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Omnipotence (from Latin: Omni Potens: "all power") is unlimited power. Monotheistic religions generally attribute omnipotence to only the deity of whichever faith is being addressed. In the monotheistic philosophies of Abrahamic religions, omnipotence is often listed as one of a deity's characteristics among many, including omniscience, omnipresence, and omnibenevolence. The presence of all these properties in a single entity has given rise to considerable theological debate, the problem of theodicy prominently included.
The term omnipotent has been used to connote a number of different positions. These positions include, but are not limited to, the following:
Under many philosophical definitions of the term "deity", senses 2, 3 and 4 can be shown to be equivalent. However, on all understandings of omnipotence, it is generally held that a deity is able to intervene in the world by superseding the laws of physics, since they are not part of its nature, but the principles on which it has created the physical world. However many modern scholars (such as John Polkinghorne) hold that it is part of a deity's nature to be consistent and that it would be inconsistent for a deity to go against its own laws unless there were an overwhelming reason to do so.
The word "Omnipotence" derives from the Latin term "Omni Potens", meaning "All-Powerful" instead of "Infinite Power" implied by its English counterpart. The term could be applied to both deities and Roman Emperors. Being the one with "All the power", it was not uncommon for nobles to attempt to prove their Emperor's "Omni Potens" to the people, by demonstrating his effectiveness at leading the Empire.
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St. Thomas Aquinas, OP acknowledged difficulty in comprehending the Deity's power: "All confess that God is omnipotent; but it seems difficult to explain in what His omnipotence precisely consists: for there may be doubt as to the precise meaning of the word 'all' when we say that God can do all things. If, however, we consider the matter aright, since power is said in reference to possible things, this phrase, 'God can do all things,' is rightly understood to mean that God can do all things that are possible; and for this reason He is said to be omnipotent." In the scholastic understanding, omnipotence is generally understood to be compatible with certain limitations or restrictions. A proposition that is necessarily true is one whose negation is self-contradictory.
St. Thomas explains that:
Omnipotence is all-sufficient power. The adaptation of means to ends in the universe does not argue, as J. S. Mill would have it, that the power of the designer is limited, but only that God has willed to manifest His glory by a world so constituted rather than by another. Indeed the production of secondary causes, capable of accomplishing certain effects, requires greater power than the direct accomplishment of these same effects. On the other hand even though no creature existed, God's power would not be barren, for "creatures are not an end to God." Regarding the Deity's power, medieval theologians contended that there are certain things that even an omnipotent deity cannot do. The statement "a deity can do anything" is only sensible with an assumed suppressed clause, "that implies the perfection of true power". This standard scholastic answer allows that acts of creatures such as walking can be performed by humans but not by a deity. Rather than an advantage in power, human acts such as walking, sitting, or giving birth were possible only because of a defect in human power. The capacity to sin, for example, is not a power but a defect or infirmity. In response to questions of a deity performing impossibilities, e.g. making square circles, St. Thomas says that "everything that does not imply a contradiction in terms, is numbered amongst those possible things, in respect of which God is called omnipotent: whereas whatever implies contradiction does not come within the scope of divine omnipotence, because it cannot have the aspect of possibility. Hence it is better to say that such things cannot be done, than that God cannot do them. Nor is this contrary to the word of the angel, saying: 'No word shall be impossible with God.' For whatever implies a contradiction cannot be a word, because no intellect can possibly conceive such a thing."
His Omnipotence means power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to him, but not nonsense. This is no limit to his power. If you choose to say 'God can give a creature free will and at the same time withhold free will from it,' you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words 'God can.'... It is no more possible for God than for the weakest of his creatures to carry out both of two mutually exclusive alternatives; not because his power meets an obstacle, but because nonsense remains nonsense even when we talk it about God.
— Lewis, 18
Early Freudianism saw a feeling of omnipotence as intrinsic to early childhood. 'As Freud and Ferenczi have shown, the child lives in a sort of megalomania for a long period...the "fiction of omnipotence"'. At birth. 'the baby is everything as far as he knows - "all powerful"...every step he takes towards establishing his own limits and boundaries will be painful because he'll have to lose this original God-like feeling of omnipotence'.
Freud considered that in a neurotic 'the omnipotence which he ascribed to his thoughts and feelings...is a frank acknowledgement of a relic of the old megalomania of infancy'. In some narcissists, the 'period of primary narcissism which subjectively did not need any objects and was entirely independent...may be retained or regressively regained..."omnipotent" behavior'.
D. W. Winnicott took a more positive view of a belief in early omnipotence, seeing it as essential to the child's well-being; and "good-enough" mothering as essential to enable the child to 'cope with the immense shock of loss of omnipotence' - as opposed to whatever 'prematurely forces it out of its narcissistic universe'.
Some monotheists reject the view that a deity is or could be omnipotent, or take the view that, by choosing to create creatures with freewill, a deity has chosen to limit divine omnipotence. In Conservative and Reform Judaism, and some movements within Protestant Christianity, including process theology and open theism, deities are said to act in the world through persuasion, and not by coercion (for open theism, this is a matter of choice—a deity could act miraculously, and perhaps on occasion does so—while for process theism it is a matter of necessity—creatures have inherent powers that a deity cannot, even in principle, override). Deities are manifested in the world through inspiration and the creation of possibility, not necessarily by miracles or violations of the laws of nature.
