Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I address the value of Ulrich et al.’s distinction between three types of second-order models. I conclude that their work contributes to the theorizing of adaptive teaching on the basis of a constructivist stance on knowing and learning.

R. S. Woolhouse; IV*—Leibniz's Reaction to Cartesian Interaction, Proceedings of the Aristotelian Society, Volume 86, Issue 1, 1 June 1986, Pages 69–82, https:/.

A comparative study of business related values among business students was conducted over the last 10 years in two neighbouring countries. Although Estonia and Finland are culturally related, according to an empirical study of managerial values, including the ethical values of business students, the two countries display significant differences. During the last decade, Estonia has changed from being a country characterised by an authoritarian, centralized, totalitarian state socialism, to a democratic country with a free market economy and different attitudes and (...) values. At the same time Finland has experienced almost a century of capitalism and democracy. It is argued that the differences in values exhibited by these two countries could be explained by using the institutional and historical context. The authors propose a model of value hierarchies in relation to institutionalism. (shrink)

Comments on:Charles T. Mathewes, Agency, Nature, Transcendence, and Moralism: A Review of Recent Work in Moral Psychology.

This chapter considers the ‘hosting question’ of how immanent universals, in contrast to transcendent universals, are ‘brought down to earth’ from ‘Plato’s heaven’. It explores the thesis that the hosting amounts to their being constituents of the states of affairs that result from their instantiations. These states of affairs are concrete complexes consisting of particulars and universals, and perhaps something that links them together. The traditional view that immanent universals are concrete is briefly defended against a recent prominent objection. On (...) relationalism, states of affairs are unified by a relation of some sort; on non-relationalism they are unified non-relationally. Roughly, these two conceptions of states of affairs are equivalent to Armstrong’s relational and non-relational versions of immanent realism, respectively. Armstrong mostly criticises the former and defends the latter. It is argued, however, that relationalism, at least potentially, answers the hosting question, whereas non-relationalism realism does not. (shrink)

This essay is one of ten contributions to a special editorial feature in The Journal of Nietzsche Studies 49.2, in which authors were invited to address the following questions: What is the future of Nietzsche studies? What are the most pressing questions its scholars should address? What texts and issues demand our urgent attention? And as we turn to these issues, what methodological and interpretive principles should guide us? The editorship hopes this collection will provide a starting point for discussions (...) about the most fruitful directions for Nietzsche scholarship to take and the most promising avenues for building on the best recent work. (shrink)

We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that FML has (...) the maximal expressive power among the logics extending FML which satisfy compactness, bisimulation invariance and the Tarski union property. (shrink)

The Oregon Basic Health Services Act of 1989 seeks to establish universal access to basic medical care for all currently uninsured Oregon residents. To control the increasing cost of medical care, the Oregon plan will restrict funding according to a priority list of medical interventions. The basic level of medical care provided to residents with incomes below the federal poverty line will vary according to the funds made available by the Oregon legislature. A rationing plan such as Oregon's which potentially (...) excludes medically necessary procedures from the basic level of health care may be just, for the right to publically-sponsored medical care is restricted by opposing rights of private property. However, the moral acceptability of the Oregon plan cannot be determined in the absence of knowing the level of resources to be provided. Finally, Oregon to date has failed to include the individuals being rationed in discussions as to how the scarce resources are to be distributed. (shrink)

In a recent paper, I argue that Perky’s famous experiments do not show what they are often taken to show. Bence Nanay has criticised my argument on two grounds. I argue against both his lines of objection.

The old question whether or no the doctrine of ‘intermediate mathematical objects’ ascribed to Plato by Aristotle is to be found in the Divided Line of Republic vi, has been recently raised again in a careful and lucid discussion by Mr. W. F. R. Hardie. I may clear the ground by saying at once that I agree with that part of Mr. Hardie's chapter which deals with those criticisms of the traditional view that have been put forward by Prof. Ferguson (...) and the late Prof. Stocks; nevertheless I do not believe that the objects of the third segment are intermediate between Forms and Sensibles: I propose to argue that they, like the objects of the highest segment, are Forms. (shrink)

I am idebted to members of the Wellington Logic Seminar for useful discussions of work of which this essay forms part, in particular to M. J. Cresswell for comments in the earlier stages of the investigation and to R. I. Goldblatt who suggested the definition ofB infD supu and made numerous other suggestions.

