24,504 research outputs found
In praise of the referee
There has been a lively debate in many fields, including statistics and
related applied fields such as psychology and biomedical research, on possible
reforms of the scholarly publishing system. Currently, referees contribute so
much to improve scientific papers, both directly through constructive criticism
and indirectly through the threat of rejection. We discuss ways in which new
approaches to journal publication could continue to make use of the valuable
efforts of peer reviewers.Comment: 13 page
The Informal Logic of Mathematical Proof
Informal logic is a method of argument analysis which is complementary to
that of formal logic, providing for the pragmatic treatment of features of
argumentation which cannot be reduced to logical form. The central claim of
this paper is that a more nuanced understanding of mathematical proof and
discovery may be achieved by paying attention to the aspects of mathematical
argumentation which can be captured by informal, rather than formal, logic. Two
accounts of argumentation are considered: the pioneering work of Stephen
Toulmin [The uses of argument, Cambridge University Press, 1958] and the more
recent studies of Douglas Walton, [e.g. The new dialectic: Conversational
contexts of argument, University of Toronto Press, 1998]. The focus of both of
these approaches has largely been restricted to natural language argumentation.
However, Walton's method in particular provides a fruitful analysis of
mathematical proof. He offers a contextual account of argumentational
strategies, distinguishing a variety of different types of dialogue in which
arguments may occur. This analysis represents many different fallacious or
otherwise illicit arguments as the deployment of strategies which are sometimes
admissible in contexts in which they are inadmissible. I argue that
mathematical proofs are deployed in a greater variety of types of dialogue than
has commonly been assumed. I proceed to show that many of the important
philosophical and pedagogical problems of mathematical proof arise from a
failure to make explicit the type of dialogue in which the proof is introduced.Comment: 14 pages, 1 figure, 3 tables. Forthcoming in Perspectives on
Mathematical Practices: Proceedings of the Brussels PMP2002 Conference
(Logic, Epistemology and the Unity of the Sciences Series), J. P. Van
Bendegem & B. Van Kerkhove, edd. (Dordrecht: Kluwer, 2004
Evolving Standards for Academic Publishing: A q-r Theory
This paper develops a model of evolving standards for academic publishing. It is motivated by the increasing tendency of academic journals to require multiple revisions of articles and by changes in the content of articles. Papers are modeled as varying along two quality dimensions: q and r. The former represents the clarity and importance of a paper's main ideas and the latter its craftsmanship and polish. Observed trends are regarded as increases in r-quality. A static equilibrium model in which an arbitrary social norm determines how q and r are weighted is developed and used to discuss comparative statics explanations for increases in r. The paper then analyzes a learning model in which referees (who have a biased view of the importance of their own work) try to learn the social norm from observing how their own papers are treated and the decisions editors make on papers they referee. The model predicts that social norms will gradually but steadily evolve to increasingly emphasize r-quality.
Environment and classical channels in categorical quantum mechanics
We present a both simple and comprehensive graphical calculus for quantum
computing. In particular, we axiomatize the notion of an environment, which
together with the earlier introduced axiomatic notion of classical structure
enables us to define classical channels, quantum measurements and classical
control. If we moreover adjoin the earlier introduced axiomatic notion of
complementarity, we obtain sufficient structural power for constructive
representation and correctness derivation of typical quantum informatic
protocols.Comment: 26 pages, many pics; this third version has substantially more
explanations than previous ones; Journal reference is of short 14 page
version; Proceedings of the 19th EACSL Annual Conference on Computer Science
Logic (CSL), Lecture Notes in Computer Science 6247, Springer-Verlag (2010
The isomorphism problem for tree-automatic ordinals with addition
This paper studies tree-automatic ordinals (or equivalently, well-founded
linearly ordered sets) together with the ordinal addition operation +.
Informally, these are ordinals such that their elements are coded by finite
trees for which the linear order relation of the ordinal and the ordinal
addition operation can be determined by tree automata. We describe an algorithm
that, given two tree-automatic ordinals with the ordinal addition operation,
decides if the ordinals are isomorphic
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