4. Hypothetical Reasoning and Deduction Architecture

Historical Materialist Hook

[RESEARCH REQUIRED: Discuss the expansion of bureaucratic logic models to incorporate hypotheticals, testing assumptions without committing to their truth value. Relate this to state administration and actuarial projection.]

Core Technical Synthesis

[RESEARCH REQUIRED: Explain the mechanics of subproofs and conditional introduction. Detail the process of algorithmic tracking—assuming premises temporarily and discharging them correctly without violating the system architecture.]

Guided Example: Conditional Introduction

A derivation utilizing a subproof:

1. P -> Q      : PR
2. Q -> R      : PR
3. | P         : AS
4. | Q         : ->E 1, 3
5. | R         : ->E 2, 4
6. P -> R      : ->I 3-5

Problem Set

Exercise 4.1

Prove hypothetical transitivity using a subproof in Carnap.

1. (A \/ B) -> C : PR
2. | A : AS
3. | A \/ B : \/I 2
4. | C : ->E 1, 3
5. A -> C : ->I 2-4

Dictionary Reference Map

For conditional frameworks and subproofs: forall x Calgary (Magnus et al. 2025, Ch. 18)
For Carnap subproof syntax: The Carnap Book (2025, Ch. 4)

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