Category Archives: Logic

What’s logical coherence for anyway?

Time for a writeup! Or something. So I’ve written before about Logical Uncertainty in a very vague way. And a few weeks ago I wrote about a specific problem of Logical Uncertainty which was presented in the MIRI workshop. I’m gonna reference definitions and results from … Continue reading

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The Gaifman Condition and the Π1-Π2 problem

So I’m at a MIRI workshop on Logical Uncertainty, and I’m gonna make a more complete post about it later, but I wanted to talk about a thing that has been on my mind. So we’re trying to build a … Continue reading

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How to prove stuff

A while ago, I wrote up a post that explained what a mathematical proof is. In short, a mathematical proof is a bunch of sentences that follow from other sentences. And when mathematicians have been trying to prove stuff for hundreds … Continue reading

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MIRI paper on logical uncertainty

Talking to raginrayguns again and he mentioned that a month and a half ago, Paul Christiano wrote a paper exactly on the subject of logical uncertainty. While I haven’t finished reading it yet, I’ll publish it here because it’s relevant. … Continue reading

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Logical Uncertainty: an addendum

And I forgot to mention one thing in the last post which is relevant. Gaifman, in his paper, states that if in  we have that then . I’ll quickly show that that’s a theorem of my approach, and, indeed, any similar … Continue reading

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Logical Uncertainty

In the past while, I’ve been talking to a friend about logical uncertainty. Specifically, how do we deal with the fact that we’re not logically omniscient? Usually, when , we have that . But what if we don’t know that ? What if we … Continue reading

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Axioms, logical pinpointing, natural numbers, and mathematical realism

One of the greatest problems people who are getting into hardcore maths face, one of the blocks, is how arbitrary the axioms look. Axioms are the fundamental truths of a mathematical system, the things we do not prove. Whenever people are introduced … Continue reading

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Propositional Logic

…is the basic form of logic whose atoms (or the basic structures upon which it acts) are propositions. A proposition is nothing more than a sentence in some language that states something. Within propositional logic, each sentence can have one of … Continue reading

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