This volume collects P. M. S. Hacker's papers on Wittgenstein and related themes written over the last decade. Hacker provides comparative studies of a range of topics--including Wittgenstein's philosophy of psychology, conception of grammar, and treatment of intentionality--and defends his own Wittgensteinian conception of philosophy.

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: Allxareyand Somexarey, There are at least as manyxasy, and There are morexthany. Herexandyrange over subsets (not elements) of a giveninfiniteset. Moreover,xandymay appear complemented (i.e., as$\bar{x}$and$\bar{y}$), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness (...) theorem. There are efficient algorithms for proof search and model construction. (shrink)

This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So in addition to assertions like All x are y and Some x are y, we also have There are at least as many x as y, and There are more x than y. Our work also allows all nouns to be complemented. We thus obtain sentences equivalent to No x are y and At least half of the universe are x. (...) We work on finite models exclusively. We formulate a syllogistic logic for our language. The main result is a soundness/completeness theorem. The logic has a rule of ex falso quodlibet, and reductio ad absurdum is admissible. There are efficient algorithms for proof search and model construction, and the logic has been implemented. (shrink)

Volume 32, Issue 3, May 2024, Page 693-697.

This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares of (...) opposition respectively. We clarify the differences between these two cubes, and discuss their gradual extensions, as well as the one of the hexagon when vertices are no longer two-valued. The second part of the paper is dedicated to the use of these structures of opposition for discussing the comparison of two items. Comparing two items usually involves a set of relevant attributes whose values are compared, and may be expressed in terms of different modalities such as identity, similarity, difference, opposition, analogy. Recently, J.-Y. Béziau has proposed an “analogical hexagon” that organizes the relations linking these modalities. Elementary comparisons may be a matter of degree, attributes may not have the same importance. The paper studies in which ways the structure of the hexagon may be preserved in such gradual extensions. As another illustration of the graded hexagon, we start with the hexagon of equality and inequality due to R. Blanché and extend it with fuzzy equality and fuzzy inequality. Besides, the cube induced by a tetra-partition can account for the comparison of two items in terms of preference, reversed preference, indifference and non-comparability even if these notions are a matter of degree. The other cube, which organizes the relations between the different weighted qualitative aggregation modes, is more relevant for the attribute-based comparison of items in terms of similarity. (shrink)

Many people think that if you're uncertain about which moral theory is correct, you ought to maximize the expected choice-worthiness of your actions. This idea presupposes that the strengths of our moral reasons are comparable across theories – for instance, that our reasons to create new people, according to total utilitarianism, can be stronger than our reasons to benefit an existing person, according to a person-affecting view. But how can we make sense of such comparisons? In this article, I (...) introduce a constructivist account of intertheoretic comparisons. On this account, such comparisons don't hold independently of facts about morally uncertain agents. They're simply the result of an ideal deliberation in terms of certain epistemic norms about what you ought to do in light of your uncertainty. If I'm right, this account is metaphysically more parsimonious than some existing proposals, and yet has plausible and strong implications. (shrink)

This paper builds upon, but substantially revises, John Harsanyi's concept of ‘extended preferences’. An individual ‘history’ is a possible life that some person (a subject) might lead. Harsanyi supposes that a given spectator, formulating her ethical preferences, can rank histories by empathetic projection: putting herself ‘in the shoes’ of various subjects. Harsanyi then suggests that interpersonal comparisons be derived from the utility function representing spectators’ (supposedly common) ranking of history lotteries. Unfortunately, Harsanyi's proposal has various flaws, including some that (...) have hitherto escaped scholarly attention. In particular, it ignores the limits of personal identity. If the subject has welfare-relevant attributes that the spectator cannot acquire without changing who she is, full empathetic identification of the latter with the former becomes impossible. This paper proposes instead to usesympathyas the attitude on a spectator's part that allows us to make sense of her extended preferences. Sympathy – an attitude of care and concern – is a psychological state quite different from empathy. We should also allow for hetereogeneity in spectators’ extended preferences. Interpersonal comparisons emerge from a plurality of sympathetic spectators, not (as per Harsanyi) from a common empathetic ranking. (shrink)

In “Slowing the slide down the slippery slope of Medical Assistance in Dying: Mutual Learnings for Canada and the US,” Daryl Pullman (2023) gets a variety of empirical, logical and legal things wro...

