Fundamentals of Formalisation level 1: Basic Logic

by toonalfrink1 min read4th May 20184 comments


Logic & Mathematics

Followup to Soon: a weekly AI Safety prerequisites module on LessWrong

(note: we have a study group running a week ahead of this series that adds important content. It turns out that to get that content ready on a weekly basis, we would have to cut corners. We prefer quality over speed. We also like predictability. So we decided to cut us some slack and publish every 2 weeks instead for the time being)

(relatedly, the challenges section of this week is not yet complete at the time of posting, so completing those will not yet imply a full understanding of the content)

Basic logic

The big ideas:

  • Sentential Logic
  • Truth Tables
  • Predicate Logic
  • Methods of Mathematical Proof

To move to the next level you need to be able to:

  • Translate informal arguments into formal logic.
  • Evaluate an argument as either valid or invalid.
  • Explain how to prove an implication/conditional, a conjunction, a disjunction, and a negation and know what this looks like informally (i.e. in words and not symbols).

Why this is important:

This builds the basic knowledge you need to be able to produce and understand mathematical proof. A firm foundation in how logical machinery operates is the best way to be assured that a proof you produce or read is correct. This also teaches the basic methods by which a proof is produced.

Without further ado: you can find the first lesson on our course platform.

Every week you have 2 options: do the whole thing, or skip to the "challenges" in the end. The latter option is for those people that suspect they already know the subject. It serves as a means of verifying that assumption.

We hope this track will facilitate aspiring AI Safety researchers in their studies. If it leads to even one success story, it will have been worth it. Maybe that success story is you!

Happy studying


4 comments, sorted by Highlighting new comments since Today at 11:16 PM
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Why oh way does this system make it so needlessly inconvenient to partake in these courses?

I just want to read the lecture material on the topics that interest me, and possibly do some of the exercises. Why do I need to create an account for that using a phony email, subscribe to courses, take tests with limited numbers of retries, and all of that? I am not aiming to get a formal diploma here, and I don't think you plan on awarding me any. So why can't I just... browse the lectures in a stateless web 1.0 fashion?

It looks to me as if is a for-profit business selling educational materials and systems to universities. The design decisions that make most sense for them are not necessarily the most convenient for students. So e.g. they may be keen to be able to distinguish one student from another, take measures against cheating, encourage and/or measure "engagement", etc. The things they do to that end may be annoying for students, but they still do them because they make their actually-paying customers happier, or make it easier to convince investors that they're doing well, or help them plan future changes.

(In other words, your question is a bit like "Why oh why do publishers charge money for mathematics textbooks, instead of making them available for free?".)

[EDITED to add:] For the avoidance of doubt, I entirely agree with you that all that stuff is annoying and that just having the material made available would be much nicer.

Thank you for your criticism. We need more of that.

I am not aiming to get a formal diploma here, and I don't think you plan on awarding me any.

A pipeline has 2 purposes: training people and identifying good students. We want to do the latter as much as the former. Not just for the sake of the institutions we ultimately wish to recommend candidates to, but also for the sake of the candidates that want to know whether they are up to the task. We recently did a poll on Facebook asking "what seems to be your biggest bottleneck to becoming a researcher" and "I'm not sure I'm talented enough" was the most popular option by far (doubling the next one).

I agree that it looks silly right now because we're a tiny startup that uploaded 2 videos and a few guides to some textbooks, and it will probably be this small for at least a year to come. You got me to consider using something more humble in the meantime. I'll bring it up in our next meeting.

Currently we can access all course materials at once. For the time being, it might be better to hide the incomplete bits so nobody can wander ahead and miss things. Slash, it might be better to force users to try one section before unlocking the next; otherwise people might eternally put off the hard sections.

That said, the platform looks new so it might not support this.