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JoHn Locke, Essay concerning Human Understanding

From Book IV, Chapter 1,

§9. Habitual Knowledge is of two degrees.

Of habitual knowledge there are, also, vulgarly speaking, two degrees:

First, The one is of such truths laid up in the memory as, whenever they
occur to the mind, it ACTUALLY PERCEIVES THE RELATION is between those
ideas. And this is in all those truths whereof we have an intuitive
knowledge; where the ideas themselves, by an immediate view, discover
their agreement or disagreement one with another.

...


Secondly, 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 a triangle are equal to two
right ones, is certain that he knows it, because he cannot doubt the
truth of it. In his adherence to a truth, where the demonstration by
which it was at first known is forgot, though a man may be thought
rather to believe his memory than really to know, and this way of
entertaining a truth seemed formerly to me like something between
opinion and knowledge; a sort of assurance which exceeds bare belief,
for that relies on the testimony of another;--yet upon a due examination
I find it comes not short of perfect certainty, and is in effect true
knowledge. That which is apt to mislead our first thoughts into a
mistake in this matter is, that the agreement or disagreement of the
ideas in this case is not perceived, as it was at first, by an actual
view of all the intermediate ideas whereby the agreement or disagreement
of those in the proposition was at first perceived; but by other
intermediate ideas, that show the agreement or disagreement of the ideas
contained in the proposition whose certainty we remember. For example:
in this proposition, that 'the three angles of a triangle are equal
to two right ones,' one who has seen and clearly perceived the
demonstration of this truth knows it to be true, when that demonstration
is gone out of his mind; so that at present it is not actually in view,
and possibly cannot be recollected: but he knows it in a different way
from what he did before. The agreement of the two ideas joined in that
proposition is perceived; but it is by the intervention of other ideas
than those which at first produced that perception. He remembers, i.e.
he knows (for remembrance is but the reviving of some past knowledge)
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 shows him, that if the three angles of a triangle were once equal
to two right ones, they will always be equal to two right ones. And
hence he comes to be certain, that what was once true in the case, 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. Upon this ground it is, that
particular demonstrations in mathematics afford general knowledge. If
then the perception, that the same ideas will ETERNALLY have the same
habitudes and relations, be not a sufficient ground of knowledge, there
could be no knowledge of general propositions in mathematics; for no
mathematical demonstration would be any other than particular: and
when a man had demonstrated any proposition concerning one triangle or
circle, his knowledge would not reach beyond that particular diagram. If
he would extend it further, he must renew his demonstration in another
instance, before he could know it to be true in another like triangle,
and so on: by which means one could never come to the knowledge of
any general propositions. Nobody, I think, can deny, that Mr. Newton
certainly knows any proposition that he now at any time reads in his
book to be true; though he has not in actual view that admirable chain
of intermediate ideas whereby he at first discovered it to be true. Such
a memory as that, able to retain such a train of particulars, may
be well thought beyond the reach of human faculties, when the very
discovery, perception, and laying together that wonderful connexion of
ideas, is found to surpass most readers' comprehension. But yet it is
evident the author himself knows the proposition to be true, remembering
he once saw the connexion of those ideas; as certainly as he knows such
a man wounded another, remembering that he saw him run him through. But
because the memory is not always so clear as actual perception, and does
in all men more or less decay in length of time, this, amongst other
differences, is one which shows that DEMONSTRATIVE knowledge is much
more imperfect than INTUITIVE, as we shall see in the following chapter.

 

INOLTRE


Book IV, Chapter 11,

§5. II. Secondly, Because we find that an Idea from actual Sensation, and
another from memory, are very distinct Perceptions.

Because sometimes I find that I CANNOT AVOID THE HAVING THOSE IDEAS
PRODUCED IN MY MIND. For though, when my eyes are shut, or windows fast,
I can at pleasure recal to my mind the ideas of light, or the sun, which
former sensations had lodged in my memory; so I can at pleasure lay by
THAT idea, and take into my view that of the smell of a rose, or taste
of sugar. But, if I turn my eyes at noon towards the sun, I cannot avoid
the ideas which the light or sun then produces in me. So that there is a
manifest difference between the ideas laid up in my memory, (over which,
if they were there only, I should have constantly the same power to
dispose of them, and lay them by at pleasure,) and those which force
themselves upon me, and I cannot avoid having
. And therefore it must
needs be some exterior cause, and the brisk acting of some objects
without me, whose efficacy I cannot resist, that produces those ideas
in my mind, whether I will or no. Besides, there is nobody who doth not
perceive the difference in himself between contemplating the sun, as
he hath the idea of it in his memory, and actually looking upon it: of
which two, his perception is so distinct, that few of his ideas are
more distinguishable one from another. And therefore he hath certain
knowledge that they are not BOTH memory, or the actions of his mind, and
fancies only within him; but that actual seeing hath a cause without.

