logic

which-came-first: logic derives from language; the formalization of logic is a development of linguistic structures into symbolic systems of inference.

Logic is the formalization of language's capacity for structured reasoning.

Reasoning is the instantiation of logical rules into a process of thought.

Inference requires the rules of logic to function; without logic, there is no systematic way to derive conclusions from premises. Remove logic and inference becomes mere guesswork.

Mathematics requires the formal rules of logic to structure its reasoning and proofs.

Paradox as a conceptual entity depends on logical frameworks to exist — a paradox is a logical contradiction made visible. Remove logic and paradoxes cease to be paradoxes.

Epistemology needs logic to operate now — without logical structure (valid inference, non-contradiction, sound reasoning), epistemological evaluation of knowledge claims cannot function. This is present-tense necessity, not just historical association.

Deduction requires logic to operate now: without a logical system (rules of inference, validity criteria), the process of deriving specific conclusions from general premises cannot function. Deduction IS a logical operation — logic is its constitutive substrate.

Knowledge representation formalizes knowledge using logical structures (ontologies, frames, semantic networks). Remove logical formalism and knowledge representation as a discipline ceases to operate.

axiom cannot function without logic — an axiom is a foundational proposition whose role is to serve as a starting point within a logical system. Remove logic and axioms lose their purpose and meaning. Constitutive necessity per Law 8.

Argumentation needs logic to operate now — without logical principles (validity, inference rules, fallacy detection), argumentation cannot function as a construct. This is present-tense necessity, not chronology.

Reductio ad absurdum is a specific kind of logical argument — the method of proving a proposition by showing its contradiction leads to absurdity. This is a clear specific→general INSTANCE_OF relationship.

Constraint-satisfaction needs logic to operate now — constraints are logical relations and satisfaction is a logical check. Remove logic and constraint-satisfaction stops working. Present-tense necessity.

Rationality as a concept depends on logic: the system of valid inference. Remove logic — remove the rules of valid reasoning — and rationality has nothing to conform to, ceasing to operate as a concept. This is not meta-level (Law 2b): rationality and logic pick out object-level concepts whose relationship is that rationality's operation presupposes logical structure.

Which-came-first test: logic predates induction as a conceptual framework. Remove logic now — does induction stop operating? Induction is a method of reasoning that operates entirely within the logical framework; without logic, inductive inference has no conceptual apparatus to function. Present-tense dependency (Law 8), not historical.

Falsifiability as a concept requires the logical framework of truth-value testing to operate. Remove logic — the system of reasoning about truth, validity, and testability — and falsifiability ceases to be a meaningful concept. It is not merely historically associated with logic; the concept's entire operation depends on logical structure (propositions, truth conditions, empirical testability).

Removal test: remove logic and abductive-reasoning stops operating — it is reasoning-by-inference, which requires logical structure to function. Abductive reasoning needs logic as its operating framework, not just historically.

Paraconsistent-logic IS a specific kind of logic — a non-classical logical system that allows contradictions without triviality. A competent speaker would say 'paraconsistent logic is a kind of logic.' Direction tested: specific→general.

SET THEORY needs LOGIC: Remove formal logic and set theory stops operating — its axioms, inference rules, and proof mechanisms all require logical reasoning. Set theory is a formal system built on logical foundations.

Deductive reasoning needs logic to operate now: it is the application of logical principles to derive conclusions from premises. Remove logic and deductive reasoning cannot function — it has no working mechanism without logical rules. Object-level dependency, not meta-level.

Tested direction: which-came-first (Law 7). Formal logic (Aristotle, Euclid) predates algorithmic-thinking by millennia. Modern algorithmic thinking derives from mathematical-logical reasoning traditions that underpin step-by-step procedure design. Y (logic) is older and fed into X (algorithmic-thinking).

Formal verification uses mathematical logic to prove properties of systems. Remove logic and formal verification ceases to operate — it has no formal machinery to work with. The removal test passes.

Burden of proof is the rule that dictates which party must produce evidence. It operates through logical reasoning — the evaluation of evidence, the assignment of responsibility for proof. Remove logic and burden of proof stops operating: there is no framework to reason about evidence, no logical structure to assign the burden. The removal test passes.