(What) Is Feminist Logic? (What) Do We Want It to Be?

Abstract

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance logic $\left({\mathsf{L}}_{\mathsf{Plum}}\mathsf{\right)}$. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest.

Keywords:

• Feminist logic
• Valerie Plumwood
• relevance logic
• anti-exceptionalism
• pedagogy

Acknowledgments

We are grateful to the audience of the Logic & Politics Workshop at UNILOG 2022 and an anonymous referee at History and Philosophy of Logic for helpful comments that contributed to the development of this paper.

Notes

1 In addition, there are historical projects that are relevant to work on feminist logic, such as identifying female logicians that have been omitted from standard histories and textbooks and assessing the impact of their work on the development of logic. Extant work along these lines includes Uckelman forthcoming on Eloise d'Argenteuil and Christine de Pisan, Gordon-Roth forthcoming on Anna Maria van Schurman and Mary Astell, Janssen-Lauret forthcoming on Christine Ladd-Franklin and Constance Jones, Beaney 2003 and Janssen-Lauret 2017 on Susan Stebbing, and Rentetzi 2010 on Rose Rand. Note, too that even if one or the other of the objections to feminist logic we discuss in Section 2 were successful, this would not rule out this sort of historical work. This sort of work would remain important even if, as is argued in Nye 1990, formal logic turns out to be a failed research project, for the same reason that historical work identifying hitherto unrecognized women in the history of alchemy would constitute important work in the history of the empirical sciences, despite alchemy being soundly debunked.

2 Here we mobilize a distinction between philosophical logic – the use of logical tools and techniques such as formalization and model-building to help us better understand philosophical concepts and debates – and the philosophy of logic – the philosophical investigation of various logical concepts, questions, and disputes. While both the distinction itself and how best to understand it have been matters of controversy, we find the distinction as we have drawn it here to usefully separate two distinct sorts of project within feminist work on logic.

3 We leave further analysis of where Trettin's scholarship falls within the history of feminist philosophy of logic to our German-speaking colleagues.

4 A number of the articles cited in this four-part taxonomy appeared in a 2010 special issue of Informal Logic titled ‘Reasoning for Change’, edited by Phyllis Rooney and Catherine Hundleby.

5 This is not to say that one could not consider other projects where the correct or best logic might be different for different groups. On such a view, one logic might be best for white men, another for white women, another for persons of color, etc. The point is that we are not concerned with such projects here. For an exploration of the idea that different logics might be correct relative to different epistemic communities, see Cook unpublished.

6 Here and below we will use $\left({\mathsf{L}}_{\mathsf{Plum}}\mathsf{\right)}$ to denote whatever relevance logic Plumwood has in mind in Plumwood 1993 and Plumwood 2002. Plumwood is far from clear regarding which of the various Australian plan logics she has in mind in these essays. But nothing really important hinges on this – either for our purposes or for Plumwood's – since the main point is that feminist considerations motivate us to embrace some non-classical logic that does not behave badly in the ways that Plumwood identifies (see our discussion in Section 3 below). It is clear from her discussion, however, that whatever logic is chosen, it must be significantly weaker than the frequently discussed relevance logic $\left(\mathsf{R}\mathsf{\right)}$, since $\left(\mathsf{R}\mathsf{\right)}$ validates excluded middle (again, see Section 3). For details on these various logics, the reader is encouraged to consult Priest 2008.

7 We focus on Nye 1990 since (i) Nye's critique is the most extensively developed argument for the rejection of logic, and (ii) Nye's monograph is Plumwood's main foil. But Nye is far from the only feminist writer to question the legitimacy of formal logic from a feminist perspective. For a particularly interesting case, see Marjorie Hass's reading of Luce Irigaray as rejecting formal logic in Hass 2002.

8 Interestingly, in later work Nye seems somewhat more amenable to project in philosophical logic, suggesting in Nye 2002 that, if formulated from a suitably feminist perspective, the tools of formal logic might be useful in clarifying various debates in the philosophy of biology.

