Many people, when asked to identify the attributes of God, will identify characteristics such as God being omniscient, omnipotent, omnipresent, infinite, eternal, and perfect along moral or emotional lines, such as having perfect mercy or perfect lovingness. But what is the basis for such contentions? These characteristics were conjured up by philosophers in the early middle ages, and the entity that is described by them is therefore called (drumroll please) the God of the Philosophers. There are only three possible sources of information from which such a determination might be made, none of which is without flaws.
First there is the nature of the Universe itself. It is vast, full of energy, and its laws of physics bear some indicia of having been designed for the specific purpose of bringing about intelligent life. Second, there are claims of information imparted to men by a god. Third, there is pure logic, and logical extrapolation from mathematical truths.
Evidence from examination of the Universe itself
Regarding the first possible basis, let us examine the Universe. It is large, but it now appears quite certain that it is not infinitely large, nor is it infinitely complex. It is not eternal, having begun at a specified time in the past. While any entity responsible for creating the Universe would have to be very powerful and very intelligent, there is simply no requirement that such an entity have more power or intellect than the immense, but decidedly finite, bare minimum required for such a creation. While it is possible to infer the existence of a powerful and intelligent Creator from the nature of the Universe (as occurs in deism and pandeism), one can not infer from the nature of the Universe alone that such a Creator must be omnipotent, omniscient, eternal, or loving.
Scientists on several fronts now theorize that humans may even develop the technology to create a new baby Universe that expands and unfolds according to laws of physics calculated by its human creators. To know that the creation of a new Universe may fall within the hands of a small group of humans on this planet, which occupies a pinprick in the whole of the Universe, puts in perspective the lack of omnipotence and infinitude necessary for the creator.
Evidence from revelation and holy texts
As for the second possible basis, there is no reason for any assertions of revelation to be believed on their face. All revelations come through the voice or hand of man, and men may be mistaken, misled, delusional, or merely dishonest. Even if some higher power exists, and a person were to correctly believe that they had received a communication from such a higher power, that person would have no way to gauge the characteristics of the source of the message beyond merely blindly trusting claims that it made. Although many holy books recount miracles said to have been performed by such higher powers, no witness is borne to any such miracle that would require the performer to be infinite in any sense, or more powerful even than many comic book heroes. Indeed, the accounts set forth in most holy texts are vague, sometimes self-contradictory, and in any event allegorical to an indeterminate degree. So it is not absolutely set forth in such texts that the creator described therein is the same entity described by the philosophers.
A higher power need not even be conscious. The power of the mind responsible for the creation of the Universe may be such that any person coming in contact with it would feel that they were experiencing conscious revelation, even though they were only touching an unconscious mind.
Evidence from mathematics and logical extrapolation
Finally, we come to the proof afforded by mathematics and logic. The most common logical arguments in favor of the existence of God, such as the cosmological argument for a prime mover or a necessary being, do not require that entity to be infinite, eternal, or omniscient. Some have attempted to craft arguments having a superficial veneer of logic and proposing that, for example the ontological argument, essentially that a perfect God can be imagined into existence. However, no such argument has withstood close logical scrutiny, if for no other reason than the ability of different minds to simultaneously conceive of imaginary beings with infinite power but contradictory characteristics such as perfect disinterest and perfect interest. No logical or mathematical formulation has yet been put forth which requires any degree of infinitude be held by a creator, nor can mathematics or logical extrapolation assign any emotional or moral characteristics to such a creator.
The only determination that logic can provide is that, because it created something at all, the creator was not so inherently perfect as to be able to continue its existence without engaging in an act of creation.