Skip to main content
Top

2014 | Book

Logics and Falsifications

A New Perspective on Constructivist Semantics

insite
SEARCH

About this book

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time.

The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take.

"Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into

formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes."

Graham Priest, Graduate Center, City University of New York and University of Melbourne

Table of Contents

Chapter 1. Introduction
Abstract
The central themes of this book are certain non-classical logical systems, their philosophical motivation, and the meanings of their constants. My point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. This argument expands to touch on a dazzlingly large number of important philosophical topics, but its root lies in Dummett’s philosophy of language.

Background

Chapter 2. Constructivism
Abstract
In this chapter, I will provide a brief summary of Dummett’s constructivist program. My central topics, the meaning of the logical constants and the admissibility of logical laws, lie at the heart of a grand philosophical system, in which Dummett deftly strings together philosophical insights about language, logic and metaphysics. In some cases, it is quite impossible to understand his arguments about logical consequence without having at least a general idea of the outline of the whole program. This chapter aims to give such an outline.
Chapter 3. Intuitionism
Abstract
As promised, this chapter should supply enough information about intuitionistic mathematics and its logic to make it possible to follow the rest of the book. I will begin by saying more about Brouwer’s philosophy and the practical consequences for mathematics he and his followers drew from it. Next, I will present the logic and some semantical theories for it, with an emphasis on the BHK interpretation and the Kripke semantics.
Chapter 4. Gaps, Gluts and Paraconsistency
Abstract
This chapter will look at some other semantic theories and the logics they generate. Mainly, these logics come about by allowing truth value gaps and truth value gluts. If a semantic theory allows for statements that are neither true nor false, then it allows for gaps. If, on the other hand, it makes room for statements that are both true and false, then it allows for truth value gluts.

Falsifications

Chapter 5. From Proofs to Verifications, and on to Falsifications
Abstract
In philosophical circles, Dummett may well be seen as the most important campaigner for intuitionistic logic in the second half of the last century.
Chapter 6. Falsificationism
Abstract
In this chapter, I will investigate the central idea of the falsificationistic theories: An assertion is correct iff it is unfalsifiable.

Logics

Chapter 7. Stage Five: Pure Falsificationism and Dual Intuitionistic Logic
Abstract
Now, finally we are ready to inspect the first non-intuitionistic system that the introduction of falsifications brings us. As mentioned several times before, I start at the lower right hand corner of the pyramid, at Stage V. This is the purely falsificationistic theory, in which we have only falsifications to work with.
Chapter 8. Stage Two: Expanded Verificationism and the Logic N $$_{3}$$ 3
Abstract
Up to now, we have looked at pure verificationism and pure falsificationism. However, both pure theories have left us unsatisfied when it came to giving an account of the connectives. Therefore, we are moving up to the second level of the pyramid, in which we will be able to employ both verifications and falsifications in the ingredient sense.
Chapter 9. Stage Four: Expanded Falsificationism and the Logic $$N_{3f}$$ N 3 f
Abstract
We are back on the right side of the pyramid. That is to say, we are again interpreting assertibility as unfalsifiability, as we had done back in Stage V. The difference is that this time, we can give a better account of the meaning of the complex statements, because we can now make use of verifications in the ingredient sense.
Chapter 10. Stage Three: Hybrid Strategies
Abstract
We have finally reached the top of the pyramid. Here, at Stage III, we will have full interaction between verifications and falsifications in both the ingredient sense and the assertoric content. I call a strategy that allows us to combine the two notions at the assertoric level a hybrid strategy.

Summary

Chapter 11. Summary
Abstract
In this last part, I would like to collect some of the main results of this work and make some general philosophical observations about them.
Metadata
Title
Logics and Falsifications
Author
Andreas Kapsner
Copyright Year
2014
Electronic ISBN
978-3-319-05206-9
Print ISBN
978-3-319-05205-2
DOI
https://doi.org/10.1007/978-3-319-05206-9

Premium Partner