Of knowledge

From the article ”Metaphysics”, Encyclopaedia Britannica, 1771

The beginning of the article Metaphysics in the Britannica of 1771. Of knowledge in general. Since the mind, in all its thoughts and reasonings, has no other immediate object but its own ideas,  which alone it does or can contemplate, it is evident that our knowledge is only conversant about them. Knowledge  then seems to be nothing but the perception of the connection and agreement, or disagreement and repugnancy of any of our ideas:  where this perception is, there is knowledge; and where it is not, there, though we fancy, guess, or believe, yet we always come short of knowledge.  When we know that white  is not black,  what do we but perceive that these two ideas  do not agree? Or that the three angles of a triangle,  are equal to two to right ones; what do we more but perceive that equality to two right ones does neccessarily agree to, and is separable from the three angles of a triangle? But to understand a little more distinctly wherein this agreement or disagreement consists, we may reduce it all to these four sorts:  1st, Identity  or diversity;  2dly, Relation;  3dly, Coexistence;  4thly, Real existence.  1. Identity  or diversity.  It is the first act of the mind, to perceive its  ideas; and so far as it perceives them, to know each whatit is, and thereby to perceive their difference, that is, the one not to be the other: by this the mind clearly perceives each idea  to agree with itself, and to be what it is; and all distinct ideas  to disagree. This it does without any pains or deduction, by its natural power of perception and distinction. This is what men of art have reduced to those general rules, viz. what is,  is; and, it is impossible for the same thing to be and not to be.  But no maxim can make a man know it clearer, that round  is not square,  than the bare perception of those two ideas,  which the mind at first sight perceives to disagree. 2. The next sort of agreement or disagreement thge mind perceives in any kind of its ideas,  may be called relative,  and is nothing but the perception of the relation between any two ideas  of what kind soever; that is, their agreement or disagreement one with another in several ways the mind takes of comparing them. 3. The third sort of agreement or disagreement to be found in our ideas, is, coexistence  or non-coexistence  in the same subject; and this belongs particularly to substances. Thus when we pronounce concerning gold,  that it is fixed, it amounts to no more but this, that fixedness, or a power to remain in the fire unconsumed, is an idea that always accompanies that particular sort of yellowness, weight, fusibility,  &c, which make our complex idea signified by the word gold.  4. The fourth sort, is that of actual and real existence  agreeing to any idea.  Within these four sorts of agreement or disagreement, is contained all the knowledge we have, or are capable of. For all that we know or can affirm concerning any idea,  is, That it is, or is not the same with some other; as, that blue is not yellow:  That it does, or does not coexist with another in the same subject; as, that iron is susceptible of magnetical impressions;  That it has that or this relation to some other ideas;  as, That two triangles, upon equal bases between two parallels, are equal:  or, that it has a real existence without the mind; as, that God is.  There are several ways wherein the mind is possessed of truth, each of which is called knowledge. First,  There is actual knowledge,  when the mind has a present view of the agreement or disagreement of any of its ideas,  or of the relation they have one with another. Secondly,  A man is said to know any proposition, when having once evidently perceived the agreement or disagreement of the ideas  whereof it consists, and so lodged it in his memory, that whenever it comes to be reflected on again, the mind assents to it without doubt or hesitation, and is certain of the truth of it. And this may be called habitual knowledge.  And thus a man may be said to know all those truths which are lodged in his memory by a foregoing, clear, and full perception. Of habitual knowledge  there are two sorts: The one is of such truths laid up in the memory, as whenever they occur to the mind, it actually perceives the relatin that is between those ideas.  And this is in all those truths, where the ideas  themselves, by an immediate view, discover their agreement or disagreement one with another. The other is of such truths, whereof the mind having been convinced, it retains the memory of the conviction, without the proofs. Thus a man that remembers certainly, that he once perceived the demonstration, that the three angles of as triangle are equal to two right ones, knows it to be true, when the demonstration is gone out of his mind, and possibly cannot be recollected: But he knows it in a different way from what he did before, namely, not by the intervention of thos eintermediate ideas,  whereby the agreement or disagreement of thois ein the proposition was at first perceived, but by remembring, i.e.  knowing that he was once certain of the truth of this proposition, that the three angles of a triangle are equal to two right ones. The immutability of the same relations between the same immutable things, is now the idea  that shews him, that if the three angles of a trianglöe were once equal to two right ones, they will always be so. And hence he comes to be certain, that what was once true, is always true; what ideas  once agreed, will always agree; and consequently, what he once knew to be true, he will always know to be true, as long as he can remember that he once knew it. Of the degrees of our knowledge. All our knowledge consisting in the view the mind has of its own ideas,  which is the utmost light and greatest certainty we are capable of, the different clearness of our knowledge  seems to lie in the different way of perception the mind has of the agreement or disagreement of any of its ideas.  