 Dec 2022

math.stackexchange.com math.stackexchange.com

My freely downloadable Beginning Mathematical Logic is a Study Guide, suggesting introductory readings beginning at subMasters level. Take a look at the main introductory suggestions on FirstOrder Logic, Computability, Set Theory as useful preparation. Tackling midlevel 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 firstorder and secondorder 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 & secondorder  modal logics  model theory<br />  nonclassical logics  intuitionistic  relevant  free  plural  arithmetic, computability, and incompleteness  set theory (naïve and less naïve)  proof theory  algebras for logic  Boolean  Heyting/pseudoBoolean  higherorder logics  type theory  homotopy type theory

 Oct 2022

www.loom.com www.loom.com

https://www.loom.com/share/a05f636661cb41628b9cb7061bd749ae
Synopsis: Maggie Delano looks at some of the affordances supplied by Tana (compared to Roam Research) in terms of providing better blockbased user interface for note type creation, search, and filtering.
These sorts of tools and programmable note implementations remind me of Beatrice Webb's idea of scientific note taking or using her note cards like a database to sort and search for data to analyze it and create new results and insight.
It would seem that many of these note taking tools like Roam and Tana are using blocks and sub blocks as a means of defining atomic notes or databaselike data in a way in which subblocks are linked to or "filed underneath" their parent blocks. In reality it would seem that they're still using a broadly defined index card type system as used in the late 1800s/early 1900s to implement a set up that otherwise would be a traditional database in the Microsoft Excel or MySQL sort of fashion, the major difference being that the user interface is cognitively easier to understand for most people.
These allow people to take a form of structured textual notes to which might be attached other smaller data or meta data chunks that can be easily searched, sorted, and filtered to allow for quicker or easier use.
Ostensibly from a mathematical (or set theoretic and even topological) point of view there should be a variety of onetoone and onto relationships (some might even extend these to "links") between these sorts of notes and database representations such that one should be able to implement their note taking system in Excel or MySQL and do all of these sorts of things.
Cascading Idea Sheets or Cascading Idea Relationships
One might analogize these sorts of note taking interfaces to Cascading Style Sheets (CSS). While there is the perennial question about whether or not CSS is a programming language, if we presume that it is (and it is), then we can apply the same sorts of class, id, and inheritance structures to our notes and their meta data. Thus one could have an incredibly atomic word, phrase, or even number(s) which inherits a set of semantic relationships to those ideas which it sits below. These links and relationships then more clearly define and contextualize them with respect to other similar ideas that may be situated outside of or adjacent to them. Once one has done this then there is a variety of Boolean operations which might be applied to various similar sets and classes of ideas.
If one wanted to go an additional level of abstraction further, then one could apply the ideas of category theory to one's notes to generate new ideas and structures. This may allow using abstractions in one field of academic research to others much further afield.
The user interface then becomes the key differentiator when bringing these ideas to the masses. Developers and designers should be endeavoring to allow the power of complex searches, sorts, and filtering while minimizing the sorts of advanced search queries that an average person would be expected to execute for themselves while also allowing some reasonable flexibility in the sorts of ways that users might (most easily for them) add data and meta data to their ideas.
Jupyter programmable notebooks are of this sort, but do they have the same sort of hierarchical "card" type (or atomic note type) implementation?
Tags
 building blocks
 integrated thinking environments
 Jupyter
 integrated development environment
 idea links
 types of notes
 Beatrice Webb
 super tags
 Roam Research
 cascading idea sheets
 user interface
 Tana
 CSS
 watch
 card index as database
 Maggie Delano
 category theory
 Boolean algebra
 scientific note taking
 programmable notes
Annotators
URL

 Mar 2019

nautil.us nautil.us

Which got McCulloch thinking about neurons. He knew that each of the brain’s nerve cells only fires after a minimum threshold has been reached: Enough of its neighboring nerve cells must send signals across the neuron’s synapses before it will fire off its own electrical spike. It occurred to McCulloch that this setup was binary—either the neuron fires or it doesn’t. A neuron’s signal, he realized, is a proposition, and neurons seemed to work like logic gates, taking in multiple inputs and producing a single output. By varying a neuron’s firing threshold, it could be made to perform “and,” “or,” and “not” functions.
I'm curious what year this was, particularly in relation to Claude Shannon's master's thesis in which he applied Boolean algebra to electronics.
Based on their meeting date, it would have to be after 1940. And they published in 1943: https://link.springer.com/article/10.1007%2FBF02478259
