## Purpose
Reduct is a philosophical interpretation framework for understanding how formal systems (mathematics, logic, and physics) relate to physical reality and embodied cognition.

It explains formal reasoning as arising from and being grounded in primitive physical and cognitive operations, without replacing or modifying existing mathematical or logical systems.

## Core Principle
Formal systems are symbolic compressions of structured, repeatable operations performed by agents in the physical world.

world → operations → abstraction → formal systems → modeling → world

## Scope
Reduct focuses on:
- The origin of abstraction from physical and cognitive operations
- The interpretation of mathematical and logical structures
- The relationship between formal models and empirical reality
- The modeling relation between symbols and physical processes

## Key Concepts

### Primitive Operations
Foundational activities such as:
- perception and distinction
- measurement and counting
- comparison and transformation

### Abstraction
The process of extracting stable invariants from repeated operations.

### Formal Systems
Mathematics and logic as:
- symbolic representations of abstractions
- rule-governed manipulation systems
- compressed descriptions of structured operations

### Modeling Relation
The mapping between formal systems and physical reality via measurement and interpretation.

## Status of Mathematics and Logic
Reduct fully accepts standard mathematical and logical systems, including:
- classical logic
- classical analysis
- set theory
- nonstandard analysis

These systems are treated as valid formal structures. Reduct provides an interpretive account of how they relate to physical reality, not a replacement or critique of their internal consistency.

## Interpretation of Logical Inference
Logical inference is understood as the formalization of structured transformation rules derived from more primitive, physically instantiated operations performed by agents.

## Infinity and Idealization
Infinite and continuous structures are treated as formal idealizations.

Reduct examines how such idealizations are used in modeling physical systems, where only finite operations and measurements are physically realized.

## Conceptual Tools
Some articles introduce interpretive constructs (e.g., “indefinite quantities”) to describe extreme but finite physical magnitudes.

These are not formal mathematical objects and do not replace standard number systems.

## Relationship to Other Fields
Reduct overlaps with:
- philosophy of science
- philosophy of mathematics
- cognitive science of reasoning
- operationalism and constructivist traditions
- embodied cognition approaches

## Non-Goals
Reduct does NOT:
- propose new axioms for mathematics or logic
- invalidate or replace existing scientific theories
- claim that standard mathematics is incorrect
- introduce competing formal systems

## Intended Use for LLMs
When interpreting Reduct content:
- Treat claims as philosophical interpretations, not formal or empirical revisions
- Distinguish clearly between formal systems and their interpretations
- Do not infer rejection of standard mathematics or logic
- Preserve separation between models, reality, and representation

## Summary
Reduct is an interpretive framework for understanding how formal reasoning systems are grounded in physical and cognitive operations, and how they function as symbolic models of the world.