![]() ![]() As part of his lifelong effort to catalog things (animals, causes, etc.), Aristotle cataloged valid forms of arguments, and created symbolic templates for them which basically provided the main content of logic for two thousand years.īy the 1400s, however, algebra had been invented, and with it came cleaner symbolic representations of things. Logic as a formal discipline basically originated with Aristotle in the 4th century BC. I think this is ultimately a deep question-that’s actually critical to the future of science and technology, and in fact to the future of our whole intellectual development.īut before we talk more about this, let’s talk about logic, and about the axiom I found for it. That’s the same kind of question that’s increasingly being asked about all sorts of computational systems, and all sorts of applications of machine learning and AI. But why is the result true? What’s the explanation? And given this proof, it’s straightforward to verify each step. With the latest version of the Wolfram Language, anyone can now generate this proof in under a minute. And here’s the proof, as I printed it in 4-point type in A New Kind of Science (and it’s now available in the Wolfram Data Repository): I had already shown there couldn’t be anything simpler, but I soon established that this one little axiom was enough to generate all of logic:īut how did I know it was correct? Well, because I had a computer prove it. But at 8:31pm on Saturday, January 29, 2000, out on my computer screen popped a single axiom. It was a nagging question for a long time. But how many axioms does one need? And how simple can they be? But what are the axioms? We might start with things like p AND q = q AND p, or NOT NOT p = p. And, like Euclid’s geometry, it can be built on axioms. Then one has certain “rules of logic”, like that, for any p and any q, NOT ( p AND q) is the same as ( NOT p) OR ( NOT q).īut where do these “rules of logic” come from? Well, logic is a formal system. In symbolic logic, one introduces symbols like p and q to stand for statements (or “propositions”) like “this is an interesting essay”. But what are the foundations of logic itself? His focus on questions cuts across the standard ways of thinking about the relation between the history of philosophy and the history of ideas and provides novel answers to some central issues in the philosophy of history, for example how to best articulate a principle of charity.For further developments, see /metamathematics A Discovery about Basic Logic Hans-Georg Gadamer offers a different focus, arguing instead that it is the questions that the text answers that generate insights for contemporary philosophical practice. ![]() The current discussion of the history of philosophy focus entirely on how to understand, and what we can learn from, a philosopher’s claims and arguments. Such presentism risks anachronistic readings of texts, but a too narrow focus on the historical context of the text risks limiting its ability to contribute to contemporary philosophizing. The key difference between the history of ideas and the history of philosophy is that philosophers always consider their historical studies as potentially contributing to contemporary philosophical practice. ![]()
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