When the mind perceives this agreement or disagreement of two ideas immediately  by themselves, without the intervention of any other, we may call it intuitive knowledge,  in which cases the mind perceives truth, as the eye does light, only by being directed towards it. Thus the mind perceives, that white is not black;  that three are more than two,  and equal to one and two.  This part of knowledge is irresistible, and, like the bright sun-shine, forces itself immediately to be perceived as soon as ever the mind turns its view that way. It is on this intuition  that depends all the certainty and evidence of our other knowledge; which certainty every one finds to be so great, that he cannot imagine, and therefore not require a greater. The next degree of knowledge, is, where the mind perceives not this agreement or disagreement immediately, or by the juxta-position,  as it were, of the ideas,  because those ideas  concerning whose agreement or disagreement the inquiry is made, cannot by the mind be so put together, as to shew it. In this case the mind is fond to discover the agreement or disagreement which it searches, by the intervention of other ideas:  And this is that which we call reasoning.  And thus, if we would know the agreement or disagreement in bigness, between the three angles of a triangle, and two right angles, we 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 or intuitive knowledge. But we must find out some other angles, to which the three angles of a triangle have equality; and finding those equal to two right ones, we come to know the equality of these three angles to two right ones. Those intervening ideas  which serve to shew the agreement of any two others, are called proofs;  and where the agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration. A quickness in the mind to find those proofs, and to apply them right, is that which is called sagacity.  This knowledge, though it be certain, is not so clear and evident as intuitive  knowledge. It requires pains and attention, and steady application of mind, to discover the agreement or disagreement of the ideas  it considers; and there must be a progression by steps and degrees, before the mind can in this way arrive at certainty. Before demonstration there was a doubt, which, in intuitive knowledge,  cannot happen to the mind that has its faculty of preception left to a degree capable of distinct ideas,  no more than it can be a doubt to the eye (that can distinctly see white  and black)  whether this ink and paper be all of a colour. Now, in every step that reason makes in demonstrative knowledge,  there is an intuitive knowledge  of that agreement or disagreement it seeks with the next intermediate idea,  which it uses as a proof; for if it were not so, that yet would need a proof; since without the perception of such agreement or disagreement, there is no knowledge produced. By which it is evident, that every step in reasoning, that produces knowledge, has intuitive certainty:  which when the mind perceives, there is no more required but to remember it, to make the agreement or disagreement of the ideas  concerning which we inquire visible and certain. This intuitive perception  of the agreement or disagreement of the intermediate ideas  in each step and progression of the demonstration, must also be exactly carried in the mind; and a man must be sure that no part is left out; which because in long deductions the memory cannot easily retain, this knowledge becomes more imperfect than intuitive,  and men often embrace falsehoods for demonstrations.

It has been generally taken for granted, that mathematicks  alone are capable of demonstrative certainty. But to have such an agreement or disagreement as may be intuitively perceived, being 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: For in whatever ideas  the mind can perceive the agreement or disagreement immediately, there it 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 the ideas  of figure, number, extension, or their modes. The reason why it has been generally supposed to belong to them only, is, because in comparing their equality or excess the modes of numbers  have every the least difference very clear and perceivable: And in extension,  though every the least excess is not so perceptible, yet the mind has found out ways to discover the just equality of two angles, extensions, or figures; and both, that is, numbers and figures, can be set down by visible and lasting marks.

