Unless we are willing to admit that two contradictories may be true, many questions which lie at the threshold of mathematics and of morals will be insoluble puzzles to us.
There can be no question of the importance of showing that two contraries or contradictories may in certain cases be both true.
Contradictories can never be both true or both false, but always one is true and the other is false.
The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato; though the Second Alcibiades, in which it is most clearly expressed (p.
On the contrary, it is impossible for the same thing to be in motion and at rest, else contradictories would be verified of the same subject.
But it is impossible for the definition to be separated from the thing defined, since this would mean that contradictories exist together.
For it would follow that contradictories can exist at the one time: for the "definition of a thing is what its name expresses," as is said in Metaph.
Of two contradictories one or other must be true: we must either affirm or deny any one thing of any other: no mean or middle is possible.
The inferences are really based on the rules of Contrary and Contradictory Opposition; Contraries cannot both be true, and of Contradictories one or other must be.
It was in view of such perplexities as these that Aristotle set forth the true contradictories of his four Modals.
It is only when Opposition is taken to mean merely difference in Quantity and Quality that there can be said to be greater opposition between Contradictories than between Contraries.
Contradictories differ both in Quantity and in Quality: Contraries, in Quality only.
Contradictories cannot both be true, nor can they both be false.
Consequently mutual contradictories seem to be true as seen by different persons at the same time.
Further, God cannot make two contradictories to be true at the same time.
And if they are both false, their subalternates are both true, being respectively thecontradictories of the universals of opposite quality, namely, I.
For contradictories are positive and negative in essence and, when least ambiguously stated, also in form.
How the taking of Contraries for Contradictoriesmay vitiate Disjunctive Syllogisms and Dilemmas has been sufficiently explained in the twelfth chapter.
It is symbolic terms, such as X and x, that are properly said to be contradictories in relation to any subject whatever, S or M.
Now if there is such an objection against our thesis we must say that the falsity of this thesis is demonstrated, and that it is impossible for us to have reasons sufficient to prove it; otherwise two contradictories would be true at once.
This necessity of accepting one of two contradictories is wholly based upon the supposed impossibility of a mean; if the mean exists, that may be true, and both the contradictories false.
But if a mean between the two contradictories be both impossible and absurd, (and we have hitherto so interpreted the law of excluded middle,) Hamilton's conditioned entirely vanishes.
This necessity of accepting one of the contradictories is wholly based upon the supposed impossibility of a mean; if a mean exists, that may be true, and both contradictories together false.
If both contradictories are equally unknown and equally unthinkable, we can not discover why, on his principles, we are bound to believe either.
Now, to mention the law of Excluded Middle and twocontradictories with a mean between them, in the same sentence, is really astounding.
But if a mean between twocontradictories be both impossible and absurd, Hamilton's 'conditioned' entirely vanishes.
Or if two contradictories cannot be true at once, by what rule of logic are we to measure the idea of that freedom which arises out of necessity.
He must of necessity, every moment choose to act, or choose to forbear acting; because two contradictories cannot possibly he true at once.
This is the famous “Law of the contradictories and excluded middle,” on the construction of which the whole fabric of religious dogma, and I may add of the higher metaphysics, must depend.
On another construction of it, one which sought to escape the dilemma of the contradictories by confining them to matters of the understanding, Hegel and Schelling believed they had gained the open field.
In the modus operandi of the emanation comes in, as I said, that partnership of the principle of totality with that of the identity of contradictories which so recommends the latter to beginners in Hegel's philosophy.
The principle of the contradictoriness of identity and the identity of contradictories is the essence of the hegelian system.
Contradictories cannot both be true--that is, cannot co-exist in nature.
His reply is this--and never pretends to be any thing else than this--"Because it is impossible to conceive that contradictories can both be true.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "contradictories" in a variety of sentences. We hope that you will now be able to make sentences using this word.
