18 episodes

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

MCMP – Metaphysics and Philosophy of Language Ludwig-Maximilians-Universität München

    • Philosophy

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

    • video
    Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

    Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

    Dietmar Zaefferer (LMU) gives a talk at the MCMP Colloquium (15 May, 2014) titled "Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist". Abstract: Despite considerable progress in formal logic and semantics conditional constructions continue to be a hotly debated topic. One reason for this difficulty of achieving a consensus could be that the problem is simply too hard to be solvable at the current state of the art, so McGee might still be right with his 1985 conjecture: „It may be that it is not possible to give a satisfactory logic of conditionals. This is not to say that it is not possible to give a linguistic account of how we use conditionals, but only to say that such an account would not give rise to a tractable theory of logical consequence.“ (McGee 1985:471) Another reason could be lack of cross-disciplinary communication: This paper looks at logicians’ discussions of counterexamples to MP an MT from the point of view of a linguist and endeavors to show at least that some of them are fallacious, and at most that a considerable amount of problems in this domain is due to insufficient care in formalization, i.e. in semantic analysis. Assume that the miniature archipelago Twin Islands, consisting of Westland and Eastland, is rarely visited, and that at present Jeff and Jane are the only visitors. Assume further that Jane is on Westland. Then the following propositions seem to be true: (P1) Jeff is not the only visitor. non q; (P2) If Jeff is on Eastland, then Jeff is the only visitor. if p then q. Application of modus tollens should lead us to the truth of: (C1) Jeff is not on Eastland. non p.However, intuitively, this does not seem to follow. So this appears to be a counterexample to modus tollens. But it isn’t. It’s easy to see why: Visitor is a relational noun. Jeff is a visitor can only be the case if there is a location Jeff is a visitor of. Uncovering the hidden parameter makes the counterexample disappear: (P1) Jeff is not the only visitor (of Twin Islands). non q; (P2) If Jeff is on Eastland, then Jeff is the only visitor (of Eastland). if p then r. Since q and r are different, there is no way of applying MT. This seems to be an easy exercise from Semantics 101, but I will argue that recent counterexamples to MT (Yalcin 2012) and MP (Kolodny&MacFarlane 2010) are subject to analogous criticism. If there is time I will also comment on the consequences of these considerations for the restrictor – operator view debate (Gillies 2010). All in all, the direction of impact of these remarks is to argue, pace McGee, that it is not only possible to give a linguistic account of how we use conditionals, but also that such an account could arguably give rise to a tractable theory of logical consequence.

    • 1 hr 18 min
    • video
    Putnam and the Multiverse

    Putnam and the Multiverse

    Timothy Bays (Notre Dame) gives a talk at the Workshop on ”Putnam's Model-Theoretic Arguments" (May 23, 2013) titled "Putnam and the Multiverse".

    • 58 min
    • video
    The Metaphysics of Lazy Worlds

    The Metaphysics of Lazy Worlds

    Benjamin Smart (Birmingham) gives a talk at the MCMP Colloquium (10 January, 2013) titled "The Metaphysics of Lazy Worlds". Abstract: Although it is not uncommon for philosophers to put the fundamental laws to one side and discuss, say, causal interactions concerning macroscopic objects like vases, matches and so on (Mumford and Anjum 2011), in this paper we are concerned with our most fundamental physical principles, and the universal laws that can be derived from these. When it comes to predicting ‘evolutions’ of physical systems, there seem to be two mathematically equivalent, but conceptually distinct kinds of what we might call ‘fundamental laws’: there are those laws we, it seems fair to say, are most used to talking about – Newtonian-style laws whereby we can take the state of a system at a time t, apply the relevant laws telling us what will happen next, and correctly predict the state of the system at time t+1. These kinds of law we refer to as ‘equations of motion’. But there is also a fundamental principle of a different nature – a teleological principle telling us that as a physical system evolves from one state to another, the path the system takes through velocity-configuration space is that which minimizes, or to be more precise, extremizes action. This teleological law is conceptually somewhat strange – how does the electron know where it’s going to end up, and what route it should take to take there to minimize the action? Nonetheless it is not a principle to be ignored by the metaphysician, purely because it is strange. We consider, from the viewpoint of four different metaphysical accounts of laws of nature, what this principle of least action (PLA) should be taken to be ontologically, its modal profile, and assuming that laws must have explanatory value, what kind of explanation it affords and where the PLA stands in the explanatory hierarchy.

