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Headword: Apodeixis
Adler number: alpha,3289
Translated headword: demonstration
Vetting Status: high
Demonstration differs from definition.[1] First, we have to investigate definition, whether it is either one method in virtue of which the definitions of all existing things can be offered, or many. And if [it is] one, which one; but if many, how many in number and what kinds. And when by means of a description or a definition we discover so many and such things, another investigation again appears to us: which methods we have to make use of with regard to which objects. And when we discover this, since definition is by genera and differentiae, [we have to establish] which the genus of the object that is set before is and which the differentiae are, in order that we can offer its definition while combining the coherent differentiae by genus. There is another difficulty too. For in whatever something is present primarily, this also belongs to it by itself. And [the expression] "by itself" means "what is according to substance".[2] But it is not the case that if something is present by itself, this also is present in a primary way. For animal belongs by itself to man, although not in a primary sense. Therefore, even though there is no man, there is animal, so animal belongs to man not in a primary sense. Similarly figure also [belongs] by itself to triangle, although not primarily. But a demonstration in the strict sense arises from what belongs to [something] by itself and in a primary sense. And without qualification,[a demonstration is what] confirms the caused effects out of causes and the particulars out of the universals. And [a demonstration] confirming causes out of caused effects is called "conclusive proof";[3] for instance, to show that the moon is spherical from of its illumination. For if it were shown that it is illuminated in this manner because it is spherical, that would be a demonstration in the strict sense. For what is caused would be shown out of a cause. But we have not made use of this mode of proof in this case, because what is caused is clearer to us than the cause. A conclusive demonstration is also to discover and understand that there is fire because there is smoke.[4] And if what is caused absolutely follows the cause, this is called "conclusive proof"; and a conclusive proof is an irrefutable sign.[5] But if [what is caused] did not absolutely follow [the cause], it would be called a sign but not a conclusive proof, because [in that case] it is not irrefutable, such as it happens in the case [of a woman] who is pale because she has given birth to a child. For having given birth to a child is not absolutely concomitant with paleness.[6] A demonstration is a deductive method through deductive arguments,[7] and it exists when a deductive argument arises from true and primary premises.
Greek Original:
Apodeixis: apodeixis horou diapherei. dei prôton zêtêsai peri horou, ara mia esti methodos, kath' hên pantôn tôn ontôn dunaton tous horous apodounai, ê pollai. kai ei mia, tis hautê: ei de pollai, posai ton arithmon kai poiai. kai hotan heurômen, tosaide kai toiaide, hupographêi ê horismôi, allê palin hêmas diadechetai zêtêsis, poiais tôn methodôn epi poiôn pragmatôn chrêsteon. kai hotan heurômen touto, epeidê ho horismos ek genôn esti kai diaphorôn, ti tou prokeimenou pragmatos to genos kai tines hai diaphorai, hina sumplexantes tas sustatikas diaphoras tôi genei, apodômen autou ton horismon. esti de kai hetera chalepotês. hôitini gar prôtôs ti enuparchei, touto kai kath' hauto huparchei. kath' hauto de esti to kat' ousian. ouketi de kai ei ti kath' hauto huparchei, touto kai prôtôs huparchei. to gar zôion tôi anthrôpôi kath' hauto men huparchei, ou prôtôs de: dio kan mê êi anthrôpos, zôion estin, hôste ou prôtôs tôi anthrôpôi to zôion huparchei. homoiôs de kai to schêma tôi trigônôi kath' hauto men, ou mentoi prôtôs. hê de kuriôs apodeixis ek tôn kath' hauto kai prôtôs huparchontôn ginetai. kai haplôs, hê ek tôn aitiôn ta aitiata pistoumenê kai ek tôn katholou ta merikôtera. hê de ek tôn aitiatôn ta aitia pistoumenê tekmêriôdês apodeixis legetai: hoion to deixai ek tôn phôtismôn tês selênês hoti sphairikê. ei gar edeiknuto, dioti sphairikê, dia touto phôtizesthai houtôs, touto an eiê kuriôs apodeixis. ek gar tou aitiou to aitiaton edeiknut' an. ou kechrêmetha de entautha têi deixei tautêi, dioti to aitiaton pros hêmas saphesteron esti tou aitiou. tekmêriôdês de apodeixis kai to ek tou kapnou to pur heurein kai katanoêsai. kai an men pantôs hepêtai to aitiaton tôi aitiôi, tekmêrion touto legetai. tekmêrion de esti to aluton sêmeion. an de mê pantôs hepoito, sêmeion men an legoito, tekmêrion de ouketi, dioti mêde aluton esti: hoion hôs to, ôchra estin, epeidê tetoken: ou pantôs gar têi ôchrotêti parakolouthei to tetokenai. apodeixis esti methodos dia sullogismôn sullogistikê, hotan ex alêthôn kai prôtôn ho sullogismos ginêtai.
