Contemporary feminist theory is at an impasse: the project of reformulating concepts of self and social identity is thwarted by an association between identity and oppression and victimhood. In Sacrificial Logics, Allison Weir proposes a way out of this impasse through a concept of identity which depends on accepting difference. Weir argues that the equation of identity with repression and domination links "relational" feminists like Nancy Chodorow, who equate self-identity with the repression of connection to others, and poststructuralist feminists like (...) Judith Butler, who view any identity as a repression of nonidentity and difference. Through readings of Chodorow, Butler, Jessica Benjamin, Luce Irigaray, Jacqueline Rose and Julia Kristeva, Weir analyzes the relation of theories of self-identity to theories of women's identity, social identity, the identity of meaning in language and feminist solidarity. Drawing particularly on the work of Julia Kristeva, she argues for a reformulation of self-identity as a capacity to participate in a social world, and sketches a model of a self-identity which depends on a capacity to accept nonidentity, difference and connections to others. (shrink)

Neo-Fregeans argue that substantial mathematics can be derived from a priori abstraction principles, Hume's Principle connecting numerical identities with one:one correspondences being a prominent example. The embarrassment of riches objection is that there is a plurality of consistent but pairwise inconsistent abstraction principles, thus not all consistent abstractions can be true. This paper considers and criticizes various further criteria on acceptable abstractions proposed by Wright settling on another one—stability—as the best bet for neo-Fregeans. However, an analogue of the embarrassment of (...) riches objection resurfaces in the metatheory and I conclude by arguing that the neo-Fregean program, at least insofar as it includes a platonistic ontology, is fatally wounded by it. (shrink)

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

How can we think about identities in the wake of feminist critiques of identity and identity politics? Allison Weir rethinks conceptions of individual and collective identities in relation to freedom.

Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and surreal-valued (...) semantics are given and the proof theory for the systems outlined. The framework is robust in the sense that no conditional, defined or primitive, which sustains the contraction principles underlying Curry paradoxes can be expressed. Classical recapture is smoothly achievable in the system which however is expressively limited and not semantically closed. The conclusion considers the issue of how to extend the system to capture full naive set theory. (shrink)

The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...) established by the neo-logicist. (shrink)

Naive set theory, as found in Frege and Russell, is almost universally believed to have been shown to be false by the set-theoretic paradoxes. The standard response has been to rank sets into one or other hierarchy. However it is extremely difficult to characterise the nature of any such hierarchy without falling into antinomies as severe as the set-theoretic paradoxes themselves. Various attempts to surmount this problem are examined and criticised. It is argued that the rejection of naive set theory (...) inevitably leads one into a severe scepticism with regard to the feasibility of giving a systematic semantics for set theory. It is further argued that this is not just a problem for philosophers of mathematics. Semantic scepticism in set theory will almost inevitably spill over into total pessimism regarding the prospects for an explanatory theory of language and meaning in general. The conclusion is that those who wish to avoid such intellectual defeatism need to look seriously at the possibility that it is the logic used in the derivation of the paradoxes, and not the naive set theory itself, which is at fault. (shrink)

The guiding idea behind formalism is that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the practice of (...) advanced mathematicians in some periods—for example, the treatment of imaginary numbers for some time after Bombelli's introduction of them, and perhaps the attitude of some contemporary mathematicians towards the higher flights of set theory. Finally, it is often the position to which philosophically naïve respondents will gesture towards, when pestered by questions as to the nature of mathematics. (shrink)

Starting with the distinction between epistemological and ontological naturalism, this chapter focuses most on Quine’s epistemological naturalism, not the ontological anti-naturalism he thought it leads to. It is argued that naturalised epistemology is not central to Quine’s epistemology. Quine’s key epistemological principle is:- follow the methods of science, and only those. Can Quine demarcate scientific methods from non-scientific ones? The problems which have been raised here, e.g. in the case of mathematics, are considered. A main theme is the relationship between (...) Quine’s naturalism and reductionist forms of ‘scientistic’ naturalism. Quine is generally taken to be an anti-reductionist, unsurprisingly given his explicit anti-reductionist pronouncements from ‘Two Dogmas’ onwards. It is argued that the situation is more complex than this and that key Quinean arguments are driven by a positivistic reductionism he never entirely broke free from. (shrink)

Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.

Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian souls. Mathematics seems both essential to science but also committed to abstract non-physical entities while methodologically it seems to have no place for experiment or empirical confirmation. The chapter critically reviews a number of responses naturalists have made including logicism, Quinean radical empiricism, and Penelope Maddy’s variant thereof and suggests some further problems both for ontological (...) and for methodological naturalists. (shrink)

In her book, Politics of Piety: The Islamic Revival and the Feminist Subject, Saba Mahmood analyzes the practices of the women in the mosque movement in Cairo, Egypt. Mahmood argues that in order to recognize the participants as agents, we need to question the assumption that agency entails resistance to norms; moreover, we need to question the feminist allegiance to an unquestioned ideal of freedom. In this paper, I argue that rather than giving up the ideal of freedom, we can (...) explore the possibility that there are different conceptions of freedom, and that the agency of the women in the mosque movement can be understood through a conception of freedom as a practice of connection, or belonging. I develop this alternative paradigm through discussions of four conceptions of freedom: Foucault's theory of agency as self-creation, positive freedom, communitarian freedom, and freedom as resistance. (shrink)

There has been much debate recently as to whether the notion of truth, as applied to one's home language, is metaphysically neutral, the interesting metaphysical questions arising elsewhere (in relation to such notions as mind-independence or objectivity or existence). ' On one side, the minimalists, as they have come to be known, favour deflationary accounts of truth such as the redundancy or disquotational theories and conclude that the notion of truth is applicable to declarative sentences in general - at least (...) where there are fairly definite standards of appropriateness for the assertion or denial of such sentences - irrespective of the metaphysical commitments of the propositions the sentences express. Opponents have criticized the minimalist account of truth or denied that it follows from this account that truth is metaphysically neutral. My sympathies in this debate lie with the minimalist but I wish to focus on a serious problem for the minimalist - that posed by the Liar paradox. This problem has featured very little in the recent debate but seems to me to yield the strongest objection to minimalism. I develop the objection in the next section, in §2 sketching what I feel to be the minimalist's best response, namely developing the position not in terms of Tarskian classical biconditionals but rather in terms of the naive rules for truth. It emerges, then, that the minimalist will be forced to repudiate classical logic. The last section, §3, deals with objections to the strategy of §2. (shrink)

Most of the time our quantifications generalise over a restricted domain. Thus in the last sentence, ‘most of the time’ is arguably not a generalisation over all times in the history of the universe but is restricted to a sub-group of times, those at which humans exist and utter quantified phrases and sentences, say. Indeed the example illustrates the point that quantificational phrases often carry an explicit restriction with them: ‘some people’, ‘all dogs’. Even then, context usually restricts to a (...) subdomain of the class specified by the count noun. Although teenagers like to have fun by being, they mistakenly think, overly literal— ‘Everyone is tired, let’s get to bed’: ‘everyone: you mean every person in the entire universe?’— competent language users have to be sensitive to context virtually all the time. But is it always the case that generalisation is over a restricted domain? On the face of it, to claim this is paradoxical. If we say. (shrink)

In this paper I argue for a theory of perception distinct both from classical sense-datum theories and from intentionalist theories, that is theories according to which one perceives external objects by dint of a relation with a propositional content. The alternative I propose completely rejects any representational element in perception. When one sees that an object has a property, the situation or state of affairs of its having that property is one's perception, so that the object and property are literally (...) part of one's mind. The most obvious objection to this view is that it embodies a rampant form of idealism. It is argued to the contrary, via consideration of the metaphysics of situations, that the theory is entirely consistent with a robustly realist view of the world. (shrink)

In this paper, Weir reconsiders identity politics and their relation to feminist solidarity. She argues that the dimension of identity as “identification-with” has been the liberatory dimension of identity politics, and that this dimension has been overshadowed and displaced by a focus on identity as category. Weir addresses critiques of identification as a ground of solidarity, and sketches a model of identity and identity politics based not in sameness, but in transformative historical process.

Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...) number and Axiom V for sets, on the one hand, then classically consistent disjunctivised versions of Axiom V which are impredicative but can prove the well-foundedness of the semantics of weaker such systems, on the other. (shrink)

Drawing on Iris Marion Young's essay, “House and Home: Feminist Variations on a Theme,” Weir argues for an alternative ideal of home that involves: the risk of connection, and of sustaining relationship through conflict; relational identities, constituted through both relations of power and relations of mutuality, love, and flourishing; relational autonomy: freedom as the capacity to be in relationships one desires, and freedom as expansion of self in relationship; and connection to past and future, through reinterpretive preservation and transformative identification.

