## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 59, Number 1 (2018), 1-33.

### The Logical Strength of Compositional Principles

#### Abstract

This paper investigates a set of issues connected with the so-called *conservativeness argument against deflationism*. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for a first-order language, taken together, have substantial logical strength, amounting to a kind of abstract consistency statement.

#### Article information

**Source**

Notre Dame J. Formal Logic Volume 59, Number 1 (2018), 1-33.

**Dates**

Received: 4 September 2014

Accepted: 28 February 2015

First available in Project Euclid: 5 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1499241609

**Digital Object Identifier**

doi:10.1215/00294527-2017-0011

**Subjects**

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

**Keywords**

truth compositionality Tarski deflationism

#### Citation

Heck Jr., Richard G. The Logical Strength of Compositional Principles. Notre Dame J. Formal Logic 59 (2018), no. 1, 1--33. doi:10.1215/00294527-2017-0011. https://projecteuclid.org/euclid.ndjfl/1499241609