# ydoaPs

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1. ## Sets vs Omniscience

This argument came up again recently, and I realized that appealing to proper classes or conglomerates won't actually help. See, the argument itself is a proof of negation, so it works in any nondegenerate topos. And it came to my attention that Cantor's Theorem generalizes from Set to an arbitrary topos. For any object Y in an arbitrary nondegenerate topos, there is no surjection f: Y -> 2Y. So you can run the exact same argument swapping out talk of sets with talk of objects and talk of subsets and members with talk of subobjects. So, the argument can be formulated for an arbitrary topos.
2. ## What made you stop believing in God?

ScienceForums(dot)Net

4. ## Why does the Christian God allow slavery in the Bible?

Because He explicitly OKed the practice all the way including sex slavery and beating slaves to within an inch of their lives. Then, in the New Testament, slavery is *still* condoned, so it's not an Old vs New thing
5. ## Why does the Christian God allow slavery in the Bible?

This an example of a pastor lying and hoping you won't actually research it. Pastors and apologists have financial incentives to lie about things like this. As pointed out below, Pastor Doug is conflating two different sets of rules for two different groups of people. The Bible actually does condone slavery as practiced in the US. It even explicitly says you can beat a slave within an inch of their lives so long as they live until morning, because they are your property.
6. ## Do you think moderators are a bit harsh sometimes when closing a thread?

You may have misspelled "years"
7. ## Oh Em Jibbers

Sayo has returned
8. ## "Law of middle" (split from De Broglie relation)

I think part of the problem here is that you've got the relation between logic and ontology backwards. It's rationality that follows nature, not the other way around. For the true description of nature to have logic at all, it has to form something called a "topos". The thing about roses, though, is most of them are intuitionistic. That is, LEM is a fairly unusual property of logics. So, the fact that the topos formed by QM is intuitionistic instead of Boolean shouldn't be that surprising. But this isn't "violating" logic in any way. It's just that the logic that falls out of QM is different than the logic that falls out of classical mechanics
9. ## "Law of middle" (split from De Broglie relation)

The topos describing QM, like most toposes, is not Boolean; LEM does not hold in QM. It has an intuitionistic logic
10. ## why do people/you bleave in the bible but refute scientific evidance

! Moderator Note As this thread serves no purpose other than to denigrate religious people, it is now closed.
11. ## What are you reading?

Algebra: Chapter 0
12. ## Sets vs Omniscience

That's the reason for set B. It takes the sets and transforms them into truths
13. ## Sets vs Omniscience

I'm not sure why you thought that was a relevant response (wrong thread, maybe?), but it's trivially wrong. That would imply that there exist infinitely many universes in which the multiverse theory is false
14. ## Sets vs Omniscience

Yes, that should have been "nonempty set from which it is generated". Good catch. I'm not sure how type theory would help here. Could you elaborate?
15. ## Sets vs Omniscience

Let A be the set of all things known by God. If God knows it, it's in A. It doesn't matter what it is; if it's a piece of God's knowledge, then it's in A. Now, let's take A and construct what's called the "Power Set" of A [we'll use "P(A)" for short]. The power set is just the set of all subsets of the set. So, if our set is {1, 2, 3}, then it's power set is {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}, {1, 2, 3}}, where ∅ is the set of nothing. An important fact to note is that there is a lot more in the power set than there is in the original set. In fact, for any set, its power set has a higher cardinality than it. This is a famous result called "Cantor's Theorem". Power sets are always bigger than the sets from which they are generated. If we take P(A), we can make a new set B = {"x is a subset of A"|x∈P(A)}. So we take an element of P(A) and the statement that this element is a subset of A is an element of B. And we do that for all elements of P(A). Since there is nothing else in B, this relation between P(A) and B is a bijection. So we know B and P(A) have the same size, which means B is bigger than A. Since the power set of A set just is the collection of subsets of the set, and B just is collection of statements asserting that each element of of P(A) is a subset of A, we know that every statement in B is true. Since B is bigger than A, we can conclude that there are truths that God cannot know. If God knows infinitely many things, in fact, there are infinitely many truths that God does not know.
16. ## Was the snake a liar?

But that's only a lie if you quote it out of context. In context, it's a denial of God's claim that they would die the day they ate the fruit. They ate it and lived throughout the week, so the serpent didn't lie. God did.
17. ## What is Time?

I thought clocks measure other clocks.
18. ## Energy, Cost and Subsidy in Power Production

! Moderator Note This thread has become nothing but Trolling/counter-Trolling/bickering. It is now closed.
19. ## How is energy conserved when length contracts?

Energy is conserved, but not invariant. Within a frame, energy in equals energy out, but between frames, energy need not have the same sum.
20. ## Italy invented the compass.

! Moderator Note This thread started off in a grey area and isn't going anywhere. Upon staff review, this thread is closed.
21. ## Could be a great idea!

! Moderator Note Link in the OP removed. If you want to discuss your speculations here, present them here.
22. ## Removal of the down-vote, yes or no?

Theoretically, improved quality means more up votes, so increased quality over time will "get rid of" the negative reputation. It's not an insurmountable task like it would be were we using the old system where a downvote from somebody with enough positive reputation *cough* swansont *cough* would have such a strong effect that the damage to the reputation would be effectively infinite. And we have both natural and artificial buffers to reputation abuse. Posters notice abuse and often upvote to counteract the unnecessary downvote. Also, we have a special user group that habitual rep abusers get put into. That being said, staff don't read all threads, so we don't notice all abuse. If you think somebody is abusing the reputation system, report a post that was abused and tell us about it. A great way to help with both issues is to be very generous with positive rep. A post doesn't need to win a Pulitzer prize to deserve some rep. The problem there is that it could lead to feuds of reputation abuse. Iirc, we had that sort of problem when you could leave a comment with your rep. Though, that was before I became a demigod. Just so you know, staff *can* see who reps what posts, and it's not always who you think. For example, a few posts above, one poster got a negative rep and the immediately following post is replying with a snide comment. One might reasonably think that the poster making the snide comment left the rep, but they didn't (I checked).
23. ## Scientific Method in climate science

! Moderator Note Upon staff review, this thread will remain closed.
24. ## quantum mechanics related problem

! Moderator Note Homework Help Rules A simple reminder to all: this is the "Homework Help" forum, not the "Homework Answers" forum. We will not do your work for you, only point you in the right direction. Posts that do give the answers may be removed.
25. ## My Favorite Proof 1 = 2 (that doesn't divide by zero)

Yeah, as far as I can tell, it's because x is being treated like a constant instead of a function on the right hand side in the first step.
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