(Cross-posted from the Teapot Atheist)

Every Sunday, rather than offering commentary on a current event as I usually do, I present an argument from scratch, either against theism writ large or against some particular religion.

Among the many properties God is said to have (for reasons critically analyzed here), omniscience is one that I don't see used as an avenue of atheistic critique enough. Perfect goodness has been extensively by me and others, as has omnipotence, but omniscience keeps getting a free pass. I'd like to try to begin correcting that gaping deficiency by expounding on the clear fact that omniscience, construed in its normal sense, is an impossible property, and ipso facto, any being whose existence entails that being's omniscience is itself impossible, and ipso facto, there is no God.

Like all of God's supposed properties, a lot of people have spent a lot of time spilling a lot of ink trying to pin down exactly what omniscience is supposed to look like. Alvin Plantinga and Stephen Davies, the only two modern philosophers of religion I know to have done much detailed work on omniscience specifically (read their work here and here, respectively), I think would implicitly accept something like:
  • A being x is omniscient if, for every proposition S, if S is true then x believes S, and if S is false then x knows S to be false and does not believe S to be true.
Basically, for everything that's true or false, God knows it, and for everything that isn't true or false (like, "kilometers are green" or "the present king of France is bald" don't seem to be either true or false), then God knows that it is true that those statements are neither true or false. This is imprecise to be sure, and the literature generated by names like the two dropped above goes into great detail on them that I haven't the space for here.

It is an interesting aside to notice that omniscience puts God in a subordinate position to the facts- God's beliefs are dependent upon the facts here; it is the truth or falsehood of S that causally determines God's beliefs about S. Hold that thought; you know where I'm going with it, but save it for below.

A reason that I think it is impossible for a being to be omniscient is that no being could ever know that it is omniscient, even though whether or not a being is omniscient is certainly true or false. Think about what it would mean to be omniscient: it would mean, if you'll accept a crude visualization, that such a being would have a list, infinitely long, of every proposition in its mind, with a "true" or a "false" (and maybe a "neither") box checked off next to it. An infinitely long list, all fixed and figured out. You look down that list and see some weird things, like, "it is true that today is Tuesday," and "it is true that on Wednesday it will be false that today is Tuesday," and ipso facto that list will eventually contain "it is true that today is Wednesday," at which pint the Tuesday checkmark will have to switch boxes, and complex and seemingly unverifiable statements like "it is true that Fred's false belief about Mary's infidelity is justified." There is some weirdness to these statements, even though they are all definitely true or false things about which an omniscient being would know the truth or falsehood thereof.

Even weirder, though, is what would happen when that being, making its checkmarks, gets to the statements "God is omniscient" and "God knows that God is omniscient." How could a being ever know that it is omniscient? It is not enough to say that it could always check its list for any pending mystery because who knows what that list is missing? Consider the following principle:
  • For any mind x, possibly that mind is massively deceived.
"Massive deception" is The Matrix, or if you like, The Truman Show- the totality of its beliefs are based on a complete deception, engineered by devious outsiders or worse. You are such a mind, since it is at least possible that you are really just a brain in a vat somewhere being fed data in order to further the plot of some elaborate intergalactic reality TV show (many interesting philosophical puzzles have arisen from this possibility). But not just you, but any being is possibly such a mind. And God would know that, too. Since the whole point of such illusions is that they are impeccable, impossible to detect as illusions, nobody within them would have even the slightest possibility of noticing the truth.

This would also be true of any being that thinks that it is God (note that the statement is that possibly it is being massively deceived, not that it is). I can't think of any reason why, if possibly I could be a brain in a vat, there could be another brain in another vat being fed all the right inputs for that brain to think that it is God. Same as I could be just getting fed all the right inputs for my brain to think that it is the Teapot Atheist's brain. As there are no good reasons to think it impossible, I think we should treat it as possible.

So imagine that you are a being that thinks its name is God and you are looking at this list with your omniscience pen in hand:

This is a bad time to be God because there is no internally consistent combination of these boxes; your checkmarks can never all be such that God is omniscient. For starters, 3 and 4 must be checked off as true: if there is a God, then such a being would have to believe that it is God since such would be true and God would be omniscient, so 3 is true, and 4 is the principal justified above, which I will take to be true barring serious objections, though the defeat of which is not necessarily fatal to this argument anyway.

And so try working your way up from 4 to get the remaining two unchecked propositions to be true at the same time, as they must be for theism to be true. For if God is omniscient and he knows it (beyond merely believing it), then it is not possible that God is being massively deceived, since that possibility would make it such that God could not know that he was omniscient. If God knows that God is omniscient, then that means that God is omniscient, meaning that God is not being massively deceived, meaning that God knows that God is not being massively deceived.

