they judged before they had examined well…. But in matters of probability we can’t always be sure that we have taken account of everything that might be relevant to the question, and that there is no evidence still to be found which could turn the probability-scales the other way, and outweigh everything that now seems to us to carry the most weight.

  1. …I the person you want to win over to your opinions is•one who examine sbefore he assents, you must allow him time to go over the account again, to recall points favouring his own side—ones he has currently forgotten—and to see on which side the advantage lies. And if he doesn’t think your arguments are good enough to indicate that he should take all that trouble reconsidering the matter, this is only what you often do insimilar cases; and you wouldn’t like it if others told to you what points you should study. … hose whohavefairly and truly examined·the grounds for their beliefs·, and have been brought by this beyond doubt about the doctrines they profess and live by, would have a fairer claim to requireothers to follow them. But there are so few of these, andthey find so little reason to be dogmatic in their opinions,that nothing insolent and bullying is to be expected from them; and there is reason to think that·in general·if men were better instructed themselves they wouldn’t push others around so much.

  2. Concerning … particular matters of fact,·I distinguish three kinds of case, to which I give a section each·. First, when something that fits with theconstant observation of ourselves and others in similarcases is supported by reports of all who mention it, weaccept it as easily and build on it as firmly as if it were certain knowledge; and we reason and act on it with as little doubt as if we had a perfect demonstration of it. Thus, if all Englishmen who have occasion to mention it were to affirm that it froze in England last winter, or that there were swallows seen there in the summer, I think one could hardly doubt this more than one does that seven and four are eleven. Thus, the first and highest degree of probability occurs when the general consent of all men in all ages, as faras it can be known, fits one’s own constant and never-failing experience in similar cases.

This is a kind of comparative probability, forming a partial order. Roughly speaking, something is regarded as more probable the more severely it has been tested. (Compare Keynes.) Note also that ‘swallows’ are species and hence abstractions, but despite that Locke argues that ceratin seeming ‘matters of fact’, if supported well enough, may reasonably be regarded as almost as certain as mathematical knowledge. (But his examples are very straightforward observations, with no deductions, inductions or abductions.)

Chapter xx: Wrong assent, or error

  1. Knowledge can be had only of visible and certain truth.So error isn’t a fault of our knowledge, but a mistake of our judgment when it gives assent to something that isn’t true.But if assent is based on likelihood, if what assent especially aims at is probability, and if probability is what I said it isin chapters xv and xvi, you will want to know how it comes about that men sometimes accept propositions that are not probable. For there’s nothing more common than contrariety of opinions; nothing more obvious than that one man wholly disbelieves what another only doubts of and a third firmly believes. The reasons for this may be very various, but Ithink they all come down to these four:
  1. Lack of proofs,·to be discussed in sections 2–4·.
  2. Lack of ability to use them,·section 5·
  3. Lack of will to use them.·section 6·.
  4. Wrong measures of probability,·sections 7–17·.

.Fourthly, there remains the last sort·of belief contrary to probability·, which occurs when people who have the real probabilities plainly laid before them nevertheless don’t accept the conclusion, and instead either suspend their assent or give it to the less probable opinion. This is the danger that threatens those who adopt wrong measures of probability. These wrong measures are

  1. Propositions that are not in themselves certain andevident, but doubtful and false, accepted as principles;·discussed in sections 8–10·.
  2. Received hypotheses;·section 1 .
  3. Predominant passions or inclinations;·sections 12–16·.
  4. Authority;·section 17·

8.The first and firmest ground of probability is the conformity something has to our own knowledge, especially the part of our knowledge that we have made our own and continueto regard as principles. These have so much influence on our opinions that it is usually by them that we judge concerning truth, and we measure probability in terms of them so strictly that if something is inconsistent with them—that is, with our ‘principles’—we count it not merely as improbable but as impossible. The reverence we give to these principles is so great, and their authority so supreme, that the testimony ofother men and even the evidence of our own senses are often rejected when they threaten to testify to something contrary to these established rules. …anyone who swallows wrong principles, blindly giving himself up to the authorityof some opinion that isn’t in itself evidently true, puts into his understanding a strong bias that will inevitably lead his assent astray.

17.The fourth and last wrong measure of probability thatI shall discuss keeps more people in ignorance or errorthan do the other three combined. I mentioned it in the foregoing chapter: it is the practice of giving our assent tothe common received opinions of our friends, our party, our neighbourhood, or our country.

18.Despite the great noise that is made about errors andopinions, I must be fair to mankind and say: There aren’t so many men with errors and wrong opinions as is commonly supposed.  ….For if we were to interrogate most partisans of most sects, so far from finding evidence that they acquired their opinions on the basis of examining arguments and the appearance of probability, we wouldn’t even find that they have any opinions of their own on the matters they are so zealous about!  … It is enough for him to obey his leaders, to have his hand and his tongue ready for the support of the common cause, in this way winning the approval of those who can give him credit, promotion, or protection in that society. Thus men become supporters of, and combatants for, opinions that they were never convinced of—indeed, ones that they never even had floating in their heads! I’m not playing down how many improbable or erroneous opinions there are out therein the world; but I am saying that there are fewer people that actually assent to them, and mistake them for truths, than there are generally thought to be.

Chapter xxi: The division of the sciences

1.All that can fall within the range of human understanding is in three categories.

  1. The nature of things as they are in themselves, their relations, and their manner of operation.
  2. What man himself ought to do, as a thinking and willing agent, for the attainment of any end, especially happiness.
  3. The ways and means by which the knowledge of each of those two is attained and communicated.

I think that science[= ‘high-level disciplined knowledge’] can properly be divided into these three sorts.

5. This is the first and most general Division of the Objects of our Understanding.

This seems to me the first and most general, as well as natural division of the objects of our understanding. For a man can employ his thoughts about nothing, but either, the contemplation of THINGS themselves, for the discovery of truth; or about the things in his own power, which are his own ACTIONS, for the attainment of his own ends; or the SIGNS the mind makes use of both in the one and the other, and the right ordering of them, for its clearer information. All which three, viz. THINGS, as they are in themselves knowable; ACTIONS as they depend on us, in order to happiness; and the right use of SIGNS in order to knowledge, being TOTO COELO different, they seemed to me to be the three great provinces of the intellectual world, wholly separate and distinct one from another.

The End

Dave Marsay

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