This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions (...) arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the truth of (...) certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

Evidential Pluralism maintains that in order to establish a causal claim one normally needs to establish the existence of an appropriate conditional correlation and the existence of an appropriate mechanism complex, so when assessing a causal claim one ought to consider both association studies and mechanistic studies. Hitherto, Evidential Pluralism has been applied to medicine, leading to the EBM+ programme, which recommends that evidence-based medicine should systematically evaluate mechanistic studies alongside clinical studies. This paper argues that Evidential Pluralism can also (...) be fruitfully applied to the social sciences. In particular, Evidential Pluralism provides (i) a new approach to evidence-based policy; (ii) an account of the evidential relationships in more theoretical research; and (iii) new philosophical motivation for mixed methods research. The application of Evidential Pluralism to the social sciences is also defended against two objections. (shrink)

There is conflicting experimental evidence about whether the “stakes” or importance of being wrong affect judgments about whether a subject knows a proposition. To date, judgments about stakes effects on knowledge have been investigated using binary paradigms: responses to “low” stakes cases are compared with responses to “high stakes” cases. However, stakes or importance are not binary properties—they are scalar: whether a situation is “high” or “low” stakes is a matter of degree. So far, no experimental work has investigated the (...) scalar nature of stakes effects on knowledge: do stakes effects increase as the stakes get higher? Do stakes effects only appear once a certain threshold of stakes has been crossed? Does the effect plateau at a certain point? To address these questions, we conducted experiments that probe for the scalarity of stakes effects using several experimental approaches. We found evidence of scalar stakes effects using an “evidence seeking” experimental design, but no evidence of scalar effects using a traditional “evidence-fixed” experimental design. In addition, using the evidence-seeking design, we uncovered a large, but previously unnoticed framing effect on whether participants are skeptical about whether someone can know something, no matter how much evidence they have. The rate of skeptical responses and the rate at which participants were willing to attribute “lazy knowledge”—that someone can know something without having to check—were themselves subject to a stakes effect: participants were more skeptical when the stakes were higher, and more prone to attribute lazy knowledge when the stakes were lower. We argue that the novel skeptical stakes effect provides resources to respond to criticisms of the evidence-seeking approach that argue that it does not target knowledge. (shrink)

Hutto and Myin claim that teleosemantics cannot account for mental content. In their view, teleosemantics accounts for a poorer kind of relation between cognitive states and the world but lacks the theoretical tools to account for a richer kind. We show that their objection imposes two criteria on theories of content: a truth-evaluable criterion and an intensionality criterion. For the objection to go through, teleosemantics must be subject to both these criteria and must fail to satisfy them. We argue that (...) teleosemantics meets the truth-evaluable criterion and is not required to meet the intensionality criterion. We conclude that Hutto and Myin’s objection fails. (shrink)

Experiences of embodied remembering are familiar and diverse. We settle bodily into familiar chairs or find our way easily round familiar rooms. We inhabit our own kitchens or cars or workspaces effectively and comfortably, and feel disrupted when our habitual and accustomed objects or technologies change or break or are not available. Hearing a particular song can viscerally bring back either one conversation long ago, or just the urge to dance. Some people explicitly use their bodies to record, store, or (...) cue memories. Others can move skilfully, without stopping to think, in complex and changing environments thanks to the cumulative expertise accrued in their history of fighting fires, or dancing, or playing hockey. The forms of memory involved in these cases may be distinct, operating at different timescales and levels, and by way of different mechanisms and media, but they often cooperate in the many contexts of our practices of remembering. (shrink)

Timothy Williamson and Sebastian Sunday-Grève discuss the question of where philosophy starts, and the idea of philosophy as a non-natural science.

