Friday, June 17, 2022

Yet another formulation of my argument against a theistic multiverse

Here’s yet another way to formulate my omniscience argument against a theistic multiverse, a theory on which God creates infinitely concretely real worlds, and yet where we have a Lewisian analysis of modality in terms of truth at worlds.

  1. Premise schema: For any first order sentence ϕ: Necessarily, ϕ if and only if God believes that ϕ.

  2. Premise schema: For any sentence ϕ: Possibly ϕ if and only if w(at w: ϕ).

  3. Premise: Possibly there are unicorns.

  4. Premise: Possible there are no unicorns.

  5. Necessarily, there are unicorns if and only if God believes that there are unicorns. (Instance of 1)

  6. Possibly, God believes that there are unicorns. (3 and 5)

  7. Possibly God believes that there are unicorns if and only if w(at w: God believes that there are unicorns). (Instance of 2)

  8. w(at w: God believes that there are unicorns). (6 and 7)

  9. w(at w: God believes that there are no unicorns). (from 1, 2, 4 in the same way 8 was derived from 1, 2, 3)

So, either there is a world at which it is the case that God both believes there are unicorns and believes that there are no unicorns, or what God believes varies between worlds. The former makes God contradict himself. The content of God’s beliefs varying across worlds is unproblematic if the worlds are abstract. But if they are concrete, then it implies a real disunity in the mind of God.

Premise schema (1) is restricted to first order sentences to avoid liar paradoxes.

23 comments:

William said...

I think that many of the steps are underspecified as to worlds, which allows
some variation in the meaning of "possible" to lead to contradiction.

Using the schema set in step 2 to specify worlds in the later steps:

3. Premise: Possible there are unicorns at a multiverse w: say, possible world w3.

4. Premise: Possible there are no unicorns at many possible multiverses w: w1, w2, w4,...

5. Necessarily, there are unicorns at w if and only if God believes that there are unicorns at w.

6. Possibly, God believes that there are unicorns at w3.

7. Possibly God believes that there are unicorns at w3 if and only if
∃w(at w3: God believes that there are unicorns at w3).

8. ∃w(at w3: God believes that there are unicorns at w3).

9. ∃w(at w1, w2, w4...): God believes that there are no unicorns at w1, w2, w4...).

So with that specification we do not get to an inconsistency.

Making it concrete, if I somehow knew there were unicorns on a planet on the other
side of the galaxy, I could still truthfully say that there are no unicorns in the
entire world, counting on Earth as the world. The same might go for a concrete
multiverse, versus our local universe.

What kind of arguments against such multiverses remain? I suppose that God could not
truly go against his nature in actions involving any universe. So there are limits in
variation in the rules or physics of such universes: they would all be made in some senses good.

Michael Birdwell said...

I don't see the problem. God knows there are toads on Earth, but not on Mars. The same type of thing is going on here. God knows there's a unicorn in w1, but not in w2. What's the contradiction?

Alexander R Pruss said...

Michael: Which premise are you denying?

Michael Birdwell said...

Alex: None, that's my problem. It looks like (in my understanding of Theistic Multiverses like Almeida's) there is w1 with unicorns, and w2 with no unicorns. Hence, God would believe there is no unicorns in w1 (p8) and no unicorns in w2 (p9). Both appear to be correct beliefs, but the premises as you wrote them create an ambiguity since you didn't differentiate between the possible worlds with unicorns and those without. If the premises are meant to say that there is a world where God believes that unicorns are impossible, then I would deny that God has such a belief (since there is a possible world with Rhinos/Unicorns in it). I think the multiverse is probably false for other reasons, but this one doesn't make much sense to me.

Alexander R Pruss said...

If you don't dispute any premise, then presumably you think some nonpremise step is invalid. Which one?

Michael Birdwell said...

Alex: Then I will reject P9. I affirm premise 8. ∃w(at w: God believes that there are unicorns). And premise 9*. ∃w2(at w2: God believes that there are no unicorns). I think that this is the actual derivation of 1, 2, and 4 (I suppose this would be a nonpremise step).

William said...

Perhaps 8. and 9. do not actually contradict one another, because they are each true in a different, underspecified context.

Alexander R Pruss said...

9 is not a premise but a conclusion from 1,2,4. And I don't see a way of accepting the derivation of 8 from 1,2,3 that doesn't in exactly the same way give a derivation of 9 from 1,2,4.

If you do accept 8 and 9, then you need to deal with the prose argument afterwards. Which we can put more precisely as:

10. ~∃w(at w: (God believes that there are unicorns AND God believes that there are no unicorns))
11. ~∃w1∃w2(at w1: God believes that there are unicorns AND at w2: ~(God believes that there are unicorns))
12. ~∃w1∃w2(at w1: God believes that there are no unicorns AND at w2: ~(God believes that there are no unicorns)).
13. Contradiction!

