Tag Archives: probability theory

Absence of evidence is evidence of absence

The W’s article about Evidence of Absence is confusing. They have an anecdote: A simple example of evidence of absence: A baker never fails to put finished pies on her windowsill, so if there is no pie on the windowsill, then … Continue reading

Posted in Basic Rationality, Mathematics, Probability Theory, Rationality | Tagged , , , , , , , | Leave a comment

Learning Bayes [part 1]

I have a confession to make. I don’t actually know Bayesian statistics. Or, any statistics at all, really. Shocking, I know. But hear me out. What I know is… Bayesian theory. I can derive Bayes’ Theorem, and I also can probably … Continue reading

Posted in Mathematics, Probability Theory | Tagged , , , , , , , , , | 5 Comments

Bayesian falsification and the strength of a hypothesis

At the end of my post about other ways of looking at probability, I showed you a graph of evidence against probability. This is the relevant graph: Looking at this graph was one of the most useful things I’ve ever … Continue reading

Posted in Mathematics, Probability Theory, Rationality | Tagged , , , , , | 4 Comments

Agreements, disagreements, and likelihood ratios

The LessWrong community has, as a sort of deeply ingrained instinct/rule, that we should never “agree to disagree” about factual matters. The map is not the territory, and if we disagree about the territory, that means at least one of … Continue reading

Posted in Basic Rationality, Mathematics, Probability Theory, Rationality | Tagged , , , | 1 Comment

Bayes’ Theorem

Bayes’ Theorem has many, many introductions online already. Those show the intuition behind using the theorem. This is going to be a step-by-step mathematical derivation of the theorem, as Jaynes explained it in his book Probability Theory: The Logic of Science. However, … Continue reading

Posted in Mathematics, Probability Theory, Rationality | Tagged , , , , , , | 4 Comments

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

Posted in Logic, Mathematics, Probability Theory, Rationality | Tagged , , , , , , , | Leave a comment

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

Posted in Logic, Mathematics, Probability Theory, Rationality | Tagged , , , , , , | 2 Comments

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

Posted in Logic, Mathematics, Probability Theory, Rationality | Tagged , , , , , , , , , | 5 Comments

Occam’s Razor

“Numquam ponenda est pluralitas sine necessitate.“ – William of Ockham (c. 1287-1347) The more famous sentence attributed to William of Ockham, “Entia non sunt multiplicanda praeter necessitatem,” translated as “Entities must not be multiplied beyond necessity,” is absent from his … Continue reading

Posted in Basic Rationality, Mathematics, Probability Theory, Rationality | Tagged , , , , , , , | 4 Comments

What is a mathematical proof?

The answer is… much simpler than one might think. A mathematical proof is just a set of steps that only produce true statements given the premises. “Huh?” Well, when you want to prove something mathematically, you start with a few … Continue reading

Posted in Intuitive Mathematics, Mathematics, Probability Theory | Tagged , , , | 4 Comments