But in other simple ideas,  whose modes and differences are made and counted by degrees, and not quantity, we have not so nice and accurate a distinction of their differences, as to perceive or find ways to measure their just equality, or the least differences: For those other simple ideas  being appearances or sensations produced in us by the size, figure, motion,  &c. of minute corpuscles singly insensible, their different degrees also depend on the variation of some, or all of those causes; which since it cannot be observed by us in particles of matter, whereof each is too subtile to be perceived, it is impossible for us to have any exact measures of the different degrees of these simple ideas.  Thus, for instance, not knowing what number of particles, nor what motion of them, is sit to produce any precise degree of whiteness,  we cannot demonstrate the certain equality of any two degrees of whiteness,  because we have no certain standard to measure them by, nor means to distinguish every the least difference; the only help we have being from our senses, which in this point fail us. But where the difference is so great as to produce in the mind ideas  clearly distinct, there ideas  of colours,  as we see in different kinds, blue  and red,  (for instance,) are as capable of demonstration as ideas  of number and extension. What is here said of colours, holds true in all secondary qalities. These two then, intuition  and demonstration,  are the degress of our knowledge;  whatever comes short of one of these, is but faith  or opinion,  not knowledge,  at least, in all general truths.  There is, indeed, another perception of the mind employed about the particular existence of finite beings  without us; which going beyond probability, but not reaching to either of the foregoing degrees of certainty, passes under the name of knowledge.

Nothing can be more certain, than that the idea  we receive from an external object is in our minds: This is intuitive knowledge;  but whether we can thence certainly infer the existence of any thing without us, corresponding to that idea,  is that whereof some men think there may be a question made, because men may have such an idea  in their minds, when no such things exist, no such object affects their senses. But its evident that we are invincibly conscious to ourselves of a different perception, when we look upon the sun  in the day, and think on it by night; when we actually taste wormwood,  or smell a rose, or only think on that savour  or odour.  So that we may add to the two former sorts of knowledge, this also of the existence of particular external objects, by that perception and consciousness we have of the actual entrance of ideas  from them, and allow these three degrees of knowledge, viz. intuitive, demonstrative,  and sensitive.

But since our knowledge is founded on, and employed about our ideas  only, will it follow thence that it must be conformable to our ideas;  and that where our ideas  are clear and distinct, obscure and confused, there our knowledge will be so too? No. For our knowledge consisting in the perception of the agreement or disagreement of any two ideas,  its clearness or obscurity consists in the clearness or obscurity of that perception, and not in the clearness or obscurity of the ideas  themselves. A man (for instance) that has a clear idea  of the angles of a triangle, and of equality to two right ones, may yet have but an obscure perception of their agreement; and so have but a very obscure knowledge of it. But obscure and confused ideas  can never produce any clear or distinct knowledge; because, as far as any ideas  are obscure or confused, so far the mind can never perceive clearly whether they agree or disagree. Of the extent of human knowledge. From what has been said concerning knowledge, it follows, First,  That we can have no knowledge farther than we have ideas. Secondly,  That we have no knowledge farther than we can have perception of that agreement or disagreement of our ideas,  either by intuition, demonstration,  or sensation.  Thirdly,  We cannot have an intuitive  knowledge that shall extend itself to all our ideas,  and all that we would know about them, because we cannot examine and perceive all the relations they have one to another, by juxta-position, or an immediate comparison one with another. Thus we cannot intuitively  perceive the equality of two extensions, the difference of whose figures makes their parts incapable of an exact immediate application. Fourthly,  Our rational  knowledge cannot reach to the whole extent of our ideas;  because between two different ideas  we would examine, we cannot always find such proofs  as we can connect one to another, with an intuitive knowledge  in all the parts of the deduction. Fifthly, Sensitive  knowledge reaching no farther than the existence of things actually present to our senses, is yet much narrower than either of the former. Sixthly,  From all which it is evident, that the extent of our knowledge,  comes not only short of the reality of things,  but even of the extent of our own ideas.  