Formality of logic and Frege’s Begriffsschrift

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’.     

Notes on Graves and Bradley’s timer algorithm

This paper presents an extension of the Graves and Bradley (1987) millisecond timer, which avoids potential measurement errors of 54.9 msec. The synchronization of the system timer count with the BIOS timer counter must be taken into account to eliminate such errors.     

Hegel’s logic of finitude

In ??Violence and Metaphysics?? Jacques Derrida suggests that ??the only effective position to take in order not to be enveloped by Hegel would seem to be??to consider false-infinity??irreducible.?? Inversely, refuting the charge of logocentrism associated with Hegelian true infinity (wahrhafte Unendlichkeit) would involve showing that Hegel??s speculative logic does not establish the infinity of being exempt from the negativity of the finite. This paper takes up Derrida??s challenge, and argues that true infinity is crucial to Hegel??s understanding of ideality as a question of normative authority, which does not fall prey to logocentrism. Through an exposition of the dialectic of the finite and the infinite in Hegel??s Science of Logic, I argue that true infinity is not an ontological category that eliminates division, but rather refers to the metalogical standpoint involved in a philosophical account of determinacy. Although fully achieved at the end of the Logic, the metalogical standpoint that Hegel elaborates in the Seinslogik under the banner of the true infinite already clarifies that determinacy is a product of normative authority that is itself precarious.     

Field’s logic of truth

T. M. Scanlon’s buck-passing account of value (BPA) has been subjected to a barrage of criticisms. Recently, to be helpful to BPA, Roger Crisp has suggested that a number of these criticisms can be met if one makes some revisions to BPA. In this paper, I argue that if advocates of the buck-passing account accepted these revisions, they would effectively be giving up the buck-passing account as it is typically understood, that is, as an account concerned with the conceptual priority of reasons or the right vis-à-vis value or the good. I conclude by addressing some of the broader implications of my arguments for the current debate about the buck-passing account of value.     

Prior’s defence of Hintikka’s theorem. A discussion of Prior’s ‘The logic of obligation and the obligations of the logician’

In his paper, The logic of obligation and the obligations of the logician, A.N. Prior considers Hintikka??s theorem, according to which a statement cannot be both impossible and permissible. This theorem has been seen as problematic for the very idea of a logic of obligation. However, Prior rejects the view that the logic of obligation cannot be formalised. He sees this resistance against such a view as an important part of what could be called the obligation of the logician. Prior argues that Hintikka??s theorem should not be seen as something paradoxical. On the contrary, it should be seen as a fully acceptable consequence of a basic and reasonable assumption in deontic logic, namely Hintikka??s rule.     

Hempel’s logic of confirmation

This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel’s cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap’s analysis.     

Boole's annotations on ‘the mathematical analysis of logic’

George Boole collected ideas for the improvement of his Mathematical analysis of logic(1847) on interleaved copies of that work. Some of the notes on the interleaves are merely minor changes in explanation. Others amount to considerable extension of method in his mathematical approach to logic. In particular, he developed his technique in solving simultaneous elective equations and handling hypotheticals and elective functions. These notes and extensions provided a source for his later book Laws of thought(1854).     

Literature and the Expressions of Being in Merleau-Ponty’s Unpublished Course Notes

In this article I examine Merleau-Ponty’s understanding of the relation between literature, being and perception. I focus especially on two of Merleau-Ponty’s courses at Collège de France: the first course, Le monde sensible et le monde de l’expression, and the unpublished course Sur le problème de la parole. In the former Merleau-Ponty presents a new understanding of perception, according to which being is expressed in perception through the style of movement of the perceived phenomenon. In the latter he advances a notion of literary writing as an expression of the being that is itself expressed to us in perception. Through a reading of Proust’s work, he discusses how the literary writer makes his experience expressive by means of a stylization of what is experienced. Hence, literature expresses perception through an enhancement of the expressiveness that it already contains. This capacity of literature will be the main focus of my investigation.     

Notes on Leitgeb’s What Truth Depends on

Studia Logica - In Hannes Leitgeb’s article What truth depends on (Leitgeb in J Philos Logic 34:155–192, 2005) the author provides a formally correct and materially adequate truth...     

Uniting model theory and the universalist tradition of logic: Carnap’s early axiomatics

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. This point is illustrated by Carnap’s early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap’s system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature.     

Soames on Russell’s logic: a reply

In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.     

Monsters in Kaplan’s logic of demonstratives

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to contain monsters. For similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift.     

A note on the deontic system DL of Jones and Pörn

I would like to thank Ingmar Pörn for valuable comments on an earlier version of this paper.     

A Comparison of Dewey’s and Russell’s Influences on China

John Dewey and Bertrand Russell visited China at around the same time in 1920. Both profoundly influenced China during the great transition period of this country. This article will focus on the differences between the two great figures that influenced China in the 1920s. This comparison will examine the following five aspects: 1. Deweyanization vs. Russellization; 2. Dewey’s “Populism” vs. Russell’s “Aristocraticism”; 3. Dewey’s “Syntheticalism” vs. Russell’s “Analyticalism”; 4. Dewey’s “Realism” vs. Russell’s “Romanticism”; 5. Dewey’s “Conservatism” vs. Russell’s “Radicalism”. This examination will highlight that, although their visit left indelible impressions among Chinese intellecturals, for the radical Marx–Leninists, any Western philosophy and socio-political theories, including Dewey’s and Russell’s, were prejudicial, outworn, and even counterrevolutionary. Soon “Marxi–Leninization” was gradually substituted for “Deweyanization” and “Russellization.”