GNOSIS Journal of Philosophy Volume 14 Issue 2
Philosophy and Environment, Science, and Policy-Making
Acknowledgements
This special issue of Gnosis highlights three outstanding student presentations from the conference “Philosophy and Environment, Science, and Policy-Making,� organized by the Graduate Philosophy Students Association (GPSA) and held on April 17-18th, 2015, at Concordia University in Montreal.
GPSA Conference Organizers Melody Mikhail Eben Hensby
Gnosis Deanne Beraldo Editor-in-Chief
Jaysen Penney Managing Editor
*Picture on cover by Rawb Leon Carlyle
Contents
Restructuring Animism: Plumwood’s Materialist Spirituality of Place and the Work of Merleau-Ponty
1 Rawb Leon Carlyle, Concordia University
The Inevitability of Care in a Posthuman World
8 Marie-Anne Casselot, McGill University
Skeptical Symmetry: A Wittgensteinian Approach to Scientific Reasoning
14 Erik Nelson, Concordia University
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Restructuring Animism: Plumwood’s Materialist Spirituality of Place and the Work of Merleau-Ponty Rawb Leon Carlyle
In her work, the late Val Plumwood calls for a “materialist spirituality of place,” invoking indigenous animism to reshape our conceptions of materiality, commodity, and death. Turning toward animist spirituality, she argues, offers us resources to combat ecological crises by restoring facets of living on Earth that have been tacitly removed from experience – such as the fact that when we die, our material bodies are appropriated by other living things. I propose that Maurice Merleau-Ponty’s account of structure from his first major work, The Structure of Behaviour, allows us to concretize Plumwood’s appeal to spirituality within a practice of philosophical interrogation. To be clear, Plumwood specifies that several examples of viable animist spirituality come to us from the traditions of the indigenous peoples of Oceania, and North and South America (among other regions). I want to preface that this appeal to indigenous animism is, in part, a recognition of some of those philosophies that have been excluded from “the Western canon” – and as such, I recognize that it’s a transgression for me to speak instead about the work of a dead white Frenchman instead of directly addressing those cultures to which Plumwood appeals (and on land seized by dead white Frenchmen, no less). Nevertheless, I wish to add Merleau-Ponty’s work to the chorus of voices that should be led by the Maori, the Mi’kmaq, the Iroquois, the Hopi, among countless others. Plumwood’s thought offers a biting critique of Western philosophy and its characteristic rejection of the non-human in favour of the human, oppression of women in favour of men, and tendency to forsake the Earth for the sake of a reductionist-modernist narrative. Plumwood claims that these differential structures – rooted in dualisms privileging spirit over matter, heaven over Earth, and life against death – are responsible for our present ecological state. As she writes, Ecological forms of both spirituality and rationality would help us recognise the way both human and earth others nourish and support our lives, would remind us that nurturers must in turn be nurtured, and prevent us from taking from that capacity to nourish more than we put back. (Environmental Culture 240) We must bear in mind that not every form of spirituality can address the present ecological crisis, or other significant facets of human life wherein we should seek to minimize violence. Frankly, Plumwood considers some forms of spirituality to be responsible for how the western tradition has informed the ecological crisis. As she points out, …it is clear that very many different kinds of earth philosophies count as spiritual on this definition. But this includes some varieties that have been deeply damaging and antipathetic to the earth and its systems of life. For examples, we can consider certain traditional forms of spirituality that are hostile to the body, to other species, to the earth, or to women, or that foster racial or religious hatred. Or we could consider certain types of ‘blood and soil’ land spiritualities that form the basis for ethnic exclusion and war. (220) Our ecological rationality and spirituality would be better off, then, embracing those aspects of reality that have been oppressed by the various dualisms perpetuated in this tradition, specifically: matter oppressed
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in favour of spirit, the earth oