Authors/Ockham/Summa Logicae/Book III-2/Chapter 31

Latin	English
CAP. 31. QUOD DEFINITIO NON POTEST A PRIORI DEMONSTRARI DE DEFINITO.	Chapter 31. That a definition cannot be demonstrated of the defined from what is prior
ƿ Ex praedictis patere potest quod definitio non potest a priori demonstrari de specie definita. Definitio enim de nullo potest prius et notius praedicari quam de definito, et per consequens per nullum medium potest demonstrari de definito a priori. Nec etiam potest talis definitio demonstrari a posteriori de specie qui sit conceptus mentis simplex et proprius praecise significatus per speciem, quia quamvis una pars talis definitionis esset demonstrabilis a posteriori de subiecto, tamen alia pars non est demonstrabilis de tali subiecto, nec a priori nec a posteriori. Verumtamen de subiecto, quale nos habemus de facto, non est forte inconveniens definitionem posse demonstrari, saltem large accipiendo demonstrationem. Et per istum varium modum probandi definitionem de definito et varium modum demonstrandi possunt exponi multae auctoritates Aristotelis, quae videntur tam inter se quam praedictis repugnare. Quandoque enim loquitur de uno modo demonstrandi, quandoque de alio; et similiter, quandoque loquitur de praedicatione definitionis de definito simplici et proprio, quandoque de praedicatione definitionis de definito composito, proprio tamen. Est igitur duplex modus deveniendi in talem definitionem.	From what has been said it is clear that a definition cannot be shown a priori of a defined species. For a definition can be predicated of nothing before and better known than of what is defined, and consequently by no means can it be demonstrated of what is defined a priori. Nor can such a definition be demonstrated a posteriori from a species which is a simple and proper concept of the mind precisely signified by the species, because although one part of such a definition is demonstrable a posteriori from the subject, yet another part is not demonstrable from such a subject, neither a priori nor a posteriori. Nevertheless, of a subject such as we have in fact, it is not perhaps inconvenient that a definition can be demonstrated, at least by taking demonstration broadly. And by means of this various method of proving the definition of the definite, and of demonstrating the various methods of demonstration, many of Aristotle's statements may be explained, which seem to contradict each other as well as the aforesaid. For sometimes he speaks of one mode of demonstration, sometimes of another; and likewise, sometimes he speaks of the predication of a definition of a simple and proper definite, sometimes of the predication of a definition of a compound definite, yet proper. There is therefore a twofold way of arriving at such a definition.
Unus est per notitiam intuitivam partium rei. Qui enim intuitive cognosceret partes rei, statim posset formare conceptus demonstrabiles, importantes illas partes in obliquo et importantes totum in recto.	One is through intuitive knowledge of the parts of a thing. For he who intuitively knew the parts of a thing, could immediately form demonstrable concepts, the important parts in the oblique and the important whole directly.
Sed adhuc non est necesse quod habeat definitionem, quia deficeret sibi genus, quod non potest haberi vel saltem non semper potest haberi nisi per notitiam intuitivam alicuius singularis alterius speciei vel aliquorum singularium ƿ diversarum specierum, quo habito potest intellectus istum conceptum praeponere aliis conceptibus demonstrabilibus, et sic habetur definitio.	But it is still not necessary that it should have a definition, because it would lack a genus, which cannot be had, or at least cannot always be had, except through the intuitive knowledge of some singular of another species, or of some singular of different species, whereby the intellect can place that concept in preference to other demonstrable concepts, and thus the definition is obtained.
Et si praedicetur de definito, erit illa propositio evidens sine omni syllogismo, et ita indemonstrabilis erit.	And if it be predicated of the definite, that proposition will be evident without any syllogism, and thus will be indemonstrable.
Si autem partes rei non omnes intuitive videantur, sed totum videatur intuitive, non tamen talis videns possit discernere inter omnes partes totius, --- si tamen hoc sit possibile ---, tunc illa pars quae est genus accipitur per notitiam illam et per notitiam alterius vel aliorum singularium. Alii autem conceptus demonstrabiles a posteriori concluduntur de definito. Et ita accipitur definitio sic quod una pars per notitiam intuitivam et aliae per effectus; et tunc, istis habitis, est talis propositio nota in qua praedicatur definitio de definito. Nec istud negat Aristoteles; sed intendit Aristoteles principaliter probare quod per nullum syllogismum a priori potest fieri evidenter notum quod talis definitio praedicatur de definito et quod sufficienter exprimit essentiam definiti.	But if the parts of a thing are not all seen intuitively, but the whole is seen intuitively, yet such a vision cannot distinguish between all the parts of the whole, if this is possible, then that part which is the genus is received by that knowledge and by the knowledge of another or other particulars. But other demonstrable concepts are concluded a posteriori from the definite. And so the definition is taken in such a way that one part is by intuitive knowledge and the other by effects; and then, having these things, there is such a well-known proposition in which a definition is predicated of the defined. Nor does Aristotle deny this; but Aristotle principally intends to prove that by no syllogism can it be evidently known a priori that such a definition is predicated of the defined and that it sufficiently expresses the essence of the defined.
