Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens¶
Frege, G. (1879). Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Commutativity
- Yang-Baxter equations (braid group and quantum-group theory rely on controlled non-commutativity). Linguistics and natural language: Some languages allow word-order permutation without changing meaning (free-word-order languages like Latin, Warlpiri); coordinated constructions "A and B" are typically interpreted commutatively; however, many constructions are non-commutative (verb-object order matters; pronoun-antecedent binding depends on order). Logic: Boolean AND, OR are commutative — Frege (1879) in Begriffsschrift gave the first formal-logical treatment establishing the symmetry of conjunction and disjunction in the underlying calculus
This sourceThe first modern predicate calculus (quantification + propositional logic); its propositional fragment yields commutative conjunction and disjunction — supports the claim that Frege gave a formal-logical treatment in which AND/OR are symmetric (note: Boole is the more direct source for the commutativity of the connectives; Frege's contribution is the formal calculus that contains them).
- Yang-Baxter equations (braid group and quantum-group theory rely on controlled non-commutativity). Linguistics and natural language: Some languages allow word-order permutation without changing meaning (free-word-order languages like Latin, Warlpiri); coordinated constructions "A and B" are typically interpreted commutatively; however, many constructions are non-commutative (verb-object order matters; pronoun-antecedent binding depends on order). Logic: Boolean AND, OR are commutative — Frege (1879) in Begriffsschrift gave the first formal-logical treatment establishing the symmetry of conjunction and disjunction in the underlying calculus
- Deductive Reasoning
- Modern formalization via Frege-Russell predicate logic
This sourceL. Nebert. The first fully formal system of quantificational (first-order predicate) logic: introduces quantified variables and a function–argument analysis of propositions, making inference itself an object of inspection; the first axiomatization of logic. WebSearch confirmed it as the inception of modern predicate logic with quantifier notation.
- Modern formalization via Frege-Russell predicate logic
- Formalization
- Logic: Translating an intuitive argument into a symbolic system where validity is decidable by form alone — the paradigm case, in which Frege's (1879) Begriffsschrift introduced a notation explicit enough to make inference itself an object of inspection rather than an exercise of intuition.
This sourceIntroduces quantification and the first modern (second-order) predicate calculus, and is the first to explicitly formulate inference rules distinct from axioms — making inference itself an object of inspection rather than intuition.
- Logic: Translating an intuitive argument into a symbolic system where validity is decidable by form alone — the paradigm case, in which Frege's (1879) Begriffsschrift introduced a notation explicit enough to make inference itself an object of inspection rather than an exercise of intuition.
- Quantifier
- A predicate. There is a property that may hold of individuals — a fragment with no truth value until its scope is fixed. A domain of discourse. There is a determinate collection of individuals over which the predicate is to be evaluated. A scope operator. Some specification fixes how much of the domain the claim covers — all, some, none, most, exactly N, a stated proportion, uniquely — turning the fragment into a claim. A fixed truth condition. Predicate and scope together determine exactly when the claim is true, which a bare predicate cannot supply. The falsification asymmetry. A universal is refuted by a single counterexample; an existential is established by a single witness; this asymmetry organises what evidence bears. The negation transformation. The negation of a quantified claim is itself quantified by a fixed rule — the negation of a universal is an existential of the negated predicate, and vice versa — so the shape of any disagreement is pre-determined.
This sourceIntroduces formal quantification and the bound-variable notation; the source of the universal/existential apparatus and the negation duality between them.
- A predicate. There is a property that may hold of individuals — a fragment with no truth value until its scope is fixed. A domain of discourse. There is a determinate collection of individuals over which the predicate is to be evaluated. A scope operator. Some specification fixes how much of the domain the claim covers — all, some, none, most, exactly N, a stated proportion, uniquely — turning the fragment into a claim. A fixed truth condition. Predicate and scope together determine exactly when the claim is true, which a bare predicate cannot supply. The falsification asymmetry. A universal is refuted by a single counterexample; an existential is established by a single witness; this asymmetry organises what evidence bears. The negation transformation. The negation of a quantified claim is itself quantified by a fixed rule — the negation of a universal is an existential of the negated predicate, and vice versa — so the shape of any disagreement is pre-determined.
- Symbolic Representation
- All depend on collective adoption of arbitrary signs for specific operations and entities, a discipline Frege (1879) inaugurated in Begriffsschrift by designing a formal symbolic notation explicitly engineered to be convention-bound and compositionally productive.
This sourceL. Nebert. Paradigm logical formalization: introduces a notation explicit enough (with quantification and the first modern predicate calculus) to make inference itself an object of inspection rather than an exercise of intuition.
- All depend on collective adoption of arbitrary signs for specific operations and entities, a discipline Frege (1879) inaugurated in Begriffsschrift by designing a formal symbolic notation explicitly engineered to be convention-bound and compositionally productive.
Verification¶
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Links previously used in the corpus¶
Before the registry existed this work was also linked 3 other ways.
- https://archive.org/details/begriffsschrifte0000freg ×1
- https://plato.stanford.edu/entries/frege-logic/ ×1
- https://www.informationphilosopher.com/solutions/philosophers/frege/Frege_Begriffsschrift.pdf ×1
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