Colloquium Mathematical Philosophy, 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.

MCMP – Metaphysics and Philosophy of Language

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

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

Putnam and the Multiverse

Colloquium Mathematical Philosophy, 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.

The Metaphysics of Lazy Worlds

Colloquium Mathematical Philosophy, 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.

Relativism and Superassertibility

Colloquium Mathematical Philosophy, 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.

Things that don't exist

Workshop on Putnam's 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".

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

Colloquium Mathematical Philosophy, Barbara Vetter (Berlin) gives a talk at the MCMP Colloquium (25 April, 2013) titled "How to be a Dispositionalist about Modality". Abstract: In recent years, metaphysicians have become increasingly attracted to the idea that modality is grounded in, or that modal statements are made true by, the dispositions of concrete objects. Some attempts have been made to formulate the view and to respond to objections. Objections typically come in the form of specific counter-examples to the view. I will raise and answer a different and, I believe, more fundamental kind of objection which has so far been neglected: the objection that dispositionalist views of modality get the logic of modality wrong. Possibilities, for instance, are closed under logical implication; but it is far from obvious that dispositions are too. (A glass, by being disposed to break, need not be disposed to be such that I am sitting or not sitting.) To answer the challenge, the metaphysics and logical behaviour of dispositions needs to be spelled out in much more detail. Answering the objection thus provides us with a deeper understanding of dispositionalism about modality.

How to be a Dispositionalist about Modality

Workshop on Putnam's Model-Theoretic Arguments, Kate Hodesdon (Bristol) gives a talk at the Workshop on ”Putnam's Model-Theoretic Arguments" (May 23, 2013) titled "Internal Realism and Structural Realism".

Internal Realism and Structural Realism

Colloquium Mathematical Philosophy, John Wigglesworth (MCMP/LMU) gives a talk at the MCMP Colloquium (16 July, 2015) titled "Mathematical Structuralism and Metaphysical Dependence". Abstract: The notion of dependence plays various roles in non-eliminative mathematical structuralism. Of particular interest is the dependence relation that is said by some structuralists to hold between an abstract mathematical structure and the various realisations that exemplify that structure. This dependence relation can be used to distinguish between different versions of non-eliminative structuralism. Ante rem structuralists say that the abstract structure is prior to and independent of any realisation of that structure. In re structuralists claim that the realisations are prior, and so the abstract structure is dependent on there being some realisation of that structure. But very little has been said about this notion of dependence. In this talk, I evaluate one account of dependence that can be found in the literature. I then propose an alternative account and use it to assess the dependence claims made by ante rem and in re structuralists.

Mathematical Structuralism and Metaphysical Dependence

Colloquium Mathematical Philosophy, Johanna Wolff (Hong Kong) gives a talk at the MCMP Colloquium (8 July, 2015) titled "Realism about Measurement and Realism about Magnitudes". Abstract: A realist about measurement, roughly speaking, holds that measurements give us information about, or epistemic access to, the way the world is. Measurement, on such an account, is objective. A realist about magnitudes, understood either as properties or relations, holds that the way measurements provide such objective knowledge is by tracking features of the world, namely certain quantitative properties or relations. Does realism about measurement require realism about magnitudes, or can we be realists about measurement without any additional commitment to magnitudes? Operationalists (Bridgman 1927, Stevens 1935) and nominalists (Field 1980) have traditionally held that it is possible to be a realist about measurement without being a realist about magnitudes. Realism about measurement without realism about magnitudes also seems to be promoted by Representationalism about measurement (Krantz et. al. 1971-90). Against these attempts to divorce realism about measurement from realism about magnitudes, Mundy (1987), Swoyer (1989), and more recently Peacocke (forthcoming) have argued that realism about measurement, while conceptually distinct from realism about magnitudes, nonetheless requires a commitment to magnitudes. My primary question in this paper is how exactly we should understand realism about measurement and realism about magnitudes respectively. A secondary aim will be to see how traditional arguments in favour of realism about magnitudes fare, depending on how we understand these two realisms.

