Previously, I introduced Inner Semantics as an alternative to popular "pointer theories" and *internal* semantical theories that dominate the philosophy of language.

Below, I'd like to explicitly describe some of the parallels of this new view in light of innovations arising from **Category Theory**.

**Category Theory** is a foundational mathematical theory that takes its inspiration from abstract algebra concepts such as *Fields*, *Groups*, and *Rings*.

Various theories have taken **Category-Theoretic** notions as the basis for formalizing concepts from abstract algebra such as *Fields*, *Groups*, and *Rings*. And some, such as *Homotopy Type Theory* have gone further in their attempt to embed traditionally *logical* concepts within such framework as well. Such formalizations place emphasis on *geometric* and *topological* notions rather than traditional *symbolic logic*.

This is a break from traditional concepts of *logic* which combine a *Language L* with a *Semantics/Interpretation/Domain/Model M* and a *Calculus/Proof/Deductive System C* - e.g. as three independent components (each representing one of the major foundational pillars of mathematics - **Logic**, **Model Theory**, and **Proof Theory** - the fourth and last is traditionally **Set Theory**) that are combined.

In such a system, the semantical objects and linguistic propositions arise from a single edifice ("top-down", as it were) rather than atomically ("bottom-up", a legacy no-doubt inherited from Russell's *Logical Atomism*).

**Connection Theory** also exhibits a similar set of properties:

- It's potentially semantically-closed.
- It can construct sub-fragments that are models of significant mathematical theories like
**Set Theory**,**Group Theory**,**Category Theory**(itself), and plain old**First Order Logic**. - As such, propositions or assertions of various
*types*(*theories*,*propositions*,*model assignments*, etc.) can be expressed and captured without recourse to external referents

I have not explored the relationship between **Thinking Notation** and **Connection Theory** much but it should be noted that **each can be generated from the other**.

- Inner Semantics
- Inner Semantics #2
- Inner Semantics #3
- Metaphors, Math, and Semantics
- Posthuman Languages
- Posthumanism and Transhumanism

##### post: 1/31/2021