This paper investigates the strange case of an argument that was directed against a positivist verification principle. We find an early occurrence of the argument in a talk by the phenomenologist Roman Ingarden at the 1934 International Congress of Philosophy in Prague, where Carnap and Neurath were present and contributed short rejoinders. We discuss the underlying presuppositons of the argument, and we evaluate whether the attempts by Carnap (especially) actually succeed in answering this argument. We think they don’t, and offer (...) instead a few sociological thoughts about why the argument seems to have disappeared from the profession’s evaluaton of the positivist criterion of verifiability. (shrink)

Rational agents face choices, even when taking seriously the possibility of determinism. Rational agents also follow the advice of Causal Decision Theory (CDT). Although many take these claims to be well-motivated, there is growing pressure to reject one of them, as CDT seems to go badly wrong in some deterministic cases. We argue that deterministic cases do not undermine a counterfactual model of rational deliberation, which is characteristic of CDT. Rather, they force us to distinguish between counterfactuals that are relevant (...) and ones that are irrelevant for the purposes of deliberation. We incorporate this distinction into decision theory to develop ‘Selective Causal Decision Theory’, which delivers the correct recommendations in deterministic cases while respecting the key motivations behind CDT. (shrink)

Being social creatures in a complex world, we do things together. We act jointly. While cooperation, in its broadest sense, can involve merely getting out of each other’s way, or refusing to deceive other people, it is also essential to human nature that it involves more active forms of collaboration and coordination (Tomasello 2009; Sterelny 2012). We collaborate with others in many ordinary activities which, though at times similar to those of other animals, take unique and diverse cultural and psychological (...) forms in human beings. But we also work closely and interactively with each other in more peculiar and flexible practices which are in distinctive ways both species-specific and culturally and historically contingent: from team sports to shared labour, from committee work to mass demonstrations, from dancing to reminiscing together about old times. (shrink)

Sebastian Sunday-Grève and Timothy Williamson discuss the question of where philosophy starts and the idea of philosophy as a non-natural science.

Social scientists often draw on a variety of evidence for their causal inferences. There is also a call to use a greater variety of evidence in social science research. This topical collection examines the philosophical foundations and implications of evidential diversity in the social sciences. It assesses the application of Evidential Pluralism in the context of the social sciences, especially its application to economics and political science. It also discusses the concept of causation in cognitive science and the implications of (...) evidential diversity for the social sciences. (shrink)

Autonomous systems are machines that can alter their behavior without direct human oversight or control. How ought we to program them to behave? A plausible starting point is given by the Reduction to Acts Thesis, according to which we ought to program autonomous systems to do whatever a human agent ought to do in the same circumstances. Although the Reduction to Acts Thesis is initially appealing, we argue that it is false: it is sometimes permissible to program a machine to (...) do something that it would be wrong for a human to do. We advance two main arguments for this claim. First, the way an autonomous system will behave can be known in advance. This knowledge can indirectly affect the behavior of other agents, while the same may not be true at the time the system actually executes its programming. Second, a lack of knowledge of the identities of the victims and beneficiaries can provide a justification during the programming phase that would be unavailable to an agent at the time the autonomous system executes its programming. (shrink)

The purpose of this essay is to offer support for the substance view of persons, the philosophical anthropology defended by Patrick Lee in his essay. In order to accomplish this the author presents a brief definition of the substance view; argues that the substance view has more explanatory power in accounting for why we believe that human persons are intrinsically valuable even when they are not functioning as such, why human persons remain identical to themselves over time, and why it (...) follows from these points that the unborn are human persons; and responds to two arguments that attempt to establish the claim that the early human being is not a unified substance until at least fourteen days after conception. (shrink)

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (...) (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3- dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance. (shrink)

Emotion is an important issue in Wittgenstein’s philosophy of psychology, yet the literature on this topic is quite small. Wittgenstein’s philosophical investigation is a grammatical one, and he tries to dissolve philosophical problems by using many philosophical methods. In this paper I examine the grammatical rules for some emotion words and the methods he employs in dealing with the philosophical problem of emotion. To facilitate this examination, I first analyze Wittgenstein’s treatment of the problem of sudden understanding, where the grammar (...) and methods are easier to comprehend. I will then show that the grammar and methods used by Wittgenstein in the cases of sudden understanding and emotion are rather similar. (shrink)