Hoc idem intendit Lincolniensis, quando dicit: ‘‘Demonstratio, quae concludit definitionem de definito, non facit nos cognoscere orationem definitivam secundum quod ipsa est definitiva, explicans quid est res, sed facit nos cognoscere solum ipsam orationem definitivam in quantum ipsa est praedicativa, dicens quoniam hoc est hoc; quamvis Lincolniensis de tali definitione non intelligat, sed de alia, de qua dicetur inferius.	This is what Lincoln intends when he says: "The demonstration which concludes the definition of the definite does not make us know the definite speech in so far as it is definite, explaining what the thing is, but makes us know only the definite speech itself in so far as it is predicative, saying that this is this;" although Lincoln does not intend such a definition, but another, which will be said below.
Sic igitur apparet per quem modum pars definitionis scitur de definito et per quem modum definitio scitur de definito. Et ad istum processum multum faciunt regulae datae in VII Topicorum.	Thus, then, it appears in what way a part of a definition is known of the defined, and in what way a definition is known of what is defined. And the rules given in the 7th Topic do much for this process.
Per istud tamen non habetur ars definiendi, sed ars definiendi accipitur per divisionem. Unde quamvis aliquis sciat evidenter omnes propositiones in quibus praedicantur partes definitionis de definito, si tamen nesciat illas partes in una oratione recto ordine ordinare, nescit definire nec habebit definitionem.	By this, however, the art of defining is not understood, but the art of defining is taken by division. Therefore, although someone clearly knows all propositions in which the parts of a definition are predicated of the defined, if he does not know how to arrange those parts in a single sentence in the correct order, he does not know how to define and will not have a definition.
Unde qui sic ordinaret partes definitionis hominis ‘rationale animal mortale’, non haberet definitionem.	Therefore, whoever would order the parts of the definition of man as a 'rational mortal animal' would not have a definition.
ƿ Est igitur ars definiendi illa per quam partes definitionis debite ordinantur. Et hoc est per divisionem: ut primo ponatur genus, deinde dividatur illud genus et accipiatur illa differentia quae scitur competere definito, quamvis hoc non sciatur per divisionem sed aliquo praedictorum modorum, de quibus dictum est prius.	It is therefore the art of defining that by which the parts of the definition are properly ordered. And this is by division: so that the genus is first posited, then that genus is divided, and that difference is taken which is known to belong to the definite, although this is not known by division but by some of the aforesaid methods, of which it was said before.
Deinde adhuc subdividatur; et sic procedendo et addendo, quousque perveniatur ad orationem convertibilem. Duobus autem modis contingit sic procedere divisive: uno modo, ut primo dividatur genus; secundo, accepta differentia quae competit definito, dividatur illa differentia vel genus convertibile cum illa differentia.	Then it is further subdivided; and by proceeding in this way and adding, until he arrives at a convertible statement. Now it happens in two ways that the division proceeds in this way: in the first way, so that the genus is first divided; secondly, having accepted the difference which belongs to the defined, that difference is divided, or the type convertible with that difference.
Deinde dividatur alia differentia vel aliud genus, ita quod semper sicut divisiones sunt diversae ita divisa sunt diversa. Sicut supposito quod homo sit substantia et homo debeat definiri, dividatur substantia per corporeum et incorporeum et addatur ‘corporeum’ substantiae et dicatur sic ‘substantia corporea’.	Then another difference or another kind is divided, so that as divisions are always different, so are the divided things different. Just as on the supposition that man is a substance and man must be defined, let the substance be divided into corporeal and incorporeal, and add the 'corporeal' substance to the substance, and thus call it 'corporeal substance'.
Deinde dividatur hoc totum ‘substantia corporea’ vel ‘corporeum’ vel hoc genus ‘corpus’, sic ‘corpus aliud animatum, aliud inanimatum’ et addatur ista differentia ‘animatum’ substantiae, sic dicendo ‘substantia corporea animata’.	Then let us divide this whole 'corporeal substance' or 'corporeal' or this kind of 'body', thus 'one body is animate, another inanimate' and this difference of 'animate' substance is added, thus saying 'animate corporeal substance'.
Deinde dividatur corpus animatum, sic ‘aliud sensibile, aliud insensibile’ et addatur ‘sensibile’ toti orationi praecedenti.	Then the animate body is divided, thus 'one sensible, another insensible', and 'sensible' is added to the whole preceding sentence.
Deinde dividatur ‘animal’, quod est genus convertibile cum sensibili, sic ‘aliud rationale, aliud irrationale’ et addatur haec differentia ‘rationale’, et tunc habetur ista definitio hominis ‘substantia corporea animata sensibilis rationalis’.	Then the 'animal' is divided, which is a type convertible with the sensible, thus 'one rational, another irrational' and this difference 'rational' is added, and then we have this definition of man as 'animate, corporeal, sensible, rational, substance'.
