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2014 | OriginalPaper | Chapter

5. From Proofs to Verifications, and on to Falsifications

Author : Andreas Kapsner

Published in: Logics and Falsifications

Publisher: Springer International Publishing

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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.

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previous chapter Gaps, Gluts and Paraconsistency
next chapter Falsificationism
Footnotes
1
Although Dummett often talks about meaning theories based on verification and falsification conditions in later works, the place where he extensively discusses falsifications is his What is a Theory of Meaning (II).
 
2
Together with the earlier chapter on intuitionistic logic, this chapter contains most of what I will have to say about purely verificationistic theories. Stage I, unlike the other stages, will thus not receive its own chapter in the third part.
 
3
Schlick (1936), p. 341.
 
4
LBM, p. 10.
 
5
Indeed, in his book Elements of Intuitionism, Dummett immediately gives “\(p\) is verified at \(w\)” as a gloss for \(v_{w}(p)=1\) (p. 139).
 
6
See Sect. 3.​6.​1.
 
7
Indeed, I do not know that Dummett addresses the question anywhere at all.
 
8
Auxier and Hahn (2007), p. 489.
 
9
Cf. also WTM, p. 78: “[T]here cannot be a piece of knowledge the possession of which by any speaker would show both that he would not be right to make a certain assertion and that he would not be wrong to make it.”
 
10
In Sect. 6.​4, I will consider and reject the idea that a verification of the impossibility to verify a statement should already count as a falsification of it.
 
11
Cf. van Benthem (2008).
 
12
When I say that this is trivial, I mean that it is easy to explain how verifications and falsifications are related to each other in the assertoric sense. The question of whether and how we can clearly separate different areas of discourse, on the other hand, is not trivial at all. Is “The number of tasty dishes on this menu is prime” a statement from the area of taste talk, or from the mathematical area? It is frequently assumed that a separation of areas of discourse is feasible, but it is actually far from clear to me how it can work in detail. However, I will not go into this problem in any depth in this book.
 
13
Not that I believe such an extremely eclectic outcome likely.
 
Metadata
Title
From Proofs to Verifications, and on to Falsifications
Author
Andreas Kapsner
Copyright Year
2014
Book
Logics and Falsifications

Print ISBN: 978-3-319-05205-2

Electronic ISBN: 978-3-319-05206-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05206-9_5

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