Logic and emergence

Introduction to Logic
by Stanford University
@coursera
https://www.coursera.org/learn/logic-introduction/home/welcome

Introduction to Mathematical Thinking
by Stanford University
@coursera
https://www.coursera.org/learn/mathematical-thinking/home/welcome

notes:

emergence in math logic - take into the account the relations between the statements, i.e. order if nothing else:

Peter threw the ball & the ball went into the hoop
(it means that Peter forced the ball into the hoop)

The ball went into the hoop & Peter threw the ball
(Peter threw the ball after the ball went through the hoop)

New information emerges from natural language, but not the mathematical.
Perhaps language (even the language of logic) should have the ability to depend on the (previous) "context".

(Shannon's information doesn't depend on previous context; maybe it should?)

Two parts of the statement are like two wave functions, each independent and on its own, but when combined they represent a new piece of information.

implication involves causality
implication = conditional + causation
causation requires relation between antecedent and consequent
statements "know" about each other the way particles in physics know about it other, but particles only appear to "know" about things as a consequence of the non-local effects, global wave function e.g.