This throws the whole enterprise of omniscience into doubt because of the simple fact that some things that are definitely truly false can never be known by a given mind to be true or false, and that there are like propositions for all minds, including God's. Some weird things will begin to follow, and they will make the picture of omniscience quite a bit uglier, especially when you realize that, even if you reject proposition 4 as false, you should at least concede it might be true, meaning that you get something real nasty-looking like:

Proposition 5 is definitely either true or false; like the others, none of them are "neithers" or "paradoxes." But this simply reboots the whole puzzle, because the mere possibility of God's non-omniscience means that any being that thinks that it is God and omniscient could not know it.

There are two temptations for escape that I can think of and neither of them will save the theist. The first is to reject 4 because, for the being that were actually God, massive deception would be impossible. Now this I agree with entirely! The only problem is that such a being would also believe itself to be God, and it is the believing to be God that incites the possibility of deception. If God did not believe it and it were true then God could not be omniscient. If God believed it, then he could not know it to be true and so could not be omniscient, since his belief could be a part of his deception.

The only other way is to suggest that I am playing on the word "know" here, as in, "you, Teapot, don't know that you aren't a brain in a vat, but you still aren't one." First, how do you know, and second, I think that God actually has better reasons to suspect that he is a brain in a vat that we do. For you see, we only have the conceptual possibility of beings utterly beyond our own spacetime manipulating things within, independent of our control, independent of our reason. God, on the other hand, knows that such things occur because he does it all the time! Our relationship to God, if there were such a being, is on par with the relationship that would exist between a deceived mind and deceiving minds. Since God would have firsthand knowledge of such things happening, God actually would have even better reasons to know that he may be the victim of massive deception, by some greater God, or he is not one at all and is only being made to think that he is, and so on.

Omniscience, then, is at its heart impossible, since it requires belief in the truth or falsity of all true or false propositions, yet there are some true or false propositions whose truth or falsity cannot be known. There are many such propositions besides the brain in the vat scenario, such as, "x would be the case if nothing familiar were true-" extrapolations from such a scenario would require recourse to the familiar, which is futile. But since such a proposition is eminently immune to our knowing its truth or falsehood, yet is true or false, not even an omniscient being could crack it, but also could not consign it to the "neither" category like "the present king of France is bald" because it describes a state of affairs that either is or isn't, period.

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Comment by Heath on July 11, 2011 at 1:26am

Your argument appears to have a subtle, but major, oversight:

There is no reason to think that an omniscient being, who by stipulation KNOWS all true propositions to be true, would deal in POSSIBILITIES. The concept of possibility makes sense for us as humans, being the epistemically deprived beings that we are. But an omniscient being has no epistemic restrictions whatsoever. There is no question of any proposition "possibly" being true, for an omniscient being would already know which propositions are true. From the standpoint of omniscience, the concept of possibility is nonsensical. Therefore propositions (4) and (5) are not candidates for inclusion among an omniscient being's knowledge base.

For an omniscient being, it is not possible that that being is "massively deceived," for an omniscient being would already know exactly which beings are massively deceived, and which one isn't: himself (herself? itself? Whatever.). If you assume at the outset that a being is omniscient and then attempt to prove that such a being cannot exist by finding a contradiction that unfolds from that being's omniscience (in other words, a reductio ad absurdum from omniscience), then you cannot sneak in epistemic uncertainty via possibilities; it undermines the very premise of your argument. Your argument then becomes a reductio ad absurdum of itself. 

Even ignoring these points, it needs to be made clear what exactly is this omniscient being's relation to time before this matter could be adequately addressed (i.e., whether it operates within time, outside of time, in some "eternal present," etc.).


As a note on your aside, an omniscient being isn't necessarily "subordinate to the facts" of reality. If that being were also omnipotent, then we could hold with Bishop Berkeley that it is the very ideas in the mind of God that make reality what it is; his knowledge is both the reason for and constitutive of all of the facts of reality. 

If you haven't read it already, I recommend that you check out "The Impossibility of God," a book edited by Michael Martin and Ricki Monnier. It's an all-around excellent volume, and includes several articles that give other reasons to think that omniscience is impossible, or at least incompatible with God's other supposed attributes.  

Comment by Chris on July 11, 2011 at 8:46am
The subtle point on possibilities is to note that the argument does not turn on beings that are omniscient (as a reductio), but on beings that believe that they are omniscient.


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