Michael Birdwell said...

Isn't it
10. ~∃w(at w: (God believes that there are unicorns AND God believes that there are no unicorns))
11. ~∃w1∃w2(at w1: God believes that there are unicorns at w1 AND at w2: ~(God believes that there are unicorns at w2))
12. ~∃w1∃w2(at w1: God believes that there are no unicorns at w1 AND at w2: ~(God believes that there are no unicorns at w2)).

I might not understand predicate logic well enough to see how there's an actual contradiction between God knowing that there are unicorns in one world and God knowing there are not unicorns in a different world, but still knowing about the unicorns in the first world

Japexican007 said...

Why is God “believing” x or y to be true.
God is omniscient he either “Knows” x or y
Is true therefore there’s no need to “believe”
X and y is true. “Believe” implies a sort of lack of knowledge
Such as when someone asks how much money do you
“Believe” I have in my wallet? I don’t think God
“Believes” something to be true he either knows it to be
True or false

Zsolt Nagy said...

You, Japexican007, are conflating "to believe in a proposition (to be true)" with "to having faith in a proposition (to be true)". In philosophy they are not quite the same thing (even when some philosophers might want to have or "believe" that to be the case).
Usually when there is an evidence for a proposition P to be true, then someone might "believe" that proposition P to be true - except for basic beliefs of some propositions P*, where proposition P* is self-evidentially, trivially, or obviously true without further evidence.
Someone might "have faith" in a proposition P' to be true, if that proposition P' is not self-evidentially true and there is no evidence in sight for that proposition P' to be true. But since there is or might be no evidence that proposition P' to be false, therefore it is not unreasonable for "having faith" in that proposition P' to be true.
You can go figure that for yourself out, if that is rational to do so or not -
"Extraordinary claims/propositions require extraordinary evidence in order for such extraordinary claims/propositions to be "believed" in to be true."

Japexican007 said...

Zsolt naggy

What is your definition of “believe” and why do you “believe” God would fall into
Having to “believe” anything rather than already know something is true, as being omniscient
Belief itself seems like holding on to a position without having data or direct experience of something
But God being omniscient would and should not be subject to “belief” if his omniscience leads him
To have direct knowledge of x thus bypassing the “belief” stage

Zsolt Nagy said...

Hm. My link didn't work the last time. So here it is again for the term "to believe in a proposition (to be true)".
I think, that I already explained, what I understand under that term. So I'm only going to reiterate here:
Someone might believe in a proposition P to be true justifiably and with a warrant, if and only if there is evidence for that proposition P to be true - except for "basic beliefs"/beliefs in some propositions P* to be true, where those propositions P* are self-evidentially, trivially or obviously true without further evidence.
(Are then "basic beliefs" justified or warranted? This is quite a good question.)
Besides that I don't believe in God, since no such extraordinary evidence have been provided for such an extraordinary proposition and I also have no faith in God, since faith in itself is unjustified and unwarranted.
So better ask that question of yours regarding God someone, who is actually believing in God or has faith in God. After all that's his or hers burden of proof of his or hers proposition about God and not mine.

Japexican007 said...

Zsolt Nagy you neither answered what I asked nor is your response related to the original post

Zsolt Nagy said...

You, Japexican007, asked "Why is God “believing” x or y to be true." and I answered, that "Someone might believe in a proposition P to be true justifiably and with a warrant, if and only if there is evidence for that proposition P to be true...".
Just put 1 plus 1 together and you get 2 or in this case:
God is 'believing" x or y to be true, because God got some evidence for x or y to be true.
You are still conflating "believing in a proposition (to be true)" with "having faith in a proposition (to be true)".
Your definition of the term "believing in a proposition (to be true)" is a thing and the philosophical definition of the same term is another.
I guess, that's all there to it here regarding your question and this post.

Japexican007 said...

Someone might believe in a proposition P to be true justifiably and with a warrant, if and only if there is evidence for that proposition P to be true...".

Sure I agree with what you said, I don’t agree with belief to be synonymous with knowing, if God knows something to be true then there is no need for God to “believe” something is true, I hold to the view that

Knowledge is all about information. Knowledge is what we gain through experience and experimentation. God knows what is true because he is omniscient

Belief on the other hand is a firmly held opinion. This does not require any information as in the case of knowledge.

Just like one can say I believe you have x amount of dollars in your wallet without any information whatsoever, this has nothing to do with knowing how much money I actually have, one is not synonymous to have a “belief” of x if one has knowledge of x. I disagree with your expression of belief and knowledge being interchangeable

Zsolt Nagy said...

Yeah, I know, that you, Japexican007, are disagreeing with the general notion of belief and knowledge. But I don't know exactly, for what reasons you are disagreeing.
It appears to me, that if you believe me having some amount of money in my wallet, then it is for some specific reasons like you knowing/believing me to be an adult working person, who usually has some money in his or hers wallet. Otherwise your believe wouldn't be justified or warranted.
By splitting hairs here you are just creating a double standard. For what specific reason is this kind of a double standard necessary? Or for what reasons exactly are justified and warranted belief and justified and warranted knowledge to be separated?

