VI. Abraham's children | do his works ------------------------+------------------------ If ye were his children | _ye would do his works_ *** 'Since all metals are elements, the most rare of all the metals must be the most rare of all the elements.'--There is a suppressed precedent to the effect that the most rare individual of a species must be the most rare of its genus, which may or may not be true. *** 'All vice is odious; but avarice is a vice; for it makes men slaves; therefore avarice is odious.' V. I. Whatever enslaves | is a vice || All vice | is odious ------------------+----------------++-------------------+--------------- Avarice enslaves | _it is a vice_ || Avarice is a vice | _it is odious_ *** 'Bucephalus is a horse; a horse is a quadruped; a quadruped is an animal; an animal is a substance; therefore Bucephalus is a substance.' All horses |are quads.|| Quads. | animals || Animal | substance -----------+----------++-----------+-----------++----------+---------- Bu. is a h.|_he is q._||B. is quad.|_he is an._||Bu. is an.|_he is subst._ This is what logicians call a _Sorites_. There may be a chain of valid arguments, in which the conclusion of one is precedent or case of the next; but the propositions just quoted do not make an argument, being merely a string of classifications. If we know what Bucephalus and substance mean, we know by perception that Bucephalus is a substance. *** 'Every being is then happy when it acquires the proper perfection of its nature; and consequently all vital beings are capable of receiving felicity that are capable of arriving at the perfection of their nature.' I. Every being that acquires | is happy --------------------------+------------------------------ All vital beings capable | _must be capable of receiving of acquiring | felicity_ This is perilously near tautology; it can be saved only by assuming that 'every being capable of happiness' is a more extensive class than 'all vital beings capable of arriving at the perfection of their nature.' *** 'The soul's debility is not owing to her lapse into matter; for as this lapse is voluntary, the soul must have sinned prior to her descent.' VI. Voluntary lapse | proves prior sin -------------------+----------------------------- Soul's lapse is v. | _her debility must have been antecedent to lapse_ *** _Cogito ergo sum._-- I. Whatever thinks | is ----------------+--------------------------- I think | _I must believe that I am_ That we exist is the most certain fact we know: it cannot be strengthened by any argumentation. If we can doubt that we _are_, we can with better reason doubt that we think. ***