This has inspired me to invent several chess variants with Philosophers and Philosopher-like pieces. Here's one; I'll post the others later:
This variant is played on a standard 8×8 board with an additonal separate 3×3 board. It uses standard chess armies (the knight pieces can be used to represent the Philosophers) plus two differently-colored markers (a pair of checkers pieces would do).
The 3×3 board is the "dialectic", and its ranks and files are numbered 0–2. The two tokens are the "Thesis" and "Antithesis". The position of the Thesis on the dialectic determines how the Philosopher moves passively, and the position of the Antithesis determines how it moves to capture. They start on squares (1,2) and (2,1), respectively (meaning that, at the start, all Philosophers move and capture as Knights). Either player may, on his or her turn, move the Thesis or Antithesis one space orthogonally instead of moving one of his or her own pieces, with the caveat that a dialectic position cannot be repeated between moves on the main board (meaning that you can't simply undo your opponent's dialectic move immediately).
The setup on the main board is identical to that of othochess, but with the Philosophers taking the place of the Knights. Philosophers are leapers (making a single step for a move, ignoring intervening pieces, like a Knight), moving according to the positions of the Thesis and Antithesis: the coordinates are interpreted as a number of spaces in any orthogonal direction followed by a number of spaces at 90° to that, e.g. if the Thesis is at (1,2) or (2,1), the Philosopher moves passively as a Knight, at (1,0) or (0,1) as a Wazir, at (1,1) as a Ferz, and at (0,0) not at all. If a Philosopher captures another Philosopher, it is promoted to a Great Philosopher. Great Philosophers behave like Philosophers, but are riders, taking any number of Philosopher steps in the same direction, rather than leapers. So, with the Thesis at (1,2) or (2,1) a Great Philosopher moves passively as a Knightrider, at (1,0) or (0,1) as a Rook, and at (1,1) as a Bishop.
The usual restrictions on moving into and in check apply to moves on the Dialectic: you cannot move the Antithesis such that it would cause an enemy Philosopher to immediately threaten your King, and if your King is in check you may only make a Dialectic move if that would remove check.
Variant: Hegelian Dialectic Chess — the Thesis and Antithesis may occupy the same square, and if they do they may be moved as a unit, called the Synthesis. This removes an odd side effect of the basic rules, which is that a Philosopher that can move passively on the diagonal cannot capture in the same way that it moves, and vice versa. It also makes a little less than half of the Dialectic pointless, so you could play with all of the Dialectic squares nothwest of the main diagonal removed, giving the Dialectic a stairstep shape.