One-dimensional F-definable sets in F((t))

We study definable sets in power series fields with perfect residue fields. We show that certain `one-dimensional' definable sets are in fact existentially definable. This allows us to apply results from previous work about existentially definable sets to one-dimensional definable sets. More precisely, let $F$ be a perfect field and let a be a tuple from $F((t))$ of transcendence degree 1 over $F$. Using the description of $F$-automorphisms of $F((t))$ given by Schilling, we show that the orbit of a under $F$-automorphisms is existentially definable in the ring language with parameters from $F(t)$. We deduce the following corollary. Let $X$ be an $F$-definable subset of $F((t))$ which is not contained in $F$, then the subfield generated by $X$ is equal to $F((t^{p^n}))$, for some $n<\omega$.Comment: 11 page

Anscombe on Acting for Reasons

This chapter discusses some of Anscombe’s contributions to the philosophy of practical reason. It focuses particularly on Anscombe’s view of what it is to act for reasons. I begin by discussing the relationship between acting intentionally and acting for reasons in Anscombe's theory of action. I then further explicate her view by discussing her rejection of two related views about acting for reasons: causalism (the view that reasons are a kind of cause of actions) and psychologism (the view that reasons are mental states like desires and beliefs). In the process, I try to show that Anscombe’s rejection of these theses does not leave us with mystery, but rather sheds light on an interesting and serious heterodox view of acting for reasons. I conclude by suggesting that though Anscombe's views have been taken sufficiently seriously by philosophers of action, they should be taken more seriously by philosophers of practical reason

Revealed Unawareness

I develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the Anscombe-Aumann approach to subjective expected utility. I observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, I characterize "impersonal" expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. I discuss in what sense impersonal expected utility can not represent unawareness.Unawareness, awareness, unforeseen contingencies, null, zero probability, subjective expected utility, Anscombe-Aumann, small worlds, extensionality of acts, event exchangeability

Anscombe on the mesmeric force of ‘ought’ and a spurious kind of moral realism

I discuss the second of the three theses advanced by Anscombe in ‘Modern Moral Philosophy’. The focus is the nature of entities to which – if Anscombe’s diagnosis is correct – ought and cognate modals are assumed by modern moral philosophers to refer. I reconstruct the alternative account offered by Anscombe of viable and justified ‘Aristotelian’ modals – as contrasted with mysterious and unjustified ‘Kantian’ modals; I discuss the nature and status of ‘Aristotelian necessity’ to which such legitimate modals refer to. I conclude with the claims that Anscombe’s account of modern moral philosophy is viciously parochial, reducing it to Oxford philosophy from the Thirties and Forties and its immediate antecedents; that her historical reconstruction is vitiated by lack of awareness of the existence of law-views of morality preceding Christian theology, artful anticipation of secularization in order to fit her picture of modern moral philosophy as the ‘day after’ of Christianity; that Aquinas’s and her own view of natural morality as made of rational moral judgments laws is incompatible with both her predilection for ‘divine law’ instead of plain down-to-earth ‘natural law’; that her strained reconstruction of a Christian-Jewish-Stoic view of morality as law promulgated by God has little to share with any reconstruction of the Biblical moral traditions meeting academic standard and in more detail there is no possible translation of Torah as Law; and that her criticism hits just targets from the old little British world she was familiar with, while leaving Kantian ethics unaffected

Decision under Uncertainty : the Classical Models

This chapiter of a collective book is dedicated to classical decision models under uncertainty, i.e. under situations where events do not have "objective" probabilities with which the Decision Marker agrees. We present successively the two main theories, their axiomatic, the interpretation and the justification of their axioms and their main properties : first, the general model of Subjective Expected Utility due to Savage (Savage, 1954), second, the Anscombe-Aumann (1963) theory, in a different framework. Both theories enforce the universal use of a probabilistic representation. We then discuss this issue in connection with the experimental result known as the Ellsberg paradox.Uncertainty, subjective probability, Subjective Expected Utility, Savage, Anscombe and Aumann, Ellsberg paradox.

The Philosophical Significance of Wittgenstein’s Experiments on Rhythm, Cambridge 1912–13

Wittgenstein’s experiments on rhythm, conducted in Charles Myers’s laboratory in Cambridge during the years 1912–13, are his earliest recorded engagement in thinking about music, not just appreciating it, and philosophizing by means of musical thinking. In this essay, I set these experiments within their appropriate intellectual, scientific, and philosophical context in order to show that, its minor scientific importance notwithstanding, this onetime excursion into empirical research provided an early onset for Wittgenstein’s career-long exploration of the philosophically pervasive implications of aspects. Dramatically moving beyond the conceptual limitations, which were inscribed by Charles Myers’s scientific program, Wittgenstein got a glimpse of a philosophical angle, which was bound to become very important to him not only in aesthetics, but also for his overarching philosophical development. He became interested in what we actually do when we re-phrase, compare, come up with good similes in order to illuminate something definite within the space of possibility, so a new aspect may come to life

Representación y conocimiento práctico

Se toman como referencia los escritos de Elizabeth Anscombe para aclarar el estatuto epistemológico de la intención, así como la relación que ésta guarda con la acción.This article explores the epistemological status of intention and its relation to human action in Elizabeth Anscombe. Central to our analysis is the notion of practical knowledge, which let us overcome a mere causalist theory of action

Awareness-Dependent Subjective Expected Utility

We develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2011a) as primitives in the Anscombe-Aumann approach to subjective expected utility. We observe that a decision maker is unaware of an event if and only if her choices reveal that the event is ``null'' and the negation of the event is ``null''. Moreover, we characterize ``impersonal'' expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. We discuss in what sense probability zero can model unawareness.unawareness, awareness, unforeseen contingencies, null, probability zero, subjective probability, Anscombe-Aumann, small worlds