An argument against creation ex nihilo

[Playfishpaste]

Take the sentence "God will create the world from nothing" and represent it as the wff C.

Call the set of worlds in which C is true {w:w⊨C}. The probability of C we'll call P(C) and we'll represent this as u({w:w ⊨ C}) where u is a function that takes as its arguments sets of worlds and outputs their probability. The probability of the set of all worlds is one. The probability of a union of disjoint sets of worlds is the sum of the probabilities of each world. The probability of a set of joint worlds is the sum of their probabilities plus the probability of their intersection.^1,2

We can split C into a very large conjunctive sentence. Call the proposition "God exists" G.

Then "C" can be written as "G ∧¬A ∧¬B ∧¬C ∧¬D...", where A,B,C, and so forth are existential propositions. We know that P(G) is 1 since God is a necessary being, and therefore exists in the set of all worlds (and the set of all worlds has a probability of 1). The probability of nothing existing at all then, is 0. Correspondingly there is only one existential proposition that is a member of the set {w:w ⊨ C}. However, if the prior probability of nothing is very low, and worlds in which there is just one true existential proposition are similar to worlds in which nothing exists, then by the similarity relation³ those worlds have a very low probability as well. We are unjustified of course, in saying the probability is zero, because they are certainly still possible worlds by most possibility criteria. So we simply say the probability of the set of w such that C is true in w is ridiculously low, or <<<<<<<1.

From this it follows that, probably, there was something around when God was making the world. Maybe meta-world stuff. A more plausible solution is that the universe simply infinitely existed, and God has sustained it forever (as in the Thomist account of christianity). Another possibility is pantheism, which implies the universe is god, or panentheism, which implies the universe is made out of God stuff and so is a piece of God.

1. Bacchus, Fahiem. "On Probability Distributions over Possible Worlds." Uncertainty in Artificial Intelligence 4 (1990). Print. (Available at citeseer:http://citeseer.ist.psu.edu/viewdoc/...10.1.1.173.620)

2. Poole, David L., and Alan K. Mackworth. "6.1." Artificial Intelligence: Foundations of Computational Agents. New York: Cambridge UP, 2010. Print. (Available online by courtesy of the authors:http://artint.info/html/ArtInt_140.html)

3. Bigelow, John C. "Semantics of Probability." Synthese 36.4 (1977): 459-72. Print. (Available at jstor:http://www.jstor.org/pss/20115242)

[The Dude]

Is this propositional logic? I'm having serious problems trying to read it without proper formatting.

[Playfishpaste]

I spiffed up the conjuncts a bit, but other then that I don't see what's wrong with the formatting.

[The Dude]

I spiffed up the conjuncts a bit, but other then that I don't see what's wrong with the formatting.

Maybe it's the way it's been taught to me here in Netherlands but it looks way different at my university. The conjucts and negations were about the only things I recognised.

[Gaidin]

Why is God a necessary being?

[Playfishpaste]

Why is God a necessary being?

dictionary?

But I mean, you could make him a contingent being, or just non existent, then the argument would just be an argument against god's existence in general, not an argument about what type of method god used to make the world.

[Gaidin]

dictionary?

But I mean, you could make him a contingent being, or just non existent, then the argument would just be an argument against god's existence in general, not an argument about what type of method god used to make the world.

Piece of advice. If you're going to stick with formal logic, state god as one of your assumptions. You didn't do that, so I was wondering where that came from and how it was shown as logically true.

[Playfishpaste]

God's being necessary entails his existence, so he has to exist. Hence why the probability was one, I figured this was trivial since everyone whose familiar with ontological arguments would see why that's so.

[Gaidin]

God's being necessary entails his existence, so he has to exist. Hence why the probability was one, I figured this was trivial since everyone whose familiar with ontological arguments would see why that's so.

