# A Manual of Logic Volume 1

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 edition. Excerpt: ...the proposition in hypothetical form--If a ball is drawn, it is either white or black--the consequents are not equally likely, owing to the preponderance in number of the white balls. And generally, this condition of equivalence can never be fulfilled when one of the alternatives simply negatives the other, owing to the indefinite range of reference of the negative term see 29 (i.)1. Indeed, such a disjunction would not fulfil the second condition given above, which requires that each alternative shall be definite. But it is necessary to enquire into the justification for Theassump-regarding the alternatives as equally likely. This justifica-alternatives tion must be found in our ignorance as to what precise con-ditions will be operative. For example, if a penny is tossed, justified by it will fall with either head or tail uppermost. Now, which tn will be uppermost in any particular throw will be exactly determined by such conditions as the position of the coin mine the at starting, how it is grasped in the fingers, the force and oven ' direction of the twist, etc. But what special form these conditions will take we are totally ignorant. We know that if S (the coin) is tossed (A), it will fall with one side upper most (X); but as we do not know the form an which A will take, we do not know whether X will appear as i (heads up) or 2 (tails up). There is, thus, in every such calculation a basis of knowledge. We know the coin will lie on one of its sides and not on its edge; but we have no reason to expect one side rather than the other to be uppermost, that is, we have no reason to believe the chances to be unequal. But further, we also know that in a long series of throws the sides which come upwards will succeed each other very...