By

**Catarina Dutilh Novaes**
(Cross-posted at NewAPPS)

This is the second and final part of my 'brief introduction' to formal methods in philosophy to appear in the forthcoming

*Bloomsbury Philosophical Methodology Reader*, being edited by Joachim Horvath. (Part I is here.) In this part I present in more detail the four papers included in the formal methods section, namely Tarski's 'On the concept of following logically', excerpts from Carnap's*Logical Foundations of Probability*, Hansson's 2000 'Formalization in philosophy', and a commissioned new piece by Michael Titelbaum focusing in particular (though not exclusively) on Bayesian epistemology.
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Some
of the pioneers in formal/mathematical approaches to philosophical questions had
a number of interesting things to say on the issue of what counts as an
adequate formalization, in particular Tarski and Carnap – hence the inclusion
of pieces by each of them in the present volume. Indeed, both in his paper on
truth and in his paper on logical consequence (in the 1930s), Tarski started
out with an informal notion and then sought to develop an appropriate formal
account of it. In the case of truth, the starting point was the correspondence
conception of truth, which he claimed dated back to Aristotle. In the case of
logical consequence, he was somewhat less precise and referred to the ‘common’
or ‘everyday’ notion of logical consequence.

These
two conceptual starting points allowed Tarski to formulate what he described as
‘conditions of material adequacy’ for the formal accounts. He also formulated
criteria of formal correctness, which pertain to the internal exactness of the
formal theory. In the case of truth, the basic condition of material adequacy
was the famous T-schema; in the case of logical consequence, the properties of
necessary truth-preservation and of validity-preserving schematic substitution.
Unsurprisingly, the formal theories he then went on to develop both passed the
test of material adequacy he had formulated himself. But there is nothing particularly
ad hoc about this, since the conceptual core of the notions he was after was
presumably captured in these conditions, which thus could serve as conceptual
‘guides’ for the formulation of the formal theories.