ฝัง
- เผยแพร่เมื่อ 12 ก.พ. 2013
- I discuss how we can impose conditions on the accessibility relation to generate new systems. I briefly analyse three such conditions and then introduce four new systems.
Errors: at about 9:25, that should be not possibly p, 1.
at about 13:52, S4 should be "M + transitivity".
I love your videos. As I was trying to grok the systems, I came up with this: K is a hypocrite's system (says things which apply to his relations, but not to him). M lives up to his word. B is for friends (true for his friends and himself). S4 is for family (grandfather's rules apply to father and me, father's to me, but my rules don't "flow back up"). S5 is for the community (same rules for everybody).
Haha, that's a good way of thinking about it. Thank you for your kind comments.
Another good way of thinking about these formulas may be the number of squares or diamonds in each characteristic formula.
We can think of these as the number of times we are travelling between worlds ( not always , just another way of remembering , say the transitivity formula , 2 squares means we travel to world 2 then world 3 and then apply whatevr we want ) ...
Why did i not find this channel when i first started my logic class. ugg! Great to have these here though thanks for posting!! I was wondering your thoughts on the S5 axiom particularly ([]P-->[]P), for im writing a paper on leibniz who uses this as a proof for his god. However i dont find it very convincing, was wondering if you could offer any help in any way.
Edit- as soon as i went to the next video in the series i got your answer in the comments ahah! Thanks!
Thanks for these!
Speaking as a theist, there are interesting arguments for God, which are neither unsound, nor in any obvious way beg the question, but it's not surprising that even theists like myself, let alone atheists, are not swayed in this way. It would be difficult for a missionary to convert the norseman with "that species of reasoning," to borrow a phrase from Hume. The value to these arguments would be intellectual capital for one's beliefs. Just as it is silly for a theist to disregard objections to arguments for God, it would also be silly for an atheist to simply disregard arguments for God in a logical system whose axioms she accepts.
Ether way, I don't think S4 and S5 will endure. Judging from various papers, they might both be dead.
+JesseMoshe
I'd like to see what papers you're reading. The feeling I get as I read the literature is that they are the majority consensus and that isn't going to change.
+Returnality
So the literature I have access to is not published yet. It is being watered down into less technical presentation. But it details how in order for S4 and S5 to hold, it must be at the expense of the simple necessity of arithmetic. If you would like to request a copy of one of the more technical proofs, please email dajohnso@yu.edu.
JesseMoshe
"It is being watered down into less technical presentation."
That's actually somewhat disappointing. Would it be possible to ever get access to all the articles in all their technical glory?
Also, do I need any connections to universities in order to get the relevant articles? I'm unfortunately not connected to anybody right now.
+Returnality
Heh. Agreed! Even logic journals that accept papers require a level of dumbing down. We're so afraid of rigor. No connection required. Just tell Dr. Johnson that you know his student, Jesse, and request his paper, "Who Mourns for S5?"
+Returnality
Hey, there! Any luck reaching him? If not I'll reach out to him myself. The other literature I've read on the weakness of S4 and S5 was from various proofs from undergrads. But I would like to get you the publishable version. Let me know if you're having trouble...
I do not understand. When you defined system K, we imposed no restrictiond or conditions on R. This from that it follows that these other systems, are just system K, and they are not extensions, but actually subsets if anything.
Nothing prevents you from drawing transitive arrows in system K.