Variations on a Montagovian theme

What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than often assumed, that they can be avoided by taking the objects of the relevant property to be coarse-grained (“sets of worlds”) propositions, and that all this has little to do with the choice between operators and predicates

Solutions to the Knower Paradox in the Light of Haack’s Criteria

The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox and its solutions.</p

The Methodological Roles of Tolerance and Conventionalism in the Philosophy of Mathematics: Reconsidering Carnap\u27s Logic of Science

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap\u27s Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of the concepts of science (including mathematics) through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap\u27s understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap\u27s logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap\u27s program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts (1992). The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language(s), and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap\u27s entire program. My third chapter argues that this reading makes Carnap\u27s program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap\u27s program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful

Conceptual graph-based knowledge representation for supporting reasoning in African traditional medicine

Although African patients use both conventional or modern and traditional healthcare simultaneously, it has been proven that 80% of people rely on African traditional medicine (ATM). ATM includes medical activities stemming from practices, customs and traditions which were integral to the distinctive African cultures. It is based mainly on the oral transfer of knowledge, with the risk of losing critical knowledge. Moreover, practices differ according to the regions and the availability of medicinal plants. Therefore, it is necessary to compile tacit, disseminated and complex knowledge from various Tradi-Practitioners (TP) in order to determine interesting patterns for treating a given disease. Knowledge engineering methods for traditional medicine are useful to model suitably complex information needs, formalize knowledge of domain experts and highlight the effective practices for their integration to conventional medicine. The work described in this paper presents an approach which addresses two issues. First it aims at proposing a formal representation model of ATM knowledge and practices to facilitate their sharing and reusing. Then, it aims at providing a visual reasoning mechanism for selecting best available procedures and medicinal plants to treat diseases. The approach is based on the use of the Delphi method for capturing knowledge from various experts which necessitate reaching a consensus. Conceptual graph formalism is used to model ATM knowledge with visual reasoning capabilities and processes. The nested conceptual graphs are used to visually express the semantic meaning of Computational Tree Logic (CTL) constructs that are useful for formal specification of temporal properties of ATM domain knowledge. Our approach presents the advantage of mitigating knowledge loss with conceptual development assistance to improve the quality of ATM care (medical diagnosis and therapeutics), but also patient safety (drug monitoring)