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Single Idea 9518

[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL ]

Full Idea

A 'theorem' of logic is the conclusion of a provable sequent in which the number of assumptions is zero.

Gist of Idea

A 'theorem' is the conclusion of a provable sequent with zero assumptions

Source

E.J. Lemmon (Beginning Logic [1965], 2.2)

Book Ref

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.50

A Reaction

This is what Quine and others call a 'logical truth'.

Related Idea

Idea 13689 'Theorems' are formulas provable from no premises at all [Sider]

The 16 ideas with the same theme [definitions of the main concepts in propositional logic]:

9517 The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon]
9516 A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon]
9518 A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon]
9519 A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon]
9529 A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon]
9531 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon]
9534 Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon]
9530 A wff is 'contingent' if produces at least one T and at least one F [Lemmon]
9532 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon]
9533 A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon]
9528 A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon]
9540 A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell]
13422 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock]
13421 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock]
13689 'Theorems' are formulas provable from no premises at all [Sider]
13520 A 'tautology' must include connectives [Wolf,RS]