 

****

Book II, chapter 27

§9: “L’identità personale: persona è un essere pensante, intelligente che possiede ragione e riflessione, e può considerare se stesso in quanto se stesso ,ossia la stessa cosa pensante ch’egli è, in tempi e luoghi diversi e ciò è possibile solo mediante la sua coscienza, che è inseparabile dal pensare (…); è impossibile per ciascuno percepire senza la consapevolezza del percepire. Quando noi vediamo, udiamo, odoriamo, gustiamo, sentiamo, meditiamo o vogliamo qualcosa , noi sappiamo quel che facciamo. … in questo modo ciascuno è perse stesso quello che chiamo io … in questo consiste l’identità di un essere razionale.”

 

****

Book IV, Chapter II.

OF THE DEGREES OF OUR KNOWLEDGE.

 

§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. …. IT IS ON THIS INTUITION THAT DEPENDS
ALL THE CERTAINTY AND EVIDENCE OF ALL OUR KNOWLEDGE; … this intuition is necessary in all the connexions of the intermediate ideas, without which we cannot
attain knowledge and certainty.


§2. II. Demonstrative.

The next degree of knowledge is, where the mind perceives the agreement
or disagreement of any ideas, but not immediately. …
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. …

 

§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.

 


§5. The demonstrated conclusion not without Doubt, precedent to the
demonstration.

… If the eyes have lost the faculty of seeing, or the mind of
perceiving, we in vain inquire after the quickness of sight in one, or
clearness of perception in the other.


§6. Not so clear as Intuitive Knowledge.

It is true, the perception produced by demonstration is also very clear;
yet it is often with a great abatement of that evident lustre and full
assurance that always accompany that which I call intuitive
: like a
face reflected by several mirrors one to another, where, as long as it
retains the similitude and agreement with the object, it produces a
knowledge; but it is still, in every successive reflection, with a
lessening of that perfect clearness and distinctness which is in the
first; till at last, after many removes, it has a great mixture of
dimness, and is not at first sight so knowable, especially to weak eyes.
Thus it is with knowledge made out by a long train of proof.

 

§15. Knowledge not always clear, where the Ideas that enter into it are
clear.

… [But ideas which, by
reason of their obscurity or otherwise, are confused, cannot produce any
clear or distinct knowledge; because, as far as any ideas are confused,
so far the mind cannot perceive clearly whether they agree or disagree.
Or to express the same thing in a way less apt to be misunderstood:
he that hath not determined ideas to the words he uses, cannot make
propositions of them of whose truth he can be certain.]


§7. Each Step in Demonstrated Knowledge must have Intuitive Evidence.

Now, in every step 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: if it
be perceived by itself, it is intuitive knowledge: if it cannot be
perceived by itself, there is need of some intervening idea, as a common
measure, to show their agreement or disagreement. By which it is plain,
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. So that to make
anything a demonstration, it is necessary to perceive the immediate
agreement of the intervening ideas, whereby the agreement or
disagreement of the two ideas under examination (whereof the one is
always the first, and the other the last in the account) is found.
This intuitive perception of the agreement or disagreement of the
intermediate ideas, in each step and progression of the demonstration,
must also be carried exactly in the mind,
and a man must be sure that no
part is left out: which, because in long deductions, and the use of
many proofs, the MEMORY does not always so readily and exactly retain;
therefore it comes to pass, that this is more imperfect than intuitive
knowledge, and men embrace often falsehood for demonstrations.


 

§30. Thirdly A third cause, Want of Tracing our ideas.

THIRDLY, Where we have adequate ideas, and where there is a certain and
discoverable connexion between them, yet we are often ignorant, for
want of tracing those ideas which we have or may have; and for want of
finding out those intermediate ideas, which may show us what habitude of
agreement or disagreement they have one with another. …. For whilst they stick in words of undetermined and uncertain
signification, they are unable to distinguish true from false, certain
from probable, consistent from inconsistent, in their own opinions.

Locke 1

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