As a powerful tool in the production of knowledge, comparing plays a crucial part in the sciences and the humanities. This volume explores the relationship between comparing and narrating in epistemic practices and clarifies the ways in which narratives enable or impede practices of comparing. It takes into account related activities, such as measuring and classifying, modeling, establishing norms and categories, as well as organizing and popularizing knowledge, to analyze the ambivalent relationship between narratives, scientific explanation, and understanding. The contributions (...) bring out the epistemic role of narratives, and elucidate how narratives are connected to comparisons and scientific explanations."--Publisher description. (shrink)

This paper explores some of the basic similarities and differences between fault-based and no-fault systems of automobile accident insurance from the perspective of a U.S. state and the laws of Macedonia. The majorities of U.S. states have adopted an at-fault system of compensation and therefore share more similarities with Macedonia than the laws of a dozen U.S. states that have adopted a no-fault system. Whereas Macedonia employs a system of nearly universal health care, such is not the case in the (...) United States. The respective states have adopted either a fault-based system or a no-fault system, but in either case issues of coverage for automobile accidents is more complicated for the lack of a nationalized health care system that at minimum acts as a safety net for treatment of injuries related to automobile accidents. It is posited that complications relating to the lack of universal health care coverage in the United States has led to significantly heightened regulatory intervention by the several states such that the similarities between the free-market approach of the states and of civil law (code) systems are greater than the differences. The paper is not based on empirical data of the legal systems or the medical systems, nor is the undeniable interrelation between a medical system and the corresponding legal system with regard to insurance coverage of primarily health-based issues considered other than to highlight how both may play a part in regulation of the automobile accident insurance industry in light the involvement of public health, safety and welfare. (shrink)

The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≥ on events that does not preclude a probabilistic interpretation, in the sense that ≥ has extensions that are probabilistically representable, we characterize the extension ≥+ of ≥ that is exactly the intersection of all probabilistically representable (...) extensions of ≥. This extension ≥+ gives us all the additional comparisons that we are entitled to infer from ≥, based on the assumption that there is some probability measure of which ≥ gives us partial qualitative information. We pay special attention to the problem of extending an order on states to an order on events. In addition to the probabilistic interpretation, this problem has a more general interpretation involving measurement of any additive quantity: e.g., given comparisons between the weights of individual objects, what comparisons between the weights of groups of objects can we infer? (shrink)

When social scientists began employing evolutionary game theory (EGT) in their disciplines, the question arose what the appropriate interpretation of the formal EGT framework would be. Social scientists have given different answer, of which I distinguish three basic kinds. I then proceed to uncover the conceptual tension between the formal framework of EGT, its application in the social sciences, and these three interpretations. First, I argue that EGT under the biological interpretation has a limited application in the social sciences, chiefly (...) because strategy replication often cannot be sensibly interpreted as strategy bearer reproduction in this domain. Second, I show that alternative replication mechanisms imply interpersonal comparability of strategy payoffs. Giving a meaningful interpretation to such comparisons is not an easy task for many social situations, and thus limits the applicability of EGT in this domain. Third, I argue that giving a new interpretation both to strategy replication and selection solves the issue of interpersonal comparability, but at the costs of making the new interpretation incompatible with natural selection interpretations of EGT. To the extent that social scientists seek such a natural selection interpretation, they face a dilemma: either face the challenge that interpersonal comparisons pose, or give up on the natural selection interpretation. By identifying these tensions, my analysis pleas for greater awareness of the specific purposes of EGT modelling in the social sciences, and for greater sensitivity to the underlying microstructure on which the evolutionary dynamics and other EGT solution concepts supervene. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...) the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)

The primary purpose of this paper is to analyze the relationship between the familiar non-Archimedean field of hyperreals from Abraham Robinson’s nonstandard analysis and Paolo Giordano’s ring extension of the real numbers containing nilpotents. There is an interesting nontrivial homomorphism from the limited hyperreals into the Giordano ring, whereas the only nontrivial homomorphism from the Giordano ring to the hyperreals is the standard part function, namely, the function that maps a value to its real part. We interpret this asymmetry to (...) mean that the nilpotent infinitesimal values of Giordano’s ring are “smaller” than the hyperreal infinitesimals. By viewing things from the “point of view” of the hyperreals, all nilpotents are zero, whereas by viewing things from the “point of view” of Giordano’s ring, nonnilpotent, nonzero infinitesimals register as nonzero infinitesimals. This suggests that Giordano’s infinitesimals are more fine-grained. (shrink)

