Omnipotence and Quantification

by

Tersur Aben

 

According to our standard pre-philosophical intuition, there is at least one being, God, who is omnipotent.  Hardly anyone would grant that God exists and deny that God is omnipotent. Yet the meaning of omnipotence remains an enigma to many philosophers.  The enigma has led many philosophers into elementary confusion over the kind of quantification to be applied to omnipotence or how to stipulate the extent to which God is power.

Initially, most philosophers parse the doctrine of divine omnipotence as stipulating:

  1.  “God has all powers.”1 

But disagreements still linger over what exactly (1) entails.  Many philosophers understand (1) as entailing unrestricted universal quantification of God’s power.  Hence they interpret (1) as:

  1.  God can do all things.2 

René Descartes is quite famous for affirming and defending (2).  Descartes writes:

I would not even dare to say that God cannot arrange that a mountain should exist without a valley, or that one and two should not make three, but I only say that he has given me a mind of such a nature that I cannot conceive a mountain without a valley or a sum of one and two which would not be three and so on, and that such things imply contradictions in my conception.3

If God has all powers, Descartes reasons, necessarily God can do all things.  If God does not have all powers, then necessarily God can do only what is within his power.  But it is incongruous to say that God lacks power, so Descartes concludes that necessarily God has all powers, which means that God can do all things.

Other philosophers cautiously restrict universal quantification of omnipotence in order to avoid predicating false propositions of God.  Restricting universal quantification of omnipotence, they parse the claim that God is omnipotent as:

3) God can do some things.

Apparently (3) avoids predicating counterintuitive assertions of God, e.g., that God do what is logically contradictory, metaphysically impossible, and morally reprehensible.4  They deny that God can:

  1.  Bring about metaphysically impossible states of affairs, such as make a mountain without a valley.
  2.  Bring about that logically contradictory statements are true, such as make true that 1+2 = 4.
  3.  Perform such morally reprehensible acts as tell a lie.5

Propositions (4-6) are contradictory, so God cannot do them.

Philosophers who read (1) as entailing (3), argue that God cannot bring it about that p and ~p are both true in the actual world (here after, W) at t.  While God can bring it about that either p or ~p is true in W at t, even God cannot bring it about that p and ~p are both truth in W at t.  But they warn against taking the function of “cannot” here to stipulate lack of power.   It simply makes factual observation about the metaphysical constitution of W, which is such that even God cannot, now, bring it about that contradictory states of affairs simultaneously obtain.  So, it does not follow from God has all powers that God can do all things.

Ontological implausibility of reading omnipotence as God can do all things is further stated through some thought experiments.  I cite a few here to show that they support (2).  

The Stone Paradox

The first thought-experiment is the stone paradox:

7)  Either God can create a stone that he cannot lift or he cannot create a stone that he cannot lift.

8)  If God can create a stone that he cannot lift, then he is not omnipotent (since he cannot lift the stone in question).

9)  But if God cannot create a stone that he cannot lift, then he is not omnipotent (since he cannot create the stone in question).

10)  Since either 8 or 9 must be the case, it follows that (either way) God is not omnipotent.6 

John L. Mackie reads the stone paradox as demonstrating the implausibility of (3).7  J. L Cowan makes a similar observation and recommends obliterating omnipotence from theology.8

C. Wade Savage reads the stone paradox differently by interpreting the statement “x cannot create a stone which x cannot lift” as “if x can create a stone, then x can lift it.”  Savage says:

If y can lift stones of any poundage, and x cannot create a stone heavier than seventy pounds, then x cannot create a stone which y cannot lift, and x is limited in power.  But if x can create stones of any poundage, and y can lift stones of any poundage, then x cannot create a stone which y cannot lift, and yet x is not thereby limited in power.9  

But Savage’s interpretation fails to convince philosophers that God can do all things.10 

Omnipotence and Freedom

Another thought experiment pertains to God’s freedom.  Peter T. Geach states it thus:

  1.  If God promises to save Israel, then either God is bound by that promise to save Israel or God is free to not save Israel.
  2.  If God is bound by his promise to save Israel, then God lacks the power to refrain from saving Israel.  
  3.  If God is free to not save Israel, then it seems that God is not keeping his promise, which shows moral defect in God.11  

Geach adds:

If God is essentially impeccable, there is no world in which he fails to fulfill a promise he has made.  But if this is so, does it not follow that, by making a promise, God limits his ability to act in future and thus renders himself less than omnipotent?”12

Thomas Flint and Alfred Freddoso explain: “God’s present belief that Israel will be saved is temporally dependent on the fact that the children of Israel will freely accept his grace and live accordingly.”13  God’s promise to save Israel simply declares God’s intent to save Israel.  God is not obligated to keep the promise, unless of course Israel meets God’s conditions.  God can help Israel meet his conditions by weakly actualizing states of affairs in which Israel freely choose to do his will.  However, if Israel freely rejects God’s will, God cannot save Israel.   

