ἑὰν δὲ προσποιούμενος ᾗ τὰ μαθήματά πως ἀπείρως προβάλλων, οὐκ ἔστιν αἰτίας ἔξω → But should one profess knowledge as he puts forward something in an inexperienced way, he is not without blame (Pappus 3.1.30.31f.)

[Sergey]

Pappus' Collection, Book III: doubting a standard translation of one sentence


Hello,

I'm trying to understand the opening philosophical/methodological remarks in Book III of the Collection of the geometer Pappus of Alexandria, and I suspect that the concluding sentence of these remarks could have been misunderstood in standard translations. It reads:

ἑὰν δὲ προσποιούμενος ᾗ τὰ μαθήματά πως ἀπείρως προβάλλων, οὐκ ἔστιν αἰτίας ἔξω.

Taking into account context and grammar, I suspect that this translates roughly as

"If however one somehow ineptly puts forward something claimed as a piece of knowledge, he is not without blame."

This is very different from three published translations of these opening remarks that I'm aware of, and they nearly agree with each other on this sentence. For example, the latest one reads

"But should he, at the same time, pretend to know something in mathematics and so to speak cast forward something in an inexperienced way, he is not without blame"

Now I don't see where in the Greek text they find anything like "to know" and "and"; conversely, nothing in their translations seems to correspond to the word ᾗ. If ᾗ were a verb (from εἰμί or ἵημι), then wouldn't it be in the infinitive? In any case, εἰμί and ἵημι don't seem to admit the meaning of "know".

Here is the full passage:



The translation above quoted is from

p.119 in A. Bernard, Sophistic Aspects of Pappus's Collection, Archive for History of Exact Sciences 57 (2003), 93-150

The other two translations are in

p.566 in Volume 2 of I. Thomas, Selections Illustrating the History of Greek Mathematics, Harvard Univ. Press, 1939;

p.170 in S. Cuomo, Pappus of Alexandria and the Mathematics of Late Antiquity, Cambridge University Press, 2000.

I would be very grateful if someone could either confirm my reading (or suggest a better one) or explain why Bernard, Thomas and Cuomo translated it the way they did. Thank you.

[billberg23]

Welcome to the Forum, Sergey!
The verb ᾗ can't be from ἵημι, because its initial phoneme is smooth breathing, not rough.  It is the present subjunctive, third person singular, of εἰμί (subjunctive to represent a general "if ever" condition).  It is used periphrastically with the present participle to represent a progressive action, so ἑὰν προσποιούμενος ᾗ τὰ μαθήματά means "if he be pretending (mathematical) knowledge," which your translators have paraphrased as "should he pretend to know something in mathematics."  The present participle προβάλλων means literally "putting forward," which your translators have rendered colloquially by converting it into an independent verbal construction "and puts forward."  You could also translate "as he puts forward," "when he puts forward," "since he puts forward," etc. 
Not that your translation is far off;  it's just that, in the Greek, the two actions "pretending knowledge" and "making some proposal" (πως προβάλλων) are gramatically separate and independent of each other.

[Sergey]

Thanks a lot, Billberg! This is what I was confused about, that the two actions must be gramatically separate, and one cannot be the object of another. I will take your word for that.

Then, from what you say, it seems that πως προβάλλων is not included in the conditional clause, and so instead of "and" it would be more accurate to say "as" or "when". This raises the issue whether τὰ μαθήματά refers to general proficiency in the field of mathematics or to a specific (mathematical) knowledge directly related to what is being put forward. Namely, if it is indeed a problem (πρόβλημα) that is being put forward, then this knowledge could be the knowledge of a solution of this problem. In this case, the sentence could be translated say as

"But should one profess knowledge as he ineptly puts forward something, he is not without blame."

This reading would not fit too well with the phrase in square brackets which the translators think is an interpolation by a scribe, but it would fit better with the rest of the passage, and especially with subsequent pages, where Pappus goes on to refute what he thinks is an incorrect solution to a certain problem. So could this new reading be correct?

[billberg23]

"But should one profess knowledge as he ineptly puts forward something, he is not without blame" seems a perfectly reasonable interpretation of the Greek.  By the way, I find yet another interpretation in the Loeb translation by Ivor Thomas, p. 567 ( https://archive.org/stream/L362GreekMathematicsIIFromAristarchusToPappus/L362-Greek%20Mathematics%20II%20From%20Aristarchus%20to%20Pappus#page/n581/mode/2up ):  "But when a man professing to know mathematics sets an investigation wrongly, he is not free from censure," which may also be in line with your thinking.  "To know mathematics" agrees with the sentence that follows, which you hadn't reproduced in your inquiry:  πρῴην γοῦν τινες τῶν τὰ μαθήματα προσποιουμένων εἰδέναι διὰ σοῦ τὰς τῶν προβλημάτων προτάσεις ἀμαθῶς ἡμῖν ὥρισαν ("At any rate, people professing to know mathematics through you recently presented us with the wrong formulations of some problems.")

[Sergey]

Thank you! As for τῶν τὰ μαθήματα προσποιουμένων εἰδέναι, it contains the additional verb εἰδέναι, in perfect infinitive, which was not in the previous sentence. So maybe something additional should also appear in the translation, if we want to preserve the precise linguistic connection between the two sentences? For example, one could write "But should one profess knowledge ... people professing to have learnt knowledge through you". Admittely, the second part sounds a bit awkward in this wording, but it seems tricky to shape it better while preserving the precise connection.

[billberg23]

"But should one profess knowledge ... people professing to have learnt knowledge through you". Admittely, the second part sounds a bit awkward in this wording, but it seems tricky to shape it better while preserving the precise connection.

Literally, εἰδέναι means "to have seen," not "to have learnt," and is to be translated into English as a simple present, "to know."  Cf. Liddell-Scott-Jones, Greek Lexicon, s.v. οἶδα (*είδω):
... pf., οἶδα, I see with the mind's eye, i.e. I know, used as pres. ... inf. εἰδέναι..
The same Lexicon lists "mathematical sciences" as a common meaning for τὰ μαθήματα, s.v. μάθημα:
.. esp. the mathematical sciences, Archyt.1,3 tit., etc. etc.
So I think we can feel perfectly comfortable translating τὰ μαθήματα εἰδέναι as "to know mathematics."

[Sergey]

OK, thanks! I agree that τῶν τὰ μαθήματα προσποιουμένων εἰδέναι refers to mathematics as a field of study. (Otherwise, this sentence would imply that the construction reviewed by Pappus was communicated to him not by a student of Pandrosion, but by someone who previosly got this very construction from Pandrosion herself. But this seems to be at odds with some later phrases, implying that the original author of the construction was a man, and that he has talked in person to Pappus about this construction.)

Still, I tend to think that in the previous sentence, προσποιούμενος ᾗ τὰ μαθήματά refers to a particular piece of mathematics rather than to mathematics as a subject. (Otherwise, I just fail to see the point of the entire discussion about problems versus theorems.) So it seems that the repeat of τὰ μαθήματά though in a slightly different meaning and with an additional verb was intended as a sort of pun, or irony. This seems to be preserved in this translation:

"But should one profess knowledge as he puts forward something in an inexperinced way, he is not without blame. At any rate, some who profess to know mathematics through you recently examined in an inexpert way the formulations of some problems."