At Discovery Institute, Michael Egnor takes note of the inherent self contradictions in materialism in the article Descarte's Blunder. We are all aware of Descarte's famous "I think therefore I am" phrase. The idea being one has to exist to think. Egnor flips the script, or more accurately, points it back a step.
"Notice that we cannot conclude that we exist unless we can conclude. That is, we must first know the principle of non-contradiction — that being is not non-being — before we can conclude that “I think therefore I am.”
The idea that "A" cannot be "non-A" is a necessary axiom for any knowledge. If we can't distinguish between this and that, we simply can't think.
Egnor discusses Aquinas and a bit of the background of the philosophy on that point but then he points to the problems with the materialist worldview. A couple of highlights.
"Materialists and atheists believe that the universe spontaneously came from nothing, and they define nothing as the laws of quantum mechanics."
This flows directly from his first point, that something has to exist beyond the mere material. It is, not coincidentally a key argument for Intelligent Design, that concept must precede product.
Related to ID:
"Materialists and atheists claim that ID is scientifically wrong, and claim that ID is not scientifically testable. But of course, in order to be scientifically wrong, ID must be scientifically testable."
And in the realm of morality:
"Materialists and atheists believe that the existence of evil disproves the existence of God, yet if there is no ultimate Source of right and wrong, there is no evil and no good; there are merely circumstances we like or dislike. Nietzsche, unlike the New Atheists, understood this."
Precisely the problem with postmodern relativism. If there are no objective standards of morality, then we cannot say that racism or rape or genocide are objectively wrong, yet the materialists of the left give us moral lectures endlessly.
He paraphrases C.S. Lewis on that point in another paragraph.
In short, materialism is irrational because it cuts itself away from the very basis of reason.
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