Socrates

The answer is 28.

Fourteen writers.
Seven scientists.
Four philosophers.
Three women.

The whole number of thinkers is X


Here's the working:

Let X be the number of thinkers.

Half X plus a quarter X plus a seventh X plus tree make up the whole amount.

Therefore:

X=   X/2 +X/4 + x/7 +3 

So

X=   X(14 + 7 + 4)     +3
      _________
             28

28X = 14X +7X +4X + 84


28X= 25X + 84


3X = 84

X=  28