what criteria for a judgment upon propositions or a set? and don't say God transcends logic

what would you think an objective (or agnostic) audience should agree to as a necessary criterion (or which necessary criteria) for evaluating any proposition (or any set of propositions)?

as to how we know anything— we know through 3 sources:
   sound sense perception,
   reliable reporting, and
   logic & reasoning.

these base principles of rationality (such as the laws of logic) are why, for example, we —logically— count by "identity"... by what each discernible, particular thing is.
these innate logical principles, which underline all meaningful communication and rational inquiry, are for supposing coherent abstraction—such as to what accepts its existence being actualised in reality: that the cause and explanation of any proposition must be non-arbitrary.

the only being that is unknown through the former two sources of sensory perception and reporting (that is Unseen — al-Ghaib), that can be directly apprehended through the latter (logic & reasoning) is the existence of the Necessary Being (the Creator) by that innate, necessary knowledge and the further exercise of its pure logical principles.

i.e. there are things that are unseen, and we innately incline —through our original disposition— to knowing the only thing we can innately know among the Unseen: the Creator.

reasoning is facilitated for us by the Necessary Being, the Uncaused Cause: He instilled in us the faculties that incline to the apprehension of truth and knowledge, especially the truth from and about Him so that we may understand it, communicate it, verify it, and act upon it [the truth].

logic is a faculty instilled in us, facilitated and enabled by the Creator, the Most Intelligent — Who knows the creation better than the creation knows itself.
The Creator is rational, not irrational; the truth —as is true belief in the Creator— is rational, not irrational.

if this innate knowledge and logical principles did not accurately reflect the nature of reality, how could we have any confidence in the conclusions we draw about the world and ourselves?
indeed, these principles (which are necessary truths by their very nature) are innate and must be grounded in the necessary cause of externality itself.

by & large, what is mental is apprehended by what we soundly perceive through the senses, and what is mental in this way was at some point not in that way (not apprehended by the mind or senses)—our (mental) application of reason to these abstractions not being committed to our perception of the extramentals, but rather to our rationality conceiving abstractions of and about the extramentals.

logic in this sense does not apply to beings, or to what is in extramental reality — we apply it to our minds, to abstractions about what is in reality or what may be real; we do not apply reason and logic to what is beyond it (the extramental — any particular being, as they transcend the reach of the faculty), but to mental abstractions of and about the extramental—perceived, or not perceived.
the attaining of knowledge of any of these particulars cannot be through reason and logic alone; as mentioned above, the sole exception to this some knowledge of God and His Existence.
logical reasoning functions, therefore, not to limit any particular extramental being — but rather to limit the mind to supposing coherently, being a coherent criteria for judgments in critical thinking.

as such, to the person who states it, I would ask: what do you mean "God transcends logic" ?

the dictionary definition of "transcendence" is "existence or experience beyond the normal or physical level"
so...is it "through logic, God is experienced beyond the normal and physical level" ?
in which case "God transcends logic" means "knowledge of God is logically coherent and directly available, beyond the normal and physical level"

if you mean "God cannot be known of or about in any way by logic alone" is what "God transcends logic" means, then
a) this is verifiably false
b) it actually only applies to everything but God
c) I am not sure why you could then find it necessary, or even possible, to reason with others about the true belief from and about God
d) it seems you are fine with the rational possibility of any (even inconsistent) set of propositions applied to your theological beliefs (and in which case I am not sure why anyone would find it necessary, or even possible, to reason with you)
e) I am not sure how you could even demonstrate that a set of propositions (which you do not claim to hold to) are not the same as what you do hold to about God (for example, how could you dispute that you are not eating God when you eat breakfast? this would involve logic that God would transcend, and it would seem possible in your paradigm. it may even kill him at any point!)