Every logical system begins with axioms: statements accepted without proof, the bedrock upon which all deduction rests.
logical.day is the space where formal reasoning meets daily practice, where the discipline of proof becomes a habit of thought.
From a conditional statement and its antecedent, derive the consequent. The simplest and most powerful inference rule: if P implies Q, and P is true, then Q must be true.
What holds for all instances holds for any particular instance. The bridge from the universal to the specific, from abstract truth to concrete application.
If P implies Q, and Q implies R, then P implies R. The chain of reasoning extends, each link forged from the one before it, reaching conclusions the premises alone could not state.
Deduction preserves truth
Contradiction implies anything
Double negation elimination
Conjunction introduction
Disjunction elimination
Existential generalization
Two proof branches converge. The assumption leads to absurdity. From contradiction, we learn: the negation of our assumption must be true. This is proof by contradiction -- the most dramatic inference, where falsehood reveals truth.
A logical day is one where every conclusion follows from its premises, where the structure of thought is visible and beautiful, where the proof is both the journey and the destination.
logical.day