User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

is this right? --GFauxPas 21:58, 11 August 2012 (UTC)
 * Made some changes. Still needs reference from Category:Propositional Logic --Andrew Salmon 22:15, 11 August 2012 (UTC)
 * It's all yours, I don't feel like finishing it. --GFauxPas 22:18, 11 August 2012 (UTC)

Space and Time
Found this interesting proof by Leibniz in a philosophy book. Does it belong on PW? It's more philosophy than logic.

Theorem
Space has no absolute substance or being. Rather, it must be entirely defined by the orders of bodies in it.

Similarly, time etc. events etc.

Proof
Let $\mathcal Q$ be the physical universe like it currently is.

Let $\mathcal Q\,'$ be a mirror image of $\mathcal Q$.

In completely empty space, one point does not differ from any other in any property at all.

Hence $\mathcal Q$ and $\mathcal Q \,'$, if they differ, differ because their respective spaces differ.

God chose to bring $\mathcal Q$ into existence.

If $\mathcal Q \ne \mathcal Q \,'$, then God arbitrarily chose to do an act without a reason. This contradicts the Principle of Sufficient Reason.

Suppose, then, "space" is not a property at all, and rather is just the order of bodies in space.

Then $\mathcal Q = \mathcal Q \,'$ from Leibniz's Law, and there is no room for inquiry of choosing one over the other.

Similar argument with time, where you take the universe and make everything happen one hour earlier.

--GFauxPas 02:04, 19 August 2012 (UTC)


 * It's more of a "philosophical argument" then a proof, like Pascal's Wager. It just has a logical bent to it. --GFauxPas 02:09, 19 August 2012 (UTC)


 * Stick it under "Philosophical Questions" like Pascal's Wager if you will (it's an interesting record on how primitive man used to think) but (a) I'm not sure it hangs together as a proof (the line "If $\mathcal Q \ne \mathcal Q \,'$, then God arbitrarily chose to do an act without a reason" does not logically follow, for example) and (b) it is not certain to be true. Presumably this is something Leibniz cam up with? --prime mover 05:35, 19 August 2012 (UTC)


 * I'm trying to do as much justice as I can to the argument that Leibniz himself presented. I'm also not convinced by his argument, but it's interesting in any event. I'm not sure how much Leibniz is using it as a proof per se. He could just be using it as an appeal to the intuition of the reader, claiming it makes more sense than the alternative. --GFauxPas 10:03, 19 August 2012 (UTC)
 * And yes, this is Leibniz's own creation, he says so explicitly. --GFauxPas 10:15, 19 August 2012 (UTC)

I'd say more interesting than the argument itself is seeing how Leibniz viewed Leibniz's law, viz. $\mathcal Q$ vs. $\mathcal Q\,'$. --GFauxPas 11:48, 19 August 2012 (UTC)


 * Bear in mind that this "proof" demands the existence of a "god" who to any rational mind is fictional. Not only does it posit the existence of such an entity (in contradiction to Occan's razor but it assumes certain qualities of such a being; those qualities, it needs to be emphasised, that specifically back up the argument Leibniz is making. Effectively: "In order to justify my belief in this statement, I assign to an arbitrary omnipotence the desire for this statement to be true." So, if this proof does go anywhere near the main pages of ProofWiki, it goes in "fallacies". Specifically which if the many and varied logical fallacies (haven't posted them up here - they are more relevant to the philosophical / rhetorical branch of logic than the symbolic / mathematical) we can leave up to the student. --prime mover 12:59, 19 August 2012 (UTC)

In Leibniz's defense, he does spend quite a lot of text addressing the issue of God's existence, benevolence etc. before getting to this issue. Though I don't agree with the argument for reasons unrelated to this conversation, you could alter it to say "there would be no reason for $\mathcal Q$ to exist rather than $\mathcal Q\,'$ to exist". --GFauxPas (talk) 13:19, 19 August 2012 (UTC)