Illogical Syllogisms

What a person believes can only be contradictory up to a point. It depends on the person to be at least minimally rational. When there's no way to decide which beliefs a person has, they have no beliefs at all. See DanielDennett, The IntentionalStance?. --MichaelSchuerig

I wonder about this. I think it suffers from the PrincipleOfTheExcludedMiddle?.

Light is a particle. Light is a wave. There are many things about which one cannot speak with much subtlety and maintain an insistence on resolving all contradictory or paradoxical appearances. These apparent contradictions are as likely as not to be constructs of incomplete understanding.

This is simply a misunderstanding. Light is not a particle. Light is not a wave. Under certain circumstances, it is useful to model it as one or the other. No contradiction.

I'm not sure that that counts as contradictory beliefs. I know that light behaves like particles under some circumstances and like waves under different circumstances. I don't see a contradiction there - just an incomplete understanding.

Or:

 1 The President of the USA is not an idiot
 2 George W Bush is an idiot
 3 George W Bush is the President of the USA

This set is somewhat interesting because it is possible to believe any two of the three without an inconsistency, but the set of all three contains a consistency: the first two imply the negation of the third, for example.

If the first is treated as a generalization, I can believe all three.

--- [OffTopic text moved to AlGoreWasRobbed?]