There is an area of mathematics called mathematical logic that studies logic using mathematics . The syllogistic logic developed by Aristotle predominated in the West until the mid-19th century , when interest in the foundations of mathematics stimulated the development of symbolic logic ( now called mathematical logic ) . In 1854 , George Boole published An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities , introducing symbolic logic and the principles of what is now known as Boolean logic .