THE CONVENIENCE OF THE TYPESETTER; NOTATION AND TYPOGRAPHY IN FREGE’S<i>GRUNDGESETZE DER ARITHMETIK</i>

Green, J. J.; Rossberg, Marcus; Ebert, Philip A.

doi:10.1017/bsl.2015.5

Cited by 4 publications

(3 citation statements)

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“…42 For an in-depth discussion of the difficulties of typesetting Frege's much more complex Begriffschrift and the importance of available type there (see Green, Rossberg, & Ebert, 2015). 43 The definition may be read as, "R and R are like relations (order isomorphic)" means that there exists a relation in the intersection of one-one relations and Ss such that S's domain is the union of the domains of R and R , and is such that R is equal to the relational product of S, R, and S. This definition mashes notation from Peano's Formulaire with some symbols Russell independently devised in his 1901 "The Logic of Relations" where he insisted on distinguishing relational products and relational intersections (Russell, 1901b, p. 315).…”

Section: By the Expressionmentioning

confidence: 99%

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The Genealogy of ‘’

Elkind¹,

Zach

2022

The Review of Symbolic Logic

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The use of the symbol $\mathbin {\boldsymbol {\vee }}$ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol $\mathbin {\boldsymbol {\vee }}$ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol $\mathbin {\boldsymbol {\vee }}$ for disjunction can be traced to Whitehead and Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of $\mathbin {\boldsymbol {\vee }}$ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed.

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Section: By the Expressionmentioning

confidence: 99%

“… 42 For an in-depth discussion of the difficulties of typesetting Frege’s much more complex Begriffschrift and the importance of available type there (see Green, Rossberg, & Ebert, 2015). …”

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The Genealogy of ‘’

Elkind¹,

Zach

2022

The Review of Symbolic Logic

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“…For an in-depth discussion of the difficulties of typesetting Frege's much more complex Begriffschrift and the importance of available type there, seeGreen, Rossberg, and Ebert (2015).…”

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The Genealogy of '$\lor$'

Elkind¹,

Zach²

2020

Preprint

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The use of the symbol ∨ for disjunction in formal logic is ubiquitous. Where did it come from? Some sources say it was introduced by Peano; others suggest it that it originates as an abbreviation of the Latin word for "or", vel. The origin of the symbol can be traced to Russell's first investigations into formal logic. Because of Principia, Russell's notation was influential in mathematical logic (through the work of the Hilbert school) as well as philosophy (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine).No topic which we have discussed approaches closer to the problem of a uniform and universal language in mathematics than does the topic of symbolic logic. The problem of efficient and uniform notations is perhaps the most serious one facing the mathematical public. No group of workers has been more active in the endeavor to find a solution of that problem than those who have busied themselves with symbolic logic . . . Each proposed a list of symbols, with the hope, no doubt, that mathematicians in general would adopt them. That expectation has not been realized. Cajori (1929, p. 314)

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“Always Mixed Together”: Notation, Language, and the Pedagogy of Frege's Begriffsschrift

Dunning

2018

Mod. Intell. Hist.

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Gottlob Frege is considered a founder of analytic philosophy and mathematical logic, but the traditions that claim Frege as a forebear never embraced his Begriffsschrift, or “conceptual notation”—the invention he considered his most important accomplishment. Frege believed that his notation rendered logic visually observable. Rejecting the linearity of written language, he claimed Begriffsschrift exhibited a structure endogenous to logic itself. But Frege struggled to convince others to use his notation, as his frustrated pedagogical efforts at the University of Jena illustrate. Teaching Begriffsschrift meant using words to explain it; rather than replacing spoken language, notation became its obverse in a bifurcated style of argument that separated deduction from commentary. Both registers of this discourse, however, remained within Frege's monologue, imposing a consequential passivity on his students. In keeping with Frege's visual understanding of notation, they learned by silently observing it, though never in isolation: notation and language were always mixed together.

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THE CONVENIENCE OF THE TYPESETTER; NOTATION AND TYPOGRAPHY IN FREGE’SGRUNDGESETZE DER ARITHMETIK

Abstract: We discuss the typography of the notation used by Gottlob Frege in hisGrundgesetze der Arithmetik.

Cited by 4 publications

References 19 publications

The Genealogy of ‘’

The Genealogy of ‘’

The Genealogy of '$\lor$'

“Always Mixed Together”: Notation, Language, and the Pedagogy of Frege's Begriffsschrift

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