# LMUcast Search

## Munich Center for Mathematical Philosophy (MCMP)

Search in progress. Just a moment ...

Conference on Paraconsistent Reasoning in Science and Mathematics , Diderik Batens (Ghent) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Transitory and Permanent Applications of Paraconsistency". Abstract: The advent of paraconsistency offers an excellent opportunity to unveil past prejudices. These do not only concern the truth or sensibility of inconsistencies, but many aspects of the nature of logic(s). My aim will be to raise questions (and possibly arrive at insights) on such topics as the following: methodological versus descriptive application contexts of logics, logical pluralism (in those application contexts), arguments for considering a specific application as suitable, truth-functionality of logical operators, sensibility of (certain uses of) classical negation, fallibilism in logic. [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Andreas Kapsner (MCMP/LMU) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Why designate gluts?". Abstract: In this talk, I want to explore the following idea: Truth value gluts should be allowed in the semantics of logical systems, as they are in many non-classical systems. However, unlike what is standard in such systems, these gluts should be treated as undesignated values. I shall give my reasons for taking this to be a view worth exploring and discuss its effects on such topics as dialetheism, paraconsistency and relevance. On the whole, it will turn out to be a surprisingly attractive view that deals well with epistemic inconsistencies and semantic paradoxes. Some of the greatest difficulties arise in the attempt to account for interesting inconsistent scientific and mathematical theories; this, then, will be the touchstone for the proposed view. [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Francesco Berto (Amsterdam) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Inconsistent Thinking, Fast and Slow". Abstract: This plays on Kahneman’s Thinking Fast and Slow. We implement two reasoning systems: our Slow system is logical-rule-based. Our Fast system is associative, context-sensitive, and integrates what we conceive via background information Slow inconsistent thinking may rely on paraconsistent logical rules, but I focus on Fast inconsistent thinking. I approach our Fast-conceiving inconsistencies in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds. The explicit content of an inconsistent conception is similar to a ceteris paribus relevant conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Maarten McKubre-Jordens (Canterbury) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Doing mathematics paraconsistently. A manifesto". Abstract: In this talk, we outline several motivations for conducting mathematics–in the style of the working mathematician–without dependence on assumptions of non-contradiction. The story involves a short analysis of theorem and counterexample, what it is to reason paraconsistently within mathematics, and takes note of some non-traditional obstacles and attempts to resolve them. In part, this will provide motivation to the mathematician to think outside the box when approaching surprising conclusions within the usual framework. Then, as we delve into the mathematics, we survey some recent results in elementary analysis when performed paraconsistently, and outline some conjectures for future research. This talk is of interest both to provide reasons and techniques for paraconsistent mathematics, and to show how rich a picture can be painted without recourse to assumptions of non-contradiction. [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Graham Priest (CUNY and St Andrews) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Models of Paraconsistent Set Theory". Abstract: Any adequate paraconsistent set theory must be able to validate at least a major part of the standard results of orthodox set theory. One way to achieve this is to take the universe or universes of sets to be such as to validate not only the naïve principles, but also all the theorems of Zermelo Fraenkel set theory. In this talk I will discuss various constructions of models of set theory which do just this. [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Itala M. Loffredo D'Ottaviano (Campinas) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Can a paraconsistent differential calculus extend the classical differential calculus?". Abstract:In 2000, da Costa proposes the construction of a paraconsistent differential calculus, whose language is the language L of his known paraconsistent logic C1, extended to the language of his paraconsistent set theory CHU1, introduced in 1986. We have studied and improved the calculus proposed by da Costa, having obtained extensions of several fundamental theorems of the classical differential calculus. From the introduction of the concept of paraconsistent super-structure X over a set X of atoms of CHU1 and of the concept of monomorphism between paraconsistent super-structures, we will present a Transference Theorem that “translates” the classical differential calculus into da Costa’s paraconsistent calculus. [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Otávio Bueno (Miami) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Inconsistent scientific Theories: A Framework". Abstract: Four important issues need to be considered when inconsistent scientific theories are under discussion: (1) To begin with, are there–and can there be–such things as inconsistent scientific theories? On standard conceptions of the structure of scientific theories, such as the semantic and the syntactic approaches (Suppe [1989], and van Fraassen [1980]), there is simply no room for such theories, given the classical underpinnings of these views. In fact, both the syntactic and the semantic approaches assume that the underlying logic is classical, and as is well known, in classical logic everything follows from an inconsistent theory. Despite this fact, it seems undeniable that inconsistent scientific theories have been entertained–or, at least, stumbled upon–throughout the history of science. So, it looks as though we need to make room for them. (2) But once some room is made for inconsistent scientific theories, how exactly should they be accommodated? In particular, it seems crucial that we are able to understand the styles of reasoning that involve inconsistencies; that is, the various ways in which scientists and mathematicians reason from inconsistent assumptions without deriving everything from them. It is tempting, of course, to adopt a paraconsistent logic to model some of the reasoning styles in question (see da Costa and French [2003], da Costa, Krause, and Bueno [2007], and da Costa, Bueno, and French [1998]). This is certainly a possibility. However, actual scientific practice is not typically done using paraconsistent logic. And if our goal is to understand that practice in its own terms, rather than to produce a parallel discourse about that practice that somehow justifies the adequacy of the latter by invoking tools that are foreign to it, an entirely different strategy is called for. (3) What are the sources of the inconsistencies in scientific theories? Do such inconsistencies emerge from empirical reasons, from conceptual reasons, from both, or by sheer mistake? By identifying the various sources in question, we can handle and assess the significance of the inconsistencies in a better way. Perhaps some inconsistencies are more important, troublesome, or heuristically fruitful than others—and this should be part of their assessment. (4) Several scientific theories become inconsistent due to the mathematical framework they assume. For example, the theories may refer to infinitesimals, as the latter were originally formulated in the early versions of the calculus (see Robinson [1974] and Bell [2005]), the theories may invoke Dirac’s delta function (Dirac [1958]), or some other arguably inconsistent mathematical framework. The issue then arises as to how we should deal with inconsistent applied mathematical theories. What is the status of these theories? Which commitments do they bring? Are we committed to the existence of inconsistent objects if we use such theories in explaining the phenomena? Can an inconsistent scientific theory ever be indispensable? Questions of this sort need to be answered so that we can make sense of the role of inconsistent theories in applications. (For an insightful discussion, see Colyvan [2009].) In this paper, I examine these four issues, and develop a framework–in terms of partial mappings (Bueno, French and Ladyman [2002], and Bueno [2006]), and the inferential conception of the application of mathematics (Bueno and Colyvan [forthcoming])–to represent and interpret inconsistent theories in science. Along the way, I illustrate how the framework can be used to make sense of various allegedly inconsistent theories, from the early formulations of the calculus through Dirac’s delta function and Bohr’s atomic model (Bohr [1913]). [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Conference on Paraconsistent Reasoning in Science and Mathematics , Holger Andreas (MCMP/LMU) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "A Paraconsistent Generalization of Carnap's Logic of Theoretical Terms". [LMUcast ID: ]

Find this and similiar clips in the video collection 'MCMP – Logic'.

Find more recordings of MCMP events and talks in the

MCMP video channels on iTunes U!