9 Note that the Independence Objection, were it correct, would entail that feminist concerns are irrelevant to logical theorizing, but not vice versa. In short, if the independence objection is right, then feminist philosophy (like all other areas of intellectual inquiry) is still constrained by logic, but not the other way around.

10 This understanding of logical consequence is a paraphrase of the immensely influential account given in Tarski 1936.

11 Of course, the reader familiar with feminist work on the philosophy of science may already be a bit worried about the comparison made in the final sentence of this argument! We will return to this thought in Section 4 below.

12 And, if this weren't the primary purpose of logic, then it is unclear why – qua philosophers – we should care about logic. At the very least, it is unclear that we should – again, qua philosophers – care about formal logics any more than, or any differently from how, we care about other abstract structures such as the subject matter of pure mathematics.

13 We note that this need not collapse into any thoroughgoing relativism. See Seidel 2014.

14 For a good survey of (Australian plan) relevance logic and related systems, see Priest 2008.

15 Adapted from Plumwood 2002, pp. 56–60.

16 It is unclear if a distinction needs to satisfy all five, or just ‘enough’, of these criteria, in order to be a dualism.

17 Plumwood formulates the logical principles that are tied to various ways of centering in terms of propositional logic. We have instead utilized first-order resources to codify the problematic rules in order to emphasize the fact that it is categorization that seems to be the primary issue here – that is, whether a logic acceptable to feminists ought to assume that everything is either $\mathrm{\Phi }\left(x\right)$ or $\mathrm{\neg \Phi }\left(x\right)$, or that nothing can be both $\mathrm{\Phi }\left(x\right)$ and $\mathrm{\neg \Phi }\left(x\right)$, etc.

18 For more detailed examinations of Plumwood's feminist version of logical revision, see Eckert and Donahue 2020, Eckert forthcoming, and Burns forthcoming.

19 Haslanger 2000 refers to these as analytic projects; Haslanger (2006, ft. nt. 5) clarifies that ‘ameliorative’ is a mere terminological update for analytic projects. In keeping with this update (and the literature), we use the term ‘ameliorative’ here, despite the fact that the quoted source identifies these as analytic projects.

20 Haslanger 2000 explores this question, settling on an account of GENDER (and RACE) that build social features such as power relations and treatment by others into the concept picked out by these terms. Jenkins 2016, Mikkola 2011, and Saul 2006 among others similarly take ameliorative approaches to GENDER.

21 Objectivity in this sense is a matter of the unity or similarity of instances of the kind in question Haslanger 2006. In this case, then, the question would concern the extent to which our actual uses of negation pick out similar operations. We can transpose Plumwood's complaint into this language: Negation, as we actually use it, is a mess of pernicious dualisms, dichotomies, and mere distinctions masquerading as a single objective kind.

22 Some notes and caveats. First, the presentation of these three distinct projects suggests bright lines between them. This is not necessarily the case, especially since ameliorative projects will generally require conceptual analysis and descriptive projects to be carried out as well. Second, the notions of ‘our concept’ and ‘legitimate purposes’ are troublesome. In both cases the reference class – who we are considering among those relevant to ‘our concept’ and who gets to determine whether purposes are legitimate – makes considerable difference to the final analysis. Much of the debate among practitioners of ameliorative projects concerns just this. In the case of GENDER, for example, Haslanger 2000 argues for a concept of gender that highlights the roles of hierarchy and social structure in the deployment of gender. In doing so, Haslanger takes this laying bare the role of society, rather than self-identification, to be of paramount importance for a concept of gender. By contrast, Jenkins 2016 rejects this account for its marginalization of trans women, arguing that inclusivity is a crucial purpose of the concept of gender. Such debates are challenging, and participants may find themselves uncertain of which moves are appropriate. Nevertheless, because these debates force us to consider the broader values etched into our concepts, we take them to be a useful consequence of undertaking ameliorative projects, rather than challenge to their general viability.

