Where does Aristotle give a definition of false premises in his logical treatises?Where does Aristotle give a definition of false premises?
He gives definitions of false premises in both THE CATEGORIES and in ON INTERPRETATION, quote
ARISTOTLE:
iv. Statements opposed as affirmation and negation belong manifestly to a class which is distinct [ie. distinct from the 3 previously mentioned kinds of opposites, which you may read for yourself in The Categories KB], for in this case, and in this case only, it is necessary for the one OPPOSITE to be TRUE and the other FALSE...
...But in the case of affirmation and negation, whether the subject exists or not, one [logical opposite] is always FALSE and the other [logical opposite is always] TRUE. For, manifestly, if Socrates exists one of the 2 propositions; (1) Socrates is ill, (2) Socrates is NOT ill; is true and the other false. This is likewise the case if he does not exist; for if he does not exist to say that he is ill is false, to say that he is not ill, is true. Thus it is in the case of those opposites only, which are opposite in the sense in which the term [ie. ';opposite'; KB] is used with reference to AFFIRMATION and NEGATION, that the rule holds good, that one of the pair must be true and the other false.';
***CATEGORIES; Ch 10. 13b lines 1-35 (in passing)***
He take up the same ';idea'; of truth vs. falsity in his next logical treatise, called ON INTERPRETATION (in English ';Peri Hermeneus'; in Greek) when he writes, quote
ARISTOTLE:
';Every sentence has meaning, not as being the natural means by which a physical faculty is realized, but, as we have said, by convention. Yet every sentence is not a proposition --- only such are propositions as have in them either TRUTH or FALSITY. Thus a prayer is a sentence, but is neither true nor false.
Let us, therefore, dismiss all other types of sentence, but the proposition, for this last [ie. propositions; or declarative sentences KB] concerns our present inquiry, whereas the investigation of the others [ie. other kinds of sentences] belongs rather to the study of rhetoric or poetry.
***Arisotle; ON INTERPRETATION 17a 1-8***
Aristotle goes on to mention the way that opposite statements may be made as either CONTRARY PROPOSITIONS, such as: ';Every man is just. vs. (on the contrary) No man is just.'; or as, by contrast, CONTRADICTORY PROPOSTIONS such as ';Socrates is just.'; vs (begging to differ) ';Socrates is NOT just.'; (or Socrates is UNjust.).
He points out that CONTRARY propositions may both be false [eg. Every human is white vs. No human is white] when their contradictory logical PROPOSTIONS are both TRUE [eg. Some human is NOT white (true; eg. President Obama) and Some human is white (true; eg. former Presdent/s Bush)], but that when one of a pair of CONTRARY propositions is TRUE [eg. Every human is an animal] its logically contrary proposition [eg. No human is an animal] must, then, be false.
In sum, Aristotle ';defines'; FALSE premises in terms of their logically opposed Affirmations or Denials which are true. In other words, a true affirmative proposition is opposed by a false denial and a true negative proposition [eg. No man is a pig; eg. Socrates is NOT foolish.] is opposed by a false affirmative proposition [eg. Every man is a pig; eg. Socrates is foolish].
Of course, the affirmative and negative propositions of arguments are called the major and minor PREMISES of arguments. His best defence of the LAW OF CONTRADICTION (true and false premises are opposed as affirmative vs. negative, contrary, or contradictory, logically opposed propositions) is in his METAPHYSICS treatise, at Bk IV, Ch. 3 1005b line 17 forward through to Ch. 8 which ends Book IV.
Kevin