Despite Flint and Freddoso’s explanation, it still appears that God cannot do all things, such as make an unconditional promise to save Israel, no matter what.  If making an unconditional promise to save Israel is something God cannot do, then it follows that God cannot do all things.

Omnipotence and Human Freedom

The last test case that I shall consider pertains to human freedom.  It can be stated thus:

14) Supposing that human beings freely build a dam across Hidden Valley Creek

15) Then building the dam across Hidden Valley Creek is something God cannot do, or

16) Human beings are forced to build the dam.  

George I. Mavrodes explains: “If someone is free then nothing can cause him or her to do what he or she does.” And Mavrodes adds: “Neither God nor anyone else can bring it about that some person freely builds a dam across Hidden Valley Creek.”14  If God brings it about that human beings build a dam across Hidden Valley Creek, then humans did not act freely, but if human beings freely build the dam across Hidden Valley Creek then that is some thing that God did not do.

A possible solution to this paradox would be to distinguish between weak and strong actualization.  Then God weakly actualizes a states of affairs in which human beings strongly actualize the state of affairs of building a dam across Hidden Valley Creek.  Although this explains how God and humans co-act, Richard Swinburne rejects it for compromising human freedom.  Swinburne: “If S acts freely, which action he performs at t1 is ultimately determined by his choice at t1 and not necessitated by earlier states.”15  So, if God brings it about at t that humans build a dam across Hidden Valley Creek at t1, the human act of building the dam at t1 cannot be free.  For humans to be genuinely free to build the dam at t1, no act prior to t1 should condition their decision to build the dam across Hidden Valley Creek at t1.

Restricted Universal Quantification

Classical theists like St. Augustine, St. Anselm, and St. Thomas Aquinas said that even though God is omnipotent God cannot do all things.  They maintain that God can only do some things.  St. Augustine clearly denies that God can do everything and he grounds his denial in Scriptural asseveration that God cannot die or deceive.  St. Augustine notes that the claim that God can do all things lacks Scriptural support.16  

Similarly, St. Anselm says that there are many things God cannot do.  For example, “God cannot be corrupted, or tell lies, or transform what is true into what is false (that is, undo what has been done).”17  And St. Thomas Aquinas names moving, falling, tiring, or altering the past among things that God cannot do.18  These theists see the limitation to what God can do as necessary for blocking off the predication of contradictory claims to God.

So, what are the things that God can do?  According to St. Augustine:

17) God can do whatever he wills.

St. Augustine says that it is because God can do whatever he wills that God is omnipotent.  Nothing stops God from carrying out his perfect will.  Rather, God freely does whatever he wills; and he freely refrains from doing whatever he wills not to do.19 So, we may rightly say that God can do whatever is necessary.

St. Thomas Aquinas says:

18) God can do whatever is possible.

But Aquinas denies that God can do what is impossible.  Aquinas notes that God always acts freely and so even God’s decision to do only what is possible is free.  Aquinas denies divine passivity, but insists that God is pure actuality.  Therefore nothing compels God to act or not to act.  So, God’s free will against doing some things does not translate into lack of power.  Rather, Aquinas says that God does not do those things because they cannot be done.20 

Peter Geach rejects as erroneous the supposition that God has all power but God can only do some things.  He judges restricted universal quantification of omnipotence inadequate and he recommends the deletion of omnipotence from theology.  Instead of omnipotence, Geach recommends that we simply say that God is almighty.21  Geach thinks that “almighty” properly depicts God’s power, God’s exaltedness or excellence, to warrant our worship of God.  

But Richard La Croix advocates keeping omnipotence in theology.  He says:

It seems reasonable, then to adopt the principle that the failure of an omnipotent being to bring about a state of affairs not brought about by an omnipotent being does not count against omnipotence or falsify the claim that a being is omnipotent.22 

La Croix recourses to weak actualization and explains that God can bring about states of affairs that can be coherently described as not brought about by God.  But George Mavrodes rejects this explanation, saying:

An agent weakly actualizes a state of affairs S just in case there is a state of affairs T such that (i) the agent strongly actualizes T, (ii) the agent’s strongly actualizing T counterfactually implies S, and (iii) the agent does not strongly actualize T. 23 

Supposing that God weakly actualizes a goat eating my flowers in my front yard, the causal chain of this event can be given without citing God and the explanation for the existence of the eaten flowers would be adequate.  Hence, weak actualization fails to sufficiently preserve divine causality, which omnipotence aims to affirm.