    • 46 min
    • video
    Relativism and Superassertibility

    Relativism and Superassertibility

    Manfred Harth (LMU) gives a talk at the MCMP Colloquium (19 June, 2013) titled "Relativism and Superassertibility". Abstract: Relativism about truth is in vogue these days. More and more areas of thought and language are considered as promising candidates for a relativistic semantics in recent years: future contingents, epistemic modals, taste-judgements, knowledge ascriptions, moral judgements etc. However, current truth-relativism is a highly contested position facing some serious problems, and given these problems a look for an alternative shape of relativism seems to be advisable for those of us who are also sceptical about contextualism for the areas in question but have relativistic inclinations all the same. In my talk, I shall explore the prospects of such an alternative for moral judgements, which is based on an epistemic account of truth as stable or superassertibility, i.e. the property of being assertible in some state of information and remaining so no matter what improvements are made to it. The straightforward road to relativism within this framework, which is proposed by Michael Lynch and Crispin Wright, is to admit that two contradictory propositions may be both stably assertible relative to divergent starting points of states of information. Yet, not too surprisingly, this requires a corresponding relativization of the truth predicate – which was to be avoided from the outset. I’ll discuss the following response to this problem: abandoning truth-relativism and limiting relativism to epistemic relativism conjoint with a restriction to intuitionistic logic. I’ll conclude that this response, which I call anti-realist epistemic relativism, may yield a promising approach to relativism in ethics that presents an alternative to truth-relativism and contextualism.

    • 46 min
    • video
    Things that don't exist

    Things that don't exist

    Tobias Rosefeldt (Berlin) gives a talk at the MCMP Colloquium (5 June, 2013) titled "Things that don't exist". Abstract: Are there things that don’t exist? Several answers seem to be possible here. You can answer ‚yes’ because you are a Mainongian and believe that existence is a discriminating property of objects, i.e. a property that some objects have and others lack. You can answer ‚no’ because you are a Quinean and believe that to exist just means to be identical to something and hence is a property of everything. Or you can be a fan of substitutional quantification and think that you can answer ‚yes’ without committing yourself to non-existing things in any ontologically interesting sense. In this paper, I want to introduce an alternative to all these views. According to this alternative, you can answer ‚yes’ to the question but nevertheless assume that (i) ‚exist’ expresses a property true of all objects and (ii) ‚there are things’ expresses objectual quantification. The reason why this is possible is that there is a literal reading of the sentence ‚There are things that don‘t exist’ in which we are using it to quantify over kinds of things and say that there are kinds that have no instances. In order to substantiate this claim, I will show that there are many cases in which natural language quantifiers such as ‚there are things’, ‚there is something’ or ‚there are Fs’ are used to quantify over kinds of things rather than individual things, and give an analysis of the intricate syntactical and semantical features of sentences in which such quantification occurs. I will then use the proposed analysis in order to show that there really is the mentioned reading of the claim that there are things that don’t exist and to explain why it has been overseen by so many philosophers. Finally, I will show how useful the insight into the linguistic structure of our talk about non-existing things is by applying it to several cases in which non-existing things are relevant in philosophy.

    • 54 min
    • video
    Naive perception, Cartesian scepticism, and the model-theoretic arguments

    Naive perception, Cartesian scepticism, and the model-theoretic arguments

    Tim Button (Cambridge) gives a talk at the Workshop on ”Putnam's Model-Theoretic Arguments" (May 23, 2013) titled "Naive perception, Cartesian scepticism, and the model-theoretic arguments".

    • 48 min

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