If someone reports that he had been thinking that he would very much like to seduce his sister, an appropriate comment might be: “Shame on you for having such a nasty idea.” But if one reports that he dreamt he seduced his sister the situation appears quite different, for while we might be repulsed by the dream shaming seems, to say the least, far less appropriate.We do not ordinarily, if ever, say things like, “It was bad of you to dream (...) that.” A child may be sent to bed without supper for saying that he hates his father, but not for reporting a dream which clearly expresses hate for his father. (shrink)

In comments on my “Moral Responsibility for Dreams,” J. F. M. Hunter claims that I fail to see that “‘Dreaming is not an action’ is a grammatical remark, [not an “empirical” one] and as such makes no assertion as to what is or may be the case in our souls, but only about how we may talk about certain psychological goings-on.” Hunter argues that ‘Dreaming is not an action’ is a logical remark in the way that ‘Bachelors are unmarried’ is (...) a logical remark. “It is not something that we notice about dreams, that they happen, as it is not something we notice about bachelors that they have no wives. It is part of the concept of a dream; and no matter what characteristics a phenomenon shares with a dream, such as being experienced while asleep, if it does not happen it is for that reason alone not a dream.”. (shrink)

Are some mental activities rational but unconscious? Psychopathological symptoms, it is said, have a sense — they are seen as compromise-formations which express the intentions of agents even though the agents are totally unaware of bringing about such symptoms. Philosophers, who often claim that such a conception is simply contradictory or incoherent, have shed little light on the puzzles and apparent paradoxes that surround the issue. It is argued here that Freud's two models of explanation — the mechanistic and the (...) intentionalistic — each fail to provide a basis for an explanatory account of the phenomenon of unconscious defense. An examination of the problem of dream composition helps explain why Freud's dependence upon rational homunculi is inappropriate and misleading. Finally, an alternative model which depends neither upon Freud's version of mechanism nor upon his lavish anthropormorphism is suggested.Ladies and Gentlemen, — It was discovered one day that the pathological symptoms of certain neurotic patients have a sense. On this discovery the psychoanalytic method of treatment was founded. It happened in the course of the treament that patients, instead of bringing forward their symptoms, brought forward dreams. A suspicion thus arose that the dreams too had a sense. (shrink)

In “Moral Responsibility for Dreams,” Harvey Mullane maintains that although there is something inappropriate about blaming people for their dreams, this is because we do not have very direct control over our dreams: but although this is the case, it is not the case that we have no control over them. We can work at having the right dreams, or not having the wrong ones, as we can work at blushing and not blushing and at loving our neighbour: and (...) therefore presumably there must be a sense in which or a degree to which we can be responsible for what we dream. There are a number of aspects of this question, and of Mullane's treatment of it, which I would like to explore further. (shrink)

Driven by interests in workforce planning and patient safety, a growing body of literature has begun to identify the reality and the prevalence of missed nursing care, also specified as care left undone, rationed care or unfinished care. Empirical studies and conceptual considerations have focused on structural issues such as staffing, as well as on outcome issues – missed care/unfinished care. Philosophical and ethical aspects of unfinished care are largely unexplored. Thus, while internationally studies highlight instances of covert rationing/missed care/care (...) left undone – suggesting that nurses, in certain contexts, are actively engaged in rationing care – in terms of the nursing and nursing ethics literature, there appears to be a dearth of explicit decision-making frameworks within which to consider rationing of nursing care. In reality, the assumption of policy makers and health service managers is that nurses will continue to provide full care – despite reducing staffing levels and increased patient turnover, dependency and complexity of care. Often, it would appear that rationing/missed care/nursing care left undone is a direct response to overwhelming demands on the nursing resource in specific contexts. A discussion of resource allocation and rationing in nursing therefore seems timely. The aim of this discussion paper is to consider the ethical dimension of issues of resource allocation and rationing as they relate to nursing care and the distribution of the nursing resource. (shrink)

Brown makes elegant use of sociological theory and of insights from language philosophy, literary criticism, and rhetoric to articulate a new theory of the human sciences, using the powerful metaphor of society as text.

