How many valid categorical syllogisms are there?



Almost all contemporary logic books I have checked (as well as Wikipedia) agree that there are 24 conditionally valid logic syllogisms (Aristotle interpretation) 6 per figure and 15 unconditionally valid syllogisms (Brentano-Boole interpretation).

Then why do I still read in a lot of resources that there are 19 valid syllogisms?

Gabriele Scarlatti

Posted 2017-12-05T10:27:47.327

Reputation: 407



See Syllogism: Aristotle's Theory:

terms can be combined in different ways to form three figures (skhemata), which Aristotle presents in the Prior Analytics. When the four categorical sentences are placed into these three figures, Aristotle ends up with the following 14 valid moods [...]

A fourth figure was discussed in ancient times as well as during the Middle Ages.

If we perform a simple calculation based on the four categorical sentences and the four figures, we find that there are 256 possible combinations of sentences. Of these, 24 have traditionally been thought to yield valid deductions. To the 19 already mentioned we must add two subalternate moods in the first figure (Barbari and Celaront), two subalternate moods in the second figure (Camestrop and Cesaro), and one subalternate mood in the fourth figure (Camenop).

See also Syllogism.


Posted 2017-12-05T10:27:47.327

Reputation: 33 575