Disputatio:Coniectura
De independentia
[fontem recensere]Ut fortasse vidistis, Lesgles, "independens axiomatum" est constructio anglica ("independent of the axioms"); nescio an "independens ex axiomatibus" melius sit. Et quam maxime consentio hanc rem paginam propriam merere -- etiamsi non inter 10,000 Paginas sit! A. Mahoney (disputatio) 22:25, 2 Decembris 2014 (UTC)
- Analogiam cogitabam "(de)pendere ex", e.g. Cic. "spes pendet ex fortuna", Sen. "ex horum (siderum) motibus fortunae populorum dependent". Nunc vero verbum "independens" in lingua antiqua non erat, sed si fuisset, fortasse hoc schema secutum esset. Lesgles (disputatio) 23:35, 3 Decembris 2014 (UTC)
- Fortasse igitur "non ex axiomatibus dependens". Andrew Dalby (disputatio) 14:56, 4 Decembris 2014 (UTC)
- Cassell's: 'free from' = vacuus abl. (nihil igni vacuum, Cic.), vel vacuus ab (ab his rebus, Cic.; vacuum oppidum ab defensoribus, Caes.). Also, liber abl. (omni metu, Liv.), vel liber ab (a delictis, Cic.), vel gen. (Verg., Hor.). But these may not be quite getting at the idea you want. Maybe you want an adverb (libere abl.), or maybe Latin would prefer some other idiom or syntactical structure altogether (e.g., axiomatibus carens). IacobusAmor (disputatio) 15:47, 4 Decembris 2014 (UTC)
- Certainly in places where Latin liber would work just as well, we should use that, but since this is a technical term (en:Independence (mathematical logic)), there might be less wiggle room. I just learned about it yesterday, though, so I don't know! Lesgles (disputatio) 17:33, 4 Decembris 2014 (UTC)
- No way "vacuus axiomatibus" or "axiomatibus carens" conveys the right meaning. That would be "something that doesn't have axioms," which is impossible in mathematics. What "independent of the axioms" means is that a given statement is consistent with the axioms, and so is its opposite -- neither the statement nor the opposite follows from the axioms. The example from geometry, in the article, is the easiest one I know to explain to non-mathematicians. Suppose you have a point p and a line l, and suppose you're in a world where all Euclid's other axioms are true (technically, a model of those axioms; I've called this exemplar elsewhere in VP). In this world, maybe Euclid's parallel postulate is also true -- so there is exactly one line l2 through point p and parallel to line l. Or maybe Euclid's rule isn't true, but instead there are no lines through p that don't meet l -- this would be the case on a sphere, where the lines are the great circles, and those always meet each other. Or maybe neither of these is true, but there are lots of lines through p that don't meet l -- this would be the case if your world is shaped like the bell of a trumpet. Given that you can make a model of the axioms of geometry in which Euclid's parallel postulate is true, and another one in which it's false, we say the parallel postulate is independent of the axioms. That's much stronger than saying that it can't be proven (by Gödel's incompleteness theorem).
