[CONTINUED]
When we speak of "no limitations" we are talking about rational categories or limitations within a rational category. Within the realm of power, we mean that God can do anything that it is logically possible for power to do. I.e., There is no limit on which powers in the category of "powers" that God can exercise. The category of powers, however, is itself restricted to the realm of things that are logically possible. This is why we are justified in using the "omni" prefix while maintaining that God cannot do anything whatsoever.
That is why even Berkhoff, while maintaining a "no limits" definition of infinite says, "There is no absolute power in Him that is divorced from His perfections". I.e., he supports the idea that there are rational restrictions on the category of "powers" when he says that there is no power of a certain kind.
Here is a definition for omnipotence as given in _The Westminster Dictionary of Christian Theology_ edited by Alan Richardson and John Bowden, 1983, Westminster Press, Philadelphia, in an article by Brian Hebblethwaite who is in turn quoting from "A.Kenny, _The God of the Philosophers_,1979:
"A more satisfactory definition has been provided by A. Kenny: omnipotence is 'the possession of all logically possible powers which it is logically possible for a being with the attributes of God to possess."
Here is a definition given in _Christian Theology, Systematic and Biblical_, arranged and compiled by Emery H. Bancroft, D.D., Late professor of Bible Doctrine and Systematic Theology at the Baptist Bible Seminary, Johnson City, New York, revised edition, 1925, on p. 68:
"C. Omnipotence. By this we mean the power of God to do all things which are objects of power, whether with or without the use of means, Gen. 17:1.
NOTE He performs natural wonders, Gen 1:1-3; Isa 44:24; Heb. 1:3; Spiritual wonders, II Cor. 4:6; Eph. 1:19; Eph. 3:20. He has power to create new things, Matt. 3:9; Rom. 4:17; after his own pleasure; Psa. 115:3; Eph. 1:11. There is nothing impossible to Him: Gen. 18:14; Matt. 19:26.
1. Omnipotence does not imply power to do that which is not an object of power; as, for example, that which is self-contradictory or contradictory to the nature of God.
NOTE Self-contradictory things are not included in the exercise of God's omnipotence.- such as the making of a past event to have not occurred (hence the uselessness of praying: "May it be that much good was done"); drawing a shorter than straight line between two given points; putting two separate mountains together without a valley between them. Things contradictory to the nature of God; for God to lie, to sin. to die. To do such things would not imply power, but impotence. God has all the power that is consistent with infinite perfection - all power to do what is worthy of Himself."
So far I have quoted only Protestants. Here is a Roman Catholic author. From _The Voice from the Whirlwind, The problem of Evil and the Modern World_ by Stephen j. Vicchio, professor of philosophy at the College of Notre Dame in Baltimore, Maryland, Christian Classics, Inc., Westminster, Maryland.
(BTW - this is a terrific book on the "problem of evil", it is essentially his Phd dissertation put out in book form.)
On p. 47, after quoting from Frederick Ferre's _Basic Modern Philosophy of Religion_, Vicchio writes:
"Ferre rightly suggests that when we say that God is omnipotent, philosophers, as well as the common man, may mean by the term one of two things. Either (a) an omnipotent being is one who can do absolutely anything, or (b) an omnipotent being is one who can do anything that is logically possible. For reasons that will become apparent later, we must also offer a third formulation of God's omnipotence: (c) an omnipotent being is one who can do anything that is logically possible and is consistent with his other attributes."
Vicchio goes on to examine each of these definitions in turn. Definition (a) which is what has been used in postings to raise objections to the existence of the Christian God, Vicchio finds used in the writings of Descartes, but not in the writings of Christian theologians such as St. Thomas Aquinas.
This leads to one of the main points of my earlier brief posting. The historical definition or understanding of omnipotence has always recognized the problems inherent in definition (a) which is why it is not the definition used by the church historically. It maybe that some Christians have held and tried to defend such a definition (such as Descartes), but for the most part, this definition is imposed on Christianity by those who wish to refute Christian conceptions by raising various objections. The objections (whether by intention or ignorance) are straw man arguments.
The definition of omnipotence like that of (b) or (c) which limits omnipotence to the category of things logically possible is the definition used by the church historically. My earlier quote from Augustine indicated as much. Here it is again, from my abridged version of _The City of God_, an abridged Version from the Translation by Gerald G. Walsh, S.J.; Demetrius B. Zema, S.J.; Grace Monahan, O.S.U.; and Daniel J. Honan on p. 109 which quotes from Augustine's book 5, chapter 10:
"We do not put the life of God and the foreknowledge of God under any necessity when we say that God must live an eternal life and must know all things. Neither do we lessen his power when we say He cannot die or be deceived. This is the kind of inability which, if removed, would make God less powerful than He is. God is rightly called omnipotent, even though He is unable to die and be deceived. We call Him omnipotent [here is the definition you did not acknowledge from the earlier post David!] because He does whatever He wills to do and suffers nothing that He does not will to suffer. He would not, of course be omnipotent, if He had to suffer anything against His will. It is precisely because He is omnipotent that for Him some things are impossible."
Aquinas has a similar conception of omnipotence. On p. 163-164 of _Summa Theologica, Volume I, ques. 15 ans. 3, (Mcgraw Hill, New York, 1963, Aquinas says:
"Whatever implies being and nonbeing simultaneously is incompatible with the absolute possibility which falls under divine omnipotence. Such a contradiction is not subject to it, not from any impotence in God, but because it simply does not have the nature of being feasible or possible. Whatever, then, does not involve a contradiction is in the realm of the possible with respect to which God is omnipotent. Whatever involves a contradiction is not within the scope of omnipotence because it cannot qualify for possibility. Better, however, to say that it cannot be done, rather than God cannot do it."
An excellent old Puritan work is _The Existence and Attributes of God_ by Stephen Charnock (1628-1680). I read a small portion of a 1979 reprint of this work published by Klock & Klock Christian Publishers of Minneapolis. He defines omnipotence in terms of God having infinite power, yet he too gives a lengthy consideration to things that are impossible for God to do.
My point is that when Christians respond to various objections to the various "omni-xxx"s of God in a way that appears to lessen the particular "omni" in question, they are not equivocating, conceding or redefining terms at all. They are only explaining what is the historic Christian teaching as found in all branches of the faith.
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http://answers.org/apologetics/omnipotence.html