As Wikipedia notes,i the term is used in everyday speech to deny a conditional (if-then statement), and it is also used in logic to mean an invalid argument. This together with the fact that in normal language people do not write the complete arguments when they argue, makes it very easy to confuse things.

Suppose that someone says “Since that global warming is undesirable, we ought to not burn more coal.” Another person then responds to that with “Non-sequitur“. What did the second person criticize? The argument structure or validity? That structure is hidden and we have to guess at what it is. (Se Note 1.) The conditional? Maybe.

We should therefore at least not use the term ‘non-sequitur’ without also clarifying what the problem is. But we ought not to use the term at all since there are better alternatives. If one means that the argument is invalid, then say “The argument is invalid”. If one means that a conditional is false, then say “The conditional is false.”. This recommendation is for discussions of a certain quality only. Chances are that if you argue with a random member of the mob, then that person will not know what it means to say that an argument is invalid or what a conditional is.

There are also similar phrases such as ‘That doesn’t follow’. Non-sequitur is latin for ‘it does not follow’.

Note 1

The principle of charity applies in that case. We don’t know which argument structure the person had in mind when making the argument. If it is member of the mob, then he or she probably doesn’t know either which structure it has. But if we should follow the aforementioned principle, then we ought to make an interpretation of the argument in question that is valid. This is sometimes a task in itself.

ihttp://en.wikipedia.org/wiki/Non_sequitur_(logic)

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