Strength increases the amount of damage you do with physical attack. Plain and simple. Nothing really seems to point at mental attributes having a similar effect on some of the disciplines. The main ones are Intelligence and Wits, in particular for the Thaumaturgy paths. They only seem to use them as a requirement for certain disciplines, to unlock their use. Does anyone know for sure if Intelligence and Wits can actually enhance the damage effects of offensive disciplines such as call lightning, hands of destruction, cauldron of blood, etc?