This paper is written for undergraduate or graduate students who are interested in philosophy of physics and quantum logic. However, I do not explain quantum logic itself. I do explain how we construct boolean lattice, based on our experiences, which is a mathematical structure behind classical logic. This is because I often find that some philosophers argue that logic does not depend on our experiences and it gives us a priori knowledge, and thus, they claim that logic governs the real world. However, this belief is baseless. We should construct boolean lattice based on the stable and empirical foundation. For this purpose, this paper introduces two ways. First, we reconstruct the concept of physical quantity, based on outcomes of measurements. You will find that physical quantities are not properties which physical objects have, and they are such as conceptual windows through which we observe the world. Second, from an epistemological point of view, you will find why boolean lattice (or classical logic) needs distributive law.
|
