First-Order Reasoning and Primitive Recursive Natural Number Notations

If the collection of models for the axioms \mathfrakA{\mathfrak{A}} of elementary number theory (Peano arithmetic) is enlarged to include not just the “natural numbers” or their non-standard infinitistic extensions but also what are here called “primitive recursive notations”, questions arise about the reliability of first-order derivations from \mathfrakA{\mathfrak{A}}. In this enlarged set of “models” some derivations usually accepted as “reliable” may be problematic. This paper criticizes two of these derivations which claim, respectively, to establish the totality of exponentiation and to prove Euclid’s theorem about the infinity of primes.     

Primitive Anxieties,Gender Madness,and Perversions of Agency in Eating Disordered Patients: Commentary on Paper by Tom Wooldridge

The following is a discussion of Tom Wooldridge’s (this issue) paper on primitive anxieties in anorexia and his metaphor of the “entropic body” as a false self “body-state” (Petrucelli, 2014) that functions to omnipotently deny dependency. The focus here is on how, for the eating disordered patient, primitive anxieties related to dependency and containment intertwine with the challenges of rapprochement, in which separation, agency, and awareness of sex difference emerge in a traumatic field. This response emphasizes the clinical utility of conceptualizing eating disorders as disorders of a gendered, agentic self. Wooldridge’s clinical material is discussed with a focus on (a) the salience of gendered enactments in work with eating disordered patients and (b) the relationship between experiences of “entropy” in the clinical dyad and the mutual disavowal of gender-inflected identifications and desires.     

Norms and Necessity

Modality presents notorious philosophical problems, including the epistemic problem of how we could come to know modal facts and metaphysical problems about how to place modal facts in the natural world. These problems arise from thinking of modal claims as attempts to describe modal features of this world that explain what makes them true. Here I propose a different view of modal discourse in which talk about what is “metaphysically necessary” does not aim to describe modal features of the world, but, rather, provides a particularly useful way of expressing constitutive semantic and conceptual rules in the object language. The result is a “modal normativist” view that enables us to avoid the epistemic problems of modality and mitigate the metaphysical worries, while also leaving open the possibility of a unified account of the function of modal language. Finally, I address a serious challenge: we have the norms we do in order to track the modal facts of the world, so that the order of explanation must go in the opposite direction. I close by showing how the normativist may answer that challenge.     

Norms and conventions

One can think of the traditional logic of blame as involving three intuitively plausible claims: (1) blame is justified only if one is deserving of blame, (2) one is deserving of blame only if one is relevantly in control of the relevant causal antecedents, and (3) one is relevantly in control only if one has libertarian freedom. While traditional compatibilism has focused on rejecting either or both of the latter two claims, an increasingly common strategy is to deny the link between blame and desert expressed in (1). While I think there is something right about many of these accounts of blame, I deny that the logic of blame can be divorced from the logic of desert. On my view, blame does have a conceptual connection to desert, but its justification is practical rather than theoretical, as the libertarian condition is a matter of adopting a stance towards a person rather than having a belief about her and the “true” causes of her action. I argue that blame fundamentally requires interacting with a person from the participant perspective and that the participant perspective, understood in terms of second-personal address, involves an ontological commitment to freedom.     

Primitive representation and misrepresentation

This paper develops a statistical approach to the problem of primitive representation. Representation of the kind commonly attributed to litmus paper, fuel gauges and tree rings occurs when, so to speak, there is a sufficiently good correlation between two variables. The fundamental distinction between misrepresentation and non-representation is explained in terms of the notion of an informationally useful correlation. The paper further argues that the statistical approach satisfactorily resolves well known puzzles such as Fodor's disjunction problem.     

Belief Norms and Blindspots

I defend the thesis that beliefs are constitutively normative from two kinds of objections. After clarifying what a “blindspot” proposition is and the different types of blindspots there can be, I show that the existence of such propositions does not undermine the thesis that beliefs are essentially governed by a negative truth norm. I argue that the “normative variance” exhibited by this norm is not a defect. I also argue that if we accept a distinction between subjective and objective norms, there need be no worrying tension between doxastic norms of truth and doxastic norms of evidence. I show how a similar approach applies to the attitude of guessing. I then suggest that if we distinguish between practical and theoretical rationality, we will prefer a negative form of norm that does not positively oblige us to form beliefs. I finish by considering an alternative possible subjunctive form of norm that would also avoid problems with blindspots, but I suggest this has a nonintuitive consequence.     

Naturalism and Conceptual Norms

The normative dimensions of concept possession pose a serious problem for naturalistic approaches to the mental. Taking Christopher Peacocke's recent proposal for a naturalistic accommodation of conceptual normativity as a stalking-horse, I argue that no proposal formulated in terms of law-like generalizations about the judgements which a concept possessor must find primitively compelling or self-evident can capture the crucial distinction between failing to possess a concept and misapplying a concept which one does actually possess.     

Agency and obligation

The purpose of this paper is to explore a new deontic operator for representing what an agent ought to do; the operator is cast against the background of a modal treatment of action developed by Nuel Belnap and Michael Perloff, which itself relies on Arthur Prior's indeterministic tense logic. The analysis developed here of what an agent ought to do is based on a dominance ordering adapted from the decision theoretic study of choice under uncertainty to the present account of action. It is shown that this analysis gives rise to a normal deontic operator, and that the result is superior to an analysis that identifies what an agent ought to do with what it ought to be that the agent does.