In this talk, I will discuss some interesting points of overlap. First, I will discuss the general proof theoretic goal of proving conservation theorems , which provide a way of comparing axiomatic theories and measuring their strength. Then I will introduce a model-theoretic notion, that of an Herbrand saturated model , and show that this notion provides a smooth and uniform way of proving a number of important conservation results. In the last part of this talk, I will show how algebraic forcing methods can be used to render the model-theoretic arguments constructive. One of the hallmarks of analytic philosophy has been the use of formal methods to address philosophical questions.
Formal methods provide a level of clarity and rigor that many find appealing.
However, the use of formal methods brings with it certain problems. This is an instance of a general problem in the use of formal models. To appreciate the problem more fully, I compare the use of formal models in the philosophy of language with the use of mathematical models in the sciences. This comparison suggests a potential solution to the problem based on the possibility of modifying the model to accommodate a lack of fit between the model and the domain or system being modeled. To the main index of resources .