text:  Yet the acknowledgment so explicitly made has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths whether of science or of daily life which we believe; while those who have avoided this inconsistency and followed out the general theorem respecting the logical value of the syllogism to its legitimate corollary have been led to impute uselessness and frivolity to the syllogistic theory itself on the ground of the _petitio principii_ which they allege to be inherent in every syllogism