## Saturday, July 14, 2007

### Is 'every man is an animal true' when there are no men?

A splendid new page in the Logic Museum here.

Ken said...

The question was how could 'every man is an animal' or 'three and four are seven' possibly be false?

“Every man is an animal” would be false if “No man is an animal” is true. This could be that animal and man are separate within a single category or that no man exists.

“Three and four are seven” would be false under a number of conditions. If the three and four are binary numbers that use the and operation such as 3 and 4, this would actually equal 0. The assumption is that “and” is acting like an “add” which may not be valid.

Augustine indicates that the number 6 is perfect if those “things” did or did not exist. This appears to say that the number six is perfect without any other statements necessary.

Because the number 6 is perfect, then other results will be true or false because 6 perfect but the same propositions may not result in the same true or false result if replaced with 5 or 7 because these are not perfect.

Is this what he is saying?

Edward Ockham said...

Augustine actually says if the 'things numbered' do not exist. I.e. if there are not six men, not six planets, and so on. Clearly other statements are necessary if 6 is to be a perfect number.