Not really. Not everyone accepts the idea of an a priori proof for this, or many other things. Mostly because it's not conceptual knowledge to be understood independent of experience. Hell if I'm reading that correctly, you're not even attempting such a proof anyway. You've assumed he exists(rightfully so for this argument, for all you don't formally state it, annoyingly), and then made the argument on what I'll phrase as the 'method of creation'. It makes for an easy misunderstanding.

[Playfishpaste]

K is a necessary existential proposition.

Let's ask of K whether it is possibly true.

Well, since K involves no contradiction, it's logically possible.

But K's being logically possible entails it's true in a possible world, and by s5, it's true in all possible worlds.

The actual world is obviously possible, by axiom B, so clearly, K is true in the actual world as well, and K says "god exists".

You might say "God exists" is not a necessary existential proposition, because it's incoherent. But again, this would take some sort of argument, and if it is incoherent than you should just reformulate the argument as a critique of creation ex nihilo in general (and not involve God in the argument at all).

[chriscase]

Well the first obvious question I have is how do you know that {w:w⊨C} is actually a set, and does it matter if it is not.

Without a lot more definitions and axioms this looks like a metaphysical thesis dressed up in mathematical clothing.

[Playfishpaste]

Well the first obvious question I have is how do you know that {w:w⊨C} is actually a set, and does it matter if it is not.

I do not know what you mean. That describes a set of possible worlds (are you familiar with modal logic?). Just like something like the set {B:B⊨R} where B denotes a member of the domain "coke bottles" and R denotes "redness" describes a set of coke bottles. Maybe you're asking if the set is empty? Or not well defined?

Without a lot more definitions and axioms this looks like a metaphysical thesis dressed up in mathematical clothing.

Well it's quite obviously a metaphysical thesis (it talks about the nature of the cosmos and the history of it), but I don't see what other axioms you need? Do you think the similarity relation is false? Do you think modal semantics are incoherent? What's the problem exactly?

[chriscase]

I do not know what you mean. That describes a set of possible worlds (are you familiar with modal logic?). Just like something like the set {B:B⊨R} where B denotes a member of the domain "coke bottles" and R denotes "redness" describes a set of coke bottles. Maybe you're asking if the set is empty? Or not well defined?

Definition of a set using this type of formalism is usually an artifact of what we refer to as naive set theory. This would allow the construction of the set of all sets and leads to Russel's paradox. So something like your set of all possible worlds appears to be a problematic collection that, strictly speaking, cannot be a set.

I'm not sure it really needs to be a set, according to the subsequent operations you do on it. That's what I was asking.

Well it's quite obviously a metaphysical thesis (it talks about the nature of the cosmos and the history of it), but I don't see what other axioms you need? Do you think the similarity relation is false? Do you think modal semantics are incoherent? What's the problem exactly?

Oh, that was merely my superficial impression. When I have a specific objection, I'll let you know.

[Playfishpaste]

Definition of a set using this type of formalism is usually an artifact of what we refer to as naive set theory. This would allow the construction of the set of all sets and leads to Russel's paradox. So something like your set of all possible worlds appears to be a problematic collection that, strictly speaking, cannot be a set.

{w:w ⊨ C} can be a statement in ZFC, NF, VBG, or KP, unless I specify which axioms I'm adopting it's not known which system I'm using, since they all have the same syntax (save some statements in NF). Typically it's assumed when people talk about sets that they are using ZFC, as it's become the convention today. ZFC avoids Russell's paradox via the axiom schema of replacement.

The set of all possible worlds is not a set of all sets, nor is it the case that a set of all possible worlds would have to include itself (sets aren't possible worlds).

I'm not sure it really needs to be a set, according to the subsequent operations you do on it. That's what I was asking.

ah I see. Well, I don't see how to define a probability measure with possible worlds without grouping them as sets. That was the idea with our function u. If you have another method that is more clear that would be better.

Oh, that was merely my superficial impression. When I have a specific objection, I'll let you know.

okay cools.

