Warning: this is an htmlized version!
The original is across this link,
and the conversion rules are here.
% (find-angg "LATEX/2017ebl-abs.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2017ebl-abs.tex"))
% (defun d () (interactive) (find-xpdfpage "~/LATEX/2017ebl-abs.pdf"))
% (defun e () (interactive) (find-LATEX "2017ebl-abs.tex"))
% (defun u () (interactive) (find-latex-upload-links "2017ebl-abs"))
% (find-xpdfpage "~/LATEX/2017ebl-abs.pdf")
% (find-pdf-text "~/LATEX/2017ebl-abs.pdf")
% (find-sh0 "cp -v  ~/LATEX/2017ebl-abs.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2017ebl-abs.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2017ebl-abs.pdf
%               file:///tmp/2017ebl-abs.pdf
%           file:///tmp/pen/2017ebl-abs.pdf
% http://angg.twu.net/LATEX/2017ebl-abs.pdf
% \documentclass[oneside]{book}
% %\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
% %\usepackage[latin1]{inputenc}
% \usepackage{amsmath}
% \usepackage{amsfonts}
% \usepackage{amssymb}
% %\usepackage{pict2e}
% %\usepackage{color}                % (find-LATEX "edrx15.sty" "colors")
% %\usepackage{colorweb}             % (find-es "tex" "colorweb")
% %\usepackage{tikz}
% %
% \usepackage{edrx15}               % (find-angg "LATEX/edrx15.sty")
% \input edrxaccents.tex            % (find-angg "LATEX/edrxaccents.tex")
% \input edrxchars.tex              % (find-LATEX "edrxchars.tex")
% \input edrxheadfoot.tex           % (find-dn4ex "edrxheadfoot.tex")
% \input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
% %
% \begin{document}

% \catcode`\^^J=10
% \directlua{dednat6dir = "dednat6/"}
% \directlua{dofile(dednat6dir.."dednat6.lua")}
% \directlua{texfile(tex.jobname)}
% \directlua{verbose()}
% %\directlua{output(preamble1)}
% \def\expr#1{\directlua{output(tostring(#1))}}
% \def\eval#1{\directlua{#1}}
% \def\pu{\directlua{pu()}}
% \directlua{dofile "edrxtikz.lua"} % (find-LATEX "edrxtikz.lua")
% \directlua{dofile "edrxpict.lua"} % (find-LATEX "edrxpict.lua")
% %L V.__tostring = function (v) return format("(%.3f,%.3f)", v[1], v[2]) end


{\bf Intuitionistic Propositional Logic For Children and
  Meta-Children, or: How Archetypal Are Finite Planar Heyting


I've been using the expression ``for children'' in titles for some
years, and with time it acquired a precise, though unusual, sense.
``Children'' are ``people without mathematical maturity'', where these
are the main aspects of mathematical maturity: ableness to 1) handle
abstract mathematical structures and 2) infinite objects; 3) work
axiomatically, 4) generalize, and 5) particularize.

Some techniques for creating versions ``for children'' of maths ``for
adults'' are described in [1]; the main one is doing two parallel
diagrams, one for the general case and another one for a particular,
hopefully ``archetypal'' case.

Finite, planar Heyting Algebras (``ZHA''s) are very good tools for
teaching Intuitionistic Propositional Logic (IPL) to children: most
non-theorems of IPL have countermodels on ZHAs that are very easy to
understand visually, and children prefer to understand tautologies and
non-tautologies first, and deductive systems later.

ZHAs are archetypal among Heyting Algebras, but in a sense of
``archetypal'' that fits only the loosest definitions in [1], sec.16.

``Meta-children'' are people who want to study the relation between
mathematics ``for children'' and ``for adults'' and produce
(meta)mathematics for adults from that. The presentation will be
mostly about teaching ZHAs and closure operators to ``children'', with
one result for meta-children in the end: that this new sense of
archetypalness can be formalized using comparisons of partial orders
([2], last sections).


[1]: Ochs, E.: {\sl Internal Diagrams and Archetypal Reasoning in
  Category Theory}. Logica Universalis, 2013.

[2]: Ochs, E: {\sl Intuitionistic Logic for Children, or: Planar
  Heyting Algebras for Children}. Preprint, 2017.


Eduardo Ochs --- UFF


Home page: \url{http://angg.twu.net/math-b.html}


% this: let D be the diagram for the partial order on positive
% modalities in S4 from Chellas's {\sl Modal Logic}, p.149; let
% $(W,R)$ be the reflexive closure of the graph $1â2â3â4â5 6â7$ and
% let $v(P):=\{2,5,6\}$. Evaluate the nodes of $D$ in the Kripke model
% $(W,R,v)$, and look the partial order of the values --- it is the
% same as $D$.

% ZHAs are archetypal among HAs, and ZHAs slashed by diagonal cuts are
% archetypal among HAs with closure operators, but in a sense of
% ``archetypal'' somewhat different from [1], that fits only the loose
% definition in sec.16.

% Local Variables:
% coding: utf-8-unix
% ee-anchor-format: "«%s»"
% End: