Impossibility Of God Arguments – Essential Indexicals.
For todays purposes I want to, simply and briefly, discuss God’s omnipotence/omniscience, but before we begin, let us define God and omnipotence:
For many theists, though not all, God is thought to be omnipotent. That is, God is all-powerful. If God is all-powerful, there is nothing that God cannot do. His power is infinite. There are no limitations. To find anything that limits God’s power would mean that God is not, after all, omnipotent. (Murray, The Atheist’s Primer, p. 111, 2010)
Murray goes on to say that the reason God is thought of this way is due to him being “more praiseworthy than anything else. If power is praiseworthy, more power is more praiseworthy. If God is the most praiseworthy thing, take any praiseworthy attribute, God has to have that attribute to the utmost degree.” (p. 111)
One response to this conception, is the so-called ‘paradox-of-the-stone’:
Can God create a stone so heavy that He cannot lift it? Is the answer is “Yes,” then here’s something God can’t do: lift this particular stone. If the answer is “No,” there here is something God can’t do: create this specific stone. Either way, God’s power is limited. Ergo, God cannot be omnipotent. (Murray, The Atheist’s Primer, p. 111, 2010)
Murray admits, that this ‘disproof’ is too petty, pedantic and disconnected to be convincing to anyone – but he does state that it makes one thing clear: “infinity ascribed to an attribute belonging to an agent is untenable.” (p. 111) But, before we even get into the paradox-of-the-stone problem, we face more immediate logical problems with God’s omnipotence :
If omnipotence means – as it certainly appears to mean – an ability to do anything, then there is an even simpler argument that there can be no omnipotent being. No being could create a square circle, or an even integer greater than two and smaller than four. Because there logically could not be such things, there could be no being that could create them. (Grim, Impossibility Arguments, p. 200, 2007)
According to Grim, Aquinas defeated this rebuttal, by stating that this is essentially a meaningless objection as God’s power requires the ability to perform any task, and that “creating a square circle” does not represent a genuine task. As a matter of principle it can be, quite generally held: ” contradictory specifications fail to specify anything – precisely because they are contradictory – rather than specifying something of a peculiarly contradictory type. If so, contradictory task specifications fail to designate genuine tasks, and thus fail to designate tasks required of an omnipotent being.” (p. 200)
Unfortunately this rebuttal to our first level objection, does not remove our second level, paradox-of-the-stone objection so easily. Grim states that the task specification is clearly not contradictory if the problem is stated as:
I could certainly create a mass of concrete too heavy for me to lift. Could God? If so, there would be something he could not do: lift that mass of concrete. If not, there is again something he could not do, though even I could do it: create such a mass of concrete. (Grim, Impossibility Arguments, p. 201, 2007)
The objection to the above becomes less about the task specification being contradictory, and more that the rebuttal contains “token inflexives or indexicals: terms that shift in their designation with the person we suppose to be performing the task.” (p.201) Some have said this objection is faulty as the tasks specification is to create a mass of concrete too heavy for one to lift, but this is not a uniform task description, as “in my case it demands only that I create a mass of concrete that I cannot lift. In God’s case it demands that God create a mass of concrete not that I cannot lift, but that God cannot.” (p.201)
But, does this objection succeed?
Grim asks, are there essentially indexical tasks? He answers that there are. Examples given are tasks undertaken in a wilderness survival course: in which a lone person is taught “building alone and without aid, a boat that both will support its builder and that its builder can easily portage.” (p. 201) The point being:
If there are any reflexive tasks of such a sort involving two inversely coordinated powers – such as creating and lifting a heavy stone – omnipotence as an ability to perform any task is simply impossible. (Grim, Impossibility Arguments, p. 201, 2007)
Perhaps, to understand this objection, we should see a more formally stated version of Grim’s argument, some clarifications and how the above also applies to omniscience too:
No one else – no one other than me – knows what I know in knowing that:
- I am making a mess.
