Passing to the blot, or pseudograph, of which you remember the meaning is that everything is true, the predication of the definition concerning the definitum is that within any even number of cuts, where the blot is any graph we please may be inserted, and within any odd number of cuts, where the blot is any graph may be erased. The blot, it is true, fills its whole area, so as to leave no room for any other graph. But there is an equivalent of it of which this is not true. For since by Permission No 1 every graph on the sheet of assertion can be transformed into the blank, it follows by the principle of contraposition that an enclosure containing nothing but a blank can when evenly enclosed be transformed into anything we please, and consequently into the pseudograph. The vacant enclosure is, therefore, a form of the pseudograph. For evenly enclosed it can be transformed [into] the blot, or the blot can be transformed into it. And since these two transformations are the reverse of one another, it follows, by the principle of contraposition, that the same is true within any odd number of cuts. When the vacant enclosure is oddly enclosed as in this figure
the enclosure on whose area it stands is evenly enclosed and can be erased by Permission No 1. But when the vacant enclosure is evenly enclosed as in the next figure

This topic was modified 7 months, 4 weeks ago by gnox.

This topic was modified 7 months, 4 weeks ago by gnox.