Difference between revisions of "Logic"
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{{: | [[wikipedia:Logic|Logic]]<ref>{{:Book/From Frege to Godel}}</ref> is a piece of data that relates a hypothetical relation between source and destination objects. It is a subject matter that uses [[abstract data]], or [[symbolic systems]]<ref>{{:BOOK/可拓逻辑初步}}</ref> to enumerate [[plausibilities]]. | ||
Based on this definition, any set of symbols that allows for the same possibility space can be thought of as the '''[[sameness|same]]''' language. This can be explained as the term: '''[[up to isomorphism]]''' in [[Category Theory]]. | |||
Some of the directly related ideas can be found here: | Some of the directly related ideas can be found here: | ||
Revision as of 08:32, 20 January 2022
Logic[1] is a piece of data that relates a hypothetical relation between source and destination objects. It is a subject matter that uses abstract data, or symbolic systems[2] to enumerate plausibilities. Based on this definition, any set of symbols that allows for the same possibility space can be thought of as the same language. This can be explained as the term: up to isomorphism in Category Theory.
Some of the directly related ideas can be found here:
Why study logic?
Logic has a unique position in the cognitive process of all systems. It is a kind of self-contained, or invariant foundation to help reason or compare against other things.
A great starting point
To learn logic, it might be easier to first play around with Lambda Calculus, since it is a small language that embeds all kinds of combinatorial powers. The best source for this is to listen to Dana Scott on Lambda Calculus. In particular, the first hour of this lecture series[3], Scott present the historical context. It will be useful to see why logic is very much computational and combinatorial in nature.
Gödel Numbering
Learning logic cannot be without learning Gödel Numbering System. This simple framing provides a number-theoretic namespace for all formal languages. The incremental addition of vocabulary to this language, also can be represented in this framing.
Interesting Dicussions
Readers can find some relevant discussions about Logic, particularly, Logicism. It can be watched on PBS Infinite Series here (starting at 5'41", just click on the following image, it will jump to that time point.):
{{#ev:youtube|KTUVdXI2vng|||||start=341}}
References
- ↑ van Heijenoort, Jean (2002). From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. local page: Harvard University Press. ISBN 9780674324497.
- ↑ 蔡文; 杨春燕; 何斌 (November 2003). 可拓逻辑初步. Beijing: 科学出版社.
- ↑ Scott, Dana (Oct 12, 2017). Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 1 of 5 - λC 2017. local page: LambdaConf.
Related Pages
Abstract data, Data, Definition/Logic, Logic Model, Meta Data, Plausibility, Symbolic systems