aristotle’s dilemmas and logical statements revisited:

all snakes(m) are reptiles(p), true, a, major

all cobras(s) are snakes(m), true, a, minor

all cobras(s) are reptiles(p), true, a, conclusion

mp/sm figure

forms encompass universal affirmative (a) & negative(e) and particular affirmative(i) & negative(o)

a. all snakes are reptiles

b. no snakes are reptiles

c. some snakes are reptiles

d. some snakes are not reptiles

contraries both cannot be true, sub-contraries both cannot be false, implications and sub-implications are both otherwise; thus contradictories are never of the same value

4 immediate inferences in deductive reasoning are converse, limited converse, obverse, and contra-positive; thus deriving

all snakes are reptiles ( proposition )

all reptiles are snakes (converse, works in e and i)

some reptiles are snakes (limited converse)

no snakes are non-reptiles (obverse, works in all)

no non-reptiles are snakes (obverse  converse)

all non-reptiles are non-snakes (contra positive, equivalent to first)

all non-snakes are non-reptiles

some non-snakes are non-reptiles (inverse)

hypothetical / conditional

if it rains(a), then the river will rise (c)

it rained(a) / the river didn’t rise (~c)

the river rose (c) / it didn’t rain (~a)

a->c, modus ponens; if antecedent, then consequent

~c->~a, modus tollens(kill), if not consequent, then not antecedent

*whew, now i have to get the other figures to match these

one has to undergo pain at times to gain knowledge


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