Experiences of embodied remembering are familiar and diverse. We settle bodily into familiar chairs or find our way easily round familiar rooms. We inhabit our own kitchens or cars or workspaces effectively and comfortably, and feel disrupted when our habitual and accustomed objects or technologies change or break or are not available. Hearing a particular song can viscerally bring back either one conversation long ago, or just the urge to dance. Some people explicitly use their bodies to record, store, or (...) cue memories. Others can move skilfully, without stopping to think, in complex and changing environments thanks to the cumulative expertise accrued in their history of fighting fires, or dancing, or playing hockey. The forms of memory involved in these cases may be distinct, operating at different timescales and levels, and by way of different mechanisms and media, but they often cooperate in the many contexts of our practices of remembering. (shrink)

Sebastian Sunday-Grève and Timothy Williamson discuss the relationship between curiosity and common sense.

Gottfried Wilhelm Leibniz presents the idea of monads, as non-communicative, self-actuating system of beings that are windowless, closed, eternal, deterministic and individualistic. For him, the whole universe and its constituents are monads and that includes humans. In fact, any ‘body’, such as the ‘body’ of an animal or man has, according to Leibniz, one dominant monad which controls the others within it. This dominant monad, he often refers to as the soul. If Leibniz’s conception of monads is accepted, it merely (...) establishes human subjectivity, idiosyncrasies, biases, prejudices and individual points of view as the norm. How then do we ensure inter-subjectivity and the kind of social interaction requisite for the achievement of social order, since Leibniz’s system forecloses the possibility of interaction and communication among monads? In this essay, we argue that just as Leibniz’s monads synchronize only through the Supreme Monad (Monas Monadum), humans as social monads should also interact through a matrix of ideals like truth, honesty, sincerity, integrity, altruism, impartiality, compassion and trust. Since social order is actualised only within the context of linked social structures, relations and values, these utopian ideals would form the fulcrum through which humans relate and the very foundation that would anchor a viable social order. Our aim here is to establish a relationship between Leibniz’s metaphysics and the physical domains of life by showing that metaphysical constructs can impinge on human social relations and wellbeing. The study employed the qualitative method of research through critical analysis of texts, library and archival materials. (shrink)

Comparison of Steve Fuller's and Alvin Goldman's social epistemologies.

This article profiles one of my mentor's research focus. The scholar has consistently published on language, teaching and learning.

Nicole Hassoun and Uriah Kriegel defend the position that infanticide is morally permissible because an infant a few days old does not have a self-concept and thus is not a person. I argue their position is flawed and cannot principally rule out the possible permissibility of slavery.

It is no surprise that the philosophy of religion, the many disciplines counted within the study of religion and theology, and religion-specific studies, all have their own methods and interests, and often proceed necessarily as conversations among small groups of experts. But the intellectual cogency and credibility of such studies also entails a problematization of the boundaries that divide them. While disciplinary distinctions are necessary and valuable, a freer flow of ideas and questions across boundaries is to the benefit of (...) all concerned. In particular, the philosophy of religion proceeds more fruitfully if, among its several dimensions, it is also intentionally comparative and inter-religious, vulnerable to the questions raised by insiders to traditions, and open to the implications of ideas for religious practice. (shrink)