Aliter contingit per divisionem procedere, ut semper idem dividatur et non diversum. Sicut si debeat definiri ternarius et accipiatur primo ƿ genus ternarii, puta numerus, et dividatur numerus primo sic ‘numerus alius par, alius impar’ et addatur ista differentia ‘impar’ isti generi ‘numerus’, sic ‘numerus impar’. Deinde dividatur idem genus, scilicet numerus et non hoc totum ‘numerus impar’, nec aliquod convertibile, sic ‘numerus alius utrobique primus, alius non utrobique primus’ et addatur ista differentia ‘utrobique primus’ isti toti ‘numerus impar’, et habetur ista oratio ‘numerus impar utrobique primus’, quae est convertibilis cum ternario.	It happens in a different way that division proceeds, so that the same thing is always divided and not something different. For example, if a ternary is to be defined and the first genus of the ternary is taken, say a number, and the number is divided by the first so that 'one number is even, another odd' and this difference 'odd' is added to this genus 'number', thus 'odd number'. Then the same kind is divided, that is, number and not the whole 'odd number', nor any convertible, thus 'another number which is prime on both sides, another which is not prime on both sides', and this difference 'primary on both sides' is added to this whole 'odd number', and we have the expression 'number odd and prime on both sides', which is convertible with the ternary.
Sic igitur patet quod duobus modis contingit definitionem per divisionem accipere. In primo processu non solum tota oratio est convertibilis cum definito sed etiam ultima differentia est convertibilis cum definito, et de tali modo accipiendi definitionem loquitur Aristoteles VII Metaphysicae. In secundo processu nulla pars definitionis est convertibilis cum definito, sed quaelibet erit in plus et tota oratio erit convertibilis. Hoc tamen generale est quod nihil scitur de definito per divisionem, nisi dicas quod tota oratio nunc scitur de definito per divisionem propter hoc quod primus intellectus non componit talem propositionem, sed quidquid scitur de definito, scitur per aliam viam. Hoc tamen habetur in fine quod scitur quod haec oratio est definito talis definiti, non tamen per hoc scitur quod haec definitio significative sumpta praedicatur de definito significative sumpto. Et hoc vult Aristoteles quando probat quod per divisionem non syllogizatur nec demonstratur definitio de definito in quantum explicans quid est definiƿtum, secundum quod eum exponit Lincolniensis.	It is clear, then, that there are two ways in which definition can be obtained by division. In the first process, not only is the whole speech convertible with the definite, but also the ultimate difference is convertible with the definite, and Aristotle speaks of such a way of receiving a definition in Metaphysics VII. In the second process, no part of the definition is convertible with the defined, but each one will be in addition and the whole sentence will be convertible. This, however, is general, that nothing is known of the definite by division, unless you say that the whole sentence is now known of the definite by division, because the first intellect does not compose such a proposition, but whatever is known of the definite is known by another way. This, however, is held in the end because it is known that this speech is defined by such a definition, yet it is not known by this that this definition taken as significant is predicated of the definite taken as significant. And this is what Aristotle means when he proves that the definition of the definite is not syllogized or demonstrated by division in so far as he explains what is defined, according to what Lincoln explains.
Unde per artem definiendi non cognoscitur definitio de definito significative sumpto, in quantum scilicet explicat quid est res, sed hoc potest praecedere artem definiendi. Sed per artem definiendi partes definitionis debite ordinantur, et per hoc scitur quod talis oratio est definitio talis definiti.	Wherefore by the art of defining is not known the definition taken from the defined significant, inasmuch as it explains what the thing is, but this may precede the art of defining. But by the art of defining the parts of the definition are duly ordered, and by this it is known that such a speech is the definition of such a defined.
Et hoc intendit Lincolniensis quando dicit: ‘‘Methodus definitiva concludit orationes tales ‘animal rationale mortale est definitio hominis’. Et haec est oratio composita ex secundis intentionibus.	And this is what Lincoln intends when he says: "The definitive method concludes such speeches as 'the rational mortal animal is the definition of man.' And this is a speech composed of secondary intentions.
Et non est haec oratio omnino definitiva, solum explicans quid est homo, sed est oratio praedicativa huius secundae intentionis ‘definitio’ de hac definitione ‘animal rationale mortale’’’.	And this speech is not completely definitive, only explaining what man is, but it is a predicative speech of this second intention, a 'definition' of this definition of 'rational mortal animal'.
Propter quod Aristoteles et Lincolniensis volunt quod numquam potest definitio demonstrari de definito per definitionem definitionis, quia per tale medium non potest demonstrari definitio de definito significative sumpto, sed semper praecise de ipsa definitione supponente pro se et non pro suo significato.	Because of this Aristotle and Lincoln want that a definition can never be shown of the defined by a definition of a definition, because by such a means a definition cannot be shown of a defined taken as a signifier, but always precisely of the definition itself suppositing for itself and not for its signified.