This entry draws largely on Philoponus, Commentary on Aristotle's de anima (28.7-18, 29.23-28, 20.12-13 and 20-26, 31.15-20 Hayduck), with a final sentence from Alexander of Aphrodisias, Commentaries on Aristotle's Topica 2.22-23.
cf. omicron 627.
[1] A demonstration is, in fact, a certain type of syllogism, for a deductive argument (or "syllogism") is a demonstration when the premises from which the deduction starts are true and primary, or are such that our knowledge of them has originally come through premises which are primary and true (see Topica 100a27-29). In more technical contexts Aristotle distinguishes o(/ros from o(rismo/s, the former meaning "term" and the latter "definition". In the present case both words are used indiscriminately, something more or less usual in Aristotle himself. For the Aristotelian definition by proximate genus and specific differentia, see Metaphysics 1037b25-1038a35 and Topica 103b14-19.
[2] As usual, the word ou)si/a is hard to render. In this context it probably means "essence", so the expression to\ kat' ou)si/an should be rendered "the essential". In the Suda example, animal belongs "by itself" (which, in accordance with the previous distinction, is the same as "essentially") to man.
[3] tekmh/rion and shmei=on are Aristotle's technical terms. A tekmh/rion is characterized as being "a necessary or always existing sign" or "a necessary sign" (Rhetoric 1357b4ff.). When people think it is impossible to refute an argument, they think they are offering a tekmh/rion, as though the matter at issue were shown and concluded (Rhetoric 1357b5-10). On the other hand, according to Aristotle, a shmei=on (sign) is meant to be a demonstrative proposition (pro/tasis a)podeiktikh/), either necessary or reputable; for anything such that when it is another thing is, or when it has come into being the other has come into being before or after, is a sign of the other's being or having coming into to being (An.Pr. 70a6-9; Oxford Translation). That is to say, given two propositions (p, q) indicating two events, p is said to be a sign of q if and only if p's verification implies q's verification. The fact that a sign is included within the domain of what "is reputable" or within the domain of "common beliefs" (e)/ndoca) shows that a sign, insofar as it is refutable, is fallible. For instance, if someone were to state that since Socrates was wise and just, it is a sign that the wise are just. Although this is a sign, it is refutable (the example is Aristotle's; Rhetoric 1357b12-14). So a sign differs from a tekmh/rion, because the former is a fallible type of demonstration while the latter is not. From the reasons offered above, a plausible translation of tekmh/rion is "conclusive proof". For further discussion on this issue see Mignucci 1969, 722.
[4] These lines are literally reproduced in tau 245, and the example is probably taken from Sextus Empiricus, Pyrrhoniae hypotyposes 2.100. The case of fire and smoke is an example of what Sextus calls "recollective sign", i.e. the one that "having been observed evidently together with the thing it signifies, at the same time as it makes an impression on us [...] it leads us to recall the thing which has been observed together with it and is not now making an evident impression on us, as in the case of smoke and fire" (Translation Barnes and Annas; see also Sextus, Adversis mathematicos 8.157). In the example, of course, smoke is the "recollective sign" of the presence of fire.
[5] This is, once more, Aristotle's position (see Rhetoric 1357b16-17, 1403a13-15.
[6] The example is taken from Aristotle, An.Pr. 70a13-16; 20-24; 35-38. The account offered by Aristotle is the following: the proof that a woman is pregnant because she is pale is meant to come through the middle figure. For since paleness follows pregnant women and is a concomitant of this woman, people suppose it has been proved that she is pregnant (An.Pr. 70a20-23).
[7] That is to say "syllogisms" (sullogismoi/; see here note 1). On the scholarly controversy with regard to the relation between demonstration and syllogistic, see Barnes (1994) xv-xviii.
Barnes, J., Aristotle: Posterior Analytics (Translated with a Commentary by Jonathan Barnes) (Oxford: Clarendon Press 1994)
Mignucci, M., Aristotele. Gli analitici primi (Traduzione, introduzione e commento di Mario Mignucci) (Napoli: Loffredo 1969)
Keywords: definition; philosophy; rhetoric; women; zoology
Translated by: Marcelo Boeri on 9 June 2001@10:51:35.
Vetted by:
David Whitehead (added note; extensive cosmetics) on 20 August 2002@07:55:21.
Marcelo Boeri (Corrected note.) on 20 November 2002@06:04:24.
Marcelo Boeri on 20 November 2002@06:08:02.
David Whitehead (more keywords; cosmetics) on 2 April 2012@04:52:38.
David Whitehead (another x-ref) on 24 January 2014@05:57:34.
David Whitehead (coding) on 27 August 2015@10:47:48.
Catharine Roth (cosmetics) on 16 September 2015@19:54:55.
Catharine Roth (tweaked translation) on 17 September 2015@00:49:21.
Catharine Roth (more tweaks) on 19 September 2015@23:39:06.


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