r/Metaphyscs

Parmenides famously claimed that what is is, and what is not is not. Leucippus believed that both what is and what is not are, namely what is is, and what is not is. He divided reality into body and space: body is what is and space is what is not. Leucippus was an ancient greek pluralist and pluralists agreed with Parmenides that the stuff that makes up reality is uncreated, indivisible, eternal and immutable, so they conceded Parmenides' claim that nothing new can ever come into or go out of existence. They also agreed with Heraclitus that there is change, motion, becoming, etc.; In order to reconciliate these views, they turned Parmenidean one into plentitude of atoms and introduced void to allow for locomotion. In fact, pluralism emerged as a reconciliatory approach between Parmenides' and Heraclitus'.

Let's make a quick reconstruction of Leucippus' argument:

1) Body is what is

2) What is is

3) Space is what is not

4) Space is as real as body

5) Therefore, what is not is (1-4)

We see that Leucippus grants the following conjunction: being is and nonbeing is.

Let's take a reconstructed version of Gorgias' argument against that:

1) Assume for reductio that being is and nonbeing is

2) Being and nonbeing are the same with respect to their being (1)

3) Nonbeing is not

4) If nonbeing is not and being and nonbeing are the same with respect to their being, then being is not

5) Therefore, being is not (2, 4)

6) Neither being nor nonbeing is (3, 5)

7) Contradiction! (1, 6)

8) Therefore, 1 is false (reductio 1-7)

Let me pull out my anti-Eleatic argument to spice things up:

1) If being is, then nonbeing is not

2) What cannot cease to be is

3) Nonbeing cannot cease to be

4) Therefore, nonbeing is (2, 3)

5) Therefore, being is not (1, 4)

Maudlin's argument against physicalism:

1) Goldbach's conjecture is either true or false

2) The truthmaker of Goldbach's conjencture is not a physical fact

3) If physicalism is true, there are no non-physical facts

4) therefore, physicalism is false (2, 3)

This is roughly how he stated the argument. I suspect some physicalists will deny commitment to a truthmaker theory or complain about the assumptions behind the second premise, and some will deny 3.

Take supervenience physicalism. Supervenience physicalism concerns the relation between a set of properties or set of facts. Namely, there is no change in non-physical properties without a change in physical properties. But mathematical truths do not require the existence of any physical facts. So, if there are mathematical truths, physicalism is false, a fortiori, supervenience physicalism is false.

One of the famous Zeno's paradoxes of motion or arguments against the possibility of motion goes as follows: in order to cross the room, you have to first get halfway to the end. Since every step takes you only halfway to the end, there is no step from any point to the end, hence you cannot cross the room, i.e., motion is impossible.

By asking "How do you ever cross the room if each step only gets you halfway to the end?", Zeno is asking a general question: "How is motion possible at all?"

The claim is that you cannot cross the room or get to the end because each step only gets you halfway to the end. But if the end of the room would be a halfway point between you and some other end, then you could cross the room. For example, let A be the starting point of whoever walks and B be the endpoint. Let AB denote the distance between A and B, i.e., the length of the interval from A to B. AB is traversable iff there is a point C such that BC=AB, AC=2AB and A, B and C are collinear.

Yet the paradox still blocks reaching halfway to any end because every halfway point is itself an end, so there is always another halfway point between you and that point no matter how many steps you take. Iow, the aforementioned reply begs the question, it would work only if motion were possible, which means it doesn't answer Zeno.