We have, then, to mark, on the larger Diagram, first, "no x are m", and secondly, "no y are m'". I think you will see, without further explanation, that the two results, separately, are ----------- ----------- | | | |0 | | | --|-- | | --|-- | | |0 | 0| | | | | | | |--|--|--|--| |--|--|--|--| | | | | | | | | | | | --|-- | | --|-- | | | | |0 | | ----------- ----------- and that these two, when combined, give us ----------- |0 | | | --|-- | | |0 | 0| | |--|--|--|--| | | | | | | --|-- | |0 | | ----------- We have now to mark the two positive portions, "some x are m'" and "some y are m". The only two compartments, available for Things which are xm', are No. 9 and No. 10. Of these, No. 9 is already marked as 'empty'; so our red counter must go into No. 10. Similarly, the only two, available for ym, are No. 11 and No. 13. Of these, No. 11 is already marked as 'empty'; so our red counter MUST go into No. 13. The final result is ----------- |0 | 1| | --|-- | | |0 | 0| | |--|--|--|--| | |1 | | | | --|-- | |0 | | ----------- And now how much of this information can usefully be transferred to the smaller Diagram? Let us take its four compartments, one by one. As to No. 5? This, we see, is wholly 'empty'. (So mark it with a grey counter.) As to No. 6? This, we see, is 'occupied'. (So mark it with a red counter.) As to No. 7? Ditto, ditto. As to No. 8? No information. The smaller Diagram is now pretty liberally marked:-- ------- | 0 | 1 | |---|---| | 1 | | ------- And now what Conclusion can we read off from this? Well, it is impossible to pack such abundant information into ONE Proposition: we shall have to indulge in TWO, this time. First, by taking x as Subject, we get "all x are y'", that is, "All Dragons are not-Scotchmen": secondly, by taking y as Subject, we get "all y are x'", that is, "All Scotchmen are not-Dragons". Let us now write out, all together, our two Premisses and our brace of Conclusions. "All Dragons are uncanny; All Scotchmen are canny. &there4 All Dragons are not-Scotchmen; All Scotchmen are not-Dragons."