Critical pedagogy is an optimistic approach for achieving transformative agency, which remains an elusive and vital aspect of civic education. Therefore, the purpose of this study was to examine the pedagogical approach of three critically identifying teachers. Specifically, this study was interested in understanding participant teacher critically civic ontological postures. The posture implies an understanding of the power inherent to civic relation and pedagogy. Participant teachers uniquely demonstrated postures that allowed them to address conceptual, personal, and material aspects of civics (...) education. Participants achieved this first by making clear temporal connections between citizenship and disciplines; second, by incorporating student experiences; and lastly by utilizing a range of instructional approaches to negate traditional civic archetypes. Findings suggest that critical civic ontological postures are dynamic, contextual, and disciplinarily situated. Authentically critically civic ontological postures include developing intellectual solidarity with students and those in educational communities. (shrink)

In this piece, the author examined the impact of ideology, experience, and privilege on pre-service Social Studies teacher disposition. Findings suggest that participants conceptually understood injustice and began to critique social antagonisms like whiteness and class. However, they continued reinforcing raced and classed ideologies in their interactions with those outside their group. When faced with the cognitive dissonance between stated ideology and their privileged position, the more liberal participants re-narrativize their political stances to adopt more critical ideological worldviews while maintaining (...) their privileged identities. More conservative participants disassociated themselves from more extreme aspects of U.S. conservative political ideology. Both groups maintained the ideologies that provided justification for social hierarchy. Upbringing/identity, understandings of power/hierarchy, emic cultural understandings, and a desire to live one’s ideology, or not, beyond the classroom, informed participant decition making. (shrink)

This paper presents the relationship between pedagogical content knowledge and political/ideological clarity as a framework for understanding the nuanced interpretations and applications of critical social studies pedagogy and practice. Using a qualitative case study research design, this study explores the decision-making process of two novice social studies teachers as they decide if and how to utilize critical historical inquiry within their classrooms. Findings indicate that teachers’ use of critical historical inquiry is informed by their subject area consciousness and political and (...) ideological clarity which is cultivated through personal, schooling, and communal experiences. However, we also find that a teacher's pedagogy is significantly strengthened when political and ideological clarity are coupled with pedagogical content knowledge to ensure a more developed enactment of critical historical inquiry is reached within the social studies classroom. (shrink)

In Davidson's example of causal deviancy, a climber knows that he can save himself from plummeting to his death by letting go of a rope connecting him to a companion who has lost his footing, but the thought of the contemplated act so upsets him that he lets go unintentionally. Causation of behavior by intentional states that rationalize it is not enough for it to count as acting. Therefore, the behavior must be caused in 'the right way' or by the (...) Right Kind of Cause. The immediate cause in Davidson's and other examples of causal immediacy is the agent's awareness or contemplation of what he or she is intending or thinking of doing, which is either caused by, or implicit in the agent's awareness of, his or her intentions or beliefs and desires. I argue that RKC can only be a mechanism-the Will-whose operation we are not directly aware of, but only indirectly once the action is underway. (shrink)

Civic engagement requires individuals to have both knowledge of democratic principles and the skills for enacting change. Acquiring the knowledge and skills necessary for a productive civic life can be difficult for students if they are not provided conceptual scaffolds and opportunities to practice citizenship. We implemented and studied an activity using Westheimer and Kahne's (2004) citizenship typology during a summer civics institute to help students grapple with their understandings of “good” citizenship. We found (1) students appropriated the language of (...) Westheimer and Kahne's citizenship typology by using it to describe their expanding understandings of citizenship; and (2) students used the citizenship typology to name and make sense of their civic identity. We discuss these findings and reflect on our use of Westheimer and Kahne's citizenship typology as a cognitive scaffold. (shrink)

The article criticises various interpretations of Epicurus's claim that belief in determinism is self-invalidating: -/- - 'The man who says that all things come to pass by necessity cannot criticise one who denies that all things come to pass by necessity, for he admits that this too happens of necessity.' - -/- especially Ted Honderich's argument that the real force of the Epicurean claim is that if belief acquisition is causally necessitated, we will be excluded from possible facts and inquiries (...) that might have produced new knowledge and might have shown some of what we take to be knowledge to be false. Honderich's argument fails to consider that undetermined inquirers might fail to make discoveries that determined inquirers could not fail to make. Determinism would not, therefore, put us in a worse position as seekers of knowledge than indeterminism. (shrink)

The argument between retributivists and consequentialists about what morally justifies the punishment of offenders is incoherent. If we were to discover that all of the contending justifications were mistaken, there is no realistic prospect that this would lead us to abandon legal punishment. Justification of words, beliefs and deeds, can only be intelligible on the assumption that if one's justification were found to be invalid and there were no alternative justification, one would be prepared to stop saying, believing or doing (...) what one has attempted to justify. Therefore, the moral standing or basis of our practices of punishing offenders can not rest on a justification of it. (shrink)

