forall x: An Introduction to Formal Logic¶
Magnus, P. D., & Ichikawa, J. J. (2018). forall x: An Introduction to Formal Logic: An Introduction to Formal Logic.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- No True Scotsman
- Begin with a contentful universal: \(\forall x\,(X(x) \rightarrow Y(x))\) — every member of category \(X\) has property \(Y\) — where \(X\) has an extension specifiable independently of \(Y\).
This sourceOpen-access logic textbook (Calgary/UBC editions). Covers universally quantified conditionals ∀x(X(x)→Y(x)) and tautology/logical truth, supporting the formal restatement and the fact that ∀x((X(x)∧Y(x))→Y(x)) is a tautology because the consequent is a conjunct of the antecedent.
- Begin with a contentful universal: \(\forall x\,(X(x) \rightarrow Y(x))\) — every member of category \(X\) has property \(Y\) — where \(X\) has an extension specifiable independently of \(Y\).
Domain-specific¶
- Rule of replacement
- The defining privilege is locality: the rule can operate within a formula rather than requiring the entire proof line to match the premise pattern of an inference rule.
This sourceOpen Logic Project. https://forallx.openlogicproject.org/
- The defining privilege is locality: the rule can operate within a formula rather than requiring the entire proof line to match the premise pattern of an inference rule.
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