In his book Man’s Vision of God, after carefully arguing his case, Charles Hartshorne make this conclusion, which I quote at length:
These things being understood, it follows that one, and only one, of the following propositions must be true:
I. There is a being in all respects absolutely perfect or unsurpassable, in no way and in no respect surpassable or perfectible. (Theism Of The First Type; absolutism, Thomism, most European theology prior to 1880.)
II. There is no being in all respects absolutely perfect; but there is a being in some respect or respects thus perfect, and in some respect or respects not so, in some respects surpassable, whether by self or others being left open. Thus it is not excluded that the being may be relatively perfect in all the respects in which it is not absolutely perfect. (Theism Of The Second Type; [neoclassical or process theism], doctrines of a “finite-infinite” or perfect-perfectible God.)
III. There is no being in any respect absolutely perfect; all beings are in all respects surpassable by something conceivable, perhaps by others or perhaps by themselves in another state. (Doctrines of a merely finite God, polytheism in some forms, atheism.)
This division is exclusive and exhaustive. To prove any two of these propositions false is to establish the truth of the remaining proposition; there can be no “higher synthesis” which combines the truth of any two or of all three of them, except as this synthesis amounts to accepting some one of the three as it stands and contradicting some part of each of the other two; that is, one of the three must be the higher synthesis.
The almost complete overlooking of the second of the three main types of doctrine has some title to be called the greatest intellectual error mankind has ever made, since it affects the most basic of all ideas, and since it escaped widespread detection for nearly the whole period of recorded philosophico-scientific development, at any rate for well over two thousand years. The only error perhaps surpassing it is indeed closely connected with it. This is the misconception of the nature and function of mathematics, the notion that mathematical knowledge is the model of all knowledge instead of merely the model of one aspect of knowledge, radically incomplete in itself, that therefore what mathematics knows is independent of everything else, pure “being” above “becoming,” and that therefore all thought about high matters should follow the mathematical pattern of deduction from easily established axioms, settled once for all, and should see as its ideal object some timeless essence, or sheer perfection, devoid, in Plato’s memorable words, of motion and life and power. These words are all the more memorable because Plato is partly responsible, as he is usually interpreted, for the error. It is a great mathematico-philosophical mind, perhaps the nearest to Plato in combination of interests that our time has produced, Alfred North Whitehead, who has most effectively criticized this mistake. The whole modern era has seen the increasing emancipation of natural science from false mathematicism or deductivism; it is not surprising that theology has also been learning the lesson, though more quietly and with inferior publicity. It is also not surprising that in both cases reaction has sometimes gone too far, and the role of the merely empirical has been exaggerated at the expense of the formerly exalted a priori element. The balance is, I believe, being found in both fields of thought.
Charles Hartshorne, Man’s Vision of God and the Logic of Theism, pp. 11-12, 28-29.