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The question Translation: that which was to have been made deals with grammatical aspects of the expression quod erat demonstrandum, but I am interested in a detailed break-down of the meaning attributed to each word. Generally this is translated as which was (necessary) to be demonstrated, but how is this meaning broken down according to each of the three individual words? More specifically, is the "necessity" aspect inherent in the gerundive "demonstrandum" or in "erat" ? Since "erat" is just past tense of "to be", it seems likely that the meaning of "necessity", if any, would be in the gerundive. Do gerundives generally carry such a connotation of necessity?

Mikhail Katz
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  • Of the European languages, its a problem in Englisch, Dutch and Low German, reduced set of constructions. But substantivation of whole phrases are now common at least in modern American (Bloomberg) English. In German it simply translates into "What was the to be made visible". Funnily, it is a religous fomula, to make the monster visible down here. In a sense, the Romans, like many ancient and some modern philologists, thought about (Greek) mathemata as a form of black magic. – Roland F Nov 21 '23 at 12:20

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Yes. In Quod erat demonstrandum the sense of necessity can be attributed completely to the gerundive. As in our case, often the gerundive is coupled with the verb esse (to be) - most famously in Censeo Carthaginem esse delendam ("I think Carthage must be destroyed").

However, the gerundive can bear a similar sense of necessity without being coupled with the verb esse, as it can be used adjectively.

So it seems that saying that the "necessity" aspect is inherent in the gerundive is a fair statement - and that usage is general indeed. This does not mean, however, that a gerundive forces a necessity as there are some other constructions in Latin where gerundive do not necessarily bear the "necessity" sense.

As for the word-breakdown. Quod=what, erat=was, demostrandum=to be demonstrated.

d_e
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  • Thanks! That's very helpful. You write that other gerundives "do not necessarily bear the 'necessity' sense." I am specifically interested in a comment by Leibniz where the gerundive "Aliter" is used. Leibniz writes: "Aliter demonstrandum quod neque majus quia non potest inveniri pars ejus finita aequalis." et cetera. Would one expect "Aliter" to have the "necessity" sense here? – Mikhail Katz Nov 21 '23 at 13:09
  • @MikhailKatz, Not sure I get what it means the adverb ""Aliter" to have the "necessity" sense here?. Do you ask if "Aliter demostrandum" means "it must be shows in another way?" Also note that "demostrandum" here is probably not gerundive but rather gerund (though still bears the necessary sense); My remark was about constructions where gerundive can use to signal "purpose", and not such as given by this Leibniz quote. You might try post here another question about this specific quote. – d_e Nov 21 '23 at 13:58
  • Yes, sorry, I was referring to "Aliter demonstrandum". – Mikhail Katz Nov 21 '23 at 14:01
  • @MikhailKatz, I can't find this quote in context in GoogleBooks. At any case, this is basically another question about a particular quote and hence I suggest to be dealt in a new question here. – d_e Nov 21 '23 at 14:10
  • I included such details in https://latin.stackexchange.com/q/21884/13902 – Mikhail Katz Nov 21 '23 at 14:13
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    Your initial statement "In Quod erat demonstrandum the sense of necessity can be attributed completely to the gerundive" is not evident. I'd rather say that this meaning is a property of the construction esse +gerundive and related ones rather than a property of the verbal adjective. See also Danesi et al (2017: 148) for a similar view: "The locus of deontic modality is not attributable to any specific lexical item or category found in the construction, but rather must be attributed to the construction as a whole. That is, the GER+(NOM+)DAT construction is semantically non-compositional". – Mitomino Nov 21 '23 at 16:24
  • Here is the relevant link to Danesi et al. (2017) paper: https://www.researchgate.net/publication/320958533_Between_the_Historical_Languages_and_the_Reconstructed_Language_An_Alternative_Approach_to_the_Gerundive_Dative_of_Agent_Construction_in_Indo-European – Mitomino Nov 21 '23 at 16:25
  • @Mitomino, I've included example (but then removed it from my answer) from Ovid : cura fuit partes velare tegendas there you have velare partes tegendas (partes cannot be in the subject because then we would expect the passive velari). there is no esse here – d_e Nov 21 '23 at 16:30
  • As pointed out by Pinkster (2015: 288-290; 298-305) and Danesi et al. (2017), i.a., the deontic value cannot be assigned to the gerundive. Otherwise, one won't be able to explain why ars carminis cantandi and many other examples with gerundives lack this meaning. Pinkster does not attribute this meaning to the gerundive but to contextual factors: this meaning can be attributed to esse +gerundive AND related constructions (see my qualification above!) like the attributive one without esse (see Pinkster (2015: 289) for examples of attributive use of gerundives with deontic meaning). – Mitomino Nov 21 '23 at 16:52
  • @Mitomino, thanks for the references, However I'm not linguistic and hence are difficult for me. Feel free to edit my answer or post a new one. I've shown two constructions with gerundives that show the "necessity" lies in the gerundive and not with esse. Now you seem to say there are other construction with the gerundive without "necessity" and that points that the "necessity" is born of the construction. I've distinctively implied that in my my answer that the gerundive is "a must" but not enough by saying that " This does not mean, however, that a gerundive forces a necessity" – d_e Nov 21 '23 at 17:06
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    @Mitomino, I created a relevant question to our discussion: – d_e Nov 21 '23 at 17:52
  • I've realized that you included a link to an interesting question about when gerundives are "used adjectively", i.e. attributively (I also included an answer to it). This set is not productive and, importantly for our present purposes, the gerundive demonstrandum would not be included in it. Following Pinkster (2015), it makes sense to attribute the deontic value of the example at issue here to contextual factors (cf. also his ex. mihi cautio est ne nucifrangibula excussit ex malis meis ‘I have to be careful that he doesn’t knock my nutcrackers out of my jaws.’ (Plaut. Bac. 597–8) – Mitomino Nov 21 '23 at 18:17
  • @Mitomino, thanks for your comments on necessity. Perhaps you would have some insight on this related question: https://latin.stackexchange.com/q/21884/13902 – Mikhail Katz Nov 22 '23 at 14:06
  • Gerundives in an attributive position don't necessarily denote necessity, so I don't think the pronounced statement is right. However, gerundives + esse do denote some type of obligation. Woodcock goes into more details and has more examples, but essentially castris capiendis is equal in force to castra capiendo, with capiendo being the gerund. No necessity necessary. – cmw Dec 01 '23 at 00:37
  • @Mitomino Does Pinkster at all comment on the confusion between gerunds and gerundives, which historically came from two separate sources? – cmw Dec 01 '23 at 00:38
  • Edit: Oh, you probably did already see this thread, right? – cmw Dec 01 '23 at 00:39
  • @cmw Pinkster (2015: 64) says the following: "There is much discussion about the relationship between the gerund and the gerundive and about which of the two was the oldest form (see also Section 5.42). They are both found from the earliest preserved texts onwards, in varying frequency. In speculations about their prehistorical development some scholars take the gerundive as the original form, others the gerund. On the whole, the latter position seems stronger." Unfortunately, Pinkster (2015) neglects Miller's (2000) important contribution: https://benjamins.com/catalog/dia.17.2.03mil – Mitomino Dec 01 '23 at 21:20
  • Bookmarking that for later. Thanks. – cmw Dec 01 '23 at 21:42