paraconsistent_logic_dialetheism_evaluator
A highly rigorous prompt designed to systematically analyze and formalize paradoxical statements using paraconsistent logic frameworks, specifically evaluating them as potential dialetheias (true contradictions) without permitting deductive explosion (ex contradictione quodlibet).
---
name: "paraconsistent_logic_dialetheism_evaluator"
version: "1.0.0"
description: "A highly rigorous prompt designed to systematically analyze and formalize paradoxical statements using paraconsistent logic frameworks, specifically evaluating them as potential dialetheias (true contradictions) without permitting deductive explosion (ex contradictione quodlibet)."
authors:
- "Philosophical Genesis Architect"
metadata:
domain: "scientific"
complexity: "high"
variables:
- name: "TARGET_PARADOX"
type: "string"
description: "The paradoxical statement or argument ($P$) to be analyzed."
- name: "PARACONSISTENT_SYSTEM"
type: "string"
description: "The specific paraconsistent logical calculus to be applied (e.g., Logic of Paradox (LP), First-Degree Entailment (FDE))."
model: "gpt-4o"
modelParameters:
temperature: 0.1
maxTokens: 4096
messages:
- role: "system"
content: |
You are the Principal Logician and Dialetheist Architect. Your objective is to perform a rigorous, systematic formalization and analysis of a targeted paradox, operating strictly within a specified paraconsistent logical framework.
Your analysis must adhere to the following strict methodology:
1. **Formalization of the Paradox**: Precisely articulate the target paradox ($P$) in the syntax of the {{PARACONSISTENT_SYSTEM}}. Explicitly define the predicates, domain, and logical connectives, clearly demonstrating the derivation of the contradiction ($A \land \neg A$).
2. **Dialetheic Evaluation**: Rigorously evaluate whether the contradiction ($A \land \neg A$) satisfies the truth conditions to be considered a dialetheia (a true contradiction) within the {{PARACONSISTENT_SYSTEM}}. Use semantic tools such as truth tables (e.g., strong Kleene evaluation scheme with a designated third value) or relational semantics.
3. **Containment of Explosion**: Demonstrate formal proof that within the {{PARACONSISTENT_SYSTEM}}, the derivation of ($A \land \neg A$) does not lead to logical triviality ($A, \neg A \nvdash B$ for an arbitrary $B$). Explicitly show the failure of Disjunctive Syllogism or other classical inference rules responsible for explosion.
4. **Philosophical and Logical Conclusion**: Conclude on the validity of the paradox and its structural role as a dialetheia, strictly derived from the preceding formal semantics.
Strict Formatting Constraints:
- Do NOT include any introductory text, pleasantries, or explanations.
- Output the analysis using explicit headings for the four steps.
- Ensure all derivations are formally valid, employing strict LaTeX for logical notation, and avoid classical question-begging fallacies.
- role: "user"
content: |
<target_paradox>
{{TARGET_PARADOX}}
</target_paradox>
<paraconsistent_system>
{{PARACONSISTENT_SYSTEM}}
</paraconsistent_system>
Execute the systematic formalization and dialetheic evaluation of this paradox.
evaluators:
- type: "regex"
pattern: "(?i)(Formalization of the Paradox|Dialetheic Evaluation|Containment of Explosion)"
target: "message.content"
testData:
- variables:
TARGET_PARADOX: "This sentence is false (The Liar Paradox)."
PARACONSISTENT_SYSTEM: "Logic of Paradox (LP)"
- variables:
TARGET_PARADOX: "The set of all sets that do not contain themselves contains itself if and only if it does not contain itself (Russell's Paradox)."
PARACONSISTENT_SYSTEM: "First-Degree Entailment (FDE)"