Munich Center for Mathematical Philosophy (MCMP)

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MCMP Curated Collections

mcmp-cc-iconMCMP Curated Collections are thematic selections from the MCMP video archives, hand-picked and carefully assembled by members of the center. As commented playlists they present guided tours through our recordings along the curator's personal perspective on a certain thread of current research in mathematical philosophy. Take your pick! And, as always, we do appreciate your feedback.

Carnap on Logic (by Georg Schiemer)

Rudolf Carnap is certainly one of the central figures in twentieth-century formal philosophy. His work covers a wide spectrum of topics and philosophical fields, ranging from the philosophy of logic and mathematics to the philosophy of language and from philosophy of science to probability theory. While Carnap’s contributions in these fields are diverse, there is a common method of doing philosophy that can be identified in his work. This is the use of logic in his approach to philosophical problems. Formal logic plays a central role in Carnap’s work throughout his career, from his early type-theoretic formulation of a constitution theory of knowledge in Der logische Aufbau der Welt to his mature work on ‘Wissenschaftslogik’, i.e. the logic of science, from the 1950s.
The present collection focuses on Carnap’s work on logic as well as on different uses of logical methods in his philosophical work. It comprises seven talks by international scholars that investigate several of Carnap’s contributions from different phases in his intellectual career. The talks selected here were originally presented at the “Carnap on Logic” conference held at the MCMP in June 2013 and co-financed by the German Research Foundation. The central objective of this conference was to investigate from different perspectives Carnap’s work on logic, its philosophical understanding, as well as on various applications of logic in the philosophies of mathematics, language, and science (among other fields). Topics discussed in Munich included his early work on logical type theory and on the metatheory of axiomatic systems as well as his later contributions to formal semantics and to modal logic. Regarding Carnap’s philosophy of logic, several talks at the conference have focused on his ‘principle of tolerance’—first expressed in 1934 in his Logical Syntax of Language—and on the logical pluralism expressed in it. I hope that the present selection of talks from the conference will provide its viewers with an overview over Carnap’s wide-ranging contributions to logic as well as over the present state of Carnap scholarship.

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Reduction and Emergence (by Sebastian Lutz)

The core idea of reduction is that a theory or a whole science can, in some possibly loose sense of the word, be inferred from some other theory or science. If, say, psychology can be reduced to neurobiology, then the claims of the former follow from the claims of the latter. Emergence, on the other hand, is often considered to be a contrary to reduction. Nonetheless, a phenomenon that is considered emergent relative to some other class of phenomena still has to have some connection to that class, often expressed as a supervenience relation.
My interest in reduction developed in parallel to my interest in definition theory, and I have always tried to understand emergence from this starting position. The talks in this collection show this predilection in that most of them present the topic in a way that connects or can be connected to the theory of definition and more generally symbolic logic—although I do not expect this connection to be always easy to achieve. The first three talks are mostly on the general nature of emergence and reduction. The remaining talks discuss reduction and emergence in and between specific sciences, roughly ordered by the size of the science’s objects of investigation.

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Nonmonotonic and Epistemic Logics (by Holger Andreas)

Classical logic is monotonic in the following sense. Suppose we have a logically valid argument from a set P of premises to a conclusion C. Then, any additional premise does not invalidate this argument. We can add as many premises as we want, without altering the validity of the argument. This condition, however, proved too restrictive for a logical analysis of everyday reasoning. In such non-mathematical contexts, we make use of nonmonotonic arguments quite frequently. That is, we use arguments that are invalidated by additional premises. In yet other words, we use defeasible arguments. These arguments are based on default axioms or default rules, which work in a fairly reliable way, but do a have a few exceptions. Nonmonotonic logics have thus been devised to study nonmonotonic arguments. These logics originated from computer science, but their relevance to philosophical questions was recognized soon by logicians working in philosophy.Dynamic epistemic logics, on the other hand, aim at a modal logic analysis of belief changes. As in nonmonotonic reasoning some conclusion may be defeated by an additional premise, so may some of our beliefs become retracted by further information. Belief revision and nonmonotonic reasoning thus turned out to be highly interrelated.

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Causes and Effects (by Roland Poellinger)

When we explain, predict, or instruct, we naturally do so by referring to causes and effects. As a truly basic semantic building block causation seems to not call for explication itself at first sight. Yet, capturing the essence of the causal nexus was David Hume's very goal when he wrote in 1748 that "we may define a cause to be an object followed by another, and where all the objects, similar to the first, are followed by objects similar to the second". This definition can be seen as point of reference for quite a variety of regularity theories of causation trying to spell out the details of Hume's approach in even more formal detail. But Hume offered an alternative, supposedly equivalent explication in defining a cause to be an object, "where, if the first object had not been, the second never had existed." This second wording has become inspiration for many philosophers to pin down the counterfactual core of causation in mathematical and logical terms. Although causal talk pervades our everyday discourse, every attempt at defining cause and effect more precisely has invited counterexamples and led to further debates about syntax, semantics, and metaphysics of these seemingly elusive concepts. For this curated collection I have selected quite different talks from the MCMP video archives in a bid to systematize current debates and give an outlook on applications and problematic cases.

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