Invalid Argument/Examples/Socrates is Mortal

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Example of Invalid Argument

This argument is technically invalid:

Socrates is a man.
Therefore, Socrates is mortal.


It may be thought that the conclusion may hence be deduced from the premise.

However, this does so purely because of the a priori knowledge that:

if $A$ is a man, then $A$ is mortal.

Hence while the conclusion follows from the premise, this does not happen purely by means of deduction from the argument itself.

Let $P$ denote the simple statement Socrates is a man..

Let $Q$ denote the simple statement Socrates is mortal..

The argument can then be expressed as:

\(\text {(1)}: \quad\) \(\ds P\) \(\) \(\ds \)
\(\text {(2)}: \quad\) \(\ds \therefore \ \ \) \(\ds Q\) \(\) \(\ds \)

But this is not a valid argument form.