These were weaknesses; but such as they were, they are a key to explicate some of his writings.

Analytical and identical propositions which merely explicate the conception of the subject, but express nothing not already known, are, in spite of their indefeasible certitude, valueless for the extension of knowledge, and when taken for more than verbal explanations, mere absurdities.

To the former class belong the objects of mathematics, the truths of which, since they are analytic (i. e., merely explicate in the predicate the characteristics already contained in the subject, and add nothing new to this), and since they concern possible relations only, not reality, possess intuitive or demonstrative certainty.

Philosophy is the science of the possible, i.e., of that which contains no contradiction; it is science from concepts, its principle, the law of identity, its form, demonstration, and its instrument, analysis, which in the predicate explicates the determinations contained in the concept of the subject.

The syllogism has the advantage of yielding universal and necessary truth, but it can only explicate and establish knowledge, not increase it.

The former explicates the concept of the subject by bringing into notice an idea already contained in it and belonging to the definition as a part thereof; it is based on the law of contradiction: an unextended body is a self-contradictory concept.

When I assert the major premise the inference proper is already made, and in the conclusion the comprehensive formula for a number of particular truths which was given in the premise is merely explicated, interpreted.

Many of the ancients explicated this severity by the fire of conflagration, which say they shall purify those souls at the day of judgment, which in this life have built upon the foundation (hay and stubble) works of folly and false opinions, states of imperfection.