If you think that bit of sly editing supports your position, I would suggest you have the greater need.
Why did you change the subject?
No need to invoke infinity.
Follow the discussion:
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Proposition: Is it possible that God is irrational because life has always been such?
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Response: God is irrational compared to our finite minds that cannot comprehend infinite reality; that is why we invent godlings and redemptionist faery-tale holy scriptures.
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Counterpoint: However, to think the infinite is necessarily incompatible with sentience represents yet another type of rhetoric/shoebox thinking.
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Response: I wouldn't necessarily disagree with the proposition, but at some point we encounter a threshold of applicability versus a range of potentials evading actualization; as
Sideshowbob↑ reminds, there is a question of faculty. Much like whether or not we have the technology to accomplish certain feats otherwise likely permissible according to physics, it is difficult to conceive of the scale at which sentient compatibility with infinitude is possible without invoking unknown physics. In terms more philosophical, something about Augustine and a rock goes here.
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Counterpoint: The very presence of sentience already establishes
unknown physics.
No need to invoke infinity. Infact you could even say the presence of physics already establishes unknown physics.
(Boldface accent added)
In discussing "God", as such, infinity is inherent, else God is not God.
When I say you're not following yourself from post to post, it is because your statement, "No need to invoke infinity", seems irrelevant or a change of subject. The other possibility, of course, as
River↑ notes, is a different definition of "God" than the monotheistic godhead usually associated with the term. And that godhead
is infinite; it's one of the classic stumbling blocks of proud faith.
As to the rest:
If the agency of omnipotence is necessarily singular (is it rational to talk about several independant omnipotent agencies?), you can automatically exclude any "greater than ..." clauses at the onset. Rejecting omnipotence because it does not have the power to destroy itself as a category is just as valid as a conversation about a square with three sides.
The first part of that, about excluding comparative clauses, does not necessarily follow. The second part is certainly interesting, but only you know whence it comes. For our purposes, Augustine's rock reminds that any human has a finite number of brain cells that operate in finite manners for finite periods, and thus cannot comprehend something infinite.
This question of comprehension derives from the proposition noted above. The perceived irrationality of God is just that,
perceived. That reality fails to make rational sense according to our human irrationality is not any great mystery. To the other, proposing that God is irrational is perfectly human, and doing so because God fails to satisfy a human even more so. And all throughout, infinitude is inherent; in the end, regardless of whether or not one "believes in God", it makes no sense to require that something be something else before we can analyze the something that it is.
Technically speaking, you are correct to say we need not invoke infinity; however, you are wrong about what the words mean; we need not invoke infinity because it is already inherently part of the consideration.
And, yes, in the context of "God", it is somewhat irrational to regard multiple omnipotent agencies. It might also be inherently improper. But this is in part because it also implies a certain manner of infinitude, and there can only be one proper infinitude.
Descartes actually answers Augustine properly, but it's not in the explicit parts about God Itself; rather, it's in Cartesian conservation. By the time we get to C.S. Lewis, the argument is a complete disaster. Wittgenstein, functionally speaking, is correct to note semantics, but like given the inevitable choice 'twixt blithering and surrender, he wisely chose the latter.
The answer is actually, "No, God cannot create a stone too heavy to lift". What complicates the answer is that a truly infinite God does little to swell our passions. As Write4U put it:
In the absence of any other demonstrable options, assigning an abstract purely mathematical system seems as good as any. There is no credible counter claim, IMO.
And that would satisfy the OP question. Yes , an abstract God could be rational, but not sentient.
The biggest challenge about explaining God might be the question of will. After all, if God is infinite, then what is all the differentiation we experience? Perhaps it is an act of will, but acts of will imply finitude; time itself is differentiation.
The resolution has to do with God being God. Without the passage of time, there is no change; if there is no change, there is no Will; the passage of time is itself a matter of differentiation.
All of which leads back to certain obvious point: God is not irrational, people are.