(1) Some islands are inhabited.
(2) Some islands are not inhabited.
§ 461. In the case of subaltern opposition the truth of the universal not only may, but must, be compatible with that of the particular.
§ 462. Immediate Inference by Relation would be a more appropriate name than Opposition; and Relation might then be subdivided into Compatible and Incompatible Relation. By 'compatible' is here meant that there is no conflict between the truth of the two propositions. Subaltern and sub-contrary opposition would thus fall under the head of compatible relation; contrary and contradictory relation under that of incompatible relation.
Relation
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Compatible Incompatible
______|_____ _____|_______
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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.