Q&A: On the Circularity Between Logic and Philosophy
On the Circularity Between Logic and Philosophy
Question
Hello Rabbi,
From what you said yesterday in the lecture “Introduction to Philosophical Thinking 1,” you distinguished between the essence of what the sciences deal with and their various branches, each of which has its own distinct subject matter, and logic, whose essence is a pattern that clarifies the form of claims, connects them, and draws conclusions.
But in practice, that itself is a philosophical activity. So really this is a circularity in which the two feed into one another.
For some reason, I’m not managing to understand the circularity that exists between logic and philosophy. I’d be happy for an explanation/example of the matter.
In addition, is there a logic underlying mathematics, or is mathematics itself that logic?
Thank you in advance.
And thank you for the first lecture—the pace and the explanation were excellent and clear!
Answer
Logic itself is circular, since it is the use of reason to investigate reason. And similarly with philosophy, which is the use of thought to investigate thought (using induction to investigate induction, and the like).
Logic is, in a certain sense, a more fundamental field, since it is the pattern that also underlies philosophy. On the other hand, even with respect to logic we make use of philosophical tools (reflecting on language and on our forms of thought is an intellectual reflection).
As for the relationship between logic and mathematics, you’re entering no small tangle. There were those who wanted to ground all of mathematics in logic, and there are arguments in every direction. But for our purposes that doesn’t matter. Mathematics as a whole is basically logic (= a formalization of our logical ways of thinking).
Excellent. As simple as it is, that’s how inspiring it is.
Thank you!