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Old January 7th, 2011, 02:50 AM
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Default Shrapnel's Unofficial Symbolic Logic Thread

I just started reading a second hand, introductory symbolic logic text book I purchased from an independent book seller associated with Amazon.com. I think I found an error in the third chapter but I don't know enough about logic to decide if the book is wrong or I am. Under the premise that it takes a relatively high level of mental brightness to be interested in TBS I thought that I might be well rewarded by fielding a query on this forum.

The proper reference to the question I will pose is best presented with a quote from Lee in Symbolic Logic: An introductory textbook for non-mathematicians (so easy a non-mathematician can do it ):

"The properties that a relation has with respect to the conditions of symmetry and those of transitivity are independent of each other. Thus, 'equals' is symmetrical and transitive, while 'ancestor of' is asymmetrical and transitive, and 'implies' is non-symmetrical and transitive. 'Next to' (in serial order) is symmetrical and in-transitive; 'father of' is asymmetrical and intransitive; 'half-brother of' is non-symmetrical and intransitive. 'Admires' is non-symmetrical and non-transitive, and so on" (-emphasis added 34).

My question is: How can the relation "half-brother of" be intransitive in the form xRy and yRz therefore xRz when x could be the half brother of y by sharing a father; y be the half brother of z by sharing that same father and x be the half-brother of z by sharing that same man again as father. It seems to me that this particular relation is non-symmetrical and non-transitive.

Works Cited:

Lee, Harold Newton. Symbolic Logic: An introductory textbook for non-mathematicians. New York: Random House, 1961. Print.
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