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→Structure of syllogisms
There are sixty-four combinations of the four vowels in each figure, thus in the three figures given by Aristotle there are one hundred and ninety-two (and in all the four figures of Aristotelian logic, two hundred and fifty six).
There are sixty-four combinations of the four vowels in each figure, thus in the three figures given by Aristotle there are one hundred and ninety-two (and in all the four figures of Aristotelian logic, two hundred and fifty six).
Not all combinations give a valid syllogism. Aristotle examines all the modes one by one, and judges whether each is valid, and gives rules which to help the memory in distinguishing the vaoid from the invalid. The first figure has only four valid modes. The major premise in this figure must be universal, and the minor affirmative, and yields conclusions of all kinds, affirmative and negative, universal and particular. The second figure also has four valid modes. Its major premise must be universal, and one of the premises must be negative. It yields universal and particular conclusions, of which all are negative. The third figure has six valid modes. Its minor must always be affirmative. It yields affirmative and negative conclusions both, all particular.
Not all combinations give a valid syllogism. Aristotle examines all the modes one by one, and judges whether each is valid, and gives rules which to help the memory in distinguishing the valid from the invalid. The first figure has only four valid modes. The major premise in this figure must be universal, and the minor affirmative, and yields conclusions of all kinds, affirmative and negative, universal and particular. The second figure also has four valid modes. Its major premise must be universal, and one of the premises must be negative. It yields universal and particular conclusions, of which all are negative. The third figure has six valid modes. Its minor must always be affirmative. It yields affirmative and negative conclusions both, all particular.
There are five rules of validity common to all syllogisms, that may be deduced from what Aristotle says.
There are five rules of validity common to all syllogisms, that may be deduced from what Aristotle says.