We present a compositionally transparent, unified semantic analysis of two kinds of so…wie-equative constructions in German, namely degree equatives and property equatives in the domain of individuals or events. Unlike in English and many other European languages (Haspelmath & Buchholz 1998, Rett 2013), both equative types in German feature the parameter marker so, suggesting a unified analysis. We show that the parallel formal expression of German degree and property equatives is accompanied by a parallel syntactic distribution (in predicative, attributive, and (...) adverbial position), and by identical semantic properties: Both equative types allow for scope ambiguities, show negative island effects out of context, and license the negative polarity item überhaupt ‘at all’ in the complement clause. As the same properties are also shared by German comparatives, we adopt the influential quantificational analysis of comparatives in von Stechow (1984ab), Heim (1985, 2001, 2007), and Beck (2011), and treat both German equative types in a uniform manner as expressing universal quantification over sets of degrees or over sets of properties (of individuals or events). Conceptually, the uniform marking of degree-related and property-related meanings is expected given that the abstract semantic category degree (type $d$) can be reconstructed in terms of equivalence classes, i.e., ontologically simpler sets of individuals (type $\langle e,t\rangle $) or events (type $\langle v,t\rangle $). These are found in any language, showing that whether or not a language makes explicit reference to degrees (by means of gradable adjectives, degree question words, degree-only equatives) does not follow on general conceptual or semantic grounds, but is determined by the grammar of that language. (shrink)

In The Metaphysics of Margaret Cavendish and Anne Conway, Marcy P. Lascano holds up the metaphysical views of two early modern women philosophers alongside one another in order to demonstrate that...

According to the doctrine of Super-Humeanism, the world’s mosaic consists only of permanent matter points and changing spatial relations, while all the other entities and features figuring in scientific theories are nomological parameters, whose role is merely to build the best law system. In this paper, I develop an argument against Super-Humeanism by pointing out that it is vulnerable to and does not have the resources to solve the well-known problem of immanent comparisons. Firstly, I show that it cannot (...) endorse a fundamentalist solution à la Lewis, since its two pillars—a minimalist ontology and a best system account of lawhood—would generate, together, a tedious problem of internal coherence. Secondly, I consider anti-fundamentalist strategies, proposed within Humeanism, and find them inapplicable to the Super-Humean doctrine. The concern is that, since it is impossible to choose the best law system within Super-Humeanism, this doctrine may be charged with incoherence. (shrink)

Students’ attitudes toward social studies as influenced by selected demographic characteristics, study habits, and parental influence, as well as attitudes toward social studies compares with attitudes toward other major subject areas were examined in this study. High school students from 20 schools took part in the study. In support of recent research findings suggested that students generally held positive attitudes toward social studies and preferred social studies over other major subject areas. Black students reported the most favorable attitudes. Attrition in (...) social studies attitudes did not occur until the senior year of high school. No differences were found in the attitudes of males and females toward social studies, but there were selected differences when social studies was compared to other major subject areas. The effects of multiculturalism and parental involvement among several issues are discussed in relation to high school students’ attitudes toward social studies. (shrink)

An important challenge to color objectivists, who hold that statements concerning color are made true or false by objective facts, is the argument from interpersonal variation in where normal observers locate the unique hues. Recently, an attractive objectivist response to the argument has been proposed that draws on the semantics of gradable adjectives and which does not require defending the idea that there is a single correct location for each of the unique hues Noûs 50: 3–40),. In ), I argued (...) that the recent objectivist response doesn’t apply to comparative occurrences of color adjectives, so a revised, comparative, version of the argument from interpersonal variation remains a powerful objection to certain types of objectivism. In this paper, I address several unsatisfactory objectivist replies to the comparative version of the argument from interpersonal variation, and offer what I think is a more plausible objectivist reply to the comparative argument from interpersonal variation. (shrink)

A recent program comparing negotiated and reciprocal forms of social exchange offers important implications for theory development. Results of these investigations show that the form of exchange studied—negotiated or reciprocal—affects many of the processes and assumptions underlying contemporary theories of exchange. Three such effects are discussed here. First, the form of exchange affects the causal mechanisms underlying power use and the relation between network structure and power. Second, whether exchange is negotiated or reciprocal affects the relative emphasis on learning or (...) rational-choice models and the breadth of motivations assumed for “self-interested” actors, including reward maximization, loss avoidance, and reciprocity. Third, the form of exchange affects the salience of the cooperative and competitive “faces” of exchange, influencing actors' subjective experiences with exchange. These results show the limitations of theories based on any single form of exchange and the need for greater understanding of the full range of exchange forms that characterize social life. (shrink)