Part one. The Dunayevskaya-Marcuse correspondence, 1954-78: the early letters: debating Marxist dialectics and Hegel's absolute idea; Dunayevskaya's Marxism and freedom and beyond; on technology and work on the eve of Marcuse's One-dimensional man; the later correspondence: winding down during the period of the New Left -- Part two. The Dunayevskaya-Fromm correspondence, 1959-78: the early letters: on Fromm's Marx's concept of man and his socialist humanism symposium; dialogue on Marcuse, on existentialism, and on socialist humanism in Eastern Europe; on Hegel, Marxism, (...) and the Frankfurt School in the period of Dunayevskaya's philosophy and revolution; the final letters: on critical theory and on Rosa Luxemburg, gender, and revolution. (shrink)

A summary of Russell’s logical atomism, understood to include both a metaphysical view and a certain methodology for doing philosophy. The metaphysical view amounts to the claim that the world consists of a plurality of independently existing things exhibiting qualities and standing in relations. The methodological view recommends a process of analysis, whereby one attempts to define or reconstruct more complex notions or vocabularies in terms of simpler ones. The origins of this theory, and its influence and reception are also (...) discussed. (shrink)

The use of Big Data—however the term is defined—involves a wide array of issues and stakeholders, thereby increasing numbers of complex decisions around issues including data acquisition, use, and sharing. Big Data is becoming a significant component of practice in an ever-increasing range of disciplines; however, since it is not a coherent “discipline” itself, specific codes of conduct for Big Data users and researchers do not exist. While many institutions have created, or will create, training opportunities to prepare people to (...) work in and around Big Data, insufficient time, space, and thought have been dedicated to training these people to engage with the ethical, legal, and social issues in this new domain. Since Big Data practitioners come from, and work in, diverse contexts, neither a relevant professional code of conduct nor specific formal ethics training are likely to be readily available. This normative paper describes an approach to conceptualizing ethical reasoning and integrating it into training for Big Data use and research. Our approach is based on a published framework that emphasizes ethical reasoning rather than topical knowledge. We describe the formation of professional community norms from two key disciplines that contribute to the emergent field of Big Data: computer science and statistics. Historical analogies from these professions suggest strategies for introducing trainees and orienting practitioners both to ethical reasoning and to a code of professional conduct itself. We include two semester course syllabi to strengthen our thesis that codes of conduct can be harnessed to support the development of ethical reasoning in, and a sense of professional identity among, Big Data practitioners. (shrink)

Why do voters seek to change the political landscape or to retain it? System justification theory proposes that a separate system motive to preserve the existing order drives support for the status-quo, and that this motivation operates independently from personal and collective interests. But how does this explanation apply to recent populist shifts in the political order such as Brexit and the emergence of Donald Trump? While the system motive may seem useful in understanding why the usual progressives may want (...) to stick with an established order, it seems insufficient to explain why the more conservative voters would want to upend the establishment. Thus, we compared SJT’s system motive explanation for the system attitudes of voters on both sides of the political divide to an alternative explanation drawn from the newer social identity model of system attitudes. According to SIMSA, the difficulty in explaining the system attitudes of Brexit/Trump and Remain/Clinton voters from SJT’s system motive standpoint can be resolved by focusing instead on the collective interests that both camps seek to satisfy with their votes. We examined these explanations in two studies conducted soon after Brexit and Trump’s election in 2016, with results providing more support for SIMSA than for SJT. (shrink)

Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of arithmetical (...) concepts. The logical system of PM sought to improve on earlier attempts by solving the contradictions found in, e.g., Frege’s system, by employing a theory of types. In this article, I also consider and critically evaluate the most common objections to Russell’s logicism, including the claim that it is undermined by Gödel’s incompleteness results, and Putnam's charge of “if-thenism”. I suggest that if we are willing to accept a slightly revisionist account of what counts as a mathematical truth, these criticisms do not obviously refute Russell’s claim to have established that mathematical truths generally are a species of logical truth. (shrink)

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...) due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...) paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, (...) including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead. (shrink)

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...) did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the earlier period where (...) Russell still made a distinction between existence and being/subsistence. But even the later Russell, including that of the Logical Atomism lectures period, would not have understood ontological questions to be first and foremost questions of quantification. He would take fundamentality to be important too, which explains in part his assertions to the effect the the values of individual variables have a reality not attributable to values of higher-order variables, even ineliminable higher-order variables. (shrink)

