Relation ______________|_____________ | | Compatible Incompatible ______|_____ _____|_______ | | | | Subaltern Sub-contrary Contrary Contradictory. § 463. It should be noticed that the inference in the case of opposition is from the truth or falsity of one of the opposed propositions to the truth or falsity of the other. § 464. We will now lay down the accepted laws of inference with regard to the various kinds of opposition. § 465. Contrary propositions may both be false, but cannot both be true. Hence if one be true, the other is false, but not vice versâ. § 466. Sub-contrary propositions may both be true, but cannot both be false. Hence if one be false, the other is true, but not vice versâ. § 467. In the case of subaltern propositions, if the universal be true, the particular is true; and if the particular be false, the universal is false; but from the truth of the particular or the falsity of the universal no conclusion can be drawn. § 468. Contradictory propositions cannot be either true or false together. Hence if one be true, the other is false, and vice versâ. § 469. By applying these laws of inference we obtain the following results-- If A be true, E is false, O false, I true. If A be false, E is unknown, O true, I unknown. If E be true, O is true, I false, A false. If E be false, O is unknown, I true, A unknown. If O be true, I is unknown, A false, E unknown. If O be false, I is true, A true, E false. If I be true, A is unknown, E false, O unknown. If I be false, A is false, E true, O true. § 470. It will be seen from the above that we derive more information from deriving a particular than from denying a universal. Should this seem surprising, the paradox will immediately disappear, if we reflect that to deny a universal is merely to assert the contradictory particular, whereas to deny a particular is to assert the contradictory universal. It is no wonder that we should obtain more information from asserting a universal than from asserting a particular. § 471. We have laid down above the received doctrine with regard to opposition: but it is necessary to point out a flaw in it.