Authors/Ockham/Summa Logicae/Book III-1/Chapter 18

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Latin English
Cap. 18. De syllogismis in secunda figura ex propositionibus de praeterito et de futuro Chapter 18. On syllogisms from propositions in the past and future [tense] in the second figure.
Circa syllogismos in secunda figura ex illis de praeterito et de futuro est sciendum quod quamvis in prima figura si maior sit de praeterito, sive subiectum supponat pro his quae sunt sive pro his quae fuerunt, non sequatur conclusio de praesenti sed tantum de praeterito, tamen aliquando ex ambabus praemissis de praeterito in secunda figura sequitur conclusio de praesenti. Regarding syllogisms in the second figure from propositions about the past and the future, it should be known that although in the first figure if the major is about the past, whether the subject supposits for things that are or for things that have been, the conclusion does not follow about the present but only about the past, nevertheless sometimes from both premises about the past in the second figure a conclusion about the present follows.
Unde sciendum quod quando ambae praemissae sunt de praeterito in secunda figura et utriusque subiectum supponit pro his quae sunt, semper sequitur conclusio de praesenti et non de praeterito. Sicut sequitur ‘nullum album fuit homo; omne nigrum fuit homo; igitur nullum nigrum, est album’, si subiectum utriusque accipiatur pro his quae sunt, quia ex opposito conclusionis et maiore sequitur oppositum minoris in prima figura, sicut ostensum est prius[1]. Sed illa de praeterito non sequitur, quia si sequeretur, tunc ex opposito conclusionis et maiore sequeretur oppositum minoris in prima figura, et per consequens in prima figura sub maiore, in qua subiectum supponit pro his quae sunt, contingeret accipere sub unam minorem de praeterito; quod ostensum est esse falsum[2]. Quod etiam talis discursus non valeat, patet per instantiam in terminis. Nam ponatur quod nihil currat nisi homo et quod nihil sit album nisi asinus et quod multi asini prius currebant, tunc haec est vera ‘omne currens fuit homo’, quia omne, quod currit, ƿ fuit homo, per casum; similiter haec est vera 'nullum album fuit homo', sumpto albo pro his quae sunt, quia quaelibet singularis est vera; et tamen haec est falsa ‘nullum album fuit currens’ sive album supponat pro his quae sunt sive pro his quae fuerunt. Hence it should be known that when both premises are about the past in the second figure and the subject of both supposits for things that are, the conclusion always follows about the present and not about the past. As follows ‘no white thing was a man; every black thing was a man; therefore no black thing is white’, if the subject of both is taken for things that are, because from the opposite of the conclusion and the major the opposite of the minor follows in the first figure, as was shown before [3]. But that does not follow about the past, because if it did follow, then from the opposite of the conclusion and the major the opposite of the minor would follow in the first figure, and consequently in the first figure under the major, in which the subject supposits for things that are, it would be possible to take under one minor from the past; which was shown to be false [4]. That such a discourse is also not valid is clear from the instantiation in the terms. For suppose that nothing runs except a man and that nothing is white except a donkey and that many donkeys ran before, then this is true ‘every running thing was a man’, because everything that runs was a man, by chance; similarly this is true ‘no white thing was a man’, taking white for things that are, because any singular is true; and yet this is false ‘no white thing was running’ whether white supposits for things that are or for things that have been.
Si autem subiectum utriusque supponat pro his quae fuerunt, tunc sequitur conclusio de praeterito, quia ex opposito conclusionis et maiore sequitur oppositum minoris. Per idem patet quod si subiectum maioris supponat pro his quae fuerunt, sequitur conclusio de praeterito. But if the subject of both supposits for things that have been, then a conclusion about the past follows, because from the opposite of the conclusion and the major the opposite of the minor follows. By the same token it is clear that if the subject of the major supposits for things that have been, a conclusion about the past follows.
Sciendum est hic quod non quilibet syllogismus talis in secunda figura est reducibilis in syllogismum primae figurae per conversionem, sine omni variatione vocis praeter solam transpositionem terminorum, sed si debet reduci per conversionem, debent propositiones converti illo modo quo dictum est prius[5] de conversione talium propositionum. It should be noted here that not every such syllogism in the second figure is reducible to a syllogism of the first figure by conversion, without any variation of the words except the mere transposition of the terms, but if it must be reduced by conversion, the propositions must be converted in the manner previously stated above,[6] concerning the conversion of such propositions.

Notes

  1. Cf. supra c.11, lin. 34-7.
  2. Supra c.17.
  3. Cf. supra c.11, lin. 34-7.
  4. Supra c.17.
  5. Supra, parte II, c. 22
  6. part II, c. 22