A question arising from the COVID-19 crisis is whether the merits of cases for climate policies have been affected. This article focuses on carbon pricing, in the form of either carbon taxes or emissions trading. It discusses the extent to which relative costs and benefits of introducing carbon pricing may have changed in the context of COVID-19, during both the crisis and the recovery period to follow. In several ways, the case for introducing a carbon price is stronger during the (...) COVID-19 crisis than under normal conditions. Oil costs are lower than normal, so we would expect less harm to consumers compared to normal conditions. Governments have immediate need for diversified new revenue streams in light of both decreased tax receipts and greater use of social safety nets. Finally, supply and demand shocks have led to already destabilized supply-side activities, and carbon pricing would allow this destabilization to equilibrate around greener production for the long-term. The strengthening of the case for introducing carbon pricing now is highly relevant to discussions about recovery measures, especially in the context of policy announcements from the European Union and United States House of Representatives. Key Policy Insights: • Persistently low oil prices mean that consumers will face lower pain from carbon pricing than under normal conditions. • Many consumers are more price-sensitive during the COVID-19 context, which suggests that a greater relative burden from carbon prices would fall upon producers as opposed to consumers than under normal conditions. • Carbon prices in the COVID-19 context can introduce new revenue streams, assisting with fiscal holes or with other green priorities. • Carbon pricing would contribute to a more sustainable COVID-19 recovery period, since many of the costs of revamping supply chains are already being felt while idled labor capacity can be incorporated into firms with lower carbon-intensity. (shrink)

This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in (...) mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the role of logic and ethics in the practice of mathematics. (shrink)

The beginning of the 21st century has seen the renewed use of aesthetics as a critical and interpretive method within various discursive spheres. Particularly, and unsurprisingly, this move has been most pronounced in the discursive systems of philosophy and the artworld. It is to this more specific re-discovery that the authors in this journal address their arguments.

In recent years, philosophy of science has witnessed a significant increase in attention directed toward the field’s social relevance. This is demonstrated by the formation of societies with related agendas, the organization of research symposia, and an uptick in work on topics of immediate public interest. The collection of papers that follows results from one such event: a 3-day colloquium on the subject of socially engaged philosophy of science (SEPOS) held at the University of Cincinnati in October 2012. In this (...) introduction, we first survey the recent history of philosophy of science’s social involvement (or lack thereof) and contrast this with the much greater social involvement of the sciences themselves. Next, we argue that the field of philosophy of science bears a special responsibility to contribute to public welfare. We then introduce as a term of art “SEPOS” and articulate what we take to be distinctive about social engagement, with reference to the articles in this collection as exemplars. Finally, we survey the current state of social engagement in philosophy of science and suggest some practical steps for individuals and institutions to support this trajectory. (shrink)

This paper seeks to defuse two claims. On the one hand, I confront the Hildebrandian claim that Thomism, by placing the principium of love in the needs and desires of the lover rather than in the beloved, denies the possibility of transcendent love; on the other, I seek to refute the Thomistic objection that Hildebrand lacks a sufficient understanding of nature and its inherent teleology. In order to accomplish this, a distinction must be made between different kinds of principium or (...) “for-its-own-sakeness.” Using St. Thomas’ theory of friendship-love, I show how every affective movement in fact has two fundamentally different principia: an “end-desired,” and an “end-for-whom” the former is desired. I next note that “value” and “bonum honestum” each encompass both of these types of “worthiness,” and that the failure to distinguish between these two has led to much of the misunderstanding between Thomists and Hildebrandians: for while the latter sometimes seem to include inanimate objects like sunsets under the higher “worthiness” (as “ends-for-whom”), the former often tend to classify even the beloved under the lower “worthiness” (as a mere “end-desired”), which are both untenable positions. It is shown, however, that for St. Thomas it is the higher, more ultimate sense of “worthiness” that is the foundation of friendship-love, and that thus love remains a truly “transcendent” or “ecstatic” phenomenon. Two objections are then addressed: 1) St. Thomas’ claim that substantial unity is the greatest cause of love, and 2) his claim that man’s primary end is Vision. In both these respects I argue that Aquinas’ position needs correction; still I maintain that neither claim should be taken to imply that, for Aquinas, man is his own center, his own chief “end-for-whom.” Finally, while Hildebrand emphatically denies that natural teleology can explain man’s transcendence (a Thomistic position), this denial seems to flow simply from confusing two ways in which “nature” can be invoked as an explanation: where he sees it invoked as the final cause, Thomists actually invoke it as simply the formal cause of our love for our true Final Cause. (shrink)

