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Adam I. Gerard
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Inner Semantics

Read: the draft paper.

Definitions

  1. Intensional definitions or sentences (whereby the predicates of assertions are described by a unifying property had by all bearing members).

  2. Extensional definitions or sentences (whereby the predicates of assertions are described by a specific list of all bearing members).

Inferentialism

The meanings of expressions, sentences, and terms are given by their inferential profiles, the inferential relationships between them define their respective meanings.

Descriptivism

The meanings of expressions, sentences, and terms are given by descriptions or definitions. Dictionary definitions (other expressions) define the meaning of linguistic items.

Correspondance

The meaning of expressions, sentences, and terms are given by reference to some item in the world.

Meaning as Use

The meaning of expressions, sentences, and terms are given by how they are used (pragmatics) within a community.

Internal Semantics

The meaning of expressions, sentences, and terms are given by the internal contents of a person’s mind.

Propositional abstraction

We take propositional abstraction to be the process of “wrapping” any statement in an n-order predicate logic where n > 0 or any declarative expression expressed in the indicative mood into a suitable data structure like JSON equipped with a truth-evaluation through a controlled semantics.

Propositional abstraction example implemented in JSON format:

var propAbstractExample = {
    "truth-value": true,
    "semantics": {
        "cat": "hat",
        "silly": "billy",
        "control": {
            "ignore": "cat"
        }
    },
    "assertion": {
        "silly": "billy"
    }
}

The semantics can be contained internally with respect to the proposition so abstracted or it can reside externally.

Which of these are preferred depends on use-case. For example, if modularity and independence are required we can stick the semantics right into the data structure. This allows each proposition so abstracted to contain different semantics.

We can then extract the truth-values to perform basic logical operations - and between two or more semantics.

Inner Semantics versus Internal Semantics

Internal semantics falls into a camp that also opposes the dominant pointer theories laid out above. Meaning is associated with some internal content with a language user’s mind.

Inner semantics, by contrast, eliminates the subjective component to internal semantics. The meaning of a sentence is fixed within the sentence itself with no external locus of meaning (whether the world, a definition, or a mental content).

Inner Semantics and Language

One way we might think about Inner Semantics is to reverse the relationship we intuitively deploy when we typically reason about languages and sentences.

We typically think about sentences as being dependent on languages (in some sense) in that sentences are some string of valid symbols and symbol arrangements forming a well-formed-formula.

What if we reverse that relationship and embed a language within a single sentence?

That, more specific articulation, helps to situate this idea into something more tangible. We're not just moving symbols within a set, we move the entire language that the sentence is expressed "within" into the sentence itself!

Of course, this works "better" for more succinct, artificial, languages.

Interesting Intersections

[I assert that] Inner Semantics, so conceived, exhibits a one-way function (with respect to the assignment of meaning).

Semantic Drift is the term I give to describe how the meanings (propositions) of sentences change over time.

Inner Semantics is also motivated by concerns similar to those found in Category Theory as well as web technologies like JSON-LD.

There are also interesting parallels with Carnap's Linguistic Frameworks.

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