Realism about Measurement and Realism about Magnitudes

Debatte zur Frage "Existiert Gott?", Winfried Löffler (Innsbruck) nimmt Stellung zum Thema "Existiert Gott?" (8. Dezember 2014) auf der gleichnamigen Veranstaltung und vertritt damit eine gegensätzliche Postion zu Norbert Hoerster (Mainz), ebenfalls Diskutant der Veranstaltung. (Hinweis: Wegen technischer Schwierigkeiten beginnt das Live-Video ab der 2. Minute.) Zusammenfassung: „Existiert Gott?“– Wenn es eine Frage gibt, über die man sich einfach nicht einig wird, dann ist es diese Frage. Aber woran liegt es, dass es in Bezug auf die Existenz Gottes seit Jahrhunderten (oder sogar Jahrtausenden) keine Einigung gibt? Liegt es daran, dass man für eine Antwort überhaupt gar nicht rational argumentieren kann? Oder kann man sehr wohl rational argumentieren, aber wir wissen letztlich nicht, welche Argumente überzeugend sind und welche nicht? Solche Fragen können – wenn überhaupt irgendjemand – nur Philosophen beantworten. Aus diesem Anlass haben wir zwei bekannte Philosophen eingeladen: Norbert Hoerster und Winfried Löffler, die beide davon überzeugt sind, dass es rationale Argumente für und wider die Existenz Gottes gibt. Winfried Löffler beantwortet die Frage „Existiert Gott?“ mit „Ja“. Seine Antwort stützt sich auf ein sogenanntes kosmologisches Argument für die Existenz Gottes. Löfflers Argumentation baut vor allem auf wissenschaftlichen Annahmen auf, die an das bekannte Standardmodell der Kosmologie anschließen. Norbert Hoerster vertritt hingegen eine skeptische Position, weil selbst das beste Pro-Argument für die Existenz Gottes (das sogenannte teleologische Argument) letztlich nicht überzeugend ist. Das Manko dieses Arguments ist laut Hoerster, dass es bekannten Einwänden nichts entgegenzusetzen hat, die bereits von David Hume vorgebracht wurden. Gegen die Existenz Gottes spricht Hoerster zufolge vor allem das noch immer ungelöste Problem des Übels in der Welt.

Existiert Gott? (Teil 2)

Colloquium Mathematical Philosophy, Thomas Ede Zimmermann (Frankfurt) gives a talk at the MCMP Colloquium (25 June, 2015) titled "Fregean Compositionality". Abstract: The distinction between transparent and opaque contexts has always played a major rôle in theories of linguistic semantics, though it has undergone a number of reformulations and precisifications since its origins in Frege’s classical substitution arguments. Most dramatically, the unfathomable distinction between Sinn and Bedeutung has been recast in more perspicuous set-theoretic terms, trading Frege’s senses for Carnap’s intensions and identifying functions with their courses of values. Still, at least part of the Fregean architecture has survived all these transformations. In particular, (i) the strategy of treating extensionality as the default case of semantic composition and invoking intensions only when need be, has become part of most common approaches to the syntax-semantics interface. On the other hand, (ii) Frege’s apparent commitment to a hierarchy of senses in the analysis of iterated opacity has been discarded for its alleged lack of cogency and coherence. In the talk I will take a closer look at both aspects of the Fregean architecture within the standard possible worlds framework of Montague’s Universal Grammar. Concerning (i), it will be argued that the Fregean strategy results in an interpretation of intensional constructions (i.e., opaque contexts) that goes beyond mere intensional compositionality in that it imposes a certain kind of uniformity on the pertinent semantic combinations. As to (ii), it will be shown how a hierarchy of intensions may help restoring compositionality when extensional and intensional scope effects appear to be out of tune. The historical background notwithstanding, the the talk will take systematic perspective, aiming at a better understanding and possible improvement of compositionality in possible worlds semantics.

Fregean Compositionality

Colloquium Mathematical Philosophy, Otávio Bueno (Miami) gives a talk at the MCMP Colloquium (22 January, 2015) titled "Logic and Metaphysical Presuppositions". Abstract: Does logic (in particular, classical logic) have metaphysical presuppositions? It may be thought that it doesn’t: logical principles and logical inferences are often taken as not requiring the existence of any objects for them to hold. Logical principles are supposedly true in any domain (so there is no reliance on the subject matter at hand), and logical inferences are traditionally understood as being similarly independent of the subject matter under consideration. As Rudolf Carnap famously pointed out: “If logic is to be independent of empirical knowledge, then it must assume nothing concerning the existence of objects (Carnap [1937], p. 140).” In this paper I examine a number of arguments to the contrary, according to which, despite appearances, logical principles and logical inferences do have metaphysical presuppositions. I consider critically these arguments and indicate how they can be resisted, and motivate an alternative that, I argue, recognizes the nature and limitations of such presuppositions. In the end, as will become clear, it does require a suitable understanding of logic and some strategies to avoid commitment to abstract objects to block such presuppositions. Left unassisted, logic may not be presupposition free after all.