Russell corresponded with Sir Michael Dummett (1925–2011) between 1953 and 1963 while the latter was working on a book on Frege, eventually published as Frege: Philosophy of Language (1973). In their letters they discuss Russell’s correspondence with Frege, translating it into English, as well as Frege’s attempted solution to Russell’s paradox in the appendix to vol. 2 of his Grundgesetze der Arithmetik. After Dummett visited the University of Münster to view Frege’s Nachlaß, he sent reports back to Russell concerning both (...) the philosophical materials Frege left behind, as well as information from Frege’s journal revealing his anti-semitic political opinions. Their interaction contains interpretive conjectures and insights on Dummett’s side, and some dark humor on Russell’s. (shrink)

In 1903, in _The Principles of Mathematics_ (_PoM_), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before _PoM_ even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...) why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (or (...) sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself. It is if and only if it is not. The other form is a contradiction involving properties. Some properties seem to apply to themselves, while others do not. The property of being a property is itself a property, while the property of being a cat is not itself a cat. Consider the property that something has just in case it is a property (like that of being a cat ) that does not apply to itself. Does this property apply to itself? Once again, from either assumption, the opposite follows. The paradox was named after Bertrand Russell, who discovered it in 1901. (shrink)

The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox, is a contradiction that arises in the logical treatment of classes and "propositions", where "propositions" are understood as mind-independent and language-independent logical objects. If propositions are treated as objectively existing objects, then they can be members of classes. But propositions can also be about classes, including classes of propositions. Indeed, for each class of propositions, there is a proposition stating that all propositions in that class are true. (...) Propositions of this form are said to "assert the logical product" of their associated classes. Some such propositions are themselves in the class whose logical product they assert. For example, the proposition asserting that all-propositions-in-the- class-of-all-propositions-are-true is itself a proposition, and therefore it itself is in the class whose logical product it asserts. However, the proposition stating that all-propositions-in-the-null-class-are-true is not itself in the null class. Now consider the class w, consisting of all propositions that state the logical product of some class m in which they are not included. This w is itself a class of propositions, and so there is a proposition r, stating its logical product. The contradiction arises from asking the question of whether r is in the class w. It seems that r is in w just in case it is not. This antinomy was discovered by Bertrand Russell in 1902, a year after discovering a simpler paradox usually called Russell's paradox ". It was discussed informally in Appendix B of his 1903 Principles of Mathematics . In 1958, the antinomy was independently rediscovered by John Myhill, who found it to plague the "Logic of Sense and Denotation" developed by Alonzo Church. (shrink)

This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics as classes, functions, meaning (...) and denotation, etc., and summarizes the correspondence between Frege and Russell and the light it sheds on the philosophical logic of both. (shrink)

Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary meta-ontological (...) and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...) thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...) Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

Fregeans face the difficulty finding a notation for distinguishing statements about the sense or meaning of an expression as opposed to its reference or denotation. Famously, in "On Denoting", Russell rejected methods that begin with an expression designating its denotation, and then alter it with a "the meaning of" operator to designate the meaning. Such methods attempt an impossible "backward road" from denotation to meaning. Contemporary neo-Fregeans, however, have suggested that we can disambiguate _with_, rather than _against_, the grain, by (...) using a notation that begins with expressions designating senses or meanings, and then alters them with a "the denotation of" operator to designate the denotation. I show that in his manuscripts of 1903–05, Russell both considered and rejected a similar notation along with the metaphysical suppositions underlying it. This discussion sheds light on the evolution of Russell's thought, and may yet be instructive for ongoing debates. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

Russell McCutcheon is one of the foremost proponents of what he calls “the critical study of religion,” that is, the shift to reflect critically on the concepts used in the academic study of religion, who invented them, and why. The critical study of religion leads to the realization that the concepts with which we think were invented by particular people, at a particular historical location, for a particular purpose. What are the philosophical implications of this? McCutcheon defends a debunking or (...) non-realist answer and contrasts this with my realist approach, and he is right to do so. This paper argues that those involved in the critical study of religion therefore face a choice between a non-realist and a realist metaphysics, that McCutcheon’s arguments against realism fail, and that those who wish to offer any kind of materialist account in which religious social structures shape human agency and subjectivity should adopt a critical study of religion that is also realist. (shrink)

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not at all (...) what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does not appear in the (...) _Principles_. I distinguish the functions and predicates versions, give a novel reading of the _Principles_, section 85, as a paradox dealing with what Russell calls _assertions_, and show that Russell's logical notation in 1902 had no way of even formulating the functions version. The propositional functions version had its origins in the summer of 1903, soon after Russell's notation had changed in such a way as to make a formulation possible. (shrink)

Review of Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context, by Anssi Korhonen (Palgrave Macmillan 2013).