We have the ideas  of a square,  a circle,  and equality;  and yet, perhaps, shall never be able to find a circle equal to a square.  The affirmations or negations we make concerning the ideas  we have, being reduced to the four sorts above mentioned, viz. identity, coexistence, relation,  and real existence,  we shall examine how far our knowledge extends in each of these. First,  As to identity and diversity,  our intuitive knowledge  is as far extended as our ideas  themselves; and there can be no idea  in the mind, which it does not presently, by an intuitive knowledge,  perceived to be what it is, and to be different from any other. Secondly,  As to the agreement or disagreement of our ideas  in coexistence:  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 substances  being nothing but certain collections of simple  ideas, coexisting in one subject,  (our idea  of flame,  for instance, is a body hot, luminous,  and moving upward;)  when we would know any thing farther concerning this, or any other sort of substance, what do we but inquire 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 coexist  with those that make up that complex idea.  The reason of this is, because the simple ideas  which make up our complex ideas  of substances, have no visible-necessary connection or inconsistense with other simple ideas  whose coexistence with them we would inform ourselves about. These ideas  being likewise, for the most part, secondary qualities,  which depend upon the primary  qualities of their minute or insensible parts, or on something yet more remote from our comprehension, it is impossible we should know which have a necessary union or inconsistency one with another, since we know not the root from whence they spring, or the size, figure, and texture of parts on which they depend, and from which they result. Besides this, there is no discoverable connection  between any secondary  quality, and those primary  qualities that it depends on. We are so far from knowing what figure, size, or motion produces (for instance) a yellow colour,  or sweet taste,  or a sharp sound,  that we can by no means conceive how any size, figure,  or motion  can possibly produce in us the idea  of any colour, taste,  or sound  whatsoever; and there is no conceivable connection between the one and the other. Our knowledge therefore of coexistence reaches little farther than experience,  Some few, indeed, of the primary  qalities have a necessary dependence and visible connection one with another; as figure  necessarily supposes extension, receiving or communicating motion by impulse  supposes solidity.  But qualities coexistent in any subject, without this dependence and connection, cannot certainly be known to coexist any farther than experience by our senses informs us. Thus, though upon trial we find gold  yellow, weighty, malleable, fusible, and fixed, yet because none of these have any evident dependence or necessary connection with the other, we cannot certainly know that where any four  of these are, the fifth  will be there also, how highly probable soever it may be: But the highest degree of probality  amounts not to certainty;  without which there can be no true knowledge: For this coexistence can be no further known, than it is perceived; and it cannot be perceived, but either, in particular  subjects, by the observation of our senses, or, in general,  by the necessary connection of the ideas  themselves. As to incompatibility,  or repugnancy to coexistence,  we may know that any subject can have of each sort of primary  qualities but one particular at once, one extension, one figure; and so of sensible ideas,  peculiar to each sense: for whatever of each kind is present in any subject, excludes all other of that fort; for instance, one subject cannot have two smells  or two colours  at the same time. As to powers of substances,  which make a great part of our inquiries about them, and are no inconsiderable branch of our knowledge; our knowledge as to these reaches little farther than experience;  because they consist in a texture and