We should seek what we can clearly intuit or deduce with certainty

We should seek not:

• what others have thought or
• what we ourselves have accepted

We should seek what we can clearly intuit or deduce with certainty.

Knowledge is acquired in no other way. Ancient books must be read, for it is a great benefit to us that we can benefit from the labors of so many people; both so that we might know those things which were rightly discovered long ago, and also so that we might be reminded what further things must be thought out in all disciplines.

However, it is very dangerous in the meantime lest perhaps the stain of errors, contracted by their too attentive reading, adhere to us no matter how unwilling and careful we may be.

Authors are inclined to this kind of thing, that, whenever they have fallen into the danger of hasty belief regarding some disputed opinion, they always try to draw us back to the same place with the most subtle arguments.

On the other hand, however, whenever they have discovered something certain and evident with success, they never present it except wrapped up in various circumlocutions, fearing indeed that the dignity of what was discovered by the simplicity of reason might be diminished, or because they envy us the clear truth.

But now, however candid and open-minded all may be, and not one ever thrust any doubt on us as true, but exhibit all things in good faith, nevertheless, since hardly anything has ever been said by one on which the contrary has not been asserted by someone else, we would always be uncertain as to whom to believe.

It would be of no avail to count votes so that we might follow the opinion which has more authors; for, if it is a difficult question, it is more credible that its truth could have been found by a few than by many. But even if all should agree among themselves, their teaching would not be sufficient; for we shall never become mathematicians, for example, though we should retain the demonstrations of all others in memory, unless we are also fitted by nature for the resolving of whatever problems may be set; nor shall we be philosophers, if we have read all the arguments of Plato and Aristotle, but cannot form a stable judgment about the matters proposed; for thus we should seem not to have learned sciences, but histories.

Furthermore, we are warned that no conjectures are ever to be mixed with our judgments concerning the truth of things. The observation of this matter is of no small importance; for there is no better reason why nothing is now found in vulgar philosophy so evident and certain that it cannot be called into question than because first the studious, not content with recognizing clear and certain things, have dared to assert even the obscure and unknown by probable conjectures; which they gradually afterward having placed full faith in, and confusing them without distinction with true and evident things, at length could conclude nothing which did not seem to depend on some such proposition, and so that which was not uncertain.

But lest we slip into the same error in the future, here are reviewed all the actions of our intellect by which we can arrive at knowledge of things without any fear of deception: only two are admitted, namely, intuition and induction.

By intuition, I understand not the wavering belief of the senses or the fallacious judgment of an ill-constructed imagination, but the easy and distinct concept of a pure and attentive mind, so that no doubt at all remains concerning what we understand; or, what is the same thing, the concept of a pure and attentive mind, not doubtful, which is born from the light of reason alone and is more certain by its own deduction, because simpler, although we have already noted that it cannot be done ill by man. Thus everyone in mind can contemplate that he exists, thinks, terminates a triangle with only three lines, a globe with only one surface, and similar things, which are much more than most people observe, because they refuse to turn their minds to so easy things.

Moreover, in case someone is moved by the novelty of the use of the word intuition and other things that I am about to be obliged to remove from the common signification in the following, I generally remind myself that I do not think at all how those words were used in the latest times in the schools, because it would be very difficult to use the same names, and to have a totally different meaning; but I only note what the individual words mean in Latin, so that, when my own are lacking, I can transfer those that seem most suitable to me.

But, indeed, this evidence and certainty of intuition do not require a method for singular enunciations alone, but also for any discourses. For example, let this be a consequence: 2 and 2 make the same thing as 3 and 1; not only must 2 and 2 be perceived to make 4, and also 3 and 1 make 4, but, moreover, from these two propositions the third necessarily follows.

Therefore, doubt can arise, why, besides intuition, another method is joined here, which is made by deduction: by which we understand that everything that is necessarily concluded from certain other things known, is.

But this had to be done, because many things are certainly known, although they are not themselves evident, provided only that they are deduced from the continuous and nowhere interrupted motion of thought of the plainest and most attentive man; nor otherwise than, if we know the end annular extremity of some long chain and the first connection of it with the same, we have contemplated all the intervening, which depend on that connection, only successively, and remember that they adhere to the next from the first to the last.

Here, therefore, we distinguish the intuition of the mind from a certain deduction, from this, that in this motion, or in that the series, as if it were a succession, is conceived; and, moreover, because the present evident necessity, which is by no means necessary, such as in the intuition, but rather from the memory it borrows its certainty somehow.

From which it is concluded that those propositions are to be said, which from the first principles are immediately concluded, under a different consideration, now by intuition, now by deduction; and the first principles themselves, only by intuition; and against remote conclusions, only by deduction.

And these two roads are to be admitted as to the most certain knowledge of things, nor on the part of genius are more to be admitted, but all other suspicions and errors are to be cast away; which yet does not prevent that the things, which have been divinely revealed, the more certain knowledge of all these, with what may be of obscure things, may be believed; for their faith, in whatever they are obscure, is not the action of the mind, but the will; and if in the understanding there are any foundations, they can be found and must be found by one of these ways, as we may show, perhaps, more fully.