23 This question – of whether and to what extent ameliorative projects (and the nearby Carnapian explication, conceptual engineering, and conceptual ethics projects) are exposed to this worry about changing the subject – is a matter of lively debate in the literature. See Strawson 1963, Cappelen 2018, and Chalmers 2020 for discussion.

24 Adapted from Quine 1986, Chapter 6.

25 One way of developing an alternative account is to argue that the meanings of the logical operators are given by some set of relatively standard introduction and elimination rule pairs for each operator. Thus, any logic that validates those rules will agree with any other logic that validates those rules with regard to the meaning of the connectives, regardless of what other inferences might also be validated by the logics in question. See Cook 2014 for discussion.

26 In response to this, proponents of an ameliorative approach might respond in two related ways. First, they might argue that the puzzle is already ill-fit to the table, and that the table really does need to be reshaped. Even if this is so, and even if it is necessary, it nevertheless seems to fall under the scope of the Quinean worry: this is changing the subject, despite the fact that the ameliorative project does not present itself as changing the subject. Second, they might construe this reshaping as simply doing what the anti-exceptionalist does. But, this is not replacing one concept with another, but rather replacing one with many, contrary to the purpose of an ameliorative project. And, even if the ameliorativist bites this bullet, they then shade into the anti-exceptionalist project we are about to outline. Recall that our goal in this discussion is not to demonstrate that any other construal is false, per se, but to show that the anti-exceptionalist approach provides the best lens through which to understand projects of feminist logical revision, like Plumwood's.

27 It is worth emphasizing that our worries about construing feminist arguments for logical revision as ameliorative projects do not generalize to all ameliorative projects. Nevertheless, these worries might apply to some projects beyond arguments regarding the correct or best logic. One potential site of such worries is Kevin Scharp's ameliorative account of truth, whereby we avoid the semantic paradoxes by replacing our single notion of truth (governed by the full Tarskian T-schema) with two distinct truth concepts: ascending truth and descending truth, each governed by one direction of the Tarskian biconditional, amongst other principles; see Scharp 2013. Whether or not the ‘changing the subject’ objection succeeds here depends, of course, on how central the notion of truth is within our conceptual scheme, and thus on the extent to which shifting from truth simpliciter to Sharp's ascending and descending truth concepts has substantial ramifications for the rest of our conceptual scheme.

28 For an alternative approach to the connections between anti-exceptionalism and feminist logic, see Russell forthcoming₁, which explores the ways that different variants of anti-exceptionalism might or might not be compatible with, or even entail, various positions regarding what feminist logic is and how it should be pursued. Russell's paper and the present essay are in many ways complementary. The papers were developed independently, but the ideas in both can be traced back in part to stimulating conversations at the Feminist Philosophy and Formal Logic Workshop at the Department of Philosophy and the Minnesota Center for Philosophy of Science at the University of Minnesota.

29 Putnam's argument is a good bit more nuanced than ‘quantum logic good, classical logic bad’, but the caricature given above is sufficient for our purposes. It is also worth noting that Quine was far from fully consistent with regard to his views on logic. As discussed earlier, in Quine 1986 he argues that any divergence from the classical logical orthodoxy amounts to changing the subject and, in effect, adopting a new language that is syntactically identical to the original but with a completely different meaning. In Quine 1951, however, he explicitly endorses the idea that logic is, like any other field, subject to refutation and thus hostage to the same sorts of challenges as any other scientific theory.

30 Adapted from Longino 1990, p. 86.

31 In fact, she could not have understood what she was doing in exactly these terms, since the term ‘anti-exceptionalist’ was not coined until after both Plumwood 1993 and Plumwood 2002 were published.

32 For further discussion of the idea that Plumwood can be fruitfully understood as endorsing a version of anti-exceptionalism, see Burns forthcoming.