motion of parts which we cannot by any means come to discover. Experience  is that which in this part we must depend on; and it were to be wished that it were more improved. As to the third sort, the agreement or disagreement of our ideas in any other relation,  this is the largest field of knowledge, and it is hard to determinate how far it may extend. This part depending on our sagacity in finding intermediate ideas  that may shew the habitudes and relations of ideas,  it is an hard matter to tell when we are at the end of such discoveries. They that are ignorant of algebra,  cannot imagine the wonders in this kind that are to be done by it; and what farther improvements and helps advantageous to other parts of knowledge the sagacious mind of man may yet find out, it is not easy to determine. The ideas  of quantity  are not those alone that are capable of demonstration and knowledge; other, and perhaps more useful parts of contemplation, would undoubtedly afford us certainty, if vices, passions, and domineering interest, did not oppose or menace endeavours of this kind. The idea  of a Supreme Being,  infinite in power, goodness, and wisdom, whose workmanship we are, and on whom we depend; and the idea  of ourselves,  as understanding rational creatures; would, if duely considered, afford such foundations of our duty,  and rules of action,  as might place morality  among the sciences capable of demonstration. The relations of other modes may certainly be perseived, as well as those of number and extension. Where there is no property, there is no injustice,  is a proposition as certain as any demonstration in Euclid:  for the idea  of property  being a right to any thing; and the idea  of injustice,  being the invasion or violation of that right; it is evident, that these ideas  being thus established, and these names annexed to them, we can as certainly know this proposition to be true, as that a triangle has three angles equal to two right ones.  Again, No government allows absolute liberty.  The idea  of government  being the establishment of society upon certain rules or laws which require conformity to them, and the idea  of absolute liberty  being for any one to do whatever he pleases, we are as capable of being certain of the truth of this proposition, as of any in mathematicks.  What has given the advantage to the ideas  of quality,  and made them thought more capable of certainty and demonstration, is, First,  That they can be represented by sensible marks which have a nearer correspondence with them than any words or sounds. Diagrams  drawn on paper are copies of the ideas,  and not liable to the uncertainty that words carry in their signification: But we have no sensible marks that resemble our moral ideas,  and nothing but words to express them by; which though when written they remain the same, yet the ideas  they stand for may change in the same man; and it is very seldom that they are not different in different persons. Secondly, Moral ideas  are commonly more complex than figures. Whence these two inconveniences follow: First,  That their names are of more uncertain signification; the precise collection of simple ideas  they stand for not being so easily agreed on, and so the sign that is used for them in communication always, and in thinking often, does not steadily carry with it the same idea. Secondly,  The mind cannot easily retain those precise combinations so exactly and perfectly as is necessary; in the examination of the habitudes and correspondencies, agreements or disagreements of several of them one with another, especially where it is to be judged off by long deductions, and the intervention of several other complex ideas,  to shew the agreement or disagreement of two remote ones. Now one part of these disadvantages in moral ideas,  which has made them be thought not capable ofdemonstration, may in good measure be remedied by definitions,  setting down that collection of simple ideas  which every term shall stand for, and then using the terms steadily and constantly for that precise collection. As to the fourth sort of knowledge, viz.  of the real actual existence of things,  we have an intuitive  knowledge of our own existence;  a demonstrative  knowledge of the existence of God;  and a sensitive  knowledge of the objects that present themselves to our senses.

From what has been said, we may discover the causes of our ignorance;  which are chiefly these three: First,  Want of ideas: Secondly,  Want of a discoverable connection between the ideas  we have: Thirdly,  Want of tracing and examining our ideas.

