39

27
31

The first three of these mean, respectively, “Nobody loves
anybody whom he does not respect,” “Somebody loves nobody
whom he does not respect,” “Somebody is loved by nobody who
does not respect him.” Those three propositions cannot be
expressed, with the same degree of analysis without the ligature
the innermost of which is within the cut that encloses both
spots. But the fourth, which means “There is somebody whom somebody does not love unless he respects him” will not have its
meaning changed by breaking both ligatures, as in the fifth
graph, so as to make it read “Either there is somebody who non-loves
somebody or else somebody respects somebody” or “If everybody
loves everybody somebody respects somebody.[”] The juncture
protruding through two cuts could be cut without altering the meaning

By putting two cuts round the
“loves” and retracting the [junctures?]
through two cuts we get the equivalent graph

The third chapter of the exposition of
existential graphs is by far the most important
and interesting of the three. The whole
gist of mathematical reasoning depends
upon it. I shall have to remit it to another

27
31

The first three of these mean, respectively, “Nobody loves
anybody whom he does not respect,” “Somebody loves nobody
whom he does not respect,” “Somebody is loved by nobody who
does not respect him.” Those three propositions cannot be
expressed, with the same degree of analysis without the ligature
the innermost of which is within the cut that encloses both
spots. But the fourth, which means “There is somebody whom somebody does not love unless he respects him” will not have its
meaning changed by breaking both ligatures, as in the fifth
graph, so as to make it read “Either there is somebody who non-loves
somebody or else somebody respects somebody” or “If everybody
loves everybody somebody respects somebody.[”] The juncture
protruding through two cuts could be cut without altering the meaning

By putting two cuts round the
“loves” and retracting the [junctures?]
through two cuts we get the equivalent graph

The third chapter of the exposition of
existential graphs is by far the most important
and interesting of the three. The whole
gist of mathematical reasoning depends
upon it. I shall have to remit it to another