i.e. I always avoid a kangaroo.
[pg164]NOTES.
[(A)] [See [p. 80]].
One of the favourite objections, brought against the Science of Logic by its detractors, is that a Syllogism has no real validity as an argument, since it involves the Fallacy of Petitio Principii (i.e. “Begging the Question”, the essence of which is that the whole Conclusion is involved in one of the Premisses).
This formidable objection is refuted, with beautiful clearness and simplicity, by these three Diagrams, which show us that, in each of the three Figures, the Conclusion is really involved in the two Premisses taken together, each contributing its share.
Thus, in Fig. I., the Premiss xm0 empties the Inner Cell of the N.W. Quarter, while the Premiss ym0 empties its Outer Cell. Hence it needs the two Premisses to empty the whole of the N.W. Quarter, and thus to prove the Conclusion xy0.
Again, in Fig. II., the Premiss xm0 empties the Inner Cell of the N.W. Quarter. The Premiss ym1 merely tells us that the Inner Portion of the W. Half is occupied, so that we may place a ‘I’ in it, somewhere; but, if this were the whole of our information, we should not know in which Cell to place it, so that it would have to ‘sit on the fence’: it is only when we learn, from the other Premiss, that the upper of these two Cells is empty, that we feel authorised to place the ‘I’ in the lower Cell, and thus to prove the Conclusion x′y1.
Lastly, in Fig. III., the information, that m exists, merely authorises us to place a ‘I’ somewhere in the Inner Square——but it has large choice of fences to sit upon! It needs the Premiss xm0 to drive it out of the N. Half of that Square; and it needs the Premiss ym0 to drive it out of the W. Half. Hence it needs the two Premisses to drive it into the Inner Portion of the S.E. Quarter, and thus to prove the Conclusion x′y′1.