A standard lighting dimmer will:
1. Not handle a high power inductive load.
2. Not hit the correct turn on points (firing angles) with a two wire connection.
3. Not allow you to set a minimum output to prevent burning out the motor when the selected voltage is too low to run the motor properly.
And the sharp inrush at turn on in each half cycle (leading edge control) will cause hum and may damage the motor.
Really old speed switches made different winding connections to the motor.