The rejection of omnipotence often follows from either philosophical or scriptural considerations, discussed below.
Process theology rejects unlimited omnipotence on a philosophical basis, arguing that omnipotence as classically understood would be less than perfect, and is therefore incompatible with the idea of a perfect deity. The idea is grounded in Plato's oft-overlooked statement that "being is power."
My notion would be, that anything which possesses any sort of power to affect another, or to be affected by another, if only for a single moment, however trifling the cause and however slight the
effect, has real existence; and I hold that the definition of being is simply power.
— Plato, 247E 
From this premise, Charles Hartshorne argues further that:
Power is influence, and perfect power is perfect influence ... power must be exercised upon something, at least if by power we mean influence, control; but the something controlled cannot be absolutely inert, since the merely passive, that which has no active tendency of its own, is nothing; yet if the something acted upon is itself partly active, then there must be some resistance, however slight, to the "absolute" power, and how can power which is resisted be absolute?
— Hartshorne, 89
The argument can be stated as follows:
For example, though someone might control a lump of jelly-pudding almost completely, the inability of that pudding to stage any resistance renders that person's power rather unimpressive. Power can only be said to be great if it is over something that has defenses and its own agenda. If a deity's power is to be great, it must therefore be over beings that have at least some of their own defenses and agenda. Thus, if a deity does not have absolute power, it must therefore embody some of the characteristics of power, and some of the characteristics of persuasion. This view is known as dipolar theism.
The most popular works espousing this point are from Harold Kushner (in Judaism). The need for a modified view of omnipotence was also articulated by Alfred North Whitehead in the early 20th century and expanded upon by the aforementioned philosopher Charles Hartshorne. Hartshorne proceeded within the context of the theological system known as process theology.
In the Authorized King James Version of the Bible, as well as several other versions, in Revelation 19:6 it is stated "...the Lord God omnipotent reigneth" (the original Greek word is παντοκράτωρ, "all-mighty"). Although much of the narrative of the Old Testament describes the Judeo-Christian God as interacting with creation primarily through persuasion, and only occasionally through force. However, it could further be argued that the ability to conflict with truth is not an appropriate representation of accepted definitions of power, which negates the assertion that a deity does not have infinite powers.
Many other verses in the Christian Bible do assert omnipotence of its deity without actually using the word itself. There are several mentions of the Christian deity being referred to as simply "Almighty", showing that the Christian Bible supports the belief of an omnipotent deity. Some such verses are listed below:
Psalms 33:8-9: Let all the earth fear the LORD: let all the inhabitants of the world stand in awe of him. For he spoke, and it was done; he commanded, and it stood fast.
Genesis 17:1: And when Abram was ninety years old and nine, the LORD appeared to Abram, and said unto him, I am the Almighty God; walk before me, and be thou perfect. (The Hebrew word used here is "shadday")
Jeremiah 32:27: Behold, I am the LORD, the God of all flesh: is there any thing too hard for me?
At his command a storm arose and covered the sea. (Psalm 107:25)
Several parts of the New Testament claim Jesus to be one with the Father, who is omnipotent, and others show Jesus to have some separation from the Father and even self-imposed limitations on his power. (Gospel of John)
A classical example goes as follows:
For He is called omnipotent on account of His doing what He wills, not on account of His suffering what He wills not; for if that should befall Him, He would by no means be omnipotent. Wherefore, He cannot do some things for the very reason that He is omnipotent.
All the above stated claims of power are each based on scriptual grounds and upon empirical human perception. This perception is limited to our senses. The power of a deity is related to its existence.There are however other ways of perception like: reason, intuition, revelation, divine inspiration, religious experience, mystical states, and historical testimony.
According to the Hindu philosophy the essence of God or Brahman can never be understood or known since Brahman is beyond both existence and non-existence, transcending and including time, causation and space, and thus can never be known in the same material sense as one traditionally 'understands' a given concept or object.
So presuming there is a god-like entity consciently taking actions, we cannot comprehend the limits of a deity's powers.
Since the current laws of physics are only known to be valid in this universe, it is possible that the laws of physics are different in parallel universes, giving a God-like entity, more power. If the number of universes is unlimited, then the power of a certain God-like entity is also unlimited, since the laws of physics may be different in other universes, and accordingly  making this entity omnipotent. Unfortunately concerning a multiverse there is a lack of empirical correlation. To the extreme there are theories about realms beyond this multiverse (Nirvana, Chaos, Nothingness).
Also trying to develop a theory to explain, assign or reject omnipotence on grounds of logic has little merit, since being omnipotent would mean the omnipotent being is above logic. A view supported by René Descartes  He issues this idea in his Meditations on First Philosophy.
Allowing assumption that a deity exists, further debate may be provoked that said deity is consciously taking actions. It could be concluded from an emanationism point of view, that all actions and creations by a deity are simply flows of divine energy (the flowing Tao in conjunction with qi is often seen as a river; Dharma (Buddhism) the law of nature discovered by Buddha has no beginning or end.) Pantheism and/or panentheism sees the universe/multiverse as 'the body of God', making 'God' everybody and everything. So if one does something, actually 'God' is doing it. We are 'God's' means according to this view.
In the Taoist religious or philosophical tradition, the Tao is in some ways equivalent to a deity or the logos. The Tao is understood to have inexhaustible power, yet that power is simply another aspect of its weakness.
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