We present two studies investigating the impact of causal perceptions and the moral emotions of anger, shame, and guilt on the justification of deviant workplace behavior. Study 1 tests our conceptual framework using a sample of undergraduate business students; Study 2 examines a population of practicing physicians. Results varied significantly between the two samples, suggesting that individual and contextual factors play an important role in shaping the perceptual and emotional processes by which individuals form reactions to undesirable affective workplace events. (...) Implications of these findings for the study of ethics, emotions, and attributions, as well as for promoting ethical behavior, are discussed. (shrink)

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has (...) proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...) The reason is interesting: if PA is slightly weakened to a subtheory P+, it admits the complex ring C as a model; thus QRF is chosen to be a theorem of PA but false in C. Inasmuch as all strictly positive theorems of R# are already theorems of P+, this nonconservativity result shows that QRF is also a nontheorem of R#. As a consequence, Ackermann's rule γ is inadmissible in R#. Accordingly, an extension of R# which retains its good features is desired. The system R##, got by adding an omega-rule, is such an extension. Central question: is there an effectively axiomatizable system intermediate between R# and R##, which does formalize arithmetic on relevant principles, but also admits γ in a natural way? (shrink)

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein. (shrink)

Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.

We now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.

J Harvey; Stereotypes and Group-claims: epistemological and moral issues, and their implications for multi-culturalism in education, Journal of Philosophy of Ed.

In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent.

Most of my intellectual efforts have focused around a single general question in the foundations of mathematics (f.o.m.). I became keenly aware of this question as a student at MIT around 40 years ago, and readily adopted it as the principal driving force behind my research.

David Harvey : On peut difficilement imaginer vérification plus spectaculaire de ce que tu prédis depuis très longtemps dans tes théories que l’actuelle crise du système financier mondial. Y a-t-il des aspects de la crise qui t’ont surpris? Giovanni Arrighi : Ma prédiction était très simple. Dans The Long Twentieth Century, je qualifiais de crise annonciatrice d’un régime d’accumulation le début de la financiarisation et je faisais remarquer qu’après un certain temps – en général environ un demi-siècle – la (...) crise terminale suivait. L’hypothèse fondamentale est que toutes ces expansions financières ne pouvaient pas tenir parce qu’elles amenaient à la spéculation plus de capital qu’il n’était possible d’en gérer – en d’autres termes, ces expansions financières avaient tendance à créer des bulles de différentes sortes. Je prévoyais que cette expansion financière mènerait à une crise terminale parce que, aujourd’hui comme dans le passé, les bulles ne peuvent pas tenir. (shrink)

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, recursion theory, and from the negative solution to Hilbert’s 10th Problem ([3], [1], and [2]).

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...) only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program. (shrink)

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.

We can equivalently present this by the recursion equations f1(n) = 2n, fk+1(1) = fk(1), fk+1(n+1) = fk(fk+1(n)), where k,n ≥ 1. We define A(k,n) = fk(n).

In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.

Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved.

Each of these theorems and concepts arose from very specific considerations of great general interest in the foundations of mathematics (f.o.m.). They each serve well defined purposes in f.o.m. Naturally, the preferred way to formulate them for mathe-matical logicians is in terms that are close to their roots in f.o.m.

We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).

1. Transfer principles from N to On. A. Mahlo cardinals. B. Weakly compact cardinals. C. Ineffable cardinals. D. Ramsey cardinals. E. Ineffably Ramsey cardinals. F. Subtle cardinals. G. From N to (...) 4. Decidability of statements on N. 5. Decidability of statements on shrink)

Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.

NOTE: This is an expanded version of my lecture at the special session on reverse mathematics, delivered at the Special Session on Reverse Mathematics held at the Atlanta AMS meeting, on January 6, 2005.

I'm Brian Harvey; I'm a Lecturer with Security of Employment in the EECS Department at the University of California at Berkeley. My main teaching assignment is our first course for CS majors, based on the Abelson and Sussman text from MIT. But I also teach "Social Implications of Computers," a course that was retired along with the professor who first taught it, and that I campaigned unsuccessfully to revive for several years until ABET, our accrediting agency, won the battle (...) for me by complaining about the lack of ethics in our curriculum. (shrink)

Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.