Death, violent or otherwise, is a matter of widespread concern with ongoing debates about such matters as euthanasia and the nature of brain death. Philosophers have often argued about the rationality of fear of death. This book argues that that dispute has been misconceived: fear of death is not something that follows or fails to follow from reason, but rather, it forms the basis of reasoning and helps to show why people must be cooperating beings who accept certain sorts of (...) facts as reasons for acting. Within the context of this account of reasons, the book gives a new understanding of brain death and of physician-assisted suicide. (shrink)

An algebraic semantics, based on factor algebras, for one-way and two-way implicative verbs is proposed. Implicative verbs denote elements of filters or of ideals generated by identity functions in factor algebras. This semantics explains in particular the problem of implicational equivalence raised by two-way implicative verbs, and shows that the negation necessary to establish the implicativity of these verbs is the negation which preserves the presuppositions of sentences with implicative verbs. In addition, it follows from the proposed semantics that any (...) two implicative verbs denoting in the same algebra but belonging to different categories, are semantically related. (shrink)

It may be hard to imagine how bullshit, or being strategically indifferent to the veracity of one’s assertions, might ever be morally permissible. Yet to categorically denounce it is to find oneself burdened with defending the impossibility of justifiable bullshit, the indefeasibility of truthfulness and the inculpability of inveterate bullshitters. A much more tenable position is to expand one’s notion of bullshit to include unintentional indifference to veracity while also characterizing bullshit (whether strategic or unintentional) as wrong only when it (...) constitutes negligence. Once bullshit is redefined in this fashion it becomes apparent that its preponderance in contemporary society is the work not of those who bullshit intentionally, but of those who uncritically consume and transmit the bullshit of others. Any attempt to disrupt the spread of negligent bullshit thus does well to consider our epistemic obligations not only as perceived experts, but as listeners. It is in this respect that the early Indian Buddhist critique of testimony proves quite helpful in reducing gullibility and, thereby, the likelihood of unintentional, yet negligent, bullshit. (shrink)

When engaging with magic, we are moved by seemingly impossible events that contradict what we believe to be possible in the real world. We are surprised, curious, and baffled when we cannot explain how the magic we are witnessing is possible. We generally understand the events to be illusions. But how is it possible to be moved by something we know to be unreal? This problem is related to the paradox of fiction in aesthetics. Here, we introduce the problem in (...) the domain of theatrical magic, discuss possible solutions, and present a tentative account that allows us to accommodate inconsistent, seemingly incompatible beliefs at different representational levels in the viewers’ mind. (shrink)

The article studies two related issues. First, it introduces the notion of the contraposition of quantifiers which is a “dual” notion of symmetry and has similar relations to co-intersectivity as symmetry has to intersectivity. Second, it shows how symmetry and contraposition can be generalised to higher order type quantifiers, while preserving their relations with other notions from generalized quantifiers theory.

The theoretical framework adopted in the exact sciences, for constructing and testing deterministic theories on the one hand, and modelling and analysis of observed phenomena on the other, is often implicitly assumed to be that of structural stability. In view of recent developments in nonlinear dynamics, it is argued here that in general it may not be possible to assume strict determinism and structural stability simultaneously; either strict determinism holds, in which case the fragility framework may turn out to be (...) the appropriate framework for the study of certain phenomena in the exact sciences, or ‘structural stability’ is restored at the expense of introducing stochasticity. In this sense a certain degree of indeterminacy may be unavoidable even at the classical level. (shrink)

The complete, or almost complete, absence from the Theaetetus of any unequivocal reference to Platonic Forms is a problem, the solution of which appeared to many scholars to have been found and convincingly presented in the late Professor Gornford's book Plato's Theory of Knowledge, published in 1935. Put briefly, his contention was that the main purpose of the dialogue is to show that no acceptable definition of knowledge can be reached if the Forms are left out of account, that there (...) are a number of passages in which any reader of the middle dialogues would see that they were deliberately being left out of account, and one or two, namely in the famous digression on the philosophic life, and in the discussion of ‘common terms’ , where they are actually brought in, though not indeed under the name of. (shrink)