2005: Volume 3
Justification of Argument Schemes
13 pages. Published July 8, 2005
Argumentation schemes are forms of argument that capture stereotypical patterns of human reasoning, especially defeasible ones like argument from expert opinion, that have proved troublesome to view deductively or inductively. Much practical work has already been done on argumentation schemes, proving their worth in AI, but more precise investigations are needed to formalize their structures. The problem posed in this paper is what form justification of a given scheme, as having a certain precise structure of inference, should take. It is argued that defeasible argumentation schemes require both a systematic and a pragmatic justification, of a kind that can only be provided by the case study method of collecting key examples of arguments of the types traditionally classified as fallacies, and subjecting them to comparative examination and analysis. By this method, postulated structures for schemes can be formulated as hypotheses to solve three kinds of problems: (1) how to classify such arguments into different types, (2) how to identify their premises and conclusions, and (3) how to formulate the critical questions used to evaluate each type of argument.
Basic Relevant Theories for Combinators at Levels I and II
Koushik Pal and Robert K. Meyer
19 pages. Published July 8, 2005
The system B+ is the minimal positive relevant logic. B+ is trivially extended to B+T on adding a greatest truth (Church constant) T. If we leave ∨ out of the formation apparatus, we get the fragment B∧T. It is known that the set of ALL B∧T theories provides a good model for the combinators CL at Level-I, which is the theory level. Restoring ∨ to get back B+T was not previously fruitful at Level-I, because the set of all B+T theories is NOT a model of CL. It was to be expected from semantic completeness arguments for relevant logics that basic combinator laws would hold when restricted to PRIME B+T theories. Overcoming some previous difficulties, we show that this is the case, at Level I. But this does not form a model for CL. This paper also looks for corresponding results at Level-II, where we deal with sets of theories that we call propositions. We adapt work by Ghilezan to note that at Level-II also there is a model of CL in B∧T propositions. However, the corresponding result for B+T propositions extends smoothly to Level-II only in part. Specifically, only some of the basic combinator laws are proved here. We accordingly leave some work for the reader.
Tonk Strikes Back
Denis Bonnay and Benjamin Simmenauer
13 pages. Published July 8, 2005
What is a logical constant? In which terms should we characterize the meaning of logical words like “and”, “or”, “implies”? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. More precisely, we favor an approach, going back to Dosen and Sambin, in which the inferential role of a logical constant is captured by a double line rule which introduces it as reflecting structural links (for example, multiplicative conjunction reflects comma on the right of the turnstyle). Rule-based characterizations of logical constants are subject to the well known objection of Prior’s fake connective, tonk. We show that some double line rules also give rise to such pseudo logical constants. But then, we are able to find a property of a double line rules which guarantee that it defines a genuine logical constant. Thus we provide an alternative answer to Belnap’s requirement of conservatity in terms of a local requirement on double line rules.
Constant Domain Quantified Modal Logics Without Boolean Negation
18 pages. Published July 8, 2005
This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s 1984 presentation of the completeness proof quite closely), but with an important twist, to do with the absence of Boolean negation.
REVIEW: Warren Goldfarb’s Deductive Logic
4 pages. Published July 11, 2005
REVIEW: Frank Markham Brown’s Boolean Reasoning: The Logic of Boolean Equations
9 pages. Published July 11, 2005
From Paradox to Judgment: towards a metaphysics of expression
32 pages. Published October 6, 2005
The Liar sentence is a singularly important piece of philosophical evidence. It is an instrument for investigating the metaphysics of expressing truths and falsehoods. And an instrument too for investigating the varieties of conflict that can give rise to paradox. It shall serve as perhaps the most important clue to the shape of human judgment, as well as to the nature of the dependence of judgment upon language use.
Playing Cards with Hintikka: An introduction to dynamic epistemic logic
H. P. van Ditmarsch, W. van der Hoek and B. P. Kooi
27 pages. Published October 6, 2005
This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the result of public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in Hintikka’s ‘Knowledge and Belief’ (1962) give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates. Our closing observations are on recent developments that link the ‘standard’ topic of (theory) belief revision, as in ‘On the Logic of Theory Change: partial meet contraction and revision functions’, by Alchourron et al. (1985), to the dynamic epistemic logics introduced here.
Copyright © 2005, Philosophy Department, University of Melbourne.
Individual papers are copyright their authors.