Reflexion in Factasia

This page describes some of the different kinds of reflexiveness which can be found in Factasia, including self-reference, as exemplified by this page, and this sentence.

Perhaps the two most familiar kinds of reflection we know are the reflection of light in mirrors (see Factasia Through the Looking Glass) and reflection as inward thought process (from which Philosophy results). Factasia deals in both these senses of reflection and many more technical ones. Looking outside Factasia, see Damjan Bojadziev's page on Mirrors.

Reflection runs through Factasia like lettering through a stick of rock. Reflection is powerful but dangerous, particularly in logic where it can push you over the edge into incoherence (as illustrated by "Russell's Paradox"). Factasia uses magic to solve hard problems (magic is probably what Dennett would call a skyhook). Many of Factasia's recipes for magic include a bit of reflection.

Vacuous, Benign and Vicious

Not all reflection works. If you want to make the most of reflexion then you have to get an understanding of how it can fail so you can spot it before it happens. Here we identify two ways it can fail and point you to some effective middle ground between them.
Reflection is a magnifying glass. If you start with something small, you end with something large. If you start with nothing, you end with nothing.

Examples of vacuous reflection include:

  1. Recursion without a base case, e.g. f(n) = n*(f(n-1))
  2. Chain letters and pyramid sales enterprises where there is no viable product.
Allways you have to ask, is the thing we are trying to build up viable, and there is no simple way to tell.
These are the ones we are looking for, and there are, I hope, many good examples in Factasia.
Sometimes you can have too much of a good thing and it all falls apart. Russell's paradox shows a kind of reflection in set theory falling apart (having sets which are members of themselves). The use of the term vicious in this context comes from Russell, and his prescription for avoiding the paradoxes was to eliminate what he called "vicious circularity". Unfortunately its not so easy to tell what is vicious, and its easy to throw out the baby with the bath water.

Self Reference
Combinatory Logic, Functional Programming
Self Application
Combinatory Logic, Functional Programming

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