The real problem here, as I see it, is the combination of “x has all powers” and “x can only do some things.”  Now, it is quite clear and even acceptable that a non-omnipotent being has limited powers and so can only do some things.  But it is hard to see that an omnipotent being can still only manage to do some things, not all things.  This problem exists because philosophers confuse the real intent of the claim God has all powers as meaning that God has, literally, every degree of powers.  

 

The Correct Meaning of “God Has All Powers”

The main challenge for us, in predicating omnipotence of God, is to justify the claim that God has all powers; yet God cannot do all things.  To meet this challenge, it is worth noting that there are three possible ways to interpret the claim that God has all powers: (a) God can do all things, (b) God can do some things and (c) God can do nothing.  We can eliminate (c) offhand because we know that God has done many things.  That leaves (a) and (b) as legitimate options.  We have shown already enough difficulties with (a), the parsing of omnipotence as the claim that God can do all things that we need not embrace it.  That leaves (b) as the best possible way of parsing the claim that God has all powers.   

Apply existential quantification to “all powers” we can interpret the claim that God has all powers to mean that there exist many types of powers, each of which God has.  The claim that God has all powers may not be read as that God possess every ounce of powers from which it follows that God can do all things.  Rather the claim that God has all powers says that there are several categories or types of powers and God has all of them.  Broadly, powers can be classified into two categories: Active and Passive.  

Active power can be defined as ability to do.  Furthermore, we can subdivide active power into creative, coercive, and influential powers:

  1.   Creative power is dynamic and explosive.  It is powerful enough to bring things into existence from nothing.  It makes what was not what is.  Both science and art show us the magnificence of creative power in the priceless quest after artistic creativity.  God created the reality in this actual world from nothing, which attests to God’s possession of maximal creative powers.  But, even though God has maximal creative power, that does not mean God can do what it logically impossible or morally reprehensible.
  2.  Coercive power pertains to the brute force that an individual may exert on another individual.  Coercive power is exerted, especially, when individuals want to compel others to do what they would otherwise not do or to stop them from doing what they want to do.  Essentially, therefore, coercive power is exerted when forcing one to act against one’s original intended will.  Hence, coercive power aims at depleting the individual’s freedom to will and act and replaces it with unquestionable obedience or servitude to the powerful individual.  God, too, has and uses coercive power, especially, on Satan and his cohorts in compelling Satan to obey God, when necessary.

iii)  Influential power is the emotive power that is generated in a benefactor by the patron.  The patron influences the benefactor to think and act in the manner that the patron thinks and act.  The transference of influential power from the patron to the benefactor is essentially amicable; hence the benefactor feels no compulsion in choosing to emulate the patron.  Yet left on their own, without the exertion of influences from the patron, the benefactor would not have been transformed into the “image” of the patron.  Teachers have and exercise influential power on students in tutorage, which is basically the transference of knowledge power from the teacher unto the students.  It is for this reason that the best teacher is one who mentors students.  God, too, has influential power and He uses it on his children by amicably enabling them to think and act like God.  God does not force his children to do his will.   He influences his children by showing them His will regarding A and B and aiding them with his Holy Spirit so they can freely choose according to God’s preferences.

 

Passive power is the power that an agent exercises by refraining from doing something.  Passive power is exemplified when one freely chooses to let another person act upon one. D. M. Armstrong explains:

A particular has passive power if, when some further particular of a certain sort is in, or comes into, a certain relation to it, certain of its properties are changed or sustained.  The brittleness of a glass is a passive power of the glass.  A radical case here is where the original particular ceases to exist.24 

Passive power is vital to animal survival.  Animals exhibit passive power when they restrain themselves from doing certain things.  Passive power is mainly useful in self-defense, especially, when animals evade enemies.  All animals use active power when hunting for food, but they use passive power when they are being hunted for food.   From the lowest to the highest, animal survival depends on ability to alternate between offense and defense or between active and passive powers.  

Passive power is also highly exhibited in sports.  When a team goes on the defense mode, it uses passive power against the opponent team.  A tennis player must have and use a lot of active and passive powers in order to win tennis matches.  When serving, the tennis player employs active power but when receiving serves, the tennis player employs passive powers.  A masterful alternation between passive and active power is vital to a tennis player’s winning of games. We are not always doing things; on many occasions things are being done for or to us.  Failing to distinguish between these modes of power spells disaster.

