[51] Plato, Euthydêm. pp. 295-296.
The base of these fallacious inferences is, That respecting the same subject, you cannot both affirm and deny the same predicate: you cannot say, A is knowing — A is not knowing (ἐπιστήμων). This is a fallacy more than verbal: it is recognised by Aristotle (and by all subsequent logicians) under the name — à dicto secundum quid, ad dictum simpliciter.
It is very certain that this fallacy is often inadvertently committed by very competent reasoners, including both Plato and Aristotle.
Again — Sophroniskus was my father — Chæredemus was the father of Patrokles. — Then Sophroniskus was different from a father: therefore he was not a father. You are different from a stone, therefore you are not a stone: you are different from gold, therefore you are not gold. By parity of reasoning, Sophroniskus is different from a father — therefore he is not a father. Accordingly, you, Sokrates, have no father.[52]
[52] Plato, Euthydêm. pp. 297-298.
But (retorts Ktesippus upon the couple) your father is different from my father. — Not at all. — How can that be? — What! is your father, then, the father of all men and of all animals? — Certainly he is. A man cannot be at the same time a father, and not a father. He cannot be at the same time a man, and not a man — gold, and not gold.[53]
[53] Plato, Euthydêm. p. 298. Some of the fallacies in the dialogue (Πότερον ὁρῶσιν οἱ ἄνθρωποι τὰ δυνατὰ ὁρᾷν ἢ τὰ ἀδύνατα; … Ἦ οὐχ οἷόν τε σιγῶντα λέγειν; p. 300 A) are hardly translatable into English, since they depend upon equivocal constructions peculiar to the Greek language. Aristotle refers them to the general head παρ’ ἀμφιβολίαν. The same about προσήκει τὸν μάγειρον κατακόπτειν, p. 301 D.
You have got a dog (Euthydêmus says to Ktesippus). — Yes. — The dog is the father of puppies? — Yes. — The dog, being a father, is yours? — Certainly. — Then your father is a dog, and you are brother of the puppies.
You beat your dog sometimes? Then you beat your father.[54]