[Krixux]

But in the end this universe, all we know , whether Created or self brought into existence is “EX NIHILO”

Thus if you assume that Creation “ex nilhilo” is impossible then this universe does not exist...
But this Universe exists, thus both Creation “ex nilhilo” and “self brought into existence ex nilhilo” are valid explanations. For as far as we know, no one can say from where, how and why this Universe came into existence.

There is presumption and lots of imagination, making the “Atheist” scenario more based on fantasy than the “Theistic” one, or the other way around , depending on one’s personal orientation ...

With other words I am retarded for believing in “intelligent design” and a Creator but believing that the known Universe came out of nothing and “just because“, its ok ...(it works both ways)

Perhaps a time will come when everything will have an explanation, but this is not that time yet.
...Till then let us respect each-other’s “fantasies“...

[chriscase]

{w:w ⊨ C} can be a statement in ZFC, NF, VBG, or KP, unless I specify which axioms I'm adopting it's not known which system I'm using, since they all have the same syntax (save some statements in NF). Typically it's assumed when people talk about sets that they are using ZFC, as it's become the convention today. ZFC avoids Russell's paradox via the axiom schema of replacement.

Of course any substantial discussion of the set theoretic basis for your argument is going to be assumed to be based on the standard ZF construction unless you explicitly state otherwise. And given how much more general use the ZF approach gets, I should think you would need to provide a reasonable justification for using an alternate foundation. Given that - under the standard model - your collection of all possible worlds does not appear to be a proper set in the first place, the very first objection you need to contend with is the sneaking suspicion that your only real motivation for abandoning the standard model is to slip a malformed set into the proof.

The set of all possible worlds is not a set of all sets, nor is it the case that a set of all possible worlds would have to include itself (sets aren't possible worlds).

How do we know that the collection of all possible worlds does not itself satisfy the definition of a "world"? What is the definition of "world" you are working from here?

As I'm sure you know, once we have the ZF axioms, the only reliable way to introduce a propositionally defined set is to qualify the elements as members of a superset that is already known to be well formed. In this case, the elements of the collection of all possible worlds have not (as far as I can tell) been shown to be members of a well-defined superset.

I don't see how to define a probability measure with possible worlds without grouping them as sets. That was the idea with our function u. If you have another method that is more clear that would be better.

Well if we can't use sets we can try for categories and morphisms. It's quite possible, however, that your measure function will have a real dependency on some set properties. In that case, the proof may not be viable.

[Marie Louise von Preussen]

"Creatio ex-nihilo" is one of these lovingly controversial points of dogma that have always many people on either sides, many of them not necessarily wrong on their perspectives. Some Christians deny it, some affirm it vehemently; theologically, it was the byproduct of an attempt (witnessed as earlier as St. Iraenaeus) to deny the pre-existence of matter, of the soul, etc... that were the common tenets of Platonism and Gnosticism current in the regions targeted by Christian proselytism.

We don't know exactly what made Iraenaeus conclude this without accepting, a priori, the authority of Scriptural passages as they were interpreted by him and consequently by the Church.

There is, of course, room for substantial interpretation in this regard. Dos Santos, in a treatise about Pythagoreanism, defines "nihil" in a classical, platonist sense (that is also current in Eastern metaphysics, Buddhism, etc) and sees creation from this "nothing" as a necessary actualization of potentialities. Now Aquinas, whose framework was primarily Aristotelian and thus encompassed a more restrictive view on the attributions of nonbeing, inevitably falls into a panentheistic metaphysics.

It's a complex problem, and perhaps a something that is not fully accessible to the content of immediate dialectical propositions. Suffice to say that it's a good reason why a tenet of faith that is not immediately self-evident is called a "mystery", and indeed, it is thought that most of the doctrine follows this rule of immediate evident unclearness. Christian theology is primarily mystical.

[chriscase]

Ok. Then according to your definition of "object", is a set an object?

[Playfishpaste]

Yes. It's a member of the class "mathematical objects".

[chriscase]

If the collection of all objects is a well-defined set, and each set is an object, then the collection of all sets should also be a well-defined set.

So how do you avoid Russel's paradox?