In September 2009, the authors of this book came together in Leiden for a workshop
called Days of Judgement . The majority of the chapters presented here are based
upon a selection of the talks held at the Leiden workshop. Right from the start, the
idea was to show the importance of the history of the notion of judgement for philosophy
today. As one may learn from Wayne Martin’s book Theories of Judgment ,
Cambridge University Press, 2006, the fi eld of judgement is broad, and one needs to
give a direction to the topic. The general idea of both the workshop and the book
presented here is to take Per Martin-L?f’s constructive type theory as a starting point,
because the notion of judgement plays a central role there. Our logical system is not
only in need of propositions; it also needs judgements in which propositions are
asserted to be true and known. According to Martin-L?f, one is entitled to make a
judgement if one has a ground for it. It is thus that the notion of judgement is related
to the notions of truth, knowledge and ground. It is precisely the relation between
these notions that has given a focus to the topic of the book presented here.
The book starts with two chapters that were not part of the workshop. In the fi rst
chapter, Martin-L?f gives a clear explanation of the way he understands the notion
of judgement, and he relates his position to that of the logical positivists. The fi rst
part of the chapter is a reprint from the paper “Veri fi cationism Then and Now”,
published in The Foundational Debate (W. DePauli-Schimanovich et al. (eds.).
Dordrecht: Kluwer, 1995, 187–196). Martin-L?f has added to the paper a postscript ,
in which he makes an amendment to the paper. G?ran Sundholm was asked to write
an afterword to his paper “Constructions, Proofs and the Meaning of the Logical
Constants”, which appeared in 1983 in the Journal of Philosophical Logic (volume
11: 151–172). In this afterword, the second chapter here, Sundholm gives an overview
of the history of constructive type theory of the last 30 years, focusing on the notions
of construction, demonstration and judgement and the ambiguities in these notions.
This afterword may help the reader to fi nd the important literature that appeared on
the notion of judgement within constructive type theory.