A Priori Proof for God's Existence

[Perplexity]

What you’ve done Vera is conducted a circular thought experiment. You did not give a deductive argument of any sort, let alone one which demonstrates that the existence of a necessary being entails a contradiction. The argument is sunk.

 

[ferdgoodfellow]

Hi Vera and Perplexity,

I really appreciate this conversation.

The proposition before us is whether it is possible to conceive of an entity which cannot fail to exist. Vera said in post #7 that all we need to do to show necessary existence is not conceivable is to “consider two different possible worlds which have nothing in common.” To illustrate he offers his reduction hypothetical (thought experiment) in #48 which results in a single proton world and a single neutron world. He then concludes: “So, we have two, physically possible worlds, without any intersection. Ergo: “no necessary being”.

Granting all the assumptions that go with possible worlds (which I don’t pretend to understand), this does seem to be a disproof of necessary existence. However, I don’t trust this conclusion on other grounds. First, thanks to Parmenides, we know that something or other must exist. Granted, it doesn’t have to be one entity. Necessary existence could be exemplified by an unending succession of contingent beings, the whole of which cannot fail to exist. But I don’t think this precludes one entity (or multiple entities) which cannot fail to exist.

Second, to deny the possibility of necessary existence is to hold that all that all existential propositions are contingent. This, of course, is the dogma of logical positivism. Put differently, it is necessarily true that “X exists” could be true or false. Logical positivists reduce all necessity to logical necessity which can only be conditional necessity (i.e. dependent on the conventions of the language being used). So how can we trust their dogma, which, by their own rules, can only be conditionally true?

This second point makes me suspect that the positivist dogma is built into Vera’s possible worlds analysis. Doesn’t it assume that in our possible world constructing we can flip the T/F or exist/doesn’t exist switch on any element of the actual world (as long as we don’t end up with something nonsensical)?

 

[Vera_Ljuba]

What you’ve done Vera is conducted a circular thought experiment. You did not give a deductive argument of any sort, let alone one which demonstrates that the existence of a necessary being entails a contradiction. The argument is sunk.

If you don’t get it…

 

[Vera_Ljuba]

The proposition before us is whether it is possible to conceive of an entity which cannot fail to exist. Vera said in post #7 that all we need to do to show necessary existence is not conceivable is to “consider two different possible worlds which have nothing in common.” To illustrate he offers his reduction hypothetical (thought experiment) in #48 which results in a single proton world and a single neutron world. He then concludes: “So, we have two, physically possible worlds, without any intersection. Ergo: “no necessary being”.

Granting all the assumptions that go with possible worlds (which I don’t pretend to understand), this does seem to be a disproof of necessary existence.

I am glad you see it. Perplexity did not. (Maybe he confuses “hypotheses” with “axioms”.) Possible world is simply an arbitrary state of affairs of ontological entities, which does not contain logically nonsensical / contradictory entities. However, it is important to stress that “concepts, ideas, abstractions, etc…” are NOT ontological entities. Ontological entities are stones, gods, leprechauns, “things”… Love (for example) or “truth” are not ontological entities.

However, I don’t trust this conclusion on other grounds. First, thanks to Parmenides, we know that something or other must exist. Granted, it doesn’t have to be one entity.

You got it right. But you don’t need to refer to anyone. If, what you say is correct, referring to outside source is not necessary. If, what you say is incorrect, referring to outside source does not help. “Nothing” is a concept, not an ontological entity. It only exists as an abstraction, not as “something”. To say “nothing exists” (where “nothing” is understood as an “ontological something”) is nonsense.

This is extremely important.

Necessary existence could be exemplified by an unending succession of contingent beings, the whole of which cannot fail to exist. But I don’t think this precludes one entity (or multiple entities) which cannot fail to exist.

You have to be careful. “Contingent” existence does not mean that entity “X” is logically or physically contingent on entity “Y”. It only means that entity “X” is present in some world “W1”, but not present in another world “W2”. For example, the existence of this post is physically “contingent” on my existence (even though my continued existence is not necessary). Once it is posted, it will continue to exist as long as the server exists, and as long as the moderators allow it to persist. In the unlucky event when the Sun goes nova, the post will disappear. We can also conceive of a different possible world, when the same post exists, but was written by someone else.

Necessary existence only means that an entity “X” exists in all different possible worlds. The usual, colloquial meaning of “it is necessary FOR something” does not apply. There are many “unfortunate” choices in the language. In mathematics, the concept of “irrational numbers” has nothing to do with rationality, it only has to do with “ratio”, the division of two numbers.

Doesn’t it assume that in our possible world constructing we can flip the T/F or exist/doesn’t exist switch on any element of the actual world (as long as we don’t end up with something nonsensical)?

Yes it does, and it has nothing to do with logical positivism, explicit or implicit.

 

[STT]

Yes, it is needed. You said that “logically possible” and “metaphysically possible” are not the same. So, prove it. What is the difference?

