Forcing with [κ] κ over a model of set theory with a strong partition cardinal, M. Spector produced a generic ultrafilter G on κ such that κ κ /G is not well-founded. Theorem. Let G be Spector-generic over a model M of $ZF + DC + \kappa \rightarrow (\kappa)^\kappa_\alpha, \kappa > \omega$ , for all $\alpha . 1) Every cardinal (well-ordered or not) of M is a cardinal of M[ G]. 2) If A ∈ M[ G] is a well-ordered subset (...) of M, then A ∈ M. Let Φ = κ κ /G. 3) There is an ultrafilter U on Φ such that every member of U has a subset of type Φ, and the intersection of any well-ordered subset of U is in U. 4) Φ satisfies Φ → (Φ) α β for all $\alpha and all ordinals β. 5) There is a linear order Φ' with property 3) above which is not "weakly compact", i.e., $\Phi' \nrightarrow (\Phi')^2$. (shrink)

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.

Potential ethical issues can arise during the process of epidemiological classification. For example, unnatural infant deaths are classified as accidental deaths or homicides. Societal sensitivity to the physical abuse and neglect of children has increased over recent decades. This enhanced sensitivity could impact reported infant homicide rates. Infant homicide and accident mortality rates in boys and girls in the USA from 1940 to 2005 were analysed. In 1940, infant accident mortality rates were over 20 times greater than infant homicide rates (...) in both boys and girls. After about 1980, when the ratio of infant accident mortality rates to infant homicide rates decreased to less than five, and the sum of infant accident and homicide rates became relatively constant, further decreases in infant accident mortality rates were associated with increases in reported infant homicide rates. These findings suggest that the dramatic decline of accidental infant mortality and recent increased societal sensitivity to child abuse may be related to the increased infant homicide rates observed in the USA since 1980 rather than an actual increase in societal violence directed against infants. Ethical consequences of epidemiological classification, involving the principles of beneficence, non-maleficence and justice, are suggested by observed patterns in infant accidental deaths and homicides in the USA from 1940 to 2005. (shrink)

The phenomena of perception have been used by philosophers to kindle and fuel doubts about the reality of ‘the external world’, a phrase which points roughly in the direction of our natural environment. After grappling with problems, which trade under this title, one often discovers that the issues have less to do with the reality of anything which might be called ‘the external world’ and more to do with the reality of the problems themselves. In this paper I propose to (...) examine three approaches to what might deserve to be labelled, ‘problems about theexternal world’. (shrink)

The phenomena of perception have been used by philosophers to kindle and fuel doubts about the reality of ‘the external world’, a phrase which points roughly in the direction of our natural environment. After grappling with problems, which trade under this title, one often discovers that the issues have less to do with the reality of anything which might be called ‘the external world’ and more to do with the reality of the problems themselves. In this paper I propose to (...) examine three approaches to what might deserve to be labelled, ‘problems about theexternal world’. (shrink)

Limits to Action: The Allocation of Individual Behavior presents the ideas and methods in the study of how individual organisms allocate their limited time and energy and the consequences of such allocation. The book is a survey of individual resource allocation, emphasizing the relationships of the concepts of utility, reinforcement, and Darwinian fitness. The chapters are arranged beginning with plants and general evolutionary considerations, through animal behavior in nature and laboratory, and ending with human behavior in suburb and institution. Topics (...) discussed include operant conditioning; the principle of diminishing returns; and issues in relation to mating strategies. Biologists, sociologists, economists, and psychologists will find the book interesting. (shrink)

The paper "Partitions of Products" [DiPH] investigated the polarized partition relation $\begin{pmatrix}\omega\\\omega\\\omega\\\vdots\end{pmatrix} \rightarrow \begin{pmatrix}\alpha_1\\\alpha_1\\\alpha_2\\\vdots \end{pmatrix}$ The relation is consistent relative to an inaccessible cardinal if every α i is finite, but inconsistent if two are infinite. We show here that it consistent (relative to an inaccessible) for one to be infinite. Along the way, we prove an interesting proposition from ZFC concerning partitions of the finite subsets of ω.

What are physical quantities, and in particular, what makes them quantitative? This book presents an original answer to this question through the novel position of substantival structuralism, arguing that quantitativeness is an irreducible feature of attributes, and quantitative attributes are best understood as substantival structured spaces.

Analogies must be symmetric. If a is like b, then b is like a. So if a has property R, and if R is within the scope of the analogy, then b (probably) has R. However, analogical arguments generally single out, or depend upon, only one of a or b to serve as the basis for the inference. In this respect, analogical arguments are directed by an asymmetry. I defend the importance of this neglected – even when explicitly mentioned – (...) feature in understanding analogical arguments. (shrink)

Manuscript Add. 3965, section 13, folios 541r–542r and 545r–546r is in the Portsmouth Collection of manuscripts and housed in the University Library, Cambridge. These drafts contain a careful account, in Newton's hand, of his views on place, time, and God. They are part of a large number of drafts relating to the three official editions of the Principia published in Newton's lifetime.

'To think often, and never to retain it so much as one moment, is a very useless sort of thinking' In An Essay concerning Human Understanding, John Locke sets out his theory of knowledge and how we acquire it. Eschewing doctrines of innate principles and ideas, Locke shows how all our ideas, even the most abstract and complex, are grounded in human experience and attained by sensation of external things or reflection upon our own mental activities. A thorough examination of (...) the communication of ideas through language and the conventions of taking words as signs of ideas paves the way for his penetrating critique of the limitations of ideas and the extent of our knowledge of ourselves, the world, God, and morals. Locke's masterpiece laid the foundation of British empiricism and is of enduring interest to anyone exploring the development of philosophical thought. This sensitive abridgement uses P. H. Nidditch's authoritative text, and together with an illuminating introduction and other features, makes Locke's arguments more accessible. (shrink)

: This article is concerned with Newton's appropriation of Descartes' ontology of true and immutable natures in developing his theory of infinitely extended space. It contends that unless the part played by the Platonic distinction between "being a nature" and "having a nature" in Newton's thinking is properly appreciated the foundation of his doctrine of space in relation to God will not be fully understood. It also contends that Newton's Platonism is consistent with his empiricism once the mediating role is (...) made clear that the geometry of moving loci play in grounding his intuitions concerning infinite natures. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.