Drawing on Iris Marion Young’s essay, “House and Home: Feminist Variations on a Theme,” Weir argues for an alternative ideal of home that involves: (1) the risk of connection, and of sustaining relationship through conflict; (2) relational identities, constituted through both relations of power and relations of mutuality, love, and flourishing; (3) relational autonomy: freedom as the capacity to be in relationships one desires, and freedom as expansion of self in relationship; and (4) connection to past and future, through reinterpretive (...) preservation and transformative identification. (shrink)

In this paper, Weir reconsiders identity politics and their relation to feminist solidarity. She argues that the dimension of identity as “identification-with” has been the liberatory dimension of identity politics, and that this dimension has been overshadowed and displaced by a focus on identity as category. Weir addresses critiques of identification as a ground of solidarity, and sketches a model of identity and identity politics based not in sameness, but in transformative historical process.

Amy Allen’s insightful and nuanced feminist critical-theoretical account of the politics of our selves could be strengthened with a more complex and differentiated account of power and of gender, and of the social as a site of multiple conflicting and contesting relations. Such an account would adhere more consistently to Allen’s own project of understanding subjects to be constituted through both relations of power and relations of interdependence and mutuality, care and solidarity. The development of this account, and of a (...) situated account of desire or motivation, is essential for a feminist critical theory of self and social transformation. (shrink)

Charles Taylor and Michel Foucault offer two very different descriptions and analyses of modern identities. While it can be argued that Taylor and Foucault are thematizing two very different aspects of identity — Taylor is focusing on first-person, subjective, affirmed identity, and Foucault is focusing on third-person, or ascribed, category identity — in practice, these two are very much intertwined. I argue that attention to identities of race, gender, class and sexual orientation demands that we combine a Foucauldian power analysis (...) with a Taylorean understanding of authenticity. Taking Nancy Fraser's and Linda Gordon's example of the `single black mother on welfare' as the `icon of dependency' in America and Charles Taylor's example of the `householder' who understands himself in relation to an ideal of independence, I show that neither individual can develop either self-knowledge or freedom without engaging in a quest for authenticity that involves both analysis of relations of power and identification with resistant identities. This requires moving beyond both Taylor and Foucault to an understanding of identity in terms of critical relations with defining communities. Key Words: authenticity • critique • Michel Foucault • freedom • identity • meaning • power • self-knowledge • social being • Charles Taylor. (shrink)

W.V. Quine's thesis of the indeterminacy of translation is the theory which launched a thousand doctorates. During the 1970s it sometimes seemed to be as firmly entrenched a dogma among North American philosophers as the existence of God was among medieval theologians. So what is the indeterminacy thesis? It is very tempting, of course, to apply a little reflexivity and deny that there is any determinate thesis of indeterminacy of translation; to charge Quine with championing a doctrine which has no (...) clear meaning, or which is hopelessly ambiguous. Such a charge is, it is argued in this article, false. His meaning is fairly clear and there is widespread agreement on what the thesis amounts to. The second section of the article looks at Quine's ‘argument from below’ for indeterminacy, then the ‘argument from above’, with concluding remarks in the last section. (shrink)

Gödel and others held that impredicative specification is illegitimate in a constructivist framework but legitimate elsewhere. Michael Dummett argues to the contrary that impredicativity, though not necessarily illicit, needs justification regardless of whether one assumes the context is realist or constructivist. In this paper I defend the Gödelian position arguing that Dummett seeks a reduction of impredicativity to predicativity which is neither possible nor necessary. The argument is illustrated by considering first highly predicative versions of the equinumerosity axiom for cardinal (...) number and Axiom V for sets, on the one hand, then classically consistent disjunctivised versions of Axiom V which are impredicative but can prove the well-foundedness of the semantics of weaker such systems, on the other. (shrink)

In this paper I highlight certain logical and metaphysical issues which arise in the characterisation of functionalism-in particular its ready coherence with a physicalist ontology, its structuralism and the impredicativity of functionalist specifications. I then utilise these points in an attempt to demonstrate fatal flaws in the functionalist programme. I argue that the brand of functionalism inspired by David Lewis fails to accommodate multiple realisability though such accommodation was vaunted as a key improvement over the identity theory. More standard accounts (...) of functionalism allow, by contrast, for far too much multiple realisability. Specifically, functionalist structures will be massively reduplicated in the human brain; so functionalism yields the absurd consequence that each human harbours large numbers of minds and exemplifies virtually all mental states. (shrink)

