Departing from and closing with reflections on issues regarding teaching practices of philosophy of mathematics, I propose a comparison between the main features of the Leibnizian notion of symbolic knowledge and some passages from the Tractatus on arithmetic. I argue that this reading allows (i) to shed a new light on the specificities of the Tractarian definition of number, compared to those of Frege and Russell; (ii) to highlight the understanding of the nature of mathematical knowledge as symbolic or formal (...) knowledge that Wittgenstein mobilizes in his book; (iii) to offer reasons for the claim that Wittgenstein can be considered the philosopher of mathematical practice avant la lettre. The paper ends with an overview, a return to the initial reflection on the connections between research and teaching, and a defense of the reading key used here in terms of its potential for the research in philosophy of mathematics. (shrink)

Music theory has to reinvent itself. Century-long paradigms have to be revisited, and recent terminologies and concepts coming from other fields of music have to find room within the traditional frameworks, particularly in connection with electronic music. In this work, I make an attempt at depicting a framework that might turn useful to further advancements in music theory, by representing the relation between electroacoustic and traditional musics within a scenario dominated by the Philosophy of Language. The Philosophy of Language is (...) herein proposed as a possible philosophical asset to counterbalance some limits of Phenomenology, which has dominated the field of electroacoustic music since its appearance. Within this scenario, the work suggests the notions of "mimesis" and "cadence" as two valid terms to help creating a common ground between the two genres, discussing them in detail and proposing new interpretations for both concepts. (shrink)

There is a famous quip of F.P. Ramsey's, which is my second epigraph. According to a widespread legend, the quip is a criticism of Wittgenstein's treatment in the Tractatus of what cannot be said. The remark is indeed Ramsey's, but he didn't mean what he is taken to mean in the legend. His quip, looked at in context, means something quite different. The legend is sometimes taken to provide support for a reading of the Tractatus according to which the nonsensical (...) propositions of the book were intended to convey what cannot be said. But, since the legend has no basis in reality, it provides no evidence in favor of any such reading of the Tractatus. The quip has great interest if it is read in the context of Ramsey's discussion of generality; it is closely related to issues of importance in the development of Wittgenstein's thought. (shrink)

In theTractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, we (...) identify three ways in which the first notational convention can be implemented, show that two of these are compatible with the text of theTractatus, and argue on systematic and historical grounds, adducing posthumous work of Ramsey’s, for one of these as Wittgenstein’s envisaged method. With respect to the second Tractarian proposal, we discuss how Wittgenstein distinguished between general and non-general propositions and argue that, claims to the contrary notwithstanding, an expressively adequate N-operator notation is implicit in theTractatuswhen taken in its intellectual environment. We finally introduce a variety of sound and complete tableau calculi for first-order logics formulated in a Wittgensteinian notation. The first of these is based on the contemporary notion of logical truth as truth in all structures. The others take into account the Tractarian notion of logical truth as truth in all structures over one fixed universe of objects. Here the appropriate tableau rules depend on whether this universe is infinite or finite in size, and in the latter case on its exact finite cardinality.As it is obviously easy to express how propositions can be constructed by means of this operation and how propositions are not to be constructed by means of it, this must be capable of exact expression.5.503. (shrink)

Dasgupta :35–67, 2009) has argued that material individuals, such as particles and laptops, are metaphysically objectionable and must be eliminated from our fundamental theories of the world. He proposes to eliminate them by redescribing all the fundamental facts of the world in a variant of predicate functor logic. We study the status, on this theory, of a putative fact particularly recalcitrant to a formulation within predicate functor logic: his own claim that there are no fundamental or primitive material individuals. We (...) consider three regimentations of the denial of primitive individuals and show that—under some plausible hypotheses about fundamental truths and the fundamentality operator—they cannot be consistently translated in predicate functor logic by Dasgupta’s usual strategy. We conclude by discussing two approaches to salvage Generalism, in the absence of such a translation. (shrink)

Ludwig Wittgenstein once wrote to G.E. Moore that he had stirred up a philosophical wasps’ nest with his paradox, associated with the sentence “I believe it’s raining and it’s not raining”. The problem is that it would be odd for a speaker to assert this thought about herself, although it could be true about her, and although the sentence is well-formed and not contradictory. -/- Making use of the notion of a sentence having sense in a context of significant use (...) (inspired by Ludwig Wittgenstein), the author explores the responses of some of the “wasps” who responded to the paradox, and the background of their reactions. -/- By using the metaphor of philosophizing from within language rather than outside of language the author explores what she calls “the user perspective” on philosophical problems. In this investigation, Moore’s paradox functions as a test case, by which the author elucidates differences in view of the role and powers of philosophical terminology. -/- The contribution of this work is meta-philosophical in being concerned with philosophical method. Its point of departure is in the therapeutic strand of the tradition after the later Wittgenstein. (shrink)

The main question addressed by this article is this: How should one understand the role of the sentences of the Tractatus, given Wittgenstein’s statement that they are nonsensical? I begin with a presentation of three general principles of interpretation in order to avoid answering the question in an inappropriate way. I then move on to a short presentation and commentary on a selection of readings – namely, the ineffabilist, resolute and elucidatory ones – and elaborate the answers given by advocates (...) of these to the question explored here. I agree on many points with resolute and elucidatory readings: the Tractatus presents an austere conception of nonsense, and is not a book that seeks to present ontological or semantic theories. I point out, however, that these readings cannot fully explain the nature of Tractarian elucidations. Then I discuss those parts of the Tractatus which refer to the sentences of the book itself. The main proposal of my own approach is this: Tractarian elucidations should be construed as rules of translation, in that they show how to substitute certain expressions for others. They enable us to construct a notation in which everything that is expressible in ordinary language can be said perspicuously. (shrink)