Logic and Metaphysical Presuppositions

Colloquium Mathematical Philosophy, Markus Werning (Bochum) gives a talk at the MCMP Colloquium (11 December, 2014) titled "Making Quotation Transparent: A Compositional Analysis of an Apparently Opaque Phenomenon". Abstract: Quotation is regarded as a paradigmatically opaque context. This is due to two failures: (i) A failure of substitution: in quotations the substitution of an expression with a synonym does not leave the meaning of the embedding context unchanged. (ii) A failure of existential generalization: in quotations the replacement of a singular term with an existentially bound variable does not constitute a valid inference. From the failure of substitution it is often inferred that quotation violates the principle of compositionality, according to which the meaning of a complex term is a syntax-dependent function of the meanings of its syntactic parts. The quoted expression, so it is concluded, does not contribute its meaning to the meaning of the embedding context. The failure of existential generalization, furthermore, is taken to entail that quoted singular terms do not introduce referents into the universe of discourse and are hence referentially vacuous. Since compositionality and referentiality are two constitutive principles of semantics, many authors view quotation as an extra-semantic and hence mainly pragmatic phenomenon. The purpose of this paper is to turn the tables and to re-establish the genuinely semantic character of quotation. In the first step I recall that in natural language many phenomena indicate that quoted expressions, at least sometimes, do contribute their meanings to the meaning of the context. This is evident in the case of mixed quotation, but arguable also the case in direct quotation and in many other cases. Moreover, it is argued that the referents of quoted singular terms can often be anaphorically referred to, not only in mixed and direct quotation, but even in some cases of pure quotation. In the second step the inference from opacity to non-compositionality and non-referentiality is reviewed with greater scrutiny. It turns out that additional premises have to be presupposed to make this inference go through. In the third step the pivotal premise that a quoted expression corresponds to a uniform syntactic part of the quotation will be rejected and replaced by the assumption that the quoted expression contributes a syntactically complex structure, which primarily contains phonological and other sub-symbolic information. However, due to a particular semantic interpretation of the quotation marks, the standard meaning and referent of the expression is recovered such that the quoted expression can contribute its standard meaning and referent to the discourse in many circumstances.

Making Quotation Transparent: A Compositional Analysis of an Apparently Opaque Phenomenon

Debatte zur Frage "Existiert Gott?", Norbert Hoerster (Mainz) nimmt Stellung zum Thema "Existiert Gott?" (8. Dezember 2014) auf der gleichnamigen Veranstaltung und vertritt damit eine gegensätzliche Postion zu Winfried Löffler (Innsbruck), ebenfalls Diskutant der Veranstaltung. Zusammenfassung: „Existiert Gott?“ – Wenn es eine Frage gibt, über die man sich einfach nicht einig wird, dann ist es diese Frage. Aber woran liegt es, dass es in Bezug auf die Existenz Gottes seit Jahrhunderten (oder sogar Jahrtausenden) keine Einigung gibt? Liegt es daran, dass man für eine Antwort überhaupt gar nicht rational argumentieren kann? Oder kann man sehr wohl rational argumentieren, aber wir wissen letztlich nicht, welche Argumente überzeugend sind und welche nicht? Solche Fragen können – wenn überhaupt irgendjemand – nur Philosophen beantworten. Aus diesem Anlass haben wir zwei bekannte Philosophen eingeladen: Norbert Hoerster und Winfried Löffler, die beide davon überzeugt sind, dass es rationale Argumente für und wider die Existenz Gottes gibt. Winfried Löffler beantwortet die Frage „Existiert Gott?“ mit „Ja“. Seine Antwort stützt sich auf ein sogenanntes kosmologisches Argument für die Existenz Gottes. Löfflers Argumentation baut vor allem auf wissenschaftlichen Annahmen auf, die an das bekannte Standardmodell der Kosmologie anschließen. Norbert Hoerster vertritt hingegen eine skeptische Position, weil selbst das beste Pro-Argument für die Existenz Gottes (das sogenannte teleologische Argument) letztlich nicht überzeugend ist. Das Manko dieses Arguments ist laut Hoerster, dass es bekannten Einwänden nichts entgegenzusetzen hat, die bereits von David Hume vorgebracht wurden. Gegen die Existenz Gottes spricht Hoerster zufolge vor allem das noch immer ungelöste Problem des Übels in der Welt.

Existiert Gott? (Teil 1)

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.

hubhopper

MCMP – Metaphysics and Philosophy of Language

hubhopper