Relativism(s) and polling
I've been enjoying recently thinking about the possible significance of polling in philosophical thought. Consider the following relatively standard way of arguing against relativism (we'll start with relativism about truth, but this might equally apply with minor modifications to, e.g. moral relativism or relativism of philosophical worth to a community of philosophical experts). I'm eager to hear from both relativists and non-relativists what might be wrong with the argument.
For the sake of argumentative simplicity, let us define relatvism (R) as the proposition that a proposition is true only if the majority agrees to it.
Since R itself is a proposition, it is self-applicable and we get the conditional:
R only if everyone agrees to it
And if you like your logic symbolic
R –> A
We are now in a position to construct the following reductio against R:
1. R (which we are assuming for the purposes of reductio aka indirect proof)
2. R –> A (which is self evident if you know what R means)
3. A ( by modus ponens from 1 and 2)
4. ~A (an empircal fact that presumably can be proved only by polling)
5. A & ~A (3 and 4 by the inference rule of conjunction)
/.: ~R (1-5 by the rule of indirect proof)
I take it to be obvious that the argument is deductively valid. And the only real question of its soundness (as far as I can tell) comes in at the question of the truth of premise 4. So, let's check: