Universally accepted logical principles plus simple formal systems can establish logic and formal-system consistency {formalism, logic}. Formalism tries to establish arithmetic, number theory, and logic consistency and foundations, without set theory.
formula
Formalism uses symbolic expressions {formula} for logical relations. Formulas connect symbols using logic rules {well-formed formula} {wff} and therefore have syntax. Formulas have truth-values. Formulas have meaning though they have no words.
schema
Sentence or formula can use term or clause placeholders {schema, logic}. Schema is not true or false, until terms or clauses substitute for placeholders.
Mathematical Sciences>Logic>Foundations
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Date Modified: 2022.0224