Science IS a materialist PHILOSOPHY - merely one of many such schools of thought.
I don't know what 'ridiculous things' logic proves, but I assure you, such conclusions proceed from fallacies or faulty reasoning.
There exist, however, formal paradoxes (skolem, banach-tarski, etc.) that represent the limits of logic, in much the same way that heisenberg's uncertainty represents the limit for which material phenomena can be measured.
In the end, all human inquiries fall prey to godel's first and second incompleteness theorems which go as follows:
"1. For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete.
2. For any formal recursively enumerable (i.e. effectively generated) theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent."
