This is untrue. The law of non-contradiction doesn't depend upon finiteness.
I was being flip. The law of non-contradiction isn’t true, because, simply put, it sometimes does not apply.
The Middle Way by Nagarjuna, is an excellent text to experience the logical methodology of the tetra-lemma. The philosopher Graham Priest has very interesting papers dealing in part with how current logic tools can illustrate the problems in ‘Classical Logic’.....sorry a non-sequitur..but if innovative advanced analytical logic is your jam....check his work out.