I am so ashamed - I just looked up non sequitur in the dictionary to get a precise meaning, and realised when I found it that I should have known it all along. I am doing a BA with a double major in linguistics and philosophy, and I am tending toward logic and applied philosophy for the latter. A non sequitur is conclusion that does not follow from the premises of the argument, literally "it does not follow". For those who have done a bit of logic, it is either deductively invalid or inductively weak.
For example:
Premise 1 - I put an undamaged loaf of bread in the kitchen last night.
Premise 2 - This morning there is a hole in the bag and the bread has big holes ripped in it.
Premise 3 - There are small droppings on the kitchen floor.
Conclusion - Therefore my house has been broken into by a bread-vandal whose trademark calling-card is to scatter rodent droppings on the floor.
That's an inductive non sequitur - an extremely weak argument. A deductive non sequitur is pretty simple:
P1 - All dogs are mammals.
P2 - All poodles are dogs.
C - Therefore, I am the King of Spain.
There you go, a quick lesson in inductive and deductive logic.
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