Why Study Philosophy?

In an Institute of Arts and Ideas article from a few years ago, Wittgenstein scholar Peter Hacker gives, well, a wittgensteinian answer:

...questions of sense precede questions of empirical truth – for if something makes no sense, it can be neither true nor false. It is just nonsense – not silly, but rather: it transgresses the bounds of sense. Philosophy patrols the borders between sense and nonsense; science determines what is empirically true and what is empirically false. What falsehood is for science, nonsense is for philosophy.

...[thus, t]he study of philosophy cultivates a healthy scepticism about the moral opinions, political arguments and economic reasonings with which we are daily bombarded by ideologues, churchmen, politicians and economists. It teaches one to detect ‘higher forms of nonsense’, to identify humbug, to weed out hypocrisy, and to spot invalid reasoning. It curbs our taste for nonsense, and gives us a nose for it instead. It teaches us not to rush to affirm or deny assertions, but to raise questions about them.