Finite is the opposite of infinite.
The same as eternal being the opposite ephemeral.
So if we are to hold the law of non contradiction to be true then two opposites would (Or could) then not be true at the same time. Wikipedia would define the law as the following.
In classical logic, the law of non-contradiction (LNC) (or the law of
contradiction (PM) or the principle of non-contradiction (PNC), or the
principle of contradiction) is the second of the three classic laws of
thought. It states that contradictory statements cannot both be true
in the same sense at the same time, e.g. the two propositions "A is B"
and "A is not B" are mutually exclusive.
So I would answer no!
Are there any defeaters for this possible belief? My impression is
that most cosmologists believe there must be a cause for a universe,
and perhaps many philosophers think the same, but I don't understand
why they do.
Well this is a rather large area of inquiry spending thousands of years. I will try and give a short history of some of the more broader schools of thought in regards to causality.
Though the ideas of causation has emerged in Pre Socratic philosophy, it was Plato who first stated the principle of causality: "everything that becomes or changes must do so owing to some cause; for nothing can come to be without a cause" (Timaeus 28a).
...and has no Becoming? And what is that which is Becoming always and
never is Existent? Now the one of these is apprehensible by thought
with the aid of reasoning, since it is ever uniformly existent;
whereas the other is an object of opinion with the aid of unreasoning
sensation, since it becomes and perishes and is never really existent.
Again, everything which becomes must of necessity become owing to some
Cause; for without a cause it is impossible for anything to attain
becoming. But when the artificer of any object, in forming its shape
and quality, keeps his gaze fixed on that which is uniform, using a
model of this kind, that object, executed in this way, must of
ARISTOTLE: FOUR TYPES OF EXPLANATION.
You could say that Aristotle was the first to make a full fledge critical account of the matter. In essence Aristotle claimed that when we ask "What is this?" We could answer the question in four ways. Each answer pertaining to a quality of the cause. (aitia)
The material cause: - that out of which
The formal cause: - the form”, “the account of what-it-is-to-be
The efficient cause: - the primary source of the change or rest
The final cause: - the end, that for the sake of which a thing is done
THE STOICS AND CAUSATION.
The stoics injected the cosmos with a logos (Divine Cause) that was ordain by the concept of fate. The stoics where firm believers in the necessity of causes to events. Which was key to there view of the coherence of the universe. Universal Causation
CAUSATION IN THE MIDDLE AGES:
Here a view contrary to Aristotle emerged. Two different views on Efficient causes which was a radical turn on the Aristotelian view,
Primary Cause: Something which is generated in of itself.
Secondary Cause: All material has been created by God and has certain intrinsic property.
Aquinas' posit five ways to argue the existence of God. His fifth way concludes from the observation of finality within natural bodies that there must be some intelligent being, God, by which all natural things are ordered to their end.
CAUSATION IN MODERN PHILOSOPHY
- Descartes: dismissal of forms
- Hobbes: causation and motion
- Spinoza: causation as necessitation
- Leibniz: sufficient reason