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outline [2016/10/15 14:21]
nikolaj 		outline [2016/10/15 14:22]
nikolaj
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 | [[An apple pie from scratch]] $\succ$ Outline ​ $\succ$ [[Drawing arrows and coding functions]] | | [[An apple pie from scratch]] $\succ$ Outline ​ $\succ$ [[Drawing arrows and coding functions]] |
 ==== Guide ==== ==== Guide ====
-* presentation of mathematical concepts in a top-down way: +Here is an outline ​structure ​(work in progress):
-The focus is on how "​mathematical data" can be set up in //set theory// and I also use //category theory// for "​structural characterizations"​.  +
- +
-(As foundational paradigms, both set- and category theory have strong merits and disadvantages. While it's possible to develop a version of categories, functors and natural transformations in set theory and a version of sets in category theory, I rather use both paradigms early on. As a side note, it's also possible to axiomatize categories in logic directly and also to specify sets in type theory, but that's pretty nonstandard and more difficult. In discussion sections, I will often use categorcal language to to characterize sets a the category of sets.) +
- +
-  * Be self-contained  +
-I start out with an more or less informal explanation of formal languages and foundational theories and common axioms. The structure ​of the presentation is summarized below. The primitive notions ​in this wiki, discussed in the first block, are summarized in [[Domain of discourse]].  +
- +
-  * Use a "two models"​ principle:  +
-For each abstract definition,  +
-I'll try to exemplify it with two different structures. +
- +
-  * Convey information in different visual language languages:  +
- +
-- proper cat'​ish drawing  +
- +
-$$ +
-\require{AMScd} +
- +
-\begin{CD} ​          +
-{\large\hbar} ​ @>​{\large{!}}>> ​     {\large{*}} ​                   +
-\\  +
-@V{{\large{m}}}VV ​     @VV{{\large\top}}V ​   +
-\\                 +
-{\large\heartsuit} ​ @>>​{\large{\chi}}> ​     {\large{\Omega}} +
-\end{CD} +
-$$ +
- +
-- drawing where you see terms, circled (the type universe is circled as well) +
- +
-- typey syntax +
- +
-- FOL/SOL +
- +
------ +
- +
-Here the structure:+
  
 === Computation and logic (presented bottom-up) === === Computation and logic (presented bottom-up) ===
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