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  • Issa Rice 11:47 pm on February 15, 2019 Permalink | Reply  


    I continued learning about causal inference.

  • Issa Rice 11:47 pm on February 15, 2019 Permalink | Reply  


    I returned to learning about causal inference, mostly from Pearl’s book but also this overview paper.

    I added a bit to the do operator page.

  • Issa Rice 10:00 pm on February 13, 2019 Permalink | Reply  


    Not much math; I spent the day relaxing, reading things, socializing, and thinking about some things.

    I made some additions to the List of important distinctions in mathematical logic page.

  • Issa Rice 9:57 pm on February 13, 2019 Permalink | Reply  


    I again didn’t do much math.

  • Issa Rice 9:56 pm on February 13, 2019 Permalink | Reply  


    I didn’t do much math; I wrote some scribbles about the page List of important distinctions in mathematical logic.

    I spent the day reading random things (I was curious about top LessWrong posts I had missed, so I spent some time looking through highly upvoted posts, e.g. the top list for 2018).

  • Issa Rice 9:53 pm on February 13, 2019 Permalink | Reply  


    I started writing List of important distinctions in mathematical logic.

    I think I read more of Peter Smith’s Gödel book.

  • Issa Rice 1:17 am on February 10, 2019 Permalink | Reply  


    I thought a bit more about the “two flavors” of incompleteness.

    I thought about the Löb’s theorem cartoon and puzzle. My take on the cartoon is that it didn’t help me understand the theorem any better, even if it is a cute cartoon; I found myself having to translate the cartoon proof back into logic, which seems like evidence against the native architecture idea that led to the cartoon (or at least, evidence against this specific execution having succeeded). I started working on a page about the puzzle.

  • Issa Rice 1:11 am on February 10, 2019 Permalink | Reply  


    I reviewed the “two flavors” of incompleteness theorems and the easy incompleteness proofs in Peter Smith’s book (chapters 6 and 7).

    I started thinking about undecidability in logic, and wrote the page for the Entscheidungsproblem. I made some embarrassing realizations, like finally understanding that all the common undecidability statements (for first-order logic) are equivalent, and also realizing that undecidability for a logic is different from undecidability for a theory. It seems totally insane to me that this isn’t emphasized in the resources I have been consulting.

  • Issa Rice 1:05 am on February 10, 2019 Permalink | Reply  


    I continued thinking about the diagonal lemma (I mostly used Peter Smith’s book, some online postings, SEP, and Gaifman’s paper). I think it was on this day that I realized that the proofs of the Rogers fixed point theorem and the diagonal lemma are basically the same, and that the theorems themselves are basically the same (I found a couple of papers and some online postings stating this connection, but I wish more textbooks talked about this).

    I wrote the diagonalization lemma page.

  • Issa Rice 1:06 am on February 7, 2019 Permalink | Reply  


    I continued trying to understand Gödel’s first incompleteness theorem, diagonalization lemma, etc. Mostly via Leary & Kristiansen’s book, but also Peter Smith’s book. Also this page on SEP.

    I started the expresses versus captures page.

  • Issa Rice 1:04 am on February 7, 2019 Permalink | Reply  


    I spent some time reading about heavy/fat/long-tailed distributions and the distinctions between these terms. I’m frustrated that people seem to use two different visualizations (the quantity vs individual visualization, and the frequency/density vs quantity visualization) but usually don’t mix the visualizations and don’t prove the equivalence between them either.

    I started the Multiplicative process page.

    I also started reading more about Gödel’s first incompleteness theorem (Leary and Kristiansen’s book).

  • Issa Rice 1:00 am on February 7, 2019 Permalink | Reply  


    I re-read the proof of existence of a computable infinite binary tree without any computable paths, in Stillwell’s Reverse Mathematics. I was able to follow the proof. If you remember, I was having trouble with this proof a while back. One of the errors I had made earlier is to assume that the tree nodes were integers, rather than finite binary sequences. Stillwell actually clarifies this in like the first sentence of the proof, but I still had the misconception! I must have been tired… A picture would have helped, and Stillwell does include one, but in an earlier section (that he references).

    I did some searching on \Delta_0 = \Sigma_0 = \Pi_0 sets/relations versus \Delta_1 = \Sigma_1\cap \Pi_1 sets/relations. They seem to be equivalent under some definitions, but I wasn’t able to figure out when they are vs when they aren’t.

    Started on the function versus algorithm page.

  • Issa Rice 11:44 pm on February 3, 2019 Permalink | Reply  


    I worked through the proof of completeness of first-order logic in Goldrei and Leary & Kristiansen. I think I was able to resolve one of the questions I had about the proof (namely, why it is that we iterate the process of adding constants rather than just adding constants once). I then started working through some of the exercises in Leary & Kristiansen for that section.

  • Issa Rice 11:42 pm on February 3, 2019 Permalink | Reply  


    I spent the day reading random things and not doing math.

  • Issa Rice 11:40 pm on February 3, 2019 Permalink | Reply  


    I did various first-day-of-the-month bureaucracies and didn’t do math.

  • Issa Rice 3:40 pm on February 1, 2019 Permalink | Reply  


    I went through more of Goldrei’s logic book (e.g. different formulations of soundness and completeness).

    I read more of Goldblatt’s Topoi but decided to not continue.

    I worked on the page Intended interpretation versus all interpretations.

  • Issa Rice 3:39 pm on February 1, 2019 Permalink | Reply  


    I spent some time reviewing some things in linear algebra (I had forgotten the justifications of some results).

    I continued a bit with logic (Goldrei’s book).

    I went through some questions I had written up, and Ankified some of the ones I was able to answer.

    I started the page Intuitiveness and simplicity tradeoff.

    I started reading Goldblatt’s Topoi: The Categorial Analysis of Logic. I suspect I will want to learn category theory at some point, even though I don’t have an immediate use for it.

  • Issa Rice 12:10 pm on January 30, 2019 Permalink | Reply  


    I continued working through Goldrei’s logic book, mostly on results leading up to the completeness theorem for propositional logic. I also read through the proof of the completeness theorem (I believe it’s called a Henkin-style proof), but I don’t understand it yet. I think I need to go back and make more of the previous results “automatic” before I can fully understand the completeness proof.

  • Issa Rice 12:07 pm on January 30, 2019 Permalink | Reply  


    I continued with logic, working out of Goldrei’s book (soundness theorem and some peripheral results).

    I also started going through the Henkin proof of completeness (for first-order logic) in Leary and Kristiansen’s book. There’s a lot of stuff going on in this proof, so I’m planning to go through it multiple times (Ankifying as I go).

  • Issa Rice 7:03 pm on January 28, 2019 Permalink | Reply  


    I worked through more of Goldrei’s logic book.

    I spent some time adding to the Models symbol page.

    I also spent a bunch of time trying to look up different definitions of semantic consequence (I think there are at least two different definitions floating around that disagree on formulas containing free variables, but I haven’t been able to find much).

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