Mathematical Mapping Theory of Truth

Reply Tue 26 Jul, 2016 05:38 am
The one directional mathematical mapping from representations of actuality (within language or memories of physical sensations) to actuality itself is TRUTH Copyright 1997 by Pete Olcott.

In laymen’s terms the curly braces indicate a term that is further defined elsewhere. When this term is on the left side of a specified axiom this axiom is defining one aspect of the meaning of this term.

This is very similar to the way that an ordinary dictionary works. We have words (terms) and their defined meanings (meaning postulates). Unlike a dictionary these meaning postulates build up a single unique meaning for a term. They do not specify different shades of meaning for a word.

The most significant key distinction between an (information science) knowledge ontology and a dictionary is that the latter is a mathematical formalization of the meanings of natural language words such that a machine can achieve understanding of these words fully equivalent to human comprehension.

(Technically the curly braces indicate a specific node in an acyclic directed graph inheritance hierarchy knowledge ontology such as the CYC project. This node is the root of the connected meaning postulates for the specified concept.)

A key distinction that we have been making is that a {DeclarativeSentence} can be incoherent, and a {Proposition} cannot be incoherent. We can determine that a {DeclarativeSentence} is incoherent because it can not be correctly mathematically mapped to a {Proposition}.

Translate {DeclarativeSentence} into {Proposition.Assertion} and {Proposition.BooleanValue}.

Axioms (meaning postulates) related to Propositions
(1) {BooleanValue} {elementOfSet} {true, false}.
(2) {Thing} Single element of the {UniversalSet}.
(3) {AbstractRepresentation} The encoding of certain aspects of a {Thing} using language.
(4) {Truth} The set of Propositions with a {BooleanValue} of {true}.

// Converting a {DeclarativeSentence} presupposition into an axiom
(5) {DeclarativeSentence} {claimsToBe} {Proposition}.
typeOf( thisThing, {TypeOfThing} )
{DeclarativeSentence} assert( typeOf( thisThing, {Proposition} )

// Converting a {DeclarativeSentence} presupposition into an axiom
(6) {DeclarativeSentence} {claimsToHave} {Proposition.BooleanValue.true}.
hasProperty( thisThing, Property)
{DeclarativeSentence} assert( hasProperty( thisThing, {Proposition.BooleanValue.true} ) )

(7) {Proposition} {hasProperty} {Assertion}.
(8) {Proposition} {hasProperty} {BooleanValue}.
(9) {Proposition} Asserted mathematical mapping from an {AbstractRepresentation} to {Thing}.

The notion of {grounded} in Saul Kripke's famous paper is formalized by the above specifications, leaving everything else as {ungrounded}.

Edit [Moderator]: Link removed
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Reply Tue 26 Jul, 2016 08:45 am
The above presentation is anchored in the ideas of the link that was removed and can not be understood without this missing material:

Outline of a Theory of Truth
Saul Kripke
The Journal of Philosophy
Vol. 72, No. 19, Seventy-Second Annual Meeting American Philosophical Association, Eastern Division (Nov. 6, 1975), pp. 690-716
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