'A number of philosophers believe' sounds right to me. Not only because philosophers is plural, but also number, while singular, has a plural meaning.
Also having the s - s ending in 'philosophers believes' is awkward because philosophers are plural and are the ones doing the believing.
'A number of philosophers believes' seems pedantically grammatically correct, since it is a number, so number is singular. But it sounds wrong to my ear.
What's the "right" way?