HoPwaG: Parmenides

Parmenides' doctrines:

• everything that exists is one;
• multiplicity an illusion, and nothing changes.

These conclusions argued for, but not from experience; purely 'rationally'. Have a division between:

• 'way of truth' (the metaphysics); and
• 'way of opinion' (what to believe about, e.g. cosmology, natural world if can't believe the way of truth).

Way of truth:

• two paths of inquiry: can ask about what "is and must be" or what "is not and can't be", but second rejected as impossible, since can't meaningfully talk about non-being, i.e. what is not;
• a third path is even worse than the second: can ask about that which "is and is not", which also entails talking about something that's not meaningful (what "is not"), but, worse, asks about something that has contradictory attributes (since anything that falls into this domain of inquiry both is and is not);
• one interpretation of this confusing distinction: Parmenides' verbs have no object, so they can apply to anything we like--i.e. Parmenides' is a maximally general level of inquiry;
• the upshot: in metaphysical inquiry, we can only talk about being and never about non-being; so any conclusion that leads us to talk about non-being is going to be false (call that Parmenides' principle of metaphysical inquiry [PPMI]);
• the argument for the conclusions: being cannot begin to be or stop being, since both involve going from being to non-being, which violates PPMI; so get conclusion that change is impossible;
• objection: not all change seems to involve change from being to non-being, e.g. of painting giraffe; 
• reply: but always need non-being to contrast different things, even where it looks to us like being hasn't been destroyed, so by PPMI (i.e. that conclusions which involve talk of non-being are false) all change;
• similarly, no change over time, no variety in what there is at any one time; and being continuous (since gaps would entail non-being); so have conclusion that being is one and multiplicity illusory;
• further, being is spherical (!), since it must be determinate, but there's interpretive dispute about why being spherical (metaphorical? or sphere as perfect shape, and since being is, must have a shape, which, since being perfect [see next argument], must be spherical);
• also have argument for perfection of being: suppose it was not; then being would lack something, i.e. we would be committed to the non-being of something which, added to what there is, would make it perfect, and since that ruled out by PPMI, being is perfect.

So this a rational deduction, starting from the axiom that can have is but not is not, and looks at consequences. So this not an explanation of the empirical world. The 'way of opinion' tries to do that, but the 'way of opinion' is, strictly, false, since it refers to the varieties of things of ordinary thought. [Note: perhaps can usefully think of Parmenides' project as something like an analysis of the concept 'being'.]