Over the last fifteen years, an ambitious explanatory framework has been proposed to unify explanations across biology and cognitive science. Active inference, whose most famous tenet is the free energy principle, has inspired excitement and confusion in equal measure. Here, we lay the ground for proper critical analysis of active inference, in three ways. First, we give simplified versions of its core mathematical models. Second, we outline the historical development of active inference and its relationship to other theoretical approaches. Third, (...) we describe three different kinds of claim -- labelled mathematical, empirical and general -- routinely made by proponents of the framework, and suggest dialectical links between them. Overall, we aim to increase philosophical understanding of active inference so that it may be more readily evaluated. -/- This the final submitted version of the Introduction to the Topical Collection "The Free Energy Principle: From Biology to Cognition", forthcoming in Biology & Philosophy. (shrink)

This paper considers negative triggers and the interpretation of simple sentences containing more than one occurrence of those items . In the most typical interpretations those sentences have more negative expressions than negations in their semantic representation. It is first shown that this compositionality problem remains in current approaches. A principled algorithm for deriving the representation of sentences with multiple negative quantifiers in a DRT framework is then introduced. The algorithm is under the control of an on-line check-in, keeping the (...) complexity of negation auto-embedding below a threshold of complexity. This mechanism is seen as a competence limitation imposing the ‘abrogation of compositionality’ observed in the so-called negative concord readings . A solution to the compositionality problem is thus proposed, which is based on a control on the processing input motivated by a limitation of the processing mechanism itself. (shrink)

We investigate the firms’ specific attributes that determine the difference in speed of adjustment (SOA) towards the cash holdings target in the Scandinavian countries: Denmark, Norway and Sweden. We examine whether Scandinavian firms maintain an optimal level of cash holdings and determine if the active cash holdings management is associated with the firms’ higher SOA and lower adjustment costs. Our findings substantiate that a higher level of off-target cost induces professional managers to rebalance their cash level towards the optimal balance (...) of cash holdings. Our results reveal that Scandinavian firms accelerate SOA towards cash targets primarily for the precautionary motive. Moreover, our results show that SOA is heterogeneous across Scandinavian firms based on adjustment cost and deviate cash holdings towards the target mainly with the support of internal financing. Furthermore, our empirical findings show that the SOA of Norwegian firms is significantly higher than the Danish and Swedish firms. (shrink)

The free energy principle is notoriously difficult to understand. In this paper, we relate the principle to a framework that philosophers of biology are familiar with: Ruth Millikan’s teleosemantics. We argue that: systems that minimise free energy are systems with a proper function; and Karl Friston’s notion of implicit modelling can be understood in terms of Millikan’s notion of mapping relations. Our analysis reveals some surprising formal similarities between the two frameworks, and suggests interesting lines of future research. We hope (...) this will aid further philosophical evaluation of the free energy principle. (shrink)

In this paper, I present the recently much discussed Value Challenge for Theories of Knowledge and formulate Generic Theistic reliabilism as a theory, which can answer this challenge, with respect to Theism and the proposition ”God exists’.

This paper aims to establish several interconnected points. First, a particular interpretation of the mathematical definition of information, known as the causal interpretation, is supported largely by misunderstandings of the engineering context from which it was taken. A better interpretation, which makes the definition and quantification of information relative to the function of its user, is outlined. The first half of the paper is given over to introducing communication theory and its competing interpretations. The second half explores three consequences of (...) the main thesis. First, a popular claim that the quantification of information in a signal is irrelevant for the meaning of that signal is exposed as fallacious. Second, a popular distinction between causal and semantic information is shown to be misleading, and I argue it should be replaced with a related distinction between natural and intentional signs. Finally, I argue that recent empirical work from microbiology and cognitive science drawing on resources of mathematical communication theory is best interpreted by the functional account. Overall, a functional approach is shown to be both theoretically and empirically well-supported. (shrink)

