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There are lots of ways we can respond to the sceptic: the Moorean approach, externalism, contextualism or deny closure. (There maybe other common responses I've forgotten.)

Very roughly, what proportion of philosophers support each of these main responses to the sceptic?

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The PhilPapers survey of professional philosophers includes these results. On the Results page you can also select only Philosophy PhDs with an expertise in epistemology for instance.

Epistemic justification: internalism or externalism?

Accept or lean toward: 
externalism 398 / 931 (42.7%)
Other   287 / 931 (30.8%)
Accept or lean toward: internalism  246 / 931 (26.4%)

External world: idealism, skepticism, or non-skeptical realism?

Accept or lean toward: 
non-skeptical realism   760 / 931 (81.6%)
Other   86 / 931 (9.2%)
Accept or lean toward: skepticism   45 / 931 (4.8%)
Accept or lean toward: idealism 40 / 931 (4.3%)
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The job of the philosopher [outside of some circles of academia] is not to defend the status quo. Thus, another response is to accept that the skeptic might be on to something and look at what our uncertainty means and what we can learn from it.

If you do know that here is one hand, we'll grant you all the rest. ---Wittgenstein, On Certainty

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