This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

One of Gottlob Frege’s most original contributions to logic and philosophy was his logical notation, his ‘Begriffsschrift’. While long criticized, dismissed, or simply ignored, the recent secondary literature contains some helpful re-evaluations and partial defenses of it. These rely largely on technical, pragmatic, or cognitive-psychological considerations. In this paper, we reconsider Frege’s own reasons for valuing his notation highly. We argue that there is a further semiotic dimension, one that matters epistemologically. This dimension becomes evident once one takes seriously, partly (...) also literally, some striking visual metaphors Frege uses. The result is an interpretation highlighting a side of Frege’s position that is not widely known. It involves his views about the indispensable role that language, or sign systems more generally, play for human thought, and especially, for logic and mathematics. More particularly and as we read Frege, a good logical notation allows for expressing conceptual/inferential relations in a ‘visually inscribed’, thus ‘perspicuous’ way, and this leads to a special kind of ‘insight’ in mathematics. Or as we elaborate this point further, it involves a kind of articulation and understanding hardly possible without it. Frege designed his Begriffsschrift with that specific goal in mind. (shrink)

According to the theory theory of metalinguistic disputes, disagreements in metalinguistic disputes are based on diverging underlying theories, opinions, or world views. An adequate description of metalinguistic disagreement needs to consider the compatibility and topics of such theories. Although topic continuity can be spelled out in terms of measurement operations, it is argued that even metalinguistic disputes about a term used in different, mutually compatible theories can be substantive because the dispute is indirectly about the virtues of the underlying theories. (...) The account is defended against externalist and holist objections. (shrink)

In componential analysis, word meanings are (partly) decomposed into other meanings, and semantic and syntactic markers. Although a theory of word meaning based on such semantic decompositions remains compatible with the linguistic labor division thesis, it is not compatible with Kripke/Putnam-style indexical externalism. Instead of abandoning indexical externalism, a Separation Thesis is defended according to which lexical meaning need not enter the truth-conditional content of an utterance. Lexical meaning reflects beliefs about word meaning shared in a speaker community, and these (...) may rest on possibly erroneous world-level theories. It is argued that this type of lexical meaning is indispensable for explaining word composition processes and the rationality of metalinguistic disputes. (shrink)

This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

The problem of value disagreement and contextualist, relativist and metalinguistic attempts of solving it are laid out. Although the metalinguistic account seems to be on the right track, it is argued that it does not sufficiently explain why and how disagreements about the meaning of evaluative terms are based on and can be decided by appeal to existing social practices. As a remedy, it is argued that original suggestions from Putnam's 'The Meaning of "Meaning"' ought to be taken seriously. The (...) resulting dual aspect theory of meaning can explain value disagreement in much the same way as it deals with disagreement about general terms. However, the account goes beyond Putnam's by not just defending a version of social externalism, but also defending the thesis that the truth conditional meaning of many evaluative terms is not fixed by experts either and instead constantly contested as part of a normal function of language. (shrink)

Keine ausführliche Beschreibung für "Religionsphilosophie katholischer Theologie" verfügbar.

In Frege's writings, the notions of truth, judgment, and objectivity are all prominent and important. This paper explores the close connections between them, together with their ties to further cognate notions, such as those of thought, assertion, inference, logical law, and reason. It is argued that, according to Frege, these notions can only be understood properly together, in their inter-relations. Along the way, interpretations of some especially cryptic Fregean remarks, about objectivity, laws of truth, and reason, are offered, and seemingly (...) opposed "realist" and "idealist" strands in his position reconciled. (shrink)

A phenomenon called perspectival disagreement is laid out and modelled on the basis of modifications to known consensus measures for qualitative representations of preferences and transitive values by binary relations. Cases of perspectival disagreement are of general philosophical interest, because they allow for the possibility that two or more agents judge the value positions of other agents differently even when their assessments are based on the same evidence. Various examples of perspectival disagreement are given, generalizations are discussed, and it is (...) argued that any representation by cardinal utilities also gives rise to some form of perspectivity. Although the examples strongly suggest that this phenomenon occurs in real life, it is concluded in the end that it does not pose any fundamental threat to representations of preferences and values as binary relations. Instead, position‐sensitive measures of disagreement ought to be taken as a modelling option for cases in which the relative importance of preference changes matters to an agent. (shrink)