But even when we are passive, we are still exerting much will power to refrain from acting.  This is why when we refrain from acting we are called powerful.  This is especially true with regards to issues of morality.  The use of passive power in restraining ourselves from acting wrongly is often taken as exhibiting strong character or moral strength.  If, for example, a young man succumbs to the temptation to commit adultery with a beautiful damsel, he will be described as weak; rather than as powerful.  

God, too, has and uses passive powers.  God employs maximal passive powers in restraining himself from doing certain things.  The biblical portraiture of God is not that of an individual who is always doing things.  On many occasions, God leaves things undone.  A significant illustrative instance of God exemplifying passive power is on Calvary, when Jesus Christ resisted the temptation by Satan and the jeering spectators to come down from the cross. Staying on Calvary and dying there was a remarkable show of strength by Jesus Christ.  

Conclusion

Existential quantification of omnipotence allows us to rightly interpret “God has all powers” as entailing “God possesses all types or kinds of powers,” but without meaning that God can do all things.  I take Anthony Kenny as supporting this view in defining omnipotence as:

 20)  (Ox) = df. For any given y, x has power over y.  

Some may object to this parsing of omnipotence on ground that it constricts God.  I deny that it constricts God; rather it rightly presents God as possessing all types of powers. Having all powers, God can freely do whatever he wills.  But God can also freely refrain from doing whatever he does not will to do.  The Scriptures list these few things that God does not will to do: change his mind, sin, sleep or die.  But even though God does not do these things, God is omnipotent.25   

1 The definition of Omnipotence as “can do” is rampant in philosophical and theological essays on omnipotence.  Boethius, St. Anslem, and Aquinas speak of omnipotence in terms of what God can do.  Aquinas says: “It remains therefore that God is called omnipotent because He can do all things which are possible absolutely.” (Summa Contra Gentiles, 1.7c).

2 Formally, [(x) (O) (GO  Gx]

3  Descartes, “Letter to Arnauld, “ 29 July, 1648, in Descartes Philosophical Letters, trans. and ed. by Anthony Kenny (Minneapolis: University of Minnesota Press, 1970), p. 236.

4 Richard R. La Croix, “The Impossibility of Defining Omnipotence,” Philosophical Studies 32 (1977): 181.

5 Thomas Aquinas, Summa Theologica. I/1.

6 C. Wade Savage, “The Paradox of the Stone,” Philosophical Review 76 (1967): 74.

7  J.L. Mackie, “Evil and Omnipotence,” Mind 64 (April, 1955): 212.

8  J.L Cowan, “The Paradox of Omnipotence,” Analysis p. 103.

9  C. Wade Savage, “The Paradox of the Stone,” p. 77.

10  G. I. Mavrodes, “Some Puzzles Concerning Omnipotence,” The Philosophical Review 72 (April 1963): 221-23.

11  P.T. Geach, “Omnipotence,” p. 16.

12  Flint and Freddoso, “Maximal Power,” p. 161.

13  Ibid., p. 162.

14  Mavrodes, “Defining Omnipotence,” Philosophical Studies 32 (1977): 197.

15 Swinburne, The Coherence of Theism (Oxford: Clarendon Press, 1993),  p. 175.

16 St. Augustine, The City of God 5:10, trans. Gerald Walsh et al; ed. Vernon Bourke (Garden City, N.Y.: Image Books, 1958), p. 109.

17 St. Anselm, Proslogion, VII, trans. M. J. Charlesworth (Notre Dame: University of Notre Dame Press, 1979), p. 1.

18St. Thomas Aquinas, Summa Contra Gentiles, I. 2.25.

19 St. Augustine, The City of God, 5:10.

20 Thomas Aquinas, Summa Theologica, 1. 25.2., trans. Thomas Gilby, Blackfrairs’ Series , vol. V. (New York: McGraw-Hill Book Company, 1966), p 165.

21  P.T Geach, “Omnipotence,”  Philosophy  48 (Jan. 1973):  8.

22 La Croix, “The Impossibility of Defining Omnipotence,” p. 182.

23


 George I. Mavrodes, “Defining Omnipotence,” p. 196.

24 D. M. Armstrong, The World of States of Affairs, Cambridge Studies in Philosophy Series (Cambridge: University Press, 1997), p. 70.

25 Anthony Kenny, “The Definition of Omnipotence,” in Thomas V. Morris, The Concept of God, (New York: Oxford University Press, 1987), p. 132.