33 For a singular exception, see Yap 2010 and Yap forthcoming, which explore the prospects for adapting Carnap's Principle of Tolerance to feminist projects.

34 There may be a singular best project, and hence a singular best logic, but the existence of such is not an assumption of the framework. Some feminist philosophers of science do explicitly deny the existence of such uniquely best projects. Denying the existence of a ‘best’ scientific project, however, is compatible with the claim that some projects are objectively better than others. Put bluntly, the point is that scientific projects can be partially ordered with respect to ‘goodness’ without there being a ‘top’ element in the ordering.

35 It should be noted, further, that this descriptive and methodologically produced indeterminacy does not necessarily dissolve into a form of anti-realism or thoroughgoing relativism. The fact that there are different logics that are correct for different projects does not amount to a claim that all projects are equally worthwhile and hence all logics are equally good. For example, the existence of an unjust, patriarchal project and a best logic for that project does not imply that any political movement – such as feminism – ought to respect that project. Moreover, we take it, even if there are genuinely worthwhile, and equally worthwhile, scientific projects with distinct best logics, this kind of indeterminacy is compatible with the sort of scientific objectivity achieved through intersubjective agreement suggested by Popper 1959 and by feminist philosophers of science, such as Longino 1990. This is our preferred understanding of the view sketched here.For the feminist philosopher who prefers a more robust, more traditional form of scientific objectivity and realism than that found in Popper, and Longino, one can focus on the fact that this indeterminacy, since it is intimately linked to the ways we do and should investigate the world, can be understood as affecting merely the methodology, but not the metaphysics, of science from within the epistemic–normative conception of logic.

36 It is also worth noting that contemporary logical pluralism was only just emerging as a serious position in philosophy of logic when Plumwood's second essay on feminist logical revision appeared.

37 We thank an anonymous referee for bringing this worry to our attention.

38 For discussion of knowledge-gathering and -creating processes in standpoint epistemology, see Collins 2002, and for methodological challenges in feminist philosophy of science, see Longino 1990.

39 The fact that the projects taken to be of central importance in extant (not explicitly feminist) anti-exceptionalist work on logical theories (formulating theories of truth, and accounting for the foundations of mathematics) are quite distinct from the projects taken to be of central importance in feminist anti-exceptionalist work such as Plumwood's (formulating adequate theories of GENDER and SEX) provides an example of such a difference.

40 We do not mean to imply that any of the anti-exceptionalist work cited in this essay is carried out from within such an anti-feminist stance, or that any of the prominent anti-exceptionalists discussed above are in any way anti-feminist. In particular, Gillian Russell has, as we have already noted, done important work on feminist logic (Russell forthcoming₂, Russell forthcoming₁), and Burns forthcoming seems to implicitly endorse anti-exceptionalism in her discussion of Plumwood's work as a sort of proto-anti-exceptionalism. Nevertheless, we do believe that much of the work on anti-exceptionalism suffers from not taking distinctly feminist considerations such as those mobilized by Plumwood into account, and from not attending sufficiently to recent work in feminist philosophy of science more generally.

41 Here, it should be emphasized that this is not Plumwood's position, as Plumwood herself is a logical monist.

42 It is worth noting that philosophers of logic who reject classical logic C in favor of some non-classical logic L for non-feminist reasons (a group that includes at least one of the authors of this essay) are faced with a superficially similar question: Can such logicians, in good conscience, teach classical logic without qualification at the introductory level? While this is a legitimate question, the stakes seem lower – at least in those cases where, unlike with feminist challenges to logic, the rejection of classical logic C is not based on more general social, political, and moral concerns.

43 Of course, there are broader questions regarding how we should teach logic that address much more than merely the decision whether to teach classical logic (or to teach it first), and answering many of these will no doubt require more carefully investigating why we teach logic to students in the first place. We cannot address such larger issues here. Hence we intend this section to be merely a brief investigation into one very rich and interesting, but admittedly narrow, aspect of this larger project.