I've been thinking about what "mathematical model" can be used to model every possible thing (including itself).

Examples: a simple neuron network models a function but doesn't model an algorithm. A list of instructions models an algorithm but doesn't model relations between elements...

You might be thinking "maybe there is nothing that can model everything" but in reality "language" does model everything including itself. The issue is that it's not an organized model and it's not clear how to create it from scratch (e.g. if you will send it to aliens that don't have any common knowledge to start with).

So what is some possible formalization of a mathematical model that models every possible thought that can be communicated?

Edit 1:

The structure formalization I'm looking for has to have a few necessary properties:

  1. Hierarchical: the representation of ideas should rely on other ideas. (E.g. an programming function is a set of programming functions, the concept "bottle of water" is sum of two concepts "water" and a "bottle"...)
  2. Uniqueness of elements: When an idea uses in its definition another idea, it must refer to one specific idea, not recreate it each time. For example, when you think of a digit "9" and the digit "8", you notice that both have a small circle at the top, you don't recreate a new concept "circle" every time, instead, you use a fixed concept "circle" for everything. By contrast, a neural network might recreate the same branch for different inputs. So two representations of concepts must be different iff they have a difference.)
  • 1
    $\begingroup$ Hi and welcome to this community! You should precisely define "everything", "thought" and "X models Y". Also, what do you mean by "in reality "language" does model everything including itself" $\endgroup$
    – nbro
    Jan 3, 2020 at 3:57
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    $\begingroup$ @nbro Your questions are helpful because I don't know what to explain more. "Everything" means thoughts, concepts, ideas and basically everything that can be expressed with language. For example, you can't explain what "the color red" is, so it doesn't count as a thought for my question. But here are examples of things I would like the same model to be able to represent: two objects have similar color or not (a relation), how to brush teeth (an algorithm), what can be considered a "3" (a classification)... Notice how I used language to make you think of those examples. $\endgroup$ Jan 3, 2020 at 10:23
  • $\begingroup$ Category Theory seems promising. There's a great free textbook Seven Sketches in Compositionality. Technically, anything can be a set, but Set Theory is mostly about cardinality and paradoxes, where Category Theory is more about functions and their relations, and more suitable for engineering. $\endgroup$
    – DukeZhou
    Jan 3, 2020 at 19:28
  • $\begingroup$ @RationalFragile I still have no idea of what you're looking for. What do you mean by "X models Y"? The language is just a means of communication in this case. $\endgroup$
    – nbro
    Jan 3, 2020 at 20:13
  • $\begingroup$ @DukeZhou I don't know almost anything about category theory, but, AFAIK, it is basically an abstract field. The only application I remember is related to functional programming languages (such as Haskell). $\endgroup$
    – nbro
    Jan 3, 2020 at 20:15


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