Japexican007 said...

I’m not sure where you get your double “standard from”, you can Google the difference between belief and knowing you don’t need to my take my word for it, it seems you just disagree because your definition doesn’t apply for every instance as I have shown

God knows x does not imply God “believes x to be true” one has data and direct experience and the other doesn’t, it’s quite simple

The definition you used “ Someone might believe in a proposition P to be true justifiably and with a warrant, if and only if there is evidence for that proposition P to be true...".

“Someone might believe in a proposition to be true justifiable and with a warrant” so what? That’s not the definition of belief that’s a reason to justifiably believe I’m something

“If and only if that proposition p to be true” this again doesn’t apply to every instance of belief such as the wallet scenario or even if have a jar with x amount of marbles, just because you believe the jar has 99 marbles doesn’t mean you’re justified in believing or have data to believe that conclusion, conversely you don’t need to have data or be justified in holding a belief to have a belief, those are two different things that you’re equating, God doesn’t need to believe something because he has the omniscience to know the instance of that something, I’m not sure what you’re arguing for here but it seems to be your own definition of “belief” incorporated with the definition of “knowledge” or knowing

Zsolt Nagy said...

I'm not arguing here for anything.
You asked a question and I simply answered it.
Sure. I am also capable of googling.
Here is what I found about this subject matter:
"Belief vs Faith (Philosophical Distinction)" by Carneades.org
At 2:46: "... In such a model, faith might be contrasted with knowledge. Both are kinds of belief. While knowledge is true, justified belief, faith is belief that may be true, but is not yet justified."
You have your own definitions. So I have my own definitions. You asked a question and I answered that question.
I reiterate: You are conflating "having a justified and warranted belief in a proposition P (to be true) in other words knowing that proposition P (to be true)" with "having an unjustified and unwarranted belief in a proposition P' (to be true) in other words having faith in that proposition P' (to be true)".
That's all, I guess.

Japexican007 said...

Belief vs faith? No one said belief vs faith
Why would God have faith vs belief
I’m sorry this is a strawman

Zsolt Nagy said...

I'm not "no one". I'm some one and I said "Belief vs Faith". Hence, not no one said "Belief vs Faith", but some one said "Belief vs Faith".
As for why would God have faiths or beliefs?
Because any one can have faiths or beliefs AND God is some particular one. Hence, some particular one can have faiths or beliefs AND God is still some particular one. Therefore, God can have faiths or beliefs.
This is not a straw man. But this is simple and plain logic.

Japexican007 said...

Your response didn’t attack my original statement of belief vs knowledge but rather you’ve made up your own dilemma, as for your reasoning
Why would God have faith? Because anyone can have faith, depends what exactly your definition of faith is, if it’s something like trust without knowledge then no because God is omniscient, but furthermore faith in what exactly? Again this strawman response is beside any conversation that anyone brought up except of course yourself, which you seem to think if you bring up an argument or response against no one but yourself then that somehow counters what others have said which has nothing to do with anything you’ve said, that’s kind of odd, someone presents 2+2= 4 and you say yea but 3*5 = 15 which has nothing to do with what was said but you want to be taken seriously rather than someone who has no idea what they’re talking about so they say whatever is on their mind to make it seem as if they’re part of the conversation, now I think you’re a troll, this is my last response, good day

Zsolt Nagy said...

You have given some arguments?!? Ah, you mean, that you have your own definitions of things.
Sure. As I have my own definitions of things.
As far as I'm concerned, I have simply answered your questions.

Besides that the claim "anyone can have faith" doesn't only depend on the definition of faith. You can and I think, you rather want to reject that claim and if so, then please do it properly: Not anyone can have faith. Or to say, that someone can not have faith and that someone supposed to be for example God, since bla, bla, bla.
If so, then my response is this: Supposedly every one except for God is created in the "image" of God and apparently every one except for God can have faith or beliefs. So then why exactly is God such an exception?!?
It should come naturally, that if every one except for God is created in the "image" of God and every creation/"image" of God can have faiths or beliefs, then also the Creator/God himself is capable of having faiths or beliefs.

Besides that you didn't presented "2+2=4". But rather asked questions like "Why is 2+2=4?".
My answer and response: Because "2+2=4" follows from some mathetical axioms - unjustified and unwarranted propositions assumed and believed to be true, not really derviable claims by any rational reasoning besides of those axioms being consistent. So it is really hard and difficult to imagine God having no faith in such mathematical axioms to be simply consistent.
Expecially if that God supposedly knows such mathematical propostions like "2+2=4" to be true like and as we do.

Have also a good day!

Best regrads,
Zsolt Nagy