“I’m moved to laughter at the thought of how presumptuous it would be to reject mathematics for philosophical reasons. How would you like the job of telling the mathematicians that they must change their ways…now that philosophy has discovered that there are no classes? Can you tell them, with a straight face, to follow philosophical argument wherever it leads? If they challenge your credentials, will you boast of philosophy’s other great discoveries: that motion is impossible, that a Being than which no greater can be conceived cannot be conceived not to exist, that it is unthinkable that anything exists outside the mind, that time is unreal, that no theory has ever been made at all probable by evidence (but on the other hand that an empirically ideal theory cannot possibly be false), that it is a wide-open scientific question whether anyone has ever believed anything, and so on, and on, ad nauseam? Not me!”
Apparently Lewis is implicitly contrasting math to some other fields where it would be OK for philosophers to correct the beliefs of others. What are those other fields?
Lewis held that our common-sense-beliefs have greater initial plausibility than every philosophical argument against them, be it in mathematics (“there are numbers”) or metaphysics (“there is time”), philosophy of mind (“there are beliefs”), ethics, etc.
Philosophy can help to find a realiser—a best candidate—for the role of numbers, beliefs, etc., but the price for “losing our moorings” (after g.e. moore), i.e., denying common-sense propositions, is almost always too high.
There is at least one case, of course, where Lewis was willing to pay: modal realism.
“I’m moved to laughter at the thought of how presumptuous it would be to reject mathematics for philosophical reasons. How would you like the job of telling the mathematicians that they must change their ways…now that philosophy has discovered that there are no classes? Can you tell them, with a straight face, to follow philosophical argument wherever it leads? If they challenge your credentials, will you boast of philosophy’s other great discoveries: that motion is impossible, that a Being than which no greater can be conceived cannot be conceived not to exist, that it is unthinkable that anything exists outside the mind, that time is unreal, that no theory has ever been made at all probable by evidence (but on the other hand that an empirically ideal theory cannot possibly be false), that it is a wide-open scientific question whether anyone has ever believed anything, and so on, and on, ad nauseam? Not me!”
-- David Lewis, ‘Parts of Classes’
Apparently Lewis is implicitly contrasting math to some other fields where it would be OK for philosophers to correct the beliefs of others. What are those other fields?
Is he? I actually didn’t get that impression.
Lewis held that our common-sense-beliefs have greater initial plausibility than every philosophical argument against them, be it in mathematics (“there are numbers”) or metaphysics (“there is time”), philosophy of mind (“there are beliefs”), ethics, etc.
Philosophy can help to find a realiser—a best candidate—for the role of numbers, beliefs, etc., but the price for “losing our moorings” (after g.e. moore), i.e., denying common-sense propositions, is almost always too high.
There is at least one case, of course, where Lewis was willing to pay: modal realism.