Capturing consequence

Author: 

Paseau, A

Publication Date: 

4 March 2019

Journal: 

Review of Symbolic Logic

Last Updated: 

2020-02-01T05:13:00.493+00:00

Issue: 

2

Volume: 

12

DOI: 

10.1017/S1755020318000291

page: 

271-295

abstract: 

First-order formalisations are often preferred to propositional ones because they are thought to underwrite the validity of more natural-language arguments. We compare and contrast the ability of some well-known logics—these two in particular—to formally capture valid and invalid natural-language arguments. We show that there is a precise and important sense in which first-order logic does <i>not</i> improve on propositional logic in this respect. We also prove some generalisations and related results of philosophical interest. The rest of the paper investigates the results' philosophical significance. A first moral is that the correct way to state the oft-cited superiority of first-order logic vis-a`-vis propositional logic is more nuanced than often thought. The second moral concerns semantic theory; the third logic's use as a tool for discovery. A fourth and final moral is that second-order logic's transcendence of first-order logic is greater than first-order logic's transcendence of propositional logic.

Symplectic id: 

923688

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article