Or so the argument goes. Since an omniscient being would be a being that knows all that is known, since I know what I know in knowing (1), and since I am not omniscient, there is no omniscient being. (Grim, Against Omniscience: The Case From Essential Indexicals, p. 349, 2003)
We can ask though, is this not the same proposition as (2) “Patrick Grim is making the mess”? Does it not contain the same information as (1)? It could be said that what is expressed in (1) is the same as what others may express in (2). Grim disagrees though, stating that this is far “too simple an account of objects of knowledge in general and of what is known in cases of (1) in particular.” (p. 351):
For the ‘I’ of the (1) is an essential indexical – essential to what it is I know or express in knowing or expressing (1). (Grim, Against Omniscience: The Case From Essential Indexicals, p. 349, 2003)
To demonstrate his point Grim articulates a scenario in which he is following a trail of spilled sugar around a tall aisle in a supermarket, in search of the person making the mess. Only to realise it is in fact himself making the mess, due to a torn sack of sugar in his cart, he is the culprit (hence (1), and (2)). It is only under (1) that all information about who is making the mess is fully expressed, whereas (2) only explains most of the information about who is making the mess (it does not include Grim’s self-realization that “he” is making the mess, and that he knows he is Patrick Grim) – which is “to reintroduce the indexical”. (p. 351)
Moreover what Patrick feels when he realises that he is making the mess can’t be “merely this impersonal matter of a named individual making a mess, because that is not what I am suddenly ashamed of or what I suddenly feel guilty about in being ashamed or feeling guilty that I am making a mess” (p.351) Grim states that others may be embarrassed by the fact that Patrick Grim is making a mess, but only he can feel the “shame and mortification of knowing that those antics are mine” (p.351)
Tying this back to omniscience:
… we see that in order to qualify as an omniscient a being must know at least all that is known. Such a being must, then, know what I know in knowing (1):
- I am making a mess
But what is known in such a case, it appears, is known by no omniscient being. The indexical ‘I”, as argued above, is essential to what I know in knowing (1). But only I can use that ‘I’ to index me – no being distinct from me can do so. I am not omniscient. But there is something I know that no being distinct from me can know. Neither I nor any being distinct from me, then, is omniscient: there is no omniscient being. (Grim, Against Omniscience: The Case From Essential Indexicals, p. 352, 2003)
Boy, wasn’t that a handful!
In an effort to avoid indexically specified tasks, some objections have moved to what Grim calls “states of affairs” (p. 201), omnipotence is redefined to mean “[one] would be able to bring about any states of affairs.” (p. 201) Grim rejects this move as well, stating that there are indexically specified states of affairs as well:
You and I may face the same state of affairs, for example, when neither of us has paid our taxes. (Grim, Impossibility Arguments, p. 201, 2007)
What has happened Grim states, is that attempts to defend a full notion of omnipotence – the ability to perform any (“consistently specifiable”) task or to bring about any consistently specifiable state of affairs – have simply been given up. Instead lesser attempts have been formulated to avoid impossibility arguments, but still retain a connection to “notions of exaggerated power to be able to claim some theological legitimacy.” (p. 201)
J.L Mackie said:
But often enough these adequate solutions are only almost adopted. The thinkers who restrict God’s power, but keep the term ‘omnipotence’, may reasonably be suspected of thinking, in other contexts, that his power is really unlimited. (Mackie, Evil and Omnipotence, p. 63, 2003)
James Rachels has stated that arguments are rarely convincing, perhaps that’s true, but make them we shall continue to do. I leave it for you to decide if any of this is compelling, if essential indexicals are enough of a reason to deny the possibility of omnipotence and omniscience and by extension a God, so defined.
Grim P. (2003). ‘Against Omniscience: The Case From Essential Indexicals”, in M Martin and R Ronnier’s, The Impossibility of God. Amherst, New York. Prometheus Books. P. 349, 351.
Grim P. (2007). ‘Impossibility Arguments’, in M Martin’s, The Cambridge Companion to Atheism. New York, New York. Cambridge University Press. Pp. 200, 201.
Mackie J.L. (2003). ‘Evil and Omnipotence‘, in M Martin and R Ronnier’s, The Impossibility of God. Amherst, New York. Prometheus Books. P. 63.
Murray M. (2010). The Atheist’s Primer. Ontario, Canada. Broadview Press. P. 111.
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