By $\mathfrak{B}_2$ we denote the $\sigma$-ideal of all subsets $A$ of the Cantor set $\{0,1\}^\omega$ such that for every infinite subset $T$ of $\omega$ the restriction $A\mid\{0,1\}^T$ is a proper subset of $\{0,1\}^T$. In this paper we investigate set theoretical properties of this and similar ideals.

By B2 we denote the σ-ideal of all subsets A of the Cantor set {0,1}ω such that for every infinite subset T of ω the restriction A∣{0,1}T is a proper subset of {0,1}T. In this paper we investigate set theoretical properties of this and similar ideals.

The main result of this paper is that if κ is not a weakly Mahlo cardinal, then the following two conditions are equivalent: 1. P(κ)/ J is κ+-complete. 2. J is a prenormal ideal. Our result is a generalization of an announcement made in [Z]. We say that J is selective iff for every J-function f: κ → κ there is a set X ∈ J such that f∣(κ - X) is one-to-one. Our theorem provides a positive partial answer to (...) a question of B. Weglorz from [BTW, p. 90], viz.: is every selective ideal J, with P(κ)/J κ+-complete, isomorphic to a normal ideal? The theorem is also true for fine ideals on $\lbrack\lambda\rbrack^{<\kappa}$ for any κ ≤ λ, i.e. if κ is not a weakly Mahlo cardinal then the Boolean algebra $\mathscr{P} (\lbrack\lambda\rbrack^{<\kappa})/\mathscr{J}$ is λ+-complete iff J is a prenormal ideal (in the sense of $\lbrack\lambda\rbrack^{<\kappa})$. (shrink)

The main result of this paper is that if $\kappa$ is not a weakly Mahlo cardinal, then the following two conditions are equivalent: 1. $\mathscr{P}(\kappa)/ \mathscr{J}$ is $\kappa^+$-complete. 2. $\mathscr{J}$ is a prenormal ideal. Our result is a generalization of an announcement made in [Z]. We say that $\mathscr{J}$ is selective iff for every $\mathscr{J}$-function $f: \kappa \rightarrow \kappa$ there is a set $X \in \mathscr{J}$ such that $f\mid(\kappa - X)$ is one-to-one. Our theorem provides a positive partial answer to (...) a question of B. Weglorz from [BTW, p. 90], viz.: is every selective ideal $\mathscr{J}$, with $\mathscr{P}(\kappa)/\mathscr{J} \kappa^+$-complete, isomorphic to a normal ideal? The theorem is also true for fine ideals on $\lbrack\lambda\rbrack^{<\kappa}$ for any $\kappa \leq \lambda$, i.e. if $\kappa$ is not a weakly Mahlo cardinal then the Boolean algebra $\mathscr{P} (\lbrack\lambda\rbrack^{<\kappa})/\mathscr{J}$ is $\lambda^+$-complete iff $\mathscr{J}$ is a prenormal ideal (in the sense of $\lbrack\lambda\rbrack^{<\kappa})$. (shrink)

It is common to account for our senses on the basis of our sensory organs. One way of glossing why Aristotle famously counted five senses—and why his count became common sense in the West and elsewhere—is because there are five rather obvious organs of sense. In more modern accounts, this organ criterion of the senses has transformed into a neurobiological criterion; that is to say, part of what it means to be a sense is to have an associated organ with (...) appropriate physiological properties. For example, part of the claim that humans have a sense of vision is that we have a non-vestigial organ (the eye) that has cells (photoreceptors) especially sensitive to the properties of electromagnetic radiation. However, the nature of this “organ criterion” is a point of some contention. Is it a sufficient criterion? Necessary? To be called “vision” need the organ mediating it give rise to “visual experiences”? This chapter will consider the neurobiological criterion as it was originally presented in Aristotle and later reconceptualized in 19th-century neurophysiologist Johannes Müller’s “Law of Specific Nerve Energies.” By understanding the role of neurobiology in these accounts, we will be able to explore the deficiencies of contemporary accounts that downplay neurobiology in differentiating the senses. We will consider one of these accounts in detail: Alva Noë’s recent arguments in favor of an enactive approach to perceptual psychology. (shrink)

In 2004 Orlando Florida was hit with an almost unprecedented series of storms and hurricanes. Within two months, Hurricanes Charley, Frances, and Jeanne hit, and Hurricane Ivan made a near miss. Billions of dollars of damage resulted from these disasters, and several dozen lives were lost. It is tempting, in the case of extreme events, to either regard them as having no need of interpretation (that is, as simply given, material events shared by everyone), or as a kind of rare (...) window on the workings of a community.1 In this paper I want to examine the public construction of the meaning of the hurricane in Orlando, particularly as represented in reports at the time in the major newspaper, the Orlando Sentinel. I am especially interested in placemaking, that is, the ways in which places gain or fail to gain meaning in times of stress. I will suggest that opportunities for place-making were lost in Orlando because of the frame the events around Hurricane Charley were given. Hurricane Frances, though, was treated differently in the Orlando press, and the discourse around the hurricanes of 2004 provides a contrast to the kind of rhetorical response that circulated during the disastrous hurricane season of 2005. In the case of some disasters, community is reinforced, and the skills of place-making are exercised. The reaction to Hurricane Charley in Orlando, on the other hand, tended not to reinforce community, and tended not to contribute to place-making. While it is extremely difficult to measure sense of place or sense of community quantitatively, it is possible to make sense out of the interpretive tools people have at their disposal in a disaster. What comes out of all this, I think, is something I want to call “place-making imagination”. This is analogous to the 1 concept of “moral imagination” in ethics (Johnson). Our moral options extend as far as our imagination will allow. A person might boil the moral universe down to polarized options – fight or flight, kill or be killed, choose A or B – when in fact a more cultivated and aware imagination may have afforded other options, perhaps better ones than either polarized one.. (shrink)

In the paper I offer a brief sketch of one of the sources of utilitarianism. Our biological ancestry is a matter of fact that is not altered by the way we describe ourselves. With philosophical theories it is otherwise. Utilitarianism can be described in ways that make it look as if it is as old as moral philosophy – as J. S. Mill thought it was. For my historical purposes, it is more useful to have an account that brings out (...) what is specific about Benthamism and its descendants. Let us try to make do with the following. First, utilitarianism asserts that the fundamental requirement of morality is that we are to maximize good, for everyone and not just for the agent. This basic principle presupposes that it makes sense to think of aggregating goods to make a total, and of comparing amounts of good thus aggregated. Second, the good to be brought about is located in feelings of pleasure, and the evil to be avoided in feelings of pain. These feelings have inherent value or disvalue regardless of how they are caused to exist and regardless of their own consequences. Third, all moral principles can be derived from the requirement that good be maximized. The principles involved in evaluating agents as well as in giving moral direction to action are nothing but applications of the basic principle. (shrink)