Recently I proposed a new argument for theism based upon a metaphysical principle connecting logic, knowledge and truth. Against this argument two specific objections can be proposed. In what follows I shall present and respond to both objections.
(A) It is also logically impossible to know that God exists (for someone could, even encountering God, believe that she is dreaming, or hallucinating, or being deceived). But then, by parallel reasoning, it also follows that, necessarily, God does not exist. And hence my argument fails. My response would be that it is not logically impossible to know that God exists. Take a possible world in which God exists. In this possible world there is a subject that knows that God exists, namely God. In that world God knows that God exists. So, it is not logically impossible to know that God exists.
(B) There might be some true mathematical Gödel sentence G that cannot be proven by any proper mathematical system. Hence, G is unknowable. But then not all truths are knowable, and therefore my principle (which entails that all truths are knowable) fails. My response would be that G is in fact knowable. For, there is a possible world in which G is known. Take again a possible world in which God exists. In that world God can be taken to know at least all mathematical truths by immediate intuition, and therefore God knows G as well.
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G would not be a Godel sentence. Godel sentences simply state that G is not provable in *some* system (comparable in "power" to the Peano arithmetic), not all possible systems.
Take any axiom of ZFC. It is not, by definition, provable. But it is also true. All proofs that are in ZFC depend on the truth of the axioms in which the proof uses.
Dear NChen,
A true mathematical sentence that is not provable in *some* system is not unknowable, since there might be another system in which that sentence is provable. Therefore, to construe an interesting objection for the atheist, I proposed that there might be some mathematical truth that is not provable in any system (and, I have no problem at all with not calling a sentence expressing this truth a Godel sentence). My response to the proposed objection was to appeal to the logical possibility of there being a God who knows all mathematical truths (i.e., there exists a logically possible world in which there is a God knowing all mathematical truths), as I explain above.
Kind regards,
Emanuel
So, let me get this straight. You are saying:
If God exists, God knows about his own existance so it is not impossible to know whether he exists, and therefore God exists.
If goed doesn't exist, it is impossible to know that goed doesn't exist, and therefore God does exist.
So whether or not God exists, God exists.
Dear Hazkan,
Your rendering of my argument is incorrect. The fact that there is a possible world in which God exists and in which God knows that God exists does not entail that God exists in the actual world. (Note that the definition of God that I assume for my new argument, i.e. personal first cause, does not include metaphysically necessary existence.)
Kind regards,
Emanuel
"Take a possible world in which God exists."
"The fact that there is a possible world in which God exists."
You are begging the question. For your response to be valid you will have to prove that there is actually a possible world in which God exists. That's not a fact a priori.
Which doesn't prove that God doesn't exist.
Dear MNb,
I'm not begging the question. For the claim that God possibly exists, i.e. that there is a logically possible world within which God exists, is quite different from the claim that God actually exists.
On prosblogion (http://bit.ly/rc7lp5) I explain why it is indeed reasonable to hold that there is a logically possible world within which God exists. See for example my responses to Aaron and Clayton.
Kind regards,
Emanuel
Dear Emanuel,
Thank you for all the reactions to my questions. So, I studied the argument a bit more and have one last question (I will stop after this, since I am assuming you may be a bit tired of the discussion by now, which is repeating itself, though I think any attention generated is always a good thing).
I looked at the argument again, and skimmed some reactions, and I think it is really great find and well argued.
The most serious problem I can find, and which emerges in the discussion, is the very strict Cartesian account of knowledge presupposed. Do you think the Cartesian account of knowledge is plausible? I think it would be very difficult to plausibly relate this conception to our modern concption of science, even in the case of mathematics, where, e.g., there may be difficulties involved in how to precisely interpret the status of axioms.
Finally, I like this blog!
Kind regards,
Hein
Dear Hein,
We do not have to concede that the cartesian conception of knowledge exhausts the analysis of knowledge in order to accept the premises of my new argument. After all, these premises are about cartesian instances of knowledge, and for accepting their plausibility we do not have to be some kind of cartesians ourselves, that is, we surely do not have to admit that there are no other types of instances of knowledge. Further I would like to thank you for your compliment regarding my blog.
Kind regards,
Emanuel
Beste Emanuel,
De vraag is of wij het begrip "bestaan" disjunctief kunnen toepassen op God.
Laten wij eens uitgaan van twee heel acceptabele aannames:
1. "God bestaat of God bestaat niet"
2. "Jan is niet God"
De disjunctie (1) lijkt compleet
Als dan het ene deel van 1 waar is dan kan het andere deel van 1 niet waar zijn.
Verder geldt: -als God bestaat dan is iemand anders dan Jan God (volgt uit 2)
-als God niet bestaat dan is Jan niet God (volgt ook uit 2)
Wij kunnen de disjunctie nu als volgt weergeven:
Ofwel iemand anders dan Jan is god (A) ...ofwel ... Jan is niet god (B)
Welnu, Als A waar is kan B niet waar zijn en vice versa.
Als A waar is, dus als iemand anders dan Jan god is dan is B niet waar, dus dan is Jan god.
Maar dit is een absurditeit die alleen maar de wereld uit te helpen is als wij de aanname 1 of 2 of allebei verwerpen.
Maar aangezien het zeer onwaarschijnlijk is dat aanname 2 verworpen zou moeten worden dient de aanname 1 verworpen te worden.
Maar betekent dat niet dat het disjunctief syllogisme, toegepast op het bestaan van God tot een absurditeit leidt?
Immers onder de zeer waarschijnlijk onjuiste aanname dat Jan God is geldt dat God bestaat, want Jan immers bestaat immers. Er is dan geen disjunctie.
En onder de zeer waarschijnlijk juiste aanname dat Jan niet God is ontstaat er een absurditeit.
Verwerpen wij de aanname (2) "Jan is niet god" dan moeten wij aannemen dat Jan god is.
Als wij nu bedenken dat wij voor "Jan" ieder willekeurig "iemand of iets" kunnen substitueren dan ontkomen wij niet aan de stelling: god bestaat niet in onze gebruikelijke zin van het woord "bestaan" of iedereen en alles is God. Pantheïsme.
Wij ontkomen, dunkt mij, niet aan de gedachte: ofwel god bestaat niet in onze gebruikelijke zin van het woord ofwel de mens en het goddelijke zijn niet van elkaar te scheiden.
Graag jouw mening hierover.
vr. groet,
Jac
Beste Jac,
Je schrijft: "Als A waar is kan B niet waar zijn". Dit is echter incorrect. A en B kunnen prima beide tegelijk waar zijn.
Groet,
Emanuel
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