## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 38, Number 3 (1997), 437-474.

### Grundgesetze der Arithmetik I §§29‒32

#### Abstract

Frege's intention in section 31 of *Grundgesetze* is to show that every well-formed expression in his formal system denotes. But it has been obscure why he wants to do this and how he intends to do it. It is argued here that, in large part, Frege's purpose is to show that the smooth breathing, from which names of value-ranges are formed, denotes; that his proof that his other primitive expressions denote is sound and anticipates Tarski's theory of truth; and that the proof that the smooth breathing denotes, while flawed, rests upon an idea now familiar from the completeness proof for first-order logic. The main work of the paper consists in defending a new understanding of the semantics Frege offers for the quantifiers: one which is objectual, but which does not make use of the notion of an assignment to a free variable.

#### Article information

**Source**

Notre Dame J. Formal Logic, Volume 38, Number 3 (1997), 437-474.

**Dates**

First available in Project Euclid: 12 December 2002

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1039700749

**Digital Object Identifier**

doi:10.1305/ndjfl/1039700749

**Mathematical Reviews number (MathSciNet)**

MR1624970

**Zentralblatt MATH identifier**

0915.03005

**Subjects**

Primary: 03-03: Historical (must also be assigned at least one classification number from Section 01)

Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}

#### Citation

Heck, Richard G. Grundgesetze der Arithmetik I §§29‒32. Notre Dame J. Formal Logic 38 (1997), no. 3, 437--474. doi:10.1305/ndjfl/1039700749. https://projecteuclid.org/euclid.ndjfl/1039700749