We generalize stochastic Kripke models and Markov transition systems to stochastic right coalgebras. These are coalgebras for a functor with as an endofunctor on the category of analytic spaces, and is the subprobability functor. The modal operators are generalized through predicate liftings which are set-valued natural transformations involving the functor. Two states are equivalent iff they cannot be separated by a formula. This equivalence relation is used to construct a cospan for logical equivalent coalgebras under a separation condition for the (...) set of predicate liftings. Consequently, behavioral and logical equivalence are really the same. From the cospan we construct a span. The central argument is a selection argument giving us the dynamics of a mediating coalgebra from the domains of the cospan. This construction is used to establish that behavioral equivalent coalgebras are bisimilar, yielding the equivalence of all three characterizations of a coalgebra’s behavior as in the case of Kripke models or Markov transition systems. (shrink)

Analytic philosophy and modern logic are intimately connected, both historically and systematically. Thinkers such as Frege, Russell, and Wittgenstein were major contributors to the early development of both; and the fruitful use of modern logic in addressing philosophical problems was, and still is, definitive for large parts of the analytic tradition. More specifically, Frege's analysis of the concept of number, Russell's theory of descriptions, and Wittgenstein's notion of tautology have long been seen as paradigmatic pieces of philosophy in this tradition. (...) This close connection remained beyond what is now often called "early analytic philosophy", i.e., the tradition's first phase. In the present chapter I will consider three thinkers who played equally important and formative roles in analytic philosophy's second phase, the period from the 1920s to the 1950s: Rudolf Carnap, Kurt Gödel, and Alfred Tarski. (shrink)

Ordinal, interval, and ratio scales are discussed and arguments for the thesis that “better than” comparisons reside on interval or ratio scales are laid out. It is argued that linguistic arguments are not conclusive since alternative rank-based definitions can be given, and that in general “better than” comparisons do not have a common scale type. Some comparison dimensions reside on ratio scales, whereas others do not show any evidence of lying on a scale stronger than an ordinal scale.

A layered approach to the evaluation of action alternatives with continuous time for decision making under the moral doctrine of Negative Utilitarianism is presented and briefly discussed from a philosophical perspective.

Nonindexical Context-Dependence and the Interpretation as Abduction Approach Inclusive nonindexical context-dependence occurs when the preferred interpretation of an utterance implies its lexically-derived meaning. It is argued that the corresponding processes of free or lexically mandated enrichment can be modeled as abductive inference. A form of abduction is implemented in Simple Type Theory on the basis of a notion of plausibility, which is in turn regarded a preference relation over possible worlds. Since a preordering of doxastic alternatives taken for itself only (...) amounts to a relatively vacuous ad hoc model, it needs to be combined with a rational way of learning from new evidence. Lexicographic upgrade is implemented as an example of how an agent might revise his plausibility ordering in light of new evidence. Various examples are given how this apparatus may be used to model the contextual resolution of context-dependent or semantically incomplete utterances. The described form of abduction is limited and merely serves as a proof of concept, but the idea in general has good potential as one among many ways to build a bridge between semantics and pragmatics since inclusive context-dependence is ubiquitous. (shrink)

A light form of value realism is defended according to which objective properties of comparison objects make value comparisons true or false. If one object has such a better-making property and another lacks it, this is sufficient for the truth of a corresponding value comparison. However, better-making properties are only necessary and usually not sufficient parts of the justifications of value comparisons. The account is not reductionist; it remains consistent with error-theoretic positions and the view that there are normative facts.

Typical puzzles for de se attitudes by Perry and Lewis are laid out and contrasted with the original version of Jackson's Knowledge Argument. It is argued, from an epistemic perspective, that de se attitudes can be explained by looking at the way internal/introspective knowledge is formed without resorting to acquaintance or making assumptions about the Mind/Body problem.

ABSTRACT. Thought experiments about de se attitudes and Jackson’s original Knowledge Argument are compared with each other and discussed from the perspective of a computational theory of mind. It is argued that internal knowledge, i.e. knowledge formed on the basis of signals that encode aspects of their own processing rather than being intentionally directed towards external objects, suffices for explaining the seminal puzzles without resorting to acquaintance or phenomenal character as primitive notions. Since computationalism is ontologically neutral, the account also (...) explains why neither Lewis’s two gods nor Mary’s surprise in the Knowledge Argument violate physicalism. (shrink)

Autonomous Weapon Systems (AWS) are artificial intelligence systems that can make and act on decisions concerning the termination of enemy soldiers and installations without direct intervention from a human being. In this article, I provide the positive moral case for the development and use of supervised and fully autonomous weapons that can reliably adhere to the laws of war. Two strong, prima facie obligations make up the positive case. First, we have a strong moral reason to deploy AWS (in an (...) otherwise just war) because such systems decrease the psychological and moral risk of soldiers and would-be soldiers. Drones protect against lethal risk, AWS protect against psychological and moral risk in addition to lethal risk. Second, we have a prima facie obligation to develop such technologies because, once developed, we could employ forms of non-lethal warfare that would substantially reduce the risk of suffering and death for enemy combatants and civilians alike. These two arguments, covering both sides of a conflict, represent the normative hill that those in favor of a ban on autonomous weapons must overcome. Finally, I demonstrate that two recent objections to AWS fail because they misconstrue the way in which technology is used and conceptualized in modern warfare. (shrink)

