Logic and philosophy of science share a long history, though contacts
have gone through ups and downs. This paper is a brief survey of some major themes
in logical studies of empirical theories, including links to computer science and current
studies of rational agency. The survey has no new results: we just try to make some
things into common knowledge.
Looking at famous 19th century authors, it is often hard to separate what we would
now call logicians from philosophers of science. Bolzano’sWissenschaftslehre (1937)
is mainly a classic in logical inference, while Mill’s famous work A System of Logic
(1843) is mainly a classic of scientific methodology. Likewise, Helmholtz’ theory
of transformations and invariants in the foundations of the empirical sciences (1868)
linked to the psychology of perception, reached mathematics, deeply influencing the
logical study of definability. But at the end of the 19th century, things changed. Modern
logic underwent an agenda contraction toward the foundations of mathematics: just
compare the small set of concerns in Frege’s Begriffsschrift (1879) as a model for the
field of logic with the Collected Papers of his contemporary Charles Sanders Peirce
(1933): a rich mixture of formal and informal themes, ranging from common sense
reasoning to science, that is still being mined today.The foundational turn made mathematics the paradigm for logical method (whichit still is) and also the major field of investigation for those methods.
Even so, a new brand of philosophers of science soon picked up on the new developments, and in the
20th century, too, many major philosophers contributed to both areas, such as Carnap,
Beth, Lewis, Hintikka, or van Fraassen. The main insights and techniques from the
foundational phase concern mathematical proof and formal systems. But in the 1930s,
members of the Vienna Circle and other groups turned these modern tools to the
empirical sciences as well, with Reichenbach and Popper as famous examples. Interests
went both ways, and for instance, Carnap also played a role in logical discussions
at the time (van Benthem 1978a). Logical methods still dominated ‘neo-positivism’
in the 1950s.
This marriage came under attack from several sides around 1960. The external
criticism of Kuhn’s The Structure of Scientific Revolutions (1962) seemed to show
that logic paints a largely false picture of the reasoning underlying actual practice and
progress in science. Added to this, influential internal critics like Suppes observed that
the formal language methodology of logic is irrelevant to scientific practice, where
one goes for the relevant structures with any symbolism at hand, by-passing systemgenerated
issues like first- versus higher-order languages that logicians delight in.
Contacts did not break off, and Philosophical Logic kept many themes alive, such as
conditional reasoning and causality, that meander through logic and the philosophy of
science. But through the 1970s, logic became friends with disciplines where languages
do play a central role, in particular, computer science and linguistics. Simultaneously,
many philosophers of science defected to probabilistic methods. Contacts between the
fields atrophied—and sometimes, even a certain animosity could be observed.
Through the 1980s and 1990s, however, many themes have emerged that are again
common to the two fields, often with a new impetus from a shared interest in computation.
I will discuss a number of these and earlier themes in this paper, and show how
a new liaison may be in the air. My emphasis will be, not on shiny new logic tools that
philosophers of science should use, but more symmetrically, on shared interests.