this is a strawman. If I don't know something, that doesn't prove it doesn't exist. The construction of the nat-nums you alude too relies on infinity as an axi

this is a strawman. If I don't know something, that doesn't prove it doesn't exist. The construction of the nat-nums you alude too relies on infinity as an axiom, so the construction itself doesn't prove jack. For all practical intents and purposes "infinity", in a very narrow sense, is indistinguishable from arbitrary large numbers. Your rhethoric question leads to contradiction: By the same line of reasoning, if I don't know what the weather will be next year, that must mean it wont exist, so time is finite, which contradicts your implications.