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Theophrastus · Fragments §63.1

A Simpler Proof of the Conversion of Universal Negatives

Passage 58 of 196 · Greek

Summary

Explains the simpler method of proof presented by Theophrastus and Eudemus to show that the universal negative proposition is convertible.

§63.1Fr. 63 Θ. μὲν καὶ Εὔδημος ἁπλούστερον ἔδειξαν τὴν καθόλου ἀποφατικὴν ἀντιστρέφουσαν ἑαυτῇ· τὴν γὰρ καθόλου ἀποφατικὴν ὠνόμασαν καθόλου στερητικὴν, τὴν δὲ δεῖξιν οὕτως ποιοῦνται.
Theophrastus and Eudemus demonstrated in a simpler way that the universal negative proposition converts with itself; for they called the universal negative a universal privative, and they make the proof as follows.
Κείσθω τὸ Α κατὰ μηδενὸς τοῦ Β· εἰ δὲ κατὰ μηδενὸς ἀπέζευκται· καὶ τὸ Β ἄρα παντὸς ἀπέζευκται τοῦ Α, εἰ δὲ τοῦτο κατʼ οὐδενὸς αὐτοῦ.
"Let A be assumed of no B; and if it is disjoined from none, B also is therefore disjoined from all of A, and if this is so, it is predicated of none of it."

Notes

  1. Fr. 63ἀντιστρέφουσαν ἑαυτῇ — A participle functioning as the complement of the verb ἔδειξαν, indicating that the proposition "converts with itself" (retains its truth value when the subject and predicate are interchanged).
  2. Fr. 63ἀπέζευκται — Perfect passive of the verb ἀποζεύγνυμι (to disjoin). In logic, it expresses the state where terms exclude each other (do not belong to one another).
  3. Fr. 63εἰ δὲ τοῦτο κατʼ οὐδενὸς αὐτοῦ — τοῦτο refers to the preceding clause ("that B is disjoined from A"). The main verb (likely ὑπάρχει or κατηγορεῖται) is omitted; supplying it yields "if this is so, [B belongs to] none of it (A)". αὐτοῦ is a genitive referring back to τὸ Α.

Cite this passage

Theophrastus, Fragments §63.1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0093.tlg010x09.humanitext-grc1:63.1

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