• Mathematics,  Philosophy,  Research

    How Meanings Change the Use of Logic

    Anyone who has even a preliminary encounter with logic believes that if A = B, then B = A. This is commonly expressed as the belief that if A is B, then B is A. This widespread use of logic is easily shown to be false when we employ two concepts, one of which is more general than the other. For example, “all men are mortal” doesn’t imply that “all…

  • Mathematics,  Overview,  Philosophy

    Numbers, Truth, Morality and God

    What is a Number? Is it an idea or a thing? This question has been debated since Greek times, and it still remains unanswered in philosophy and science. This post examines the nature of the problem, and what its likely resolution will look like. It illustrates how the problem of numbers leads to the problem of choice, which then results in the problem of morality, which then results in questions of…

  • Biology,  Computing,  Mathematics,  Physics

    Evolution and Mechanism – Are They Compatible?

    A computer is a canonical example of a machine. Every machine can be described by a mathematical theory, and every mathematical theory can be automated on a computer. Therefore if you could describe something mathematically, you could also automate it in a computer. People often suppose that this means if we had a mathematical description of nature, that description could also be automated on a machine. In the case of…

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