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One of the funniest/coolest theorems ever:
Definability is not well-defined
interesting link:
http://www.rudi.net/bookshelf/classics/city/alexander/alexander1.shtml
(I read parts of it and skimmed the rest). Interesting discussion of how people try to reduce semilattice structures to tree-structures. A few pictures, some succinct ways of describing the restrictiveness of trees:
"Whenever we have a tree structure, it means that within this structure no piece of any unit is ever connected to other units, except through the medium of that unit as a whole.
The enormity of this restriction is difficult to grasp. It is a little as though the members of a family were not free to make friends outside the family, except when the family as a whole made a friendship. "
, an interesting psych experiment 2/3s down page 2 involving pictures, showing that the difficulty for humans of thinking in semilattices may be fundamental.
http://www.geom.umn.edu/docs/outreach/4-cube/
beginning symbolic logic links:
the top three are the ones I recommend.
-- http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/logic/logicintro.html
good intro stuff. concise presentation of new material, and exercises with solutions.
-- this one looks pretty good (read the .pdf "slides"). Looks short but still starts from the beginning:
http://www.cs.ualberta.ca/~isaac/cmput272/s03/272.html
don't bother reading past may 20, much of the remaining stuff is CS or math specific.
--- http://www.stanford.edu/class/cs103a/
Also pretty concise. The problem is that it looks like the solutions to the problems aren't on the web (so I'd still recommend doing some problems from http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/logic/logicintro.htm\ l in addition to reading this one, if you read this one).
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http://www.columbia.edu/~av72/symboliclogic/
this one looks good, too (the "lectures" folder), but it has a lot of material on how the english language uses "logical" words to mean things other than formal logic means with those words (I think this is part of the study of "semantics"). And later on in the course it uses some extra terminology.
I'd recommend the first two instead of this because it omits this "extra" stuff and so is more compact.
--- http://www.trentu.ca/academic/math/sb/pcml/welcome.html
this one is dense and goes further than the above. it gets into more technical/mathematical proofs ABOUT logic, rather than just showing you how to use it.
i wouldn't recommend this one until you've read some basic stuff about reading/using predicate logic & first order logic (i.e. the stuff in the other links). Or, if you have someone to ask questions of, I guess you could jump into this one. (you could ask me via email if you could stand waiting for a reply -- probably intolerable though). Either way it's still dense and I'm not sure I'd recommend it at all unless you are itching for more after learning the other basic stuff.
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http://www.sjsu.edu/faculty/carranza/
This one describes old fashioned/medeval logic. I don't know this stuff, I'd be interested in learning! I think that this stuff is half-obsolete today because the modern formalism is considered simpler/easier/more concise. But I think there's might be value in looking at things in multiple ways (i.e. in learning this too).
Anyway, I wouldn't recommend it until after you learn the modern formalisms. It's like a baroque way of saying the same thing. But it's neat.
--- http://www.gotmath.com/notes.html
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example of math being a cool language:
once you learn about convolution (or before, if you want to reason it out), a meaningless looking equation such as
$y(t) = \int_0^t e^{-\tau} u(t - \tau) d \tau$
(where t=time, u(t) = the input to a system, y(t) is the output)
can become a beautiful expression (or maybe metaphor) of something such as perhaps the way that a thought fades from memory.
http://www.tricki.org/tricki/map
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https://rjlipton.wordpress.com/2009/12/26/mathematical-embarrassments/
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https://www.quora.com/What-is-it-like-to-understand-advanced-mathematics/answers/873950?srid=p6KQ&share=1 but see also https://news.ycombinator.com/item?id=12286960
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