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Modus Ponens: (Latin for: mood that affirms.)  In its basic form, an argument that runs ‘If p, then q. p.  Therefore q.’

For example,

If today is Tuesday, then I will go to work.

Today is Tuesday.

Therefore, I will go to work.

Modus Tollens: (Latin for: mood that denies.)  In its basic form, an argument that runs ‘If p, then q.  But not-q.  Therefore not-p.’

For example,

If I miss the train, I take a taxi.

I didn’t take a taxi.

Therefore, I didn’t miss the train.

Definitions, but not examples, taken from Antony Flew, ed., A Dictionary of Philosophy, rev. 2nd ed., 236.

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