- As for how to express this in Latin, I agree that my original English calque doesn't work, and I note (with some surprise) that I don't actually find independens in the PHI corpus, though it's not rare in Vicipaedia! So I'll edit. A. Mahoney (disputatio) 20:05, 4 Decembris 2014 (UTC)
- It's absent from Ainsworth's, L&S, White's, Cassell's, and Traupman. Merriam-Webster says independent is first known in English only in 1611, somewhat late for a descendant of a genuinely classical term to have entered the English vocabulary. What would independens mean to Cicero? 'not down-hanging'?! Perhaps a Vicipaedian squad should go on a search-and-destroy mission! IacobusAmor (disputatio) 22:50, 4 Decembris 2014 (UTC)
- Verecunde — nam scio me rerum mathematicarum imperitum esse — hanc propono dictionem: "Coniectura aliqua potest esse nec vera, nec falsa, sed in axiomatibus non posita" (vel fortasse "Coniectura aliqua potest esse nec vera, nec falsa, neque in axiomatibus posita.") (???) Neander (disputatio) 06:22, 5 Decembris 2014 (UTC)
- It's absent from Ainsworth's, L&S, White's, Cassell's, and Traupman. Merriam-Webster says independent is first known in English only in 1611, somewhat late for a descendant of a genuinely classical term to have entered the English vocabulary. What would independens mean to Cicero? 'not down-hanging'?! Perhaps a Vicipaedian squad should go on a search-and-destroy mission! IacobusAmor (disputatio) 22:50, 4 Decembris 2014 (UTC)
- Certainly in places where Latin liber would work just as well, we should use that, but since this is a technical term (en:Independence (mathematical logic)), there might be less wiggle room. I just learned about it yesterday, though, so I don't know! Lesgles (disputatio) 17:33, 4 Decembris 2014 (UTC)
- Cassell's: 'free from' = vacuus abl. (nihil igni vacuum, Cic.), vel vacuus ab (ab his rebus, Cic.; vacuum oppidum ab defensoribus, Caes.). Also, liber abl. (omni metu, Liv.), vel liber ab (a delictis, Cic.), vel gen. (Verg., Hor.). But these may not be quite getting at the idea you want. Maybe you want an adverb (libere abl.), or maybe Latin would prefer some other idiom or syntactical structure altogether (e.g., axiomatibus carens). IacobusAmor (disputatio) 15:47, 4 Decembris 2014 (UTC)
- Fortasse igitur "non ex axiomatibus dependens". Andrew Dalby (disputatio) 14:56, 4 Decembris 2014 (UTC)
De verbo "independens"
[fontem recensere]Verbum Anglicum fortasse e Francogallico mutuatum est, de quo Dictionnaire historique (Rey) haec dicit s.v. dépendre: "L'adjectif, l'adverbe et le nom ont suscité des antonymes ... indépendant (1584) ..." Sublineavi ego. Vicipaedianus/a supra (prima A.Mahoney?) participium verbi activi finxit, id quod difficile est conceptu. Aegre possumus independere. Sed adiectivum "independens" substantivumque "independentia" apud scriptores Latinos recentiores crebriter reperiuntur, illud ab anno 1656, hoc ab 1741, fortasse antea.
Quomodo Cicero de his vocabulis iudicaturus sit, nescio, sed ego in re politica accipio. De usu mathematico nihil dico, quod mathematicus non sum :) Andrew Dalby (disputatio) 10:07, 5 Decembris 2014 (UTC)
- Verbum etiam invenio apud Rodericum de Arriga, anno 1632: hic "independentem" vidimus
- Apud Cartesium quoque, etiamsi sensu theologico tantum, ut videtur: hic in Vicifonte francogallica
- Non est in Thesauro Linguae Latinae.
- Quod notio mathematica recentior est, verbum proprium latinum invenire non exspecto. Nec Cartesius nec Gauss, qui ambo de rebus mathematicis latine scripserunt, de axiomatibus cogitabant ceu nunc facimus. Sciverunt utrum propositio quaedam ex axiomatibus demonstranda sit, sed propositio si non demonstratur, secundum tales mathematicos, vel est falsa vel demonstrationem habet difficiliorem et nondum inventam. Saeculo 20 tantum mathematici talia propositiones et axiomata invenerunt, qualia hic describimus. Alii mathematici, ergo, verbum latinum nobis non praebent. Id "independens" (quod confiteor verbum post Ciceronis aetatum factum) simile est verbis aliarum linguarum (lectores igitur intellegent); "non ab axiomatibus pendens" fortasse rectius dicitur sed, ut dicit Andrew supra, "in-dependens" (et non "im-pendens," quod hoc verbum alium sensum habet) fit verbum oppositum. (Mathematica olim fui et hac in parte laboravi.)
- Verbum activum "independere" autem non video, nec finxi; adiectivo vel participio usa sum. A. Mahoney (disputatio) 14:14, 5 Decembris 2014 (UTC)
- Bene, bene. Meo iudicio verbis "independens, independentia" interdum uti necesse est. Andrew Dalby (disputatio) 19:59, 5 Decembris 2014 (UTC)