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We didn't replace Euclid's axioms. I'm sorry that you think so, because it is a common misconception that mathematics "believes in a set of axioms". The euclide

by ouid 4y ago

We didn't replace Euclid's axioms. I'm sorry that you think so, because it is a common misconception that mathematics "believes in a set of axioms". The euclidean axioms are a foundation for the logical system of euclidean geometry. Eucliden geometry is not only unchanged, but is actually a system which has been proven to be consistent and decideable. https://en.wikipedia.org/wiki/Tarski%27s_axioms https://en.wikipedia.org/wiki/Tarski%27s_axioms. This makes it rather uninteresting, which is why we now study a different system. Empiricism, likewise, is an axiom that goes. That which I observe exists, and then if you would like to keep that axiom, you're going to have to throw away anything else that is shown to be inconsistent as a result. Which is in bounds.

guerrilla 4y ago
I think you misunderstood what I said and may have demonstrated a little ignorance at the same time. Hilbert's axioms are axioms for Euclidean geometry, like Tarski's and Birkhoff's. > That which I observe exists This isn't even close to what empiricism is. You named a (very poor) ontological principle. Empiricism is a set of epistemological principles.
- ouid 4y ago
  First point: this is why I wrote the logical system of Euclidean geometry. Propositions in that language, and the proofs therein, have not changed. Second point: That is most definitely what empiricism is. Moreover, I have just given you a set of epistemological beliefs. It's a set with a single element, and it in fact characterizes empiricism. I don't know what else to tell you.
  - guerrilla 4y ago
    > First point: this is why I wrote the logical system of Euclidean geometry. Propositions in that language, and the proofs therein, have not changed. The point was that the axioms we used changed. Read further back up the thread. You're off track. > Second point: That is most definitely what empiricism is. Moreover, I have just given you a set of epistemological beliefs. It's a set with a single element, and it in fact characterizes empiricism. I don't know what else to tell you. No, please take an introduction to philosophy. Empericism is an epistemology, it has nothing to do with what exists which is an ontology. Ffs open Wikipedia or something. This is embarrassing Dunning-Kruger effect here.

by ouid 4y ago

guerrilla 4y ago

I think you misunderstood what I said and may have demonstrated a little ignorance at the same time. Hilbert's axioms are axioms for Euclidean geometry, like Tarski's and Birkhoff's. > That which I observe exists This isn't even close to what empiricism is. You named a (very poor) ontological principle. Empiricism is a set of epistemological principles.

ouid 4y ago
First point: this is why I wrote the logical system of Euclidean geometry. Propositions in that language, and the proofs therein, have not changed. Second point: That is most definitely what empiricism is. Moreover, I have just given you a set of epistemological beliefs. It's a set with a single element, and it in fact characterizes empiricism. I don't know what else to tell you.
- guerrilla 4y ago
  > First point: this is why I wrote the logical system of Euclidean geometry. Propositions in that language, and the proofs therein, have not changed. The point was that the axioms we used changed. Read further back up the thread. You're off track. > Second point: That is most definitely what empiricism is. Moreover, I have just given you a set of epistemological beliefs. It's a set with a single element, and it in fact characterizes empiricism. I don't know what else to tell you. No, please take an introduction to philosophy. Empericism is an epistemology, it has nothing to do with what exists which is an ontology. Ffs open Wikipedia or something. This is embarrassing Dunning-Kruger effect here.