Home > Atheism, Philosophy, Skepticism, Theism > Impossibility Of God Arguments – Essential Indexicals.

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:

  1. 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):

  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.

  1. January 13, 2012 at 4:40 am

    Detailed post – Thanks.

  2. January 13, 2012 at 4:46 am

    Hi Rob. An interesting post, though I must admit I find it is easy to get lost in the logic and lose the plot, so to speak. Thank you for referring to my two blogs on the subjects of omnipotence and omniscience (The God Franchise). I know they are simple, and that they tie in with other blogs about God that I have posted, Omnipotence has to be defined to be as powerful as it gets, i.e., there is nothing more powerful, because otherwise we get into the square circle and heavy rock arguments. Unless we can find something more powerful than God, then God’s level of power can be defined as omnipotence.

    Omniscience is a little easier as I see that everyone or everything that has knowledge is effectively a subset of God, and the whole has to know all that the subsets have collected in knowledge. Once again, since God therefore knows all that can be known, then let’s call that omniscience. Refering to your quote from Grim, I believe that God knows everything that I know as I am a subset of Him, so while I am not God, God is me (along with everyone and everything else). I therefore say that Grim has not proved his case about distinct beings.

    Thank you for this discussion. It is important for us all to understand these terms and the qualities of this Consciousness that is our essence, and who has been named God (a name which is often misunderstood)!

    • January 13, 2012 at 8:12 am

      Thankyou for your thoughts and comments Alan!

  3. December 17, 2014 at 6:02 pm

    In my article ‘Omnipotent God and The Paradox of the Stone’ I showed that the paradox of the stone could be answered negatively or affirmatively without causing any problem to God’s omnipotence.

    Greatest Being theological concept of God is that of a being with maximal excellence in respect to power(omnipotence), presence (omniprence), knowledge (omniscient) and moral perfection.

    Now, could God create a stone that God could not lift? Yes. Actual God could create a 0.1 k.g. stone and vow not to lift it. Because God is moral perfect then God cannot break His vow. Thus God has created a stone He cannot lift. That He cannot lift does not reflect lack of power, but moral perfection. Thus God is has the ability(power) to lift it but not the capability(morality).

    Again, could God create a stone that God could not lift? No. Because for every stone with weight x God possess power y to lift x. The state of failing to lift x is not an ability but disability or liability. Thus God not being able to lift x is not because of lack of power but actually the opposite because of such power.

    So either way the paradox is solved. Tooley also offered an atheistic solution to this problem. 🙂

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