On What There is—Infinitesimals and the Nature of Numbers

Abstract

This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics.     

There is no ‘Is’ of constitution

I defend the view that ordinary objects like statues are identical to the pieces of matter from which they are made. I argue that ordinary speakers assert sentences such as ‘this statue is a molded piece of clay’. This suggests that speakers believe propositions which entail that ordinary objects such as statues are the pieces matter from which they are made, and therefore pluralism contradicts ordinary beliefs. The dominant response to this argument purports to find an ambiguity in the word ‘is’, such that ‘is’ in these sentences means the same as ‘constitutes or is constituted by’. I will use standard tests for ambiguity to argue that this strategy fails. I then explore and reject other responses to the argument.     

On the Alleged Ambiguity of ‘Now’ and ‘Here’

It is argued that, in order to account for examples where the indexicals `now' and `here' do not refer to the time and location of the utterance, we do not have to assume (pace Quentin Smith) that they have different characters (reference-fixing rules), governed by a single metarule or metacharacter. The traditional, the fixed character view is defended: `now' and `here' always refer to the time and location of the utterance. It is shown that when their referent does not correspond to the time and/or location of the utterance, `now' and `here' work in an anaphoric way, inheriting their reference from another noun phrase. The latter may be explicit or implicit in the discourse. It is also shown that `now' and `here' can inherit their reference from a presupposed or tacit reference. In that case, they are coreferential with what will be labeled a `tacit initiator'. This anaphoric interpretation has the merit of fitting within the Kaplanian distinction between pure indexicals (`now', `here', `today', etc.) and demonstratives (`this', `that', `she', etc.).     

On ‘what is said to be’

I wish to thank Arnold Koslow and David Rosenthal for helpful comments.     

Estrangement,Nature and ‘the Flesh’

In this paper I address the question of what it is to be alienated from nature. The focus is alienation in the sense of estrangement, a ‘being cut off from’ a wider world. That we are so estranged is a claim associated with ecological critique of contemporary society. But what is it to be estranged from nature given that everything we are, do and produce, always remains within a wider nature? I explore the possibility that this might be understood with reference to Merleau-Ponty’s notion of ‘flesh’. I set the scene for this with some discussion of Honneth’s recent account of reification as a ‘distorted praxis’ and then, drawing upon Merleau-Ponty’s phenomenology of perception and especially his later ontology of flesh, develop the idea of estrangement from the natural world as an inadequate participation in a ‘primordial’ perceptual relation. This idea of estrangement brings together various elements of ecological critique. However, I argue that although this idea of estrangement might inform and help to articulate such a critique, it cannot be the sole concern of an environmental political philosophy: other kinds of alienation within the humanised environmental context need to be considered too.     

On ‘there is’

Philosophical Studies -     

The Crimes and Punishments of the ‘Enemies of the Church’ and the Nature of Russia’s Desecularising Regime1

Following a longstanding sociological tradition, this paper looks at reactions to nonconformity in order to understand the nature of social norms. In particular, it explores the patterns and scope of intolerance towards the perceived ‘enemies of the Church’ in order to understand social norms emerging in post-atheist Russia. Utilising the ‘social drama’ approach, the paper offers a comparative case study of increasingly repressive reactions by the Russian Orthodox Church (ROC) and state to two art exhibitions at the Sakharov Museum and anti-clerical publications by a blogger in Karelia, along with an in-depth analysis of the recent (2012) Pussy Riot action at Christ the Saviour Cathedral in Moscow and the resulting trial and punishment of three of the band’s members, as well as of a variety of events that have followed this initial action. We then utilise national and cross-national representative survey data to suggest that these repressive reactions were congruent with an intolerant public sentiment towards opponents of the ROC. Ultimately, we draw on Durkheim’s dialectic of norm and deviance, work on disciplinary modalities of power by Foucault and Agamben, desecularisation analysis and social identity theory to argue that the severe punishment of the perceived ‘enemies of the Church’ and the popular support for it reflect the crystallisation of a new normative system brought about by the desecularising regime in Russia, a regime which is characterised by a symbiosis of the ROC and the state.     

‘Nature’ and ‘Elementary Nature’ in Phenomenology and Sāṅkhya

Journal of Indian Council of Philosophical Research - This is a comparative study. It is in two parts: ‘nature’ and ‘elementary nature’. ‘Nature (of things)’ as...     

On the Proximity of the Logical and ‘Objective Bayesian’ Interpretations of Probability

In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly similar. Second, I argue that the logical interpretation is not manifestly inferior, at least for the reasons that Williamson offers. I suggest that the key difference between the logical and ‘Objective Bayesian’ views is in the domain of the philosophy of logic; and that the genuine disagreement appears to be over Platonism versus nominalism (within weak psychologism).

---

What is learning? On the nature and merits of a functional definition of learning

Learning has been defined functionally as changes in behavior that result from experience or mechanistically as changes in the organism that result from experience. Both types of definitions are problematic. We define learning as ontogenetic adaptation—that is, as changes in the behavior of an organism that result from regularities in the environment of the organism. This functional definition not only solves the problems of other definitions, but also has important advantages for cognitive learning research.     

On the formation and function of the category ‘religion’ in anarchist writing

Recent works by Asad, McCutcheon and Fitzgerald have sought to call into question the category ‘religion’ in social anthropology and religious studies. The purpose of this essay is to explore the formation and function of the category religion in anarchist writing. Taking the mid‐nineteenth century as a rough point of departure, I demonstrate that the formation and function of religion as a category in anarchist writing reflects wider constructions and imaginings of modernity through which religion emerges as a cipher for thinking about the past. I will argue that the function of the category religion in anarchist writing is to order relations between past and present. Specifically, where ‘anarcho‐modernist’ writing broadly constitutes religion and the past as conditions to be overcome, ‘anarcho‐romanticist’ writing articulates a generalised nostalgia for religion and the past, although it should be noted that religion is rarely dealt with in any systematic way in anarchist writing. I will conclude by suggesting that although anarchist writing is a marginal corpus of literature, the category religion is constituted along similar lines and fulfils similar functions in both anthropological and phenomenological writings on religion.     

On the measurement of priming: What is the correct baseline?

Abstract

We argue, contrary to Ostergaard (this issue), that the baseline for measuring priming effects in “recognition/identification” experiments is correctly estimated by the subjects’ performance with non-primed items. There is no reason to assume, as Ostergaard (this issue) does, that priming that occurs in a single presentation of the target item is qualitatively different from priming that occurs, in the same experimental situation, in two or more presentations, or that empirical findings, such as stochastic independence between recognition and primed identification, are affected by the number of presentations of the target items at study.     

Pascal’s Wager and the Nature of God

This paper argues that Pascal’s formulation of his famous wager argument licenses an inference about God's nature that ultimately vitiates the claim that wagering for God is in one’s rational self-interest. Specifically, it is argued that if we accept Pascal’s premises, then we can infer that the god for whom Pascal encourages us to wager is irrational. But if God is irrational, then the prudentially rational course of action is to refrain from wagering for him.