When experimental participants are given the chance to reflect and revise their initial judgments in a dynamic conversational context, do their responses to philosophical scenarios differ from responses to those same scenarios presented in a traditional static survey? In three experiments comparing responses given in conversational contexts with responses to traditional static surveys, we find no consistent evidence that responses differ in these different formats. This aligns with recent findings that various manipulations of reflectiveness have no effect on participants’ judgments (...) about philosophical scenarios. Although we did not find a consistent quantitative effect of format (conversation vs. static survey), conversational experiments still provide qualitative insights into debates about how participants are understanding (or misunderstanding) the scenarios they read in experimental studies, whether they are replacing difficult questions with questions that are more easily answered, and how participants are imagining the scenarios they read in ways that differ from what is explicitly stated by experimenters. We argue that conversational experiments—"Socratic questionnaires"—help show what is going on “under the hood” of traditional survey designs in the experimental investigation of philosophical questions. (shrink)

John Rawls is arguably the most important political philosopher of the past century. His theory of justice has set the agenda for debate in mainstream political philosophy for the past forty years, and has had an important influence in economics, law, sociology, and other disciplines. However, despite the importance and popularity of Rawls's work, there is no clear picture of what a society that met Rawls's principles of justice would actually look like. This article sets out to explore that question.

The main concern of this paper is the proper analysis of the NP celui-ci in French. The contribution of L. Tasmowski to this discussion is well known. In my view, this contribution makes two important points: 1) in its anaphoric uses, celui-ci cannot be analysed as a "nominal anaphoric" along the lines suggested by Corblin for its exophoric uses. This point is also made in Kleiber, Zribi-Hertz, Imoto ; 2) eventhough celui-ci like pronouns and definite NPS must be linked in (...) its anaphoric uses to a familiar discourse referent, it involves "une rupture de familiarité" [a familiarity break]. Basically, I will argue in this paper that these two points are correct, although they seem to draw the analysis of celui-ci in two opposite directions and look somewhat paradoxical. In this paper, I propose a solution to those difficulties which is based on the analysis of celui-ci as a "mentional NP". Other mentional NPs in French are, for instance, le premier, le second, ce dernier. Mentional NPS, it will be claimed, are just NPs which are associated to a previously established discourse referent by using only the properties of the previous mention having evoked this discourse referent in the discourse context. I will claim that there is a strong association between mentionals and NPs without a noun in French, namely that mentional references are achieved by NPs without a noun. I will show moreover that this specific kind of reference based on contingent properties of a discourse referent is the key for understanding how a coindexed NP produces the break in topic continuity noted by Tasmowski. (shrink)

Many instances have presented mathematics as a difficult subject for students, and some of these difficulties have been perceived as an injustice to those who suffer from it. Meanwhile, no child is to be left behind in building a just society if all were to experience the collective good of mathematics. For this reason, it became necessary to explore pre-service teachers’ perceptions of mathematics as social justice in their lived experiences. In doing this, the qualitative interpretive approach was adopted, where (...) qualitative data was collected, transcribed, and analysed using the case study design. A sample of eleven pre-service teachers were involved in the study. The findings indicated that the pre-service teachers had experienced severe issues of mathematics as social justice in their previous schooling that were unfair to them. However, they now felt mathematics could be interesting if delivered in a manner that let their voices be heard in the delivery process. (shrink)

Prominent views about representation share a premise: that mathematical communication theory is blind to representational content. Here I challenge that premise by rejecting two common misconceptions: that Claude Shannon said that the meanings of signals are irrelevant for communication theory (he didn't and they aren't), and that since correlational measures can't distinguish representations from natural signs, communication theory can't distinguish them either (the premise is true but the conclusion is false; no valid argument can link them).