- Dec 2022
My freely downloadable Beginning Mathematical Logic is a Study Guide, suggesting introductory readings beginning at sub-Masters level. Take a look at the main introductory suggestions on First-Order Logic, Computability, Set Theory as useful preparation. Tackling mid-level books will help develop your appreciation of mathematical approaches to logic.
This is a reference to a great book "Beginning Mathematical Logic: A Study Guide [18 Feb 2022]" by Peter Smith on "Teach Yourself Logic A Study Guide (and other Book Notes)". The document itself is called "LogicStudyGuide.pdf".
It focuses on mathematical logic and can be a gateway into understanding Gödel's incompleteness theorems.
I found this some time ago when looking for a way to grasp the difference between first-order and second-order logics. I recall enjoying his style of writing and his commentary on the books he refers to. Both recollections still remain true after rereading some of it.
It both serves as an intro to and recommended reading list for the following: - classical logics - first- & second-order - modal logics - model theory<br /> - non-classical logics - intuitionistic - relevant - free - plural - arithmetic, computability, and incompleteness - set theory (naïve and less naïve) - proof theory - algebras for logic - Boolean - Heyting/pseudo-Boolean - higher-order logics - type theory - homotopy type theory
- incompleteness theorems
- homotopy type theory
- nonclassical logic
- Peter Smith
- type theory
- mathematical logic
- Oct 2022
If you give a title to your notes, "claim notes" are simply notes with a verb. They invite you to say: "Prove it!" - "The positive impact of PKM" (not a claim) - "PKM has a positive impact in improving writer's block" (claim) A small change with positive mindset consequences
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If you give a title to your notes, "claim notes" are simply notes with a verb.<br><br>They invite you to say: "Prove it!"<br><br>- "The positive impact of PKM" (not a claim)<br>- "PKM has a positive impact in improving writer's block" (claim)<br><br>A small change with positive mindset consequences— Bianca Pereira | PKM Coach and Researcher (@bianca_oli_per) October 6, 2022
Bianca Pereira coins the ideas of "concept notes" versus "claim notes". Claim notes are framings similar to the theorem or claim portion of the mathematical framing of definition/theorem(claim)/proof. This set up provides the driving impetus of most of mathematics. One defines objects about which one then advances claims for which proofs are provided to make them theorems.
Framing one's notes as claims invites one to provide supporting proof for them to determine how strong they may or may not be. Otherwise, ideas may just state concepts which are far less interesting or active. What is one to do with them? They require more active work to advance or improve upon in more passive framings.
link to: - Maggie Delano's reading framing: https://hypothes.is/a/4xBvpE2TEe2ZmWfoCX_HyQ