First,  There are some things we are ignorant of for want of ideas.  All the simple ideas  we have are confined to the observations of our senses, and the operations of our own minds that we are conscious of in ourselves. What other ideas  it is possible other creatures may have, by the assistance of other senses and faculties more or perfecter than we have, or different from ours, it is not for us to determine; but to say or think there are no such, because we conceive nothing of them, is no better an argument, than if a blind man should be positive in it, that there was no such thing as sight and colours, because he had no manner of idea  of any such thing. What faculties therefore other species of creatures have to penetrate into the nature and inmost constitutions of things, we know not. This we know, and certainly find, that we want other views of them, besides those we have, to make discoveries of them more perfect. The intellectual  and sensible  world are in this perfectly alike, that the parts which we see of either of them, hold no proportion with that we see not; and whatsoever we can reach with our eyes or our thoughts of either of them, is but a point almost nothing in comparison of the rest. Another great cause of ignorance, is the want of ideas that we are capable of.  This keeps us in ignorance of things we conceive capable of being known. Bulk, figure, and motion we have ideas  of; yet not knowing what is the particular bulk, motion, and figure of the greatest part of the bodies of the universe, we are ignorant of the several powers, efficacies, and ways of operation, whereby the effects we daily see are produced. These are hid from us in some things, by being too remote;  in others, by being too minute.  When we consider the vast distance of the known and visible parts of the world, and the reasons we have to think that what lies within our ken is but a small part of the immense universe, we shall then discover an huge abyss of ignorance. What are the particular fabricks of the great masses of matter, which make up the whole stupenduous frame of corporeal beings; how far they are extended; and what is their motion, and how continued; and what influence they have upon one another; are contemplations, that at first glimpse our thoughts lose themselves in. If we confine our thoughts to this little system of our sun, and the grosser masses of matter that visibly move about it; what several sorts of vegetables, animals, and intellectual corporeal beings, infinitely different from those of our little spot of earth, may probably be in other planets,  to the knowledge of which, even of their outward figures and parts, we can no way attain, whilst we are confined to this earth, there being no natural means, either by sensation or reflection, to convey their certain ideas  into our minds? There are other bodies in the universe, 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 all their secondary  qualities and operations, our want of precise distinct ideas  of their primary  qualities keeps us in incurable ignorance of what we desire to know about them. Did we know the mechanical affections of rhubarb  and opium,  we might as easily account for their operations of purging  or causing sleep,  as a watchmaker can for the motions of his watch. The dissolving of silver in aqua fortis,  or gold  in aqua regia,  and not vice versa,  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 operations: Nor can we be assured about them any farther 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 matters of fact. And therefore, how far soever human industry may advance useful and experimental philosophy  in physical things, yet scientifical  will still be out of our reach; because we want perfect and adequate ideas  of those very bodies which are nearest to us, and most under our command. This, at first sight, shews us how disproportionate our knowledge is to the whole extent, even of material  beings; to which if we add the consideration of that infinite number of spirits  that may be, and probably are, which are yet more remote from our knowledge, whereof we have no cognizance; we shall find this cause of ignorance conceal from us, in an impenetrable obscurity, almost the whole intellectual  world, a greater certainly, and a more beautiful world than the material:  For bating some very few ideas  of spirit we get from our own mind by reflection, and from thence the best we can collect of the Father of all spirits,  the Author of them and us and all things, we have no certain information so much as of the existence of other spirits but by revelation; much less have we distinct ideas  of their different natures, states, powers, and several constitutions, wherein they agree or differ one from another, and from us: And therefore in what concerns their different species and properties, we are under an absolute ignorance. The second  cause of ignorance, is the want of discoverable connection  between those ideas  we have: Where we want that, we are utterly incapable of universal  and certain  knowledge: and are, as in the former case, left only to observation  and experiment.  Thus the mechanical affections of bodies having no affinity at all with the ideas  they produce in us, we can have no distinct knowledge of such operations beyond our experience; and can reason no otherwise about them, than as the effects or appointment of an infinitely wise agent,  which perfectly surpass our comprehensions.

The operation of our minds upon our bodies, is as inconceivable. How any thought  should produce a motion in body,  is as remote from the nature of our ideas,  as how any body  should produce any thought in the mind.  That it is so, if experience did not convince us, the consideration of the things themselves would never be able in the least to discover to us.