There could be an underlying reality. Physics is not complete yet. We have serious problem in understanding consciousness. The standard model is not anomaly free. String theory and its family also failed.

 

[STT]

Vera said in post #7 that all we need to do to show necessary existence is not
conceivable is to “consider two different possible worlds which have nothing in common.”

Why that is correct?

First, thanks to Parmenides, we know that something or other must exist. Granted, it doesn’t have to be one entity.

Where this has been showed. You can also show that the “nothing” is impossible. Do you have an argument for that? God started from nothing.

 

[ferdgoodfellow]

Hi STT,

Vera said in post #7 that all we need to do to show necessary existence is not
conceivable is to “consider two different possible worlds which have nothing in common.”

You ask, “Why that is correct?”

I don’t think it is, it but has been challenging for me to articulate why. Given sheer conceivability, it does seem like you can construct two possible worlds with no commonality.

I am starting to get my thoughts together in light of what Vera said three posts back. In the mean time, what do you think?

 

[ferdgoodfellow]

Hi STT,

Parmenides showed that all references to nothing are relative. Attempts to refer to absolute nothingness end in contradiction. For example, “The box contains absolutely nothing.” But then that would mean that the sides of the box would be collapsed and touching, in which case it wouldn’t be a box.

 

[Vera_Ljuba]

There could be an underlying reality.

“Could be” is not an argument. However, be as it may, in my proof I did not use either one. The process of elimination results in two non-overlapping worlds, which are “physically” possible…

 

[STT]

Hi STT,

Vera said in post #7 that all we need to do to show necessary existence is not
conceivable is to “consider two different possible worlds which have nothing in common.”

You ask, “Why that is correct?”

I don’t think it is, it but has been challenging for me to articulate why. Given sheer conceivability, it does seem like you can construct two possible worlds with no commonality.

I am starting to get my thoughts together in light of what Vera said three posts back. In the mean time, what do you think?

What Vera said doesn’t make any sense to me.

 

[Vic_Taltrees_UK]

Concepts representing infinitesimals or approximations to infinity are often expressed with absolute terminology hence in many circumstances confusion over e.g “nothing”.

 

[Vic_Taltrees_UK]

Vera’s arguments in her post 7 have in my view a tendency to be convincing, in this context.

(Though much of the subsequent argumentation is illuminating.)

The real clincher for the existence of God will be what Christians do or don’t do for fellow Christians. If we don’t want to, why should anyone else believe?

 

[Vic_Taltrees_UK]

God couldn’t be greatest before act of creation since He is the only one who exists. Therefore the argument fails.

If He is great enough to be before then, surely He is greater than those that didn’t manage that feat?

 

[STT]

Hi STT,

Parmenides showed that all references to nothing are relative.

Hi Ferd,

What do you mean with that? Could you please elaborate?

Attempts to refer to absolute nothingness end in contradiction.

How?

For example, “The box contains absolutely nothing.” But then that would mean that the sides of the box would be collapsed and touching, in which case it wouldn’t be a box.

I think we can conceive nothing, no thing, no volume etc.

In any case, if you accept that “nothing” cannot exist then existence is necessary. This means that God could exist but it is also means that the universe could exist without God intervention too. I however have a argument against the act of creation I can present it here). Adding that argument to what is discussed one can conclude that God (creator) does not exist.

 

[STT]

“Could be” is not an argument. However, be as it may, in my proof I did not use either one. The process of elimination results in two non-overlapping worlds, which are “physically” possible…

I didn’t get your argument. Could you please elaborate?

 

[STT]

If He is great enough to be before then, surely He is greater than those that didn’t manage that feat?

What do you mean with those? Moreover what we call beginning has an intrinsic problem. One cannot initiate the beginning. That is true since we need time in order to initiate things but time itself an element of universe.

 

[ferdgoodfellow]

Hi STT,

You said: What Vera said doesn’t make any sense to me.

Refer back to Vera’s post at #48

Not just incorrect, but these two worlds are physically possible. Let’s start with the existing world, which is clearly possible, since it exists. Taking any possible world, we can freely remove any subset of the world, without a logical impossibility “creeping in”. For example, we could remove the Magellan cloud, and the remaining world would still be possible. Or all the galaxies, except the Milky Way. Using this “removal” method, we can arrive at any “sub-world”. One of them can result in a “single-electron” world, the other one can result in a “single-positron” world. Or, if you prefer (because positrons are “rare”) the other end-world could be one with a “single-neutron” world.
So, we have two, physically possible worlds, without any intersection. Ergo: “no necessary being”.

