Much of philosophy is concerned with providing a rigorous foundation to truths

Much of philosophy is concerned with providing a rigorous foundation to truths

Much of philosophy is concerned with providing a rigorous foundation to truths which are otherwise intuitive and uncontroversial; think of philosophy of math, for instance. Do philosophers believe that, absent an appreciation of such foundational principles, laymen don't actually "know" such truths, e.g., that 1+1=2; and if laymen do know such truths, how do they know them?

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