In some of our ideas  there are certain relations, habitudes, and connections, so visibly included in the nature of the ideas  themselves, that we cannot conceive them separable from them by any power whatsoever: In these only we are capable of certain and universal knowledge. Thus the idea  of a right lined triangle,  neccessarily carries with it an equality of its angles to two right ones.  But the coherence and continuity of the parts of matter, the production of sensation in us of colours  and sounds,  &c. by impulse and motion, being such wherein we can discover no natural connection with any ideas  we have, we cannot but ascribe them to the arbitrary will and good pleasure of the wise Architect. The things that we observe constantly to proceed regularly, we may conclude to act by a law set them; but yet by a law that we know not; whereby, though causes work steadily, and effects constantly flow from them, yet their connections and dependencies being not discoverable in our ideas,  we can have but an experimental knowledge of them. The third cause of ignorance, is our want of tracing those ideas we have  or may have, and finding out those intermediate ideas  which may shew us what habitude of agreement or disagreement they may have one with another: And thus many are ignorant of mathematical  truths, for want of application in inquiring, examining, and by due ways comparing those ideas.  Hitherto we have examined the extent  of our knowledge, in respect of the several sorts of beings that are: There is another extent  of it, in respect of universality,  which will also deserve to be considered; and in this regard our knowledge follows the nature of our ideas.  If the ideas  are abstract,  whose agreement or disagreement we perceive, our knowledge is universal.  For what is known of such general ideas,  will be true of every particular thing in which that essence,  that is abstract idea,  is to be found: And what is once known of such ideas,  will be perpetually, and for ever true. So that, as to all general knowledge, we must search and find it only in our own minds: And it is only the examining of our own ideas  that furnishes us with that. Truths belonging to essences of things, (that is, to abstract ideas),  are eternal,  and are to be found out by the contemplation only of those essences, as the existence of things is to be known only from experience. Of the reality of our knowledge. The reader by this time may be ready to object, 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: It is no matter how things are, so a man observe but the agreement of his own imaginations, and talk conformably: it is all truth, all certainty. To this it is answered, that if our knowledge of our ideas  should terminate in them, and reach no farther, where there is something farther intended, our most serious thoughts would be of little more use than the reveries  of a crazy brain. But it is evident, that this way of certainty,  by the knowledge of our own ideas,  goes a little farther than bare imagination: and that all the certainty of general truths a man has, lies in nothing else but this knowledge of our ideas.  It is evident, that the mind knows not things immediately, but by the intervention of the ideas  it has of them. Our knowledge therefore is real,  only so far as there is a conformity between our ideas  and the reality of things. But how shall we know when our ideas  agree with things themselves? There are two sorts  of ideas,  that we may be assured agree with things: These are, First, Simple  ideas; which since the mind can by no means make to itself, must be the effect of things operating upon the mind in a natural way, and producing therein those perceptions, which, by the will of our Maker, they are ordained and adapted to. Hence it fullows, that simple ideas  are not fictions of our fancies, but the natural and regular productions of things without us, really operating upon us; which carry with them all the conformity our state requires, which is to represent things under those appearances they are fitted to produce in us. Thus the idea  of whiteness,  as it is in the mind, exactly answers that power which is in any body to produce it there. And this conformity between our simple ideas,  and the existence of things, is sufficient for real knowledge. Secondly,  All our complex ideas,  except those of substances, being archetypes  of the mind´s own making, and not referred to the existence of things as to their originals, cannot want any conformity neccessary to real knowledge: For that which is not designed to reprecent any thing but itself, can never be capable of a wrong representation. Here the ideas  themselves are considered as archetypes, and things no otherwise regarded than as they are conformable to them. Thus the mathematician  considers the truth and properties belonging to a rectangle,  or circle,  only as they are ideas  in his own mind, which possibly he never found existing mathematically, that is, precisely true; yet his knowledge is not only certain, but real;  because real things are no farther concerned, nor intended to be meant by any such propositions, than as things really agree to those archetypes  in his mind. It is 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 exists:  What is true of those figures  that have barely an ideal  existence in his mind, will hold true of them also when they come to have a real  existence in matter.

