To every affirmative proposition there is thus opposed a contradictory negative proposition; to every negative a contradictory affirmative. This pair of contradictory opposites may be called an _Antiphasis_; always assuming that the predicate and subject of the two shall be really the same, without equivocation of terms--a proviso necessary to guard against troublesome puzzles started by Sophists.[13] And we must also distinguish these propositions opposite as _Contradictories_, from propositions opposite as _Contraries_. For this, it has to be observed that there is a distinction among things ([Greek: pra/gmata]) as universal or singular, according as they are, in their nature, predicable of a number or not: _homo_ is an example of the first, and _Kallias_ is an example of the second. When, now, we affirm a predicate universally, we must attach the mark of universality to the subject and not to the predicate; we must say, Every man is white, No man is white. We cannot attach the mark of universality to the predicate, and say, Every man is every animal; this would be untrue.[14] An affirmation, then, is _contradictorily_ opposed to a negation, when one indicates that the subject is universally taken, and the other, that the subject is taken not universally, _e.g. Omnis homo est albus_, _Non omnis homo est albus_; _Nullus homo est albus_, _Est aliquis homo albus_. The opposition is _contrary_, when the affirmation is universal, and the negation is also universal, _i.e._, when the subject is marked as universally taken in each: for example, _Omnis homo est albus_, _Nullus homo est albus_. Of these contrary opposites, both cannot be true, but both may be false. Contradictory opposites, on the other hand, while they cannot both be true, cannot both be false; one must be false and the other true. This holds also where the subject is a singular term, as Sokrates.[15] If, however, an universal term appear as subject in the proposition _indefinitely_, that is, without any mark of universality whatever, _e.g._, Est albus homo_, _Non est albus homo_, then the affirmative and negative are not necessarily either contrary or contradictory, though they may be so sometimes: there is no opposition, properly speaking, between them; both may alike be true. This last observation (says Aristotle) will seem strange, because many persons suppose that _Non est homo albus_ is equivalent to _Nullus homo est albus_; but the meaning of the two is not the same, nor does the truth of the latter follow from that of the former,[16] since _homo_ in the former may be construed as not universally taken. [Footnote 13: Ibid. p. 17, a. 33: [Greek: _kai\ e)/stô a)nti/phasis tou=to_, kata/phasis kai\ a)po/phasis ai( a)ntikei/menai.] It seems (as Ammonius observes, Schol. p. 112, a. 33) that [Greek: a)nti/phasis] in this sense was a technical term, introduced by Aristotle.]