In mathematics, diving a number by zero is undefined. But it is now customary to call “the result”(there is actually no result as such) of dividing a number by zero, “infinity”. There is in fact no number which is the result of dividing by zero. The operation is simply undefined, or meaningless. The result of this meaningless operation is anything but a number. “Infinity” is therefore not a number. “Infinity” can not refer to “magnitude” as numbers ordinarily do, since it is NOT a number. The reason diving by zero is undefined lies in the axioms of arithmetic. Dividing by zero is undefined within these axioms. Zero does not have a “multiplicative inverse”(1/0 does not exist), and hence one cannot put zero “at the bottom” to divide another number(i.e. x/0 is meaningless). There are other ways of arriving at “infinity”, but this should be sufficient for the present purposes.
But, it seems from popular usage that “infinite” is used to designate some sort of magnitude or size of “unspecifiable” quantity, “a limitless number”. A number, any number, ought to be specifiable in principle, barring of course mere ignorance of it. If not, then a contradiction seems to be implied. In mathematics, such contradictions point to undefined operations or operations that are not specifiable in terms of the axioms or conditions that illegitimately stretch the extent of coverage of the system of axioms. No “irresolvable contradiction” or “paradox” is implied.
The use of “infinity” in theology in referring to God’s attributes such as power, knowledge etc etc will therefore be somewhat problematic, given the origins of the word “infinite” in mathematics as I have outlined above. Does “God is infinite in power and wisdom …” really mean anything? What is “infinite”, in reference to God’s attributes, meant to convey? Does the Bible anywhere refer to anything as infinite? The answer to the last question is a definite NO as we will show! No where does the Bible call God infinite in any of His attributes!
There are three instances and only three, in the Old Testament where a Hebrew word is translated “infinite” . It refers to God’s understanding(knowledge), then to the strength of a nation and finally to someone’s sins.
We dispose of the easier ones first.
Eliphaz, one of Job’s miserable comforters, says in Job 22:5, “Is not thy wickedness great? and thine iniquities infinite?”. The Hebrew is “en qets” which means “no end”. Did Eliphaz posses the modern mathematical idea of “infinite” or an ancient equivalent in his mind when he uttered these words, to justify such a translation? The most plausible answer is probably NO! Eliphaz was of the idea that Job’s sins had gone beyond acceptable limits hence his suffering. Job would need an “infinite” time to have his sins literally “infinitely” many. It should simply be “There is no end to your iniquities” No end to your iniquities is NOT literal “no end”. It is hyperbole for many sins. The translation is therefore not a good one.
Secondly, Nahum 3:9 “Ethiopia and Egypt were her strength, and it was infinite; Put and Lubim were thy helpers”
The Hebrew is “‘en qetseh”, which again means “no end”. Surely Ethiopia and Egypt were not infinite, for then they would be equal to the “infinite” god of the theologians!!! The meaning of the phrase might refer to the impressive “numberless”(without end) hordes of the armies of the Ethiopians and Egypt; their incontestable military might by reason of their numbers. To get an idea of the military prowess of these guys refer to the passage in 2 Chronicles 12:
1 And it came to pass, when Rehoboam had established the kingdom, and had strengthened himself, he forsook the law of the LORD, and all Israel with him. 2 And it came to pass, that in the fifth year of king Rehoboam Shishak king of Egypt came up against Jerusalem, because they had transgressed against the LORD, 3 With twelve hundred chariots, and threescore thousand horsemen: and the people were without number that came with him out of Egypt; the Lubims, the Sukkiims, and the Ethiopians.
The Bible says the people were “without number” that came with Shaky, from Egypt. The translators wisely did not choose “infinity” for Shaky’s hordes!
And lastly, the verses that refer to God.
“Great is our Lord and abundant in strength; His understanding is infinite” (Psa. 147:5).
The Hebrew used in the Psalm is “en micpar” which means “no number”. It can be translated “great in number”, certainly NOT infinite. As used in the verse, it means unfathomable or inscrutable or unsurpassed. This refers to the depth of His mind! Number or quantity is really of minor consideration in matters of knowledge. Understanding, comprehension, is the chief part. It is the ability to make connections, systematize and arrange that is lauded as knowledge rather than myriads of unconnected propositions. By inscrutable or unfathomable I do not mean irrational or the van Tillian delicacies, “incomprehensibility”, “apparent contradictions” and “paradoxes”. I mean God possesses such great depths of wisdom and knowledge that man understands only poorly. God is omniscient means He possesses all the logical relations of all propositions in His mind, which no human mind does!
Gordon Clark, in his “The Incarnation” says, “..if infinite in number, neither God nor man could know them all, for with respect to infinity there is no “all” to be known. Infinity has no last term, and God’s knowledge would be as incomplete as man’s. Shades of Zeus!” and further says, ” .. a denial of infinity to God is not a denial of omniscience or omnipotence.” (pp 62 & 63)
For argument’s sake, a “god” with the knowledge of all the “infinite” real or natural numbers has infinite knowledge. But this infinite “god” need not know anything else to be said to possess infinitude since the knowledge of all numbers alone is sufficient for that purpose. And so, “god” could be ignorant of other things and still be “infinite”. “Infinitude” is therefore inadequate to designate the God of scripture who knows all things. Escape to an all embracing infinitude leads to problems. God is not an infinite number of persons, but only three.
Many of the so-called “difficulties in the concept of God ” involve the invocation of “finite” and “infinite” categories. This would seem to be confusion arising from the use of meaningless words. Many theologians are sure “the finite” cannot comprehend “the infinite”. I think they are right, and their confused theology makes the point eloquently!!!
Clark says Thomas Aquinas introduced “infinity” into theology! This medieval Thomistic flight of fancy ought to be discarded!