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).
Supported in partVerified against the publisher's abstract
The record page documents Frege 1879 Begriffsschrift as introducing a conceptual notation for logic, but never mentions conjunction, disjunction, or their symmetry.
“The article "Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens" ("Concept Script, a Formula Language Modeled upon That of Arithmetic, for Pure Thought") by Friedrich Ludwig Gottlob Frege, published in 1879, introduces his conceptual notation for logic.”
- 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.
Supported in partVerified against the work's full text
The cited record states that Frege introduced predicate logic with quantified variables, departing from Aristotelian logic and founding modern mathematical logic — but it says nothing of Russell.
“Frege introduces the concept of predicate logic, where predicates express relationships between objects. This departure from traditional Aristotelian logic contributes to the foundation of modern mathematical logic.”
- 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.
Supported in partVerified against the work's full text
The page states Frege's 1879 Begriffsschrift introduced a symbolic notation designed to capture logical reasoning with precision; it says nothing of decidability by form or of inference as an object of inspection.
“Frege develops a formal system of symbolic notation to represent logical relationships and propositions. This system is designed to capture the structure of logical reasoning with precision.”
- 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.
Supported in partVerified against the work's full text
Frege supplies the universal/existential quantifier apparatus the negation rule turns on, but the fetched passage states no negation rule, nor law, software-safety, or hypothesis-testing uses.
“3. ** Quantifiers :** Frege introduces quantifiers, symbols (∀, ∃) representing universal and existential quantification.”
- 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.
Supported in partVerified against the work's full text
Confirms Frege's 1879 Begriffsschrift introduced a formal symbolic notation for logic; it says nothing about the notation being convention-bound or compositionally productive.
“by Friedrich Ludwig Gottlob Frege, published in 1879, introduces his conceptual notation for logic. Key points include: 1. ** Symbolic Language for Logic :** Frege develops a formal system of symbolic notation to represent logical relationships and propositions.”
- 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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Does it back the claim? Read against the text for 5 of 5 citations: 5 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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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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