ABSTRACT

In the mid-1800s, George Boole developed a theory of logic as an instrument for representing the structure of mathematical problems. One of the key insights of Boole’s method is that the epistemic status of logical laws can be established by studying logic’s application to solving problems in mathematics. William Thomson’s Outlines begins with an explicit statement that logical reasoning is prior to logical laws, which is why logic is a science. In 1854, five years after the publication of Thomson’s Outlines, Boole published An Investigation of the Laws of Thought. Boole’s Investigation responds explicitly to the New Analytic tradition. The influence of the New Analytic on Boole is deep but also mixed. Boole’s approach, of showing the justification of the laws of thought as laws of logic, owes a great deal to the New Analytic. “General logic for Immanuel Kant contains the ‘absolutely necessary rules of thinking, without which no use of the understanding takes place’.