In December 1984 Angela Weir and Elizabeth Wilson, two founding members of Feminist Review, published an article assessing contemporary British feminism and its relationship to the left and to class struggle. They suggested that the women's movement in general, and socialist-feminism in particular, had lost its former political sharpness. The academic focus of socialist-feminism has proved more interested in theorizing the ideological basis of sexual difference than the economic contradictions of capitalism. Meanwhile the conditions of working-class and black women have (...) been deteriorating. In this situation, they argue, feminists can only serve the general interests of women through alliance with working-class movements and class struggle. Weir and Wilson represent a minority position within the British Communist Party (the CP), which argues that ‘feminism’ is now being used by sections of the left, in particular the dominant ‘Eurocommunist’ left in the CP, to justify their moves to the right, with an accompanying attack on traditional forms of trade union militancy. Beatrix Campbell, who is aligned to the dominant position within the CP, has been one target of Weir and Wilson's criticisms. In several articles from 1978 onwards, and in her book Wigan Pier Revisited, Beatrix Campbell has presented a very different analysis of women and the labour movement. She has criticized the trade union movement as a ‘men's movement’, in the sense that it has always represented the interests of men at the expense of women. And she has described the current split within the CP as one extending throughout the left between the politics of the ‘old’ and the ‘new’: traditional labour movement politics as against the politics of those who have rethought their socialism to take into account the analysis and importance of popular social movements – in particular feminism, the peace and anti-racist movements. In reply to this debate, Anne Phillips has argued that while women's position today must be analysed in the context of the capitalist crisis, it is not reducible to the dichotomy ‘class politics’ versus ‘popular alliance’. Michèle Barrett, in another reply to Weir and Wilson, has argued that they have presented a reductionist and economistic approach to women's oppression, which caricatures rather than clarifies much of the work in which socialist-feminists have been engaged. To air these differences between socialist-feminists over the question of feminism and class politics, and to see their implications for the women's movement and the left, Feminist Review has decided to bring together the main protagonists of this debate for a fuller, more open discussion. For this discussion Feminist Review drew up a number of questions which were put to the participants by Clara Connolly and Lynne Segal. (Michèle Barrett was present in a personal capacity.) They cover the recent background to socialist-feminist politics, the relationship of feminism to Marxism, the role of feminists in le ft political parties and the labour movement, the issue of racism and the prospects for the immediate future. The discussion was lengthy and what follows is an edited version of the transcript. (shrink)

Olav Gjelsvik: Quine on Observationality: This chapter discusses the role of the observationality of objects in Quine's philosophy. It does it by providing an overview of some of the milestones in Quine's thoughts about observation and observation sentences, and in connection with each milestone it identifies some of the philosophical problems Quine responds to and deals with. To help us understand how his thinking developed, the chapter discusses some of these problems and evaluates his responses. The final part discusses both (...) details and the bigger picture, partly by relating Quine to philosophers before him and after him. (shrink)

[Alan Weir] This paper addresses the problem of how to account for objective content-for the distinction between how we actually apply terms and the conditions in which we ought to apply them-from within a naturalistic framework. Though behaviourist or dispositionalist approaches are generally held to be unsuccessful in naturalising objective content or 'normativity', I attempt to restore the credibility of such approaches by sketching a behaviouristic programme for explicating objective content. /// [Alexander Miller] Paul Boghossian (1989, 1990) has argued, on (...) grounds concerning the holistic nature of belief fixation, that there are principled reasons for thinking that 'optimal conditions' versions of reductive dispositionalism about content cannot hope to satisfy a condition of extensional accuracy. I discern three separable strands of argument in Boghossian's work-the circularity objection, the open-endedness objection, and the certification objection-and argue that each of these objections fails. My conclusion is that for all that Boghossian has shown, 'optimal conditions' versions of reductive dispositionalism have to be assessed on a case-by-case basis. (shrink)

I revisit my 1993 paper on Putnam and mathematical realism focusing on the indispensability argument and how it has fared over the years. This argument starts from the claim that mathematics is an indispensable part of science and draws the conclusion, from holistic considerations about confirmation, that the ontology of science includes abstract objects as well as the physical entities science deals with.