I have seen one recent proof that Supreme being exists based on higher order logic and reasonable axioms, which is verified by computer, and shows that necessarily there is at least Simplified Supreme being:
Here's paper of proof:
https://arxiv.org/abs/2001.04701
It has removed almost all problems from Godel proof, such as removing axioms 2, 4 and 5, and required only 3 axioms, which are very reasonable.
Here's are axioms of paper, as it requires only 3 axioms and are very reasonable which doesn't implies other axioms which are controversial:
(Quote)
A1’ Self-identity is a positive property, self-difference is not.
A2’ A property entailed or necessarily entailed by a positive property is positive.
A3 The conjunction of any collection of positive properties is positive.
(Unquote)
If we can state instead of positive property, second order P property is such as it satisfies above axioms, as someone may object word positive.
First axioms I think is uncontroversial, which can be accepted by reasonable person. It only divides properties in such a way that properties which has same interpretation as self identity is P property, and has same as self difference are not P property.
As self identity and self difference are not same, but different and of opposite, it is possible to divide them into two groups, such as P property, and not P.
And interpretation of P can be such as properties who's negation is contradictory are not P property, like self difference is not P property. Or there can be other way to partition or divides it in such a way that first axioms should be uncontroversial.
Second and third axioms are also such that whole system is consistent, which means it is possible to have such property or to divides property in such a way that can satisfy axioms, and is possible in some world.
Now as it proves that necessary being exist, if it is possible the it is necessary, and thus, it proves that simplified Supreme being exist necessarily.
It's not clear that the conjunction of positive properties is positive. For instance, knowing that Trump is president seems positive as does knowing that Trump is not president (of course, the latter property can only be had in a world where Trump is not president). But the conjunction of these two properties is contradictory, and hence not positive.
I think this problem may be solved if we can modify definition of positive property, or P property.
Author has removed axiom 2 of previous, which means it isn't necessary that property is either positive or it's negation is positive. And author also checked for proof by which it isn't implies.
So, we can interpret P property in different ways such as neither of "knowing Trump is president" or "not knowing Trump is president" is P property.
As author has given alternative way to state P property:
(Quote)
An alternative to A1’ would be: The universal property (λx.>) is a positive property, and the empty property (λx.⊥) is not.
(Unquote)
Now property of "not being identical to itself" implies contradiction. Or it is empty property as it is self difference. But same is not case for "not knowing that Trump is president" or "knowing that Trump is president", neither of property is universal property or empty property.
And if having self identity, which is P property doesn't entail possibly or necessarily that "knowing Trump is president" then we don't need to divide it as positive or not positive. And thus all property, which entails by self identity or universal property, and whatever property after entails, only needs to be positive property. But if property of "Knowing Trump is president" doesn't entails by any property which first entails by universal property or self identity, then we not need to divide it as positive and not positive. And thus such conjunctions of such properties which is firstly entails by universal property or self identity only need to be such as conjunction of them don't becomes empty property.
Or my second thought is property that "knowing Trump is not president" is not possible, because to know something one needs absolute knowledge, and knowing that brain is not vat, not simulation, one isn't being deceived, one is not in hallucinations, one not facing illusions, and all other state of affairs exactly in all ways, such as that knowledge may not possible. And there can't exists such property.
"Knowing that self identity is P property" is entails by self identity, and thus it may be P property, or "Knowing that universal property is P property" is entails by Universal property, and thus P property, but I can't think a way by which such sequence can leads to Knowing that Trump is president or it's opposite, and if it doesn't then it doesn't have to one of two, or not need to P property or not P property, and thus it may not problem.
Thanks for the insightful lecture on beauty, Prof. Pruss! I'm curious, why not include feminine beauty? That seems like a universal paradigm of beauty.
That's great. Can you provide the slides here?
ReplyDeleteDone.
ReplyDeleteThanks a lot. That's some good stuff
ReplyDeleteThanks so much for doing this, Alex.
ReplyDeleteHello,
ReplyDeleteI have seen one recent proof that Supreme being exists based on higher order logic and reasonable axioms, which is verified by computer, and shows that necessarily there is at least Simplified Supreme being:
Here's paper of proof:
https://arxiv.org/abs/2001.04701
It has removed almost all problems from Godel proof, such as removing axioms 2, 4 and 5, and required only 3 axioms, which are very reasonable.
Please see it at least once.
Jay Sri Krishna
Here's are axioms of paper, as it requires only 3 axioms and are very reasonable which doesn't implies other axioms which are controversial:
Delete(Quote)
A1’ Self-identity is a positive property, self-difference is not.
