Thursday, 13 October 2005

Fewtril #31

We usually deplore a man for his lack of reason, but given that he holds a set of self-righteous and false premises, one ought to be thankful that at least he cannot find his way to a logical conclusion.


Anonymous said...

The pedant general has suggested I seek your help in translating this passage:

Arthur Seat

Anonymous said...

Logically, any conclusion (including a false one) is entailed by a set of false premises. One ought to be concerned, not thankful!

Deogolwulf said...

No. An argument is valid if and only if its conclusion follows logically from its premises. Otherwise it is invalid. An argument is sound if and only if it is both valid and its premises are true. Otherwise it is unsound.

One can of course have a valid but unsound argument. Thus:

If all Englishmen are cockroaches, then all Englishmen should be exterminated,
All Englishmen are cockroaches,
Therefore, all Englishmen should be exterminated.

Now, I for one, being an Englishman, would be thankful if someone who believed the premises to be true could not draw the logical conclusion - or even more thankful if they produced a non sequitor such as "All Englishmen should be given lots of money". Now, this is a simple illustration only, designed to show that one should be thankful that some people cannot draw logical conclusions from their false beliefs. Is it not then conceivable to you that there is any regretable thing in the world that is the result of conclusions following from false premises? A moment's thought should throw up many examples. And it as such that one might be thankful for non sequitors. That is my point.