Hense it follows, that moral  knowledge is as capable of real certainty  as mathematicks:  For certainty  being nothing but the perception of the agreement or disagreement of our ideas,  and demonstration nothing but the perception of such agreement by the intervention of other ideas,  our moral ideas,  as well as mathematical,  being archetypes  themselves, and so adequate or complete ideas,  all the agreement or disagreement we shall find in them will produce real  knowledge, as well as in mathematical figures.  That which is requisite to make our knowledge certain,  is the clearness of our ideas:  and that which is required to make it real,  is, that they answer their archetypes.

Thirdly,  But the complex ideas,  which we refer to archetypes  without us, may differ from them, and so our knowledge about them may come short of being real; and such are our ideas  of substances.  These must be taken from something that does or has existed, and not be made up of ideas  arbitrarily put together, without any real pattern. Herein, therefore, is founded the reality of our knowledge concerning substances,  that all our complex ideas  of them must be such, and such only, as are made up of such simple ones as have been discovered to coexist in nature. And our ideas  being thus true, tho' not perhaps very exact copies, are the subjects of the real  knowledge of them. Whatever ideas  we have, the agreement we find they have with others will be knowledge. If those ideas  be abstract, it will be general  knowledge. But to make it real  concerning substances,  the ideas  must be taken from the real existence of things. Wherever, therefore, we perceive the agreement or disagreement 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 truth in general. Truth, in the proper import of the world, signifies the joining or separating of signs, as the things signified by them do agree or disagree one with another, The joining or separating of signs, is what we call propositions:  so that truth  properly belongs only to propositions:  Whereof there are two sorts, mental  and verbal;  as there are two  sorts of signs commonly made use of, ideas  and words.

It is difficult to treat of mental  propositions without verbal;  because, in speaking of mental,  we must make use of words,  and then they become verbal.  Again, men commonly in their thoughts and reasonings use words  instead of ideas:  especially if the subject of their meditation contains in it complex ideas.  If we have occasion to form mental  propositions about white, black, circle,  &c. we can, and often do, frame in our minds the ideas  themselves, without reflecting on the names:  But when we would consider, or make propositions about the more complex ideas,  as of a man, vitriol, fortitude, glory,  &c. we usually put the name  for the idea;  because the idea  these names  stand for being for the most part confused, imperfect, and undetermined, we reflect on the names  themselves, as being more clear, certain, and distinct, and readier to occur to our thoughts, than pure ideas;  and so we make use of these words  instead of the ideas  themselves, even when we would meditate and reason within ourselves, and make tacit mental propositions.

We must then observe two sorts of propositions  that we are capable of making: First. Mental propositions,  wherein the ideas  in our understandings are put together or separated by the mind perceiving or judging of their agreement or disagreement. Secondly, Verbal propositions;  which are words put together or separated in affirmative or negative sentences: So that proposition  consists in joining or separating signs; and truth  consists in putting together or separating these signs, according as the things they stand for agree or disagree. Truth,  as well as knowledge, may well come under the distinction of verbal  and real;  that being only verbal truth,  wherein terms are joined according to the agreement or disagreement of the ideas  they stand for, without regarding whether our ideas  are such as really have or are capable of having an existence in nature. But then it is they contain real truth,  when these signs are joined as our ideas  agree: and when our ideas are such as, we know, are capable of having an existence in nature; which in substances we cannot know, but by knowing that such have existed. Truth  is the marking down in words the agreement or disagreement of ideas  as it is: Falsehood  is the marking down in words the agreement or disagreement of ideas  otherwise than it is; and so for as these ideas,  thus marked by sounds, agree to their archetypes,  so far only is the truth real.  The knowledge of this truth  consists in knowing what ideas  the words stand for, and the perception of the agreement or disagreement of those ideas,  according as it is marked by those words. Besides truth  taken in the strict sense before mentioned, there are other sorts of truths:  As, first, Moral truth;  which is speaking things according to the persuasion of our own minds. Secondly, Metaphysical truth;  which is nothing but the real existence of things conformable to the ideas  to which we have annexed their names. These considerations of truth  either having been before taken notice of, or not being much to our present purpose, it may suffice here only to have mentioned them.