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On the Improvement of Understanding, by Benedict de Spinoza, [1883], at


[19] (1) Reflection shows that all modes of perception or knowledge may be reduced to four:—I. (2) Perception arising from hearsay or from some sign which everyone may name as he please.

II. (3) Perception arising from mere experience—that is, form experience not yet classified by the intellect, and only so called because the given event has happened to take place, and we have no contradictory fact to set against it, so that it therefore remains unassailed in our minds.

III. (19:4) Perception arising when the essence of one thing is inferred from another thing, but not adequately; this comes when [f] from some effect we gather its cause, or when it is inferred from some general proposition that some property is always present.

IV. (5) Lastly, there is the perception arising when a thing is perceived solely through its essence, or through the knowledge of its proximate cause.

[20] (1) All these kinds of perception I will illustrate by examples. (2) By hearsay I know the day of my birth, my parentage, and other matters about which I have never felt any doubt. (3) By mere experience I know that I shall die, for this I can affirm from having seen that others like myself have died, though all did not live for the same period, or die by the same disease. (4) I know by mere experience that oil has the property of feeding fire, and water of extinguishing it. (5) In the same way I know that a dog is a barking animal, man a rational animal, and in fact nearly all the practical knowledge of life.

[21] (1) We deduce one thing from another as follows: when we clearly perceive that we feel a certain body and no other, we thence clearly infer that the mind is united [g] to the body, and that their union is the cause of the given sensation; but we cannot thence absolutely understand [h] the nature of the sensation and the union. (2) Or, after I have become acquainted with the nature of vision, and know that it has the property of making one and the same thing appear smaller when far off than when near, I can infer that the sun is larger than it appears, and can draw other conclusions of the same kind.

[22] (1) Lastly, a thing may be perceived solely through its essence; when, from the fact of knowing something, I know what it is to know that thing, or when, from knowing the essence of the mind, I know that it is united to the body. (2) By the same kind of knowledge we know that two and three make five, or that two lines each parallel to a third, are parallel to one another, &c. (3) The things which I have been able to know by this kind of knowledge are as yet very few.

[23] (1) In order that the whole matter may be put in a clearer light, I will make use of a single illustration as follows. (2) Three numbers are given—it is required to find a fourth, which shall be to the third as the second is to the first. (23:3) Tradesmen will at once tell us that they know what is required to find the fourth number, for they have not yet forgotten the rule which was given to them arbitrarily without proof by their masters; others construct a universal axiom from their experience with simple numbers, where the fourth number is self-evident, as in the case of 2, 4, 3, 6; here it is evident that if the second number be multiplied by the third, and the product divided by the first, the quotient is 6; when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional.

[24] (1) Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid's proposition, but intuitively, without going through any process.

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