# Invalid Argument/Examples/Socrates is Mortal

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## Example of Invalid Argument

This argument is technically invalid:

## Proof

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.

$\blacksquare$

## Sources

- 1988: Alan G. Hamilton:
*Logic for Mathematicians*(2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives: Example $1.1$