A2’ A property entailed or necessarily entailed by a positive property is positive.
A3 The conjunction of any collection of positive properties is positive.
(Unquote)
If we can state instead of positive property, second order P property is such as it satisfies above axioms, as someone may object word positive.
First axioms I think is uncontroversial, which can be accepted by reasonable person. It only divides properties in such a way that properties which has same interpretation as self identity is P property, and has same as self difference are not P property.
As self identity and self difference are not same, but different and of opposite, it is possible to divide them into two groups, such as P property, and not P.
And interpretation of P can be such as properties who's negation is contradictory are not P property, like self difference is not P property. Or there can be other way to partition or divides it in such a way that first axioms should be uncontroversial.
Second and third axioms are also such that whole system is consistent, which means it is possible to have such property or to divides property in such a way that can satisfy axioms, and is possible in some world.
Now as it proves that necessary being exist, if it is possible the it is necessary, and thus, it proves that simplified Supreme being exist necessarily.
It's not clear that the conjunction of positive properties is positive. For instance, knowing that Trump is president seems positive as does knowing that Trump is not president (of course, the latter property can only be had in a world where Trump is not president). But the conjunction of these two properties is contradictory, and hence not positive.
ReplyDeleteHello sir,
ReplyDeleteI think this problem may be solved if we can modify definition of positive property, or P property.
Author has removed axiom 2 of previous, which means it isn't necessary that property is either positive or it's negation is positive. And author also checked for proof by which it isn't implies.
So, we can interpret P property in different ways such as neither of "knowing Trump is president" or "not knowing Trump is president" is P property.
As author has given alternative way to state P property:
(Quote)
An alternative to A1’ would be: The universal property (λx.>) is a positive property, and the empty property (λx.⊥) is not.
(Unquote)
Now property of "not being identical to itself" implies contradiction. Or it is empty property as it is self difference. But same is not case for "not knowing that Trump is president" or "knowing that Trump is president", neither of property is universal property or empty property.
And if having self identity, which is P property doesn't entail possibly or necessarily that "knowing Trump is president" then we don't need to divide it as positive or not positive. And thus all property, which entails by self identity or universal property, and whatever property after entails, only needs to be positive property. But if property of "Knowing Trump is president" doesn't entails by any property which first entails by universal property or self identity, then we not need to divide it as positive and not positive. And thus such conjunctions of such properties which is firstly entails by universal property or self identity only need to be such as conjunction of them don't becomes empty property.
Or my second thought is property that "knowing Trump is not president" is not possible, because to know something one needs absolute knowledge, and knowing that brain is not vat, not simulation, one isn't being deceived, one is not in hallucinations, one not facing illusions, and all other state of affairs exactly in all ways, such as that knowledge may not possible. And there can't exists such property.
ReplyDeleteOne more thought is:
ReplyDelete"Knowing that self identity is P property" is entails by self identity, and thus it may be P property, or "Knowing that universal property is P property" is entails by Universal property, and thus P property, but I can't think a way by which such sequence can leads to Knowing that Trump is president or it's opposite, and if it doesn't then it doesn't have to one of two, or not need to P property or not P property, and thus it may not problem.
I converted Prof. Alexander Pruss' Wilde lectures in natural theology (2019) from video (mp4) to audio (mp3) to share on Google Drive:
ReplyDelete1. The argument from beauty
2. The argument from the falsity of scepticism
3. New work for natural law in metaphysics, ethics, and epistemology, part 1
4. New work for natural law in metaphysics, ethics, and epistemology, part 2
5. Did God make the natural numbers?
Yay! I was looking for these the other day, and thought maybe they weren't recorded.
ReplyDeleteHere are the direct links to the videos:
ReplyDeletehttps://www.theology.ox.ac.uk/sites/default/files/theology/videos/media/wilde_lecture_1_2019.mp4
https://www.theology.ox.ac.uk/sites/default/files/theology/videos/media/wilde_lecture_2_2019.mp4
https://www.theology.ox.ac.uk/sites/default/files/theology/videos/media/wilde_lecture_3_2019.mp4
https://www.theology.ox.ac.uk/sites/default/files/theology/videos/media/wilde_lecture_4_2019.mp4
https://www.theology.ox.ac.uk/sites/default/files/theology/videos/media/lecture_5.mp4
Thanks for the insightful lecture on beauty, Prof. Pruss! I'm curious, why not include feminine beauty? That seems like a universal paradigm of beauty.
ReplyDelete