Diversity Reading List

Abstract:
Some personal thoughts and opinions on what “good quality mathematics” is and whether one should try to define this term rigorously. As a case study, the story of Szemer´edi’s theorem is presented.

Abstract:

Logicians have always found inspiration for new research in the ordinary language that is used on a daily basis and acquired naturally in childhood. Whereas the logical issues in the foundations of mathematics motivated the development of mathematical logic with its emphasis on notions of proof, validity, axiomatization, decidability, consistency, and completeness, the logical analysis of natural language motivated the development of philosophical logic with its emphasis on semantic notions of presupposition, entailment, modality, conditionals, and intensionality. The relation between research programs in both mathematical and philosophical logic and natural language syntax and semantics as branches of theoretical linguistics has increased in importance throughout the last fifty years. This chapter reviews the development of one particularly interesting and lively area of interaction between formal logic and linguistics—the semantics of natural language. Research in this emergent field has proved fruitful for the development of empirically, cognitively adequate models of reasoning with partial information, sharing or exchanging information, dynamic interpretation in context, belief revision and other cognitive processes.

Abstract: Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.

Abstract:

Many of us think that ordinary objects – such as tables and chairs – exist. We also think that
ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we
are committed to the (seemingly innocuous) thesis that ordinary objects are composed of parts, we
then open ourselves up to a whole host of philosophical problems, most of which center on what
exactly this composition relation is. Composition as Identity (CI) is the view that the composition
relation is the identity relation. While such a view has some advantages, there are many arguments
against it. In this essay, I discuss several versions of the most common objection against CI, and
show how the CI theorist can maintain that these arguments – contrary their initial intuitive
appeal – are nonetheless unsound.

Abstract:

The chapter portrays how contextual examples are relevant to methods of teaching that empower understanding. Focusing on argument from Vine Deloria, jr’s Red Earth, White Lies, Native students inspire one another to learn critical thinking skills, as they discover ways to determine whether Deloria’s concerns with the logic of Western thought are shown to be justified. In the context of teaching about a particular critical thinking fallacy, students grasp the application of logical skills in their own meaningful
cultural context. The point driven home is that the meaningful and culturally relevant contextual content of examples used to teach critical thinking can excite and inspire Native students to learn. Thus philosophers can reinforce the acquisition of critical thinking skills for Native students by using meaningful, familiar content to reinforce understanding and praxis, for the recognition of cognitively false conclusions. This chapter implies an ethical maxim: using examples only from Western thought to teach critical thinking skills may prejudice students of other traditions in their acquisition of these skills.

Abstract:
The object of this paper is the study, in some of its aspects, of the structure of scientific inquiry. The subject is a large one and covers the major part of the field of scientific methodology. We shall confine our attention more particularly to the consideration of those problems of scientific structure which occur in the case of more advanced sciences and merely outline the corresponding problems which occur primarily in sciences in the more elementary stage

Abstract: The argument from multiple realization is currently considered the argument against intertheoretic reduction. Both Little and Kincaid have applied the argument to the individualism-holism debate in support of the antireductionist holist position. The author shows that the tenability of the argument, as applied to the individualism-holism debate, hinges on the descriptive constraints imposed on the individualist position. On a plausible formulation of the individualist position, the argument does not establish that the intertheoretic reduction of social theories is highly unlikely. Nonetheless, the reductive project may run into other potential obstacles. For this reason, it is concluded that the prospect of intertheoretic reduction is uncertain rather than unlikely.