There are certain beliefs we as humans hold which form the foundations of how we think. Most of the truly axiomatic beliefs, the ones so integral to the human mind that it is not possible to think without them, are, unsurprising, not thought about all too much. In many cases, these beliefs are so obvious, so intuitive that we do not even recognize them as beliefs but rather blindly accept them as rules valid thinking must follow. For example, the (axiomatic) rule "If A is true, then A is true".
In certain cases, these axiomatic beliefs come into conflict. For example, it seems extraordinarily difficult to belief in causality, that all events in the world occur due to a web of causation stretching back to the beginning of time. while simultaneously believing in free will, the ability of people to make choices*. After all, if all things are determined by previous events then the same applies to our desires and our actions.
It seems to me that far too much of philosophy is comprised of attempts to solve intractable problems such as this. This would not be a problem if those attempts were successful or at least failed. The problem is that many of these attempts inevitably degenerate into language games where the meaning of words is debated rather than the actual incompatibility between the concepts those words represent.
* It is important to note that free-will and personhood are two sides of the same coin. If you don't believe in free will, you must believe that a person is no more than a certain pattern of cause and effect which reacts to stimuli in a deterministic fashion. At this point, it becomes impossible to meaningfully distinguish between a person and any other pattern existing in the natural world.
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