Back in #65 I tried to explain my understanding of possible worlds this way:

My naive understanding of PW’s is to begin imagining a world truth table with brazillions upon brazillions of statements describing the actual world. E.g. Donald Trump is president of the US is true. Hillary is president is false. There are penguins is true. There are unicorns is false. Melania’s inaugural outfit is powder blue is true, and so on. A possible world involves taking any one or more of the brazillions upon brazillions of statements and changing the truth value. The result will be deemed a “possible world” as long as the world truth table contains only statements which are logically possible. A truth table which assigns T to “There are round squares” cannot be a possible world. So the cardinal rule for constructing a possible world is “Don’t put into your World Truth Table any statements that are nonsense.”
Now if we posit the possibility of necessary existence, we are asking, in possible worlds lingo, whether it is possible for there to be an X such that “There is an X” is true in every possible world. Not knowing anything about X, we quite naturally think that we can assign a truth value of false to that particular statement in our World Truth Table. For all we know, it could be T or F. If there is nothing nonsensical about assigning F to this statement, we’ve got a possible world.

Back in #82 I said

Doesn’t it assume that in our possible world constructing we can flip the T/F or exist/doesn’t exist switch on any element of the actual world (as long as we don’t end up with something nonsensical)?

And Vera agreed in #84.
So it does seem that possible worlds semantics, as presented by Vera, has a built-in assumption that no existential propositions can be necessary. Sheer conceivability is the only criterion for deeming a something a possible world.

 

[ferdgoodfellow]

So I have to ask: Why can’t there be at least one entity which exists necessarily?

We’ve examined this question in terms of possible worlds. X would have to be present in every possible world. But, via Vera’s world reduction thought experiment, we can conceive of two worlds with nothing in common, which would mean there is at least one world with no X in it.

But we learned that the construction of possible worlds assumes that a world without X is always possible. In other words, it assumes there is no X which exists in all possible worlds. It assumes there can’t be at least one entity which exists necessarily. So we can’t use possible worlds analysis to disprove necessary existence. Putting our question through possible worlds analysis amounts to asking a system of thought which assumes necessary existence is impossible whether necessary existence is possible. We know what the answer will be.

I have therefore come around to Perplexity’s conclusion that Vera’s possible world’s disproof is circular. The impossiblity of the “necessarily existing object” is supposed to be the end result of the dis-proving process, not a beginning assumption of that process.

 

[reggieM]

We’ve examined this question in terms of possible worlds. X would have to be present in every possible world. But, via Vera’s world reduction thought experiment, we can conceive of two worlds with nothing in common, which would mean there is at least one world with no X in it.

I’m sorry I haven’t followed this sufficiently but perhaps an additional thought could help.

In order to have, for example, a “single electron”, there are a number of things that must exist. Space. Dimension. Individuality. Difference. Distinction, Uniqueness, Order, Movement, Energy, Distance, Contingency, Causality, Time, Physicality.

I do not believe we can conceive of two worlds with nothing in common.

In order to even distinguish one world from another, they both must have something in common (factors that allow for the distinction of one from another).

If the two worlds had nothing in common, we could not use the same measure of possibility for them (they are plotted within a shared space of what is possible).

Please correct this if I have missed the key argument.

 

[Vera_Ljuba]

So I have to ask: Why can’t there be at least one entity which exists necessarily?

We’ve examined this question in terms of possible worlds. X would have to be present in every possible world. But, via Vera’s world reduction thought experiment, we can conceive of two worlds with nothing in common, which would mean there is at least one world with no X in it.

But we learned that the construction of possible worlds assumes that a world without X is always possible. In other words, it assumes there is no X which exists in all possible worlds. It assumes there can’t be at least one entity which exists necessarily. So we can’t use possible worlds analysis to disprove necessary existence. Putting our question through possible worlds analysis amounts to asking a system of thought which assumes necessary existence is impossible whether necessary existence is possible. We know what the answer will be.

I have therefore come around to Perplexity’s conclusion that Vera’s possible world’s disproof is circular. The impossiblity of the “necessarily existing object” is supposed to be the end result of the dis-proving process, not a beginning assumption of that process.

You are mistaken. It starts with the assumption that “necessary existence” IS possible.

All I can do is direct your attention to the “disproof” of the hypothesis that “p/q = sqrt(2)” - where p and q are integers without a common divisor. (If there are common divisors, we simplify the fraction by dividing both the numerator and the divisor with the common divider.) The elimination process described in post #80 explicitly assumes that such integers exist. During the process all we do is “square” the equation, divide by 2, etc. the hypothesis is not used.

THEN, at the end of the process we arrive at a contradiction, and that proves the impossibility of the hypothesis. This process is called “indirect proof”.

The very same happens in the “disproof” of necessary existence. We start with the assumption that necessary existence IS possible. The starting scenario is our current, existing world, which is possible, since it exists. Eliminating physical objects does not change the “possibility” feature of the world. Adding something (like a 4 sided triangle) could change it, but eliminating cannot. At the end process we have our contradiction, two physically possible worlds with nothing on common.

When we start with a possible world, we can always eliminate something without getting a logical contradiction - just like when we simplify both the numerator and the divisor by dividing them with the common divisor.

The two final worlds are physically possible. If you still have doubts, feel free to ask.