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Thu 20 Mar, 2003 03:56 pm
I always loved 'sorites' : A form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. Here is one from Lewis Carroll's 'Symbolic Logic':
All my sons are slim.
No child of mine is healthy who takes no exercise.
All gluttons, who are children of mine, are fat.
No daughter of mine takes any exercise.
Conclusion?
My daughters are not healthy. It is possible that some of my sons are also not healthy. I cannot see that it is necessary that any daughters are fat - unless the "all gluttons who are children of mine" line is logically implying that there ARE children of his who are gluttons. If it does imply this, then we know that all the daughters are unhealthy and at least one, possibly more, is fat.
None of the sons is a glutton.
The key element is whether the line I mention DOES imply the necessity of these girls existing.
That is what I think, anyway!
Theorem:
If my child exists, the child is a slim boy or an unhealthy girl.
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