forall x: An Introduction to Formal Logic

Magnus, P. D., Button, T., Trueman, R., Zach, R., & Thomas-Bolduc, A. (2018). forall x: An Introduction to Formal Logic: Calgary.

Type

Book

Intellectual base

Review or monograph

Year

2018

Pages cited

2-27

Link

https://forallx.openlogicproject.org/html/Ch31.html

Cited from

philosophy

Cited by

6 citations across 5 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.

Domain-specific

• Atomic Sentence
  • In first-order logic (FOL), $F(a)$ can pass both, while $F(x)$ is an atomic formula but not a sentence if $x$ is free.
• Existential Quantification
  • This is a truth condition, not a demand that a proof or computation exhibit the object.
• Quantifier Shift
  • The error is treating the weaker case-wise premise as if it alone guaranteed the stronger common-witness conclusion.
• 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/

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Links previously used in the corpus

Before the registry existed this work was also linked 3 other ways.

• https://forallx.openlogicproject.org/ ×1
• https://forallx.openlogicproject.org/html/Ch27.html ×1
• https://forallx.openlogicproject.org/html/Ch6.html ×1

Registry ID ref:f50607f7d754 · see in the full table