Disclaimers

This is a stub. I am having exams right now and do not have the time to write the full article. I'll update (not any time soon) after I've resolved the problems in this article.

The original post was supposed to be part of my "Meditations in Ontology" sequence (I planned on starting the sequence next year at earliest, probably later). I'll probably write a few other stubs to address the recent discussion about existence and truth.

I have learned neither computability theory nor information theory; if I make a mistake somewhere, please correct me.

There has been recent discussion about what it means to "exist". I realised that I have an answer to that question, and decided to briefly explain it here.

Useful Concepts

Object

For the purposes of this post it is sufficient to understand an object as "anything".

Structural Equivalence

Two systems are structurally equivalent if they are composed of the same components.

Functional Equivalence

Two systems are functionally equivalent if they have the same domain, the same range and the same image for all inputs.

Two structurally equivalent systems are functionally equivalent, yet two systems can be functionally equivalent and structurally similar. Sometimes, the semantic content of a concept refers to its function (e.g a clock). At other times, the semantic content might refer to its structure (e.g an atom). Yet still, some concepts may be defined according to both form and structure (e.g a gold watch).

Simulation

When we say that one object $X$ simulates another object $Y$ , we say that $X$ (or a specific output of $X$ (if $X$ is a computational system) is a perfect fidelity model of $Y$ . That is, in all ontologies $X$ (or said output of $X$ ) and $Y$ are indistinguishable and interchangeable.

A Note on Computation

The output of a computation has no inherent meaning. There is no global semantic content to the output of a given computation. When I run a program, the stream of binary code sent to the output devices have no meaning. Only after they have passed the output device, and have been translated from binary to a language I understand, can I "read" the information therein. If I thought in binary, perhaps my monitor would just display the binary stream directly.

Observer

For a given computational process, the semantic content of the output is defined relative to an obser... ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,