A typical response to global skepticism (skepticism which claims that we can

A typical response to global skepticism (skepticism which claims that we can

A typical response to global skepticism (skepticism which claims that we can know nothing), is that such a position is self-defeating. However, couldn't the global skeptic respond by stating that such an objection relies on the objector having knowledge of the truth of the law of non-contradiction, which the skeptic claims we don't know? Thus, the skeptic could argue that they know nothing can be known while having the privilege of also incoherently claiming that they still know certain things. Would it even be possible to even intelligibly respond to such a claim, since it seems when one begins to reject things like the laws of logic, then intelligible discourse becomes impossible and were left with assumptions?

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