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 $1.1$