Fitch notation

Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a method of presenting natural deduction proofs in propositional calculus and first-order logics using a structured, line-by-line format that explicitly shows assumptions, inferences, and their scope. It was invented by Frederic Brenton Fitch in the 1930s and later popularized through his textbook Symbolic Logic (1952). Fitch notation is notable for its use of indentation or boxes to indicate the scope of subordinate assumptions, making it one of the most pedagogically accessible systems for teaching formal logic.

Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a method of presenting natural deduction proofs in propositional calculus and first-order logics using a structured, line-by-line format that explicitly shows assumptions, inferences, and their scope. It was invented by Frederic Brenton Fitch in the 1930s and later popularized through his textbook Symbolic Logic (1952). Fitch notation is notable for its use of indentation or boxes to indicate the scope of subordinate assumptions, making it one of the most pedagogically accessible systems for teaching formal logic. The null assumption, i.e., we are proving a tautology Our first subproof: we assume the l.h.s. to show the r.h.s. follows A subsubproof: we are free to assume what we want. Here we aim for a reductio ad absurdum We now have a contradiction We are allowed to prefix the statement that "caused" the contradiction with a not Our second subproof: we assume the r.h.s. to show the l.h.s. follows We invoke the rule that allows us to remove an even number of nots from a statement prefix From 1 to 4 we have shown if P then not not P, from 5 to 6 we have shown P if not not P; hence we are allowed to introduce the biconditional in 7, where iff stands for if and only if

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