PHIL 738

Philosophical Logic


Please note: this is archived course information from 2015 for PHIL 738.

Description

Beyond the classical.

Classical first-order logic is an elegant, well-behaved, formal system that is capable of expressing a great deal of mathematics, but it can only establish the validity of an embarrassingly small subset of the valid arguments expressible in ordinary language.

Can we make it better? Can we make its language more expressive without introducing intractable technical or conceptual problems?

In undergraduate classes, we add modal operators, but there are other, less familiar, upgrades. These include: plural quantifiers (which let us say that there are Fs without this being just another way of saying that there is at least one F), generalised quantifiers (which translate words like "most" and "several"), second-order quantifiers, predicate modifiers and definite descriptions. There are also special predicates for capturing set membership and the relationshp between parts and wholes. We will explore these extensions to first-order languages, provide a semantics for each of them and add some rules of inference to classical logic so that they can demonstrate the validity of more arguments. We will also reflect on these formal enrichments and ask the following questions about each of them: Do they qualify as part of logic, rather than, say, part of mathematics, linguistics or physics? Are there metaphysical costs associated with adopting them – must we commit ourselves to the existence of dodgy stuff? Are there severe metatheoretic costs – such as the failure of completeness or compactness?

A strong background in formal logic is needed, including papers at Stage III.

Availability 2015

Not taught in 2015

Lecturer(s)

TBA

Reading/Texts

Readings will be mostly from online sources

Points

PHIL 738: 15 points