In recent years a number of works have explored the similarities and differences between Western philosophy and Confucianism. While works that compare the thought of Confucius and Western philosophy are diverse, they share the view that comparative study is worthwhile and seek to address in various ways some of the common challenges that comparative studies face. In light of this body of work, this chapter examines different answers to the question of why comparative philosophy is worthwhile, and highlights three different (...) kinds of challenges that frequently arise in comparative philosophy. (shrink)

Bayesian nested-model comparisons involve an assessment of the probabilities for a relatively simple model and a more general encompassing model. Since the simpler model can be viewed as a subset of the more complex model it is nested in, Popper has argued that the axioms of probability are violated when the simpler model is nonetheless assigned a higher prior probability. While Popper raised this objection in the context of assigning prior probabilities to models, we argue that Popper’s objection does (...) not just concern the priors, but Bayesian model comparisons more generally. We term this ‘the subset problem’. A variety of solutions have been proposed in the literature. We discuss some of these solutions and combine them into a new Bayesian account, in which both the probability assignments and the algebra over which they are assigned receive a specific interpretation. Finally, we discuss a new non-Bayesian solution, in which nested models are assigned an attractiveness measure that need not be additive. (shrink)

Research into robotic social learning, especially that concerned with imitation, often focuses at differing ends of a spectrum from observational learning at one end to following or matched-dependent behaviour at the other. We study the implications and differences that arise when carrying out experiments both at the extremes and within this spectrum. Physical Khepera robots with minimal sensory capabilities are used, and after training, experiments are carried out where an imitating robot perceives the dynamic movement behaviours of another model robot (...) carrying a light source. It learns the movement behaviour of the model by either statically observing the model, dynamically observing the model or by following the model. It finally re-enacts the learnt behaviour. We compare the results of these re-enactments and illustrate the differences and trade-offs that arise between static observational and reactive following learning methods. We also consider circumstances where, for this robotic embodiment, dynamic observation has both advantages and disadvantages when compared to static observation. We conclude by discussing the implications that arise from using and combining these types of social learning. (shrink)

An important challenge to color objectivists, who hold that statements concerning color are made true or false by objective (non-subject-involving) facts, is the argument from interpersonal variation in where normal observers locate the unique hues. Recently, an attractive objectivist response to the argument has been proposed that draws on the semantics of gradable adjectives and which does not require defending the idea that there is a single correct location for each of the unique hues (Gómez-Torrente, 2016). In Hansen (2015), I (...) argued that the recent objectivist response doesn’t apply to comparative occurrences of color adjectives, so a revised, comparative, version of the argument from interpersonal variation remains a powerful objection to certain types of objectivism. In this paper, I address several unsatisfactory objectivist replies to the comparative version of the argument from interpersonal variation, and offer what I think is a more plausible objectivist reply to the comparative argument from interpersonal variation. (shrink)

This paper is about the relevance, to the definition of freedom, of values or goods other than freedom. In this respect,its subject matter is not at all new. However, I do believe that new light can be thrown on the nature of this relationship by paying more attention to another relationship – one which exists within the concept of freedom itself. There are two senses in which we can be said to possess freedom. Firstly, there is the sense in which (...) we can be said to be free to do a certain particular thing. Secondly,there is the sense in which we can be said to possess a certain ‘amount’,‘degree’ or ‘quantity’ of freedom, in some overall sense.1 I believe that most recent accounts of the relationship between freedom and other goods are inconsistent, because they see those other goods as affecting the truth value of claims about freedom in the second sense, but not in the first. (shrink)

Democracy is not in steady state and democratizations are open-ended processes; they depend on structures and functions in systemic contexts that idiosyncratically evolve in tone, tenor, direction, and pace. They affect and are affected by scores of determinants, both perceived and hypothetical. In interlinked chapters that span a number of disciplines, this volume reexamines the basic traits, the comparable outcomes, and the self-defining dynamics of some of the more widely attempted versions of democracy across the world. It discusses some of (...) the controversies that can speed up or slow democratizations. The crucial question these chapters address is whether democratization is possible without an understanding of what is expected from a mode of citizenship inseparable from an ethic of freedom. (shrink)

This collection of "comparisons and contrasts" explores Heinz Kohut's self psychology in relation to a wide-ranging group of modern thinkers, both inside and outside of analysis. Separate sections analyze self psychology alongside Freud and the first generation of psychoanalytic dissidents; British object relations theorists; and contemporary theorists like Kernberg, Mahler, Lacan, and Masterson.