Independent study guide to logic for philosophers and mathematicians


Originally published at:


Sounds like a good mix of the logic I got in philosophy and the set theory I got in computer science.

Was it Russell who deduced that all mathematics reduces to logic plus set theory? I’m pretty sure he’s the one who figured out that numbers are fundamentally defined as a kind of set.


I’m reminded that when Trump was elected, there was a mad scramble to produce syllabi of varying quality on totalitarianism. I remember thinking at the time that I wished more people would build open syllabi about more topics.


This study guide on logic is 95 pages long.

A manifesto describing why the Earth is flat is considerably shorter, some as short as tweet. /s

Why should I waste time with a well thought out guide to logic when the “true secrets of the universe” can be mine with little thought or work?

Why ?

Critical thinking is the art of analyzing and evaluating thinking with a view to improving it.
From. Critical Thinking, Tools and Concepts. By Paule and Elder. link below

Critical Thinking, Tools and Concepts PDF from [The Foundation For Critical Thinking] (

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We should probably feel lucky that it’s countable and finite; given the topic.


He famously worked in this area, but he wasn’t the originator. Grassmann and Peano both preceded him and Russell’s work was related to Hilbert’s program to axiomatize mathematics. (contemporaneous)


written on the assumption of very little education in either maths or philosophy.

Honestly this is a pretty optimistic evaluation. I know most of these books (and have taught out of a couple); many are serious books at the graduate level, and few aren’t at least at the level of a senior class for math majors.


ah, see. This study guide is a for a very particular set of persons. If I may?

  1. L1. If you have only done an ‘informal logic’ or ‘critical reasoning course’, then you’ll probably need to read a good introductory formal logic text before tackling the more advanced work covered in this Guide. See below.
  2. L2. If you have taken a logic course with a formal element, but it was based on some really, really, elementary text book like Sam Guttenplan’s The Languages of Logic, Howard Kahane’s Logic and Philosophy, or Patrick Hurley’s Concise Introduction to Logic (to mention some frequently used texts), then you might still struggle with the initial suggestions in this Guide – though this will of course vary a lot from person to person. So the best advice is probably just to make a start and see how you go. If you do struggle, one possibility would be to use Intermediate Logic by Bostock mentioned in §3.3 to bridge the gap between what you know and the beginnings of mathematical logic. Or again, try one of the books I’m about to mention, skipping quickly over what you already know.
    L3. If you have taken an elementary logic course based on a substantial text like the ones mentioned in just a moment, then you should be well prepared.

And I speak as a first level character. See?

That was my CTY text.

Never got around to formal introductions.


Two choices always hard.

The effect of equipollence on the skeptic does not consist in his being equally persuaded by both accounts, but in his being unable to determine by which account he ought to be persuaded, irrespective of which account in fact persuades him.


I wanted to study rhetoric when I was at university. I was at one of the last universities in the U.S. that had a program in rhetoric, and my R.A., somebody that was a mentor, was in the program. At the worst of my failing , if I had just looked at what I enjoyed, I should have made the switch instead of being lead by my own ego and by pushed along by others with something to prove. At that time, I just wanted to persuade people, damn the ethics, and I loved the art of argument.

Nice quote, and it is also a reminder that a good skeptic is critical of one’s own thought- something I remind myself constantly, but like somebody that is new to meditation, I rarely do it without conscious thought as I let my thoughts wonder and I don’t interrogate all that is presented to me.


I dunno, I always go with the account that aligns with my programmed ideation. Failing that, the one that is most entertaining.


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