Logic and Foundations of Mathematics Commons^™

Magicicada And Mathematics: What The Parochiality Of Our Explanations Means For The Indispensability Argument, Jadyn Malone

Philosophy Senior Theses

This thesis examines whether the indispensability argument justifies belief in the existence of mathematical entities. I adopt ontological naturalism, arguing that we should believe in entities that feature in our best scientific theories, which are determined through inference to the best explanation. The indispensability argument contends that because mathematical entities are explanatorily indispensable to our best scientific theories – as demonstrated by examples like the prime number explanation of cicada life cycles – we should believe they exist just as we believe in electrons and stars.

However, I identify a challenge: our scientific explanations are inherently parochial, shaped by human …

Logical Pluralism From A Pragmatic Perspective, Teresa Kouri Kissel

Philosophy Faculty Publications

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.

A New Interpretation Of Carnap's Logical Pluralism, Teresa Kouri

Philosophy Faculty Publications

Rudolf Carnap’s logical pluralism is often held to be one in which corresponding connectives in different logics have different meanings. This paper presents an alternative view of Carnap’s position, in which connectives can and do share their meaning in some (though not all) contexts. This re-interpretation depends crucially on extending Carnap’s linguistic framework system to include meta-linguistic frameworks, those frameworks which we use to talk about linguistic frameworks. I provide an example that shows how this is possible, and give some textual evidence that Carnap would agree with this interpretation. Additionally, I show how this interpretation puts the Carnapian position …

Why There Can't Be A Logic Of Induction, Stuart Glennan

Scholarship and Professional Work - LAS

Carap's attempt to develop an inductive logic has been criticized on a variety of grounds, and while there may be some philosophers who believe that difficulties with Carnap's approach can be overcome by further elaborations and modifications of his system, I think it is fair to say that the consensus is that the approach as a whole cannot succeed. In writing a paper on problems with inductive logic (and with Carnap's approach in particular), I might therefore be accused of beating a dead horse. However, there are still some (e.g., Spirtes, Glymour and Scheines 1993) who seem to believe that …