In Plato's Parmenides, we have the 8 Deductions that go something like this (this applies, as best as I can see, to both the standard and non-standard models that the SEoP describes. All this is shamelessly lifted from the SEoP site):
- If the G is, then the G is not F and not con-F in relation to itself.
- If the G is, then the G is F and con-F in relation to the others.
- If the G is, then the others are F and con-F in relation to the G.
- If the G is, then the others are not F and not con-F in relation to themselves.
- If the G is not, then the G is F and con-F in relation to the others.
- If the G is not, then the G is not F and not con-F in relation to itself.
- If the G is not, then the others are F and con-F in relation to the G.
- If the G is not, then the others are not F and not con-F in relation to themselves.
I decided to plot these out on a truth table.
What interests me here is the latter two columns; "Others to G" and "Others to Themselves".
Looking at these, we can see that Deductions 3 and 7, along with Deductions 4 and 8, actually have the exact same results and implications (EDIT) and do not care about the state of G.
My question is; does this not mean that we can simplify the Deductions down to a total of 6, like this?:
- If the G is, then the G is not F and not con-F in relation to itself.
- If the G is, then the G is F and con-F in relation to the others.
- If the G is not, then the G is F and con-F in relation to the others.
- If the G is not, then the G is not F and not con-F in relation to itself.
- The others are F and con-F in relation to the G.
- The others are not F and not con-F in relation to themselves.
There's likely something super obvious I don't get, I'm not a trained or educated philosopher. I just came across this and found it interesting, was wondering if someone with a bigger thinking sponge than mine could explain!
