I was reading Aristotle's Metaphysics, and I'm stumped on this passage:

Yet the acquisition of it [wisdom, knowledge of first causes and principles] must in a sense end in something which is the opposite of our original inquiries. For all men begin, as we said, by wondering that things are as they are, as they do about self-moving marionettes, or about the solstices or the incommensurability of the diagonal of a square with the side; for it seems wonderful to all who have not yet seen the reason, that there is a thing which cannot be measured even by the smallest unit. But we must end in the contrary and, according to the proverb, the better state, as is the case in these instances too when men learn the cause; for there is nothing which would surprise a geometer so much as if the diagonal turned out to be commensurable.

It's the last paragraph of Part 2 in Book I.

Translation from this link: http://classics.mit.edu/Aristotle/metaphysics.1.i.html

Earlier on, he mentioned that men begin to search for such knowledge out of wonder and puzzlement. Is he saying that the end of the "original inquiries" ends in certainty, which would be the opposite of puzzlement?

  • Another answer to your question on Aristotle's 'Metaphysics'.
    – Geoffrey Thomas
    Jan 6, 2018 at 21:40

3 Answers 3


Go to Thomas! He's the great commentator on Aristotle. Here's what he says on that passage (Sententia Metaphysicæ lib. 1 l. 3 n. 66-68):

  1. But it is necessary (33).

    He [Aristotle] now gives the goal toward which this science moves. He says that its progression comes to rest, or is terminated, in the contrary of what was previously found in those who first sought this science, as also happens in the case of natural generations and motions. For each motion is terminated in the contrary of that from which the motion begins. Hence, since investigation is a kind of movement towards knowledge, it must be terminated in the contrary of that from which it begins. But, as was stated above (53), the investigation of this science began with man’s wonder about all things, because the first philosophers wondered about less important matters and subsequent philosophers about more hidden ones. And the object of their wonder was whether the case was like that of strange chance occurrences, i.e., things which seem to happen mysteriously by chance. For things which happen as if by themselves are called chance occurrences. For men wonder most of all when things happen by chance in this way, supposing that they were foreseen or determined by some cause. For chance occurrences are not determined by a cause, and wonder results from ignorance of a cause. Therefore when men were not yet able to recognize the causes of things, they wondered about all things as if they were chance occurrences; just as they wondered about changes in the course of the sun, which are two in number, namely, the solstices, that of winter and that of summer. For at the summer solstice the sun begins to decline toward the south, after previously declining toward the north. But at the winter solstice the opposite occurs. And they wondered also that the diagonal of a square is not commensurable with a side. For since to be immeasurable seems to belong to the indivisible alone (just as unity alone is what is not measured by number but itself measures all numbers), it seems to be a matter of wonder that something which is not indivisible is immeasurable, and consequently that what is not a smallest part is immeasurable. Now it is evident that the diagonal of a square and its side are neither indivisible nor smallest parts. Hence it seems a matter of wonder if they are not commensurable.

  2. Therefore, since philosophical investigation began with wonder, it must end in or arrive at the contrary of this, and this is to advance to the worthier view, as the common proverb agrees, which states that one must always advance to the better. For what that opposite and worthier view is, is evident in the case of the above wonders, because when men have already learned the causes of these things they do not wonder. Thus the geometrician does not wonder if the diagonal is incommensurable with a side. For he knows the reason for this, namely, that the proportion of the square of the diagonal to the square of a side is not as the proportion of the square of a number to the square of a number [d²/s²≠a²/b², where s,a,b ∈ ℕ], but as the proportion of two to one [d²/s²=2/1, assuming s=1]. Hence it follows that the proportion of a side to the diagonal is not as the proportion of number to number [s/d≠c/e, where c,e ∈ ℕ]. And from this it is evident that they cannot be made commensurable. For only those lines are commensurable which are proportioned to each other as number to number [i.e., s/d=c/e]. Hence the goal of this science to which we should advance will be that in knowing the causes of things we do not wonder about their effects.

  3. From what has been said, then, it is evident what the nature of this science is, namely, that it is speculative and free, and that it is not a human possession but a divine one; and also what its aim is, for which the whole inquiry, method, and art must be conducted. For its goal is the first and universal causes of things, about which it also makes investigations and establishes the truth. And by reason of the knowledge of these it reaches this goal, namely, that there should be no wonder because the causes of things are known.


I think that A is pointing at the principle that real causes are often different from appearences.

The search for wisdom moves from what we see or think beeing obvious and asking for reason or causes ("wondering that things are as they are").

He uses the geometrical example (the wonderful discovery by greek mathematicians of the incommensurability of diagonal and side of the square) to show that, against the "common sense" of lay people assuming that all lenghts are "measurable" (in greek sense : with integer numbers) the experienced geometer knows that it is not so.

He has achieved wisdom because he has found the proof (the reason why) of the incommensurabilty of the two lenghts.


You are using Sir David Ross' translation, which some of us find harder to make out than the Greek original. Hugh Lawson Tancred's Penguin translation is more helpful, not least in its insertion of commentaries on the chapters. But this bit of Aristotle looks exceptionally knotty. In fact as Geremia suggests, Aquinas has the root of it.

Philosophy begins in wonder. The 'contrary' state at which metaphysics aims (and will deliver if achieved) is one of understanding the ultimate causes and principles of things. Given this understanding, whatever it may be, which of course Aristotle has not yet told us, the matters which puzzle the person now caught in wonder will be as clear of day. To the person who has achieved the clarity of metaphysical knowledge the puzzlement of the original inquirer will itself be as puzzling as that original puzzlement itself was. Once we know we do not wonder why things are so; the wonder would be if they were otherwise. The state of mind of the geometer is a parallel illustration. The geometer once puzzled over the the relations of the lines of a right-angled triangle to one another. When the Pythagorean theory had been proved, it was obvious that in any right-angled triangle the sum of the squares of the sides of the right angle equals the square of the hypotenuse - that there is this commensurability. The geometer, at first baffled how any systematic relation could hold and baffled by what it might be, would now be baffled (would be in a state of painful wonder) if the precise commensurability s/he had discovered did NOT hold.

This help ?

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