The areas of interest of the scholar of religious studies, Karl E. Grozinger, are diverse. His research is concentrated on the religious and cultural history of Judaism throughout the ages: Israel in antiquity, the era of rabbinical traditional literature, philosophy of religion during the Middle Ages, the kabbalistic tradition, as well as Jewish thinkers and devout movements in contemporary times. On the occasion of Professor Grozinger's seventieth birthday, numerous scholars present the first fruits of their current research as a first (...) look into the tendencies of future research in Jewish studies. In accordance with this scholar's broad interests, the volume Jewish Lifeworlds and Jewish Thought, edited by Nathanael Riemer, is comprised of contributions to a wide variety of topics of Jewish cultural history.With contributions by Hermann Lichtenberger, Hanna Liss, Ronit Meroz, Yoav Elstein, Susanne Talabardon, Nathanael Riemer, Giuseppe Veltri, Dirk Westerkamp, Thomas Meyer, Daniel Jutte, Frederek Musall, Robert Jutte, J. Friedrich Battenberg, Admiel Kosman, Rella Kushelevsky, Elvira Grozinger, Simon Bronner, Avidov Lipsker, Jascha Nemtsov, Rebekka Denz, Micha Brumlik, Micha? Galas, Manja Herrmann, Hans-Michael Haussig, Anat Feinberg, Adam Lipszyc, Vivian Liska, Julius H. Schoeps, Edward D'browa, Ewa Geller, Manfred Voigts, Mordechai Lewy and Stanislaw Krajewski. (shrink)

Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the motivations (...) for its core ideas; the step-by-step development of these ideas, from Begriffsschrift through Die Grundlagen der Arithmetik and Grundgesetze der Arithmetik to Frege's very last writings, indeed even beyond those, to a number of recent "neo-Fregean" proposals for how to update them. One main development, or break, in Frege's views occurred after he was informed of Russell's antinomy. His attempt to come to terms with this antinomy has found some attention in the literature already. It has seldom been analyzed in connection with earlier changes in his views, however, partly because those changes themselves have been largely ignored. Nor has it been discussed much in connection with Frege's basic motivations, as formed in reaction to earlier positions. Doing both in this paper will not only shed new light on his response to Russell's antinomy, but also on other aspects of his views. In addition, it will provide us with a framework for comparing recent updates of these views, thus for assessing the remaining attraction of Frege's general approach. I will proceed as follows: In the first part of the paper (§1.1 and §1.2), I will consider the relationship of Frege's conception of the natural numbers to earlier conceptions, in particular to what I will call the "pluralities conception", thus bringing into sharper focus his core ideas and their motivations. In the next part (§2.1 and §2.2), I will trace the order in which these ideas come up in Frege's writings, as well as the ways in which his position gets modified along the way, both before and after Russell's antinomy.. (shrink)

Principles are investigated that allow one to establish a preference ordering between possible actions based on the question of whether the acting agent himself or other agents will benefit or be harmed by the consequences of an action. It is shown that a combination of utility maximization, an altruist principle, and weak negative utilitarianism yields an ordering that seems to be intuitively appealing, although it does not necessarily reflect common everyday evaluations of actions.

The word ‘concept’ is sometimes used as a synonym for ‘property’, but many authors use it in a more specific sense, for example as standing for unsaturated entities whose extensions are sets and classes, for Fregean senses, or for abstract objects. Although there is no universal agreement on a definition of concepts, a viable theory of concepts has to address a number of formal issues: How to deal with counterfactual and possibly contradictory concepts, how to restrict comprehension schemes in higher-order (...) logic to avoid semantic paradoxes like the Paradox of Predication, how to nominalize concepts, and how to express similarity and typicality of concepts. The article gives a brief survey of the most important problems in concept theory and their possible solutions. (shrink)

It is well known that Frege and his writings were an important influence on Wittgenstein. There is no agreement, however, on the nature and scope of this influence. In this paper, I clarify the situation in three related ways: by tracing Frege's and Wittgenstein's actual interactions, i.e., their face‐to‐face meetings and their correspondence between 1911 and 1920; by documenting Wittgenstein's continued study of Frege's writings, until the very end of his life in 1951; and by constructing, on that basis, a (...) new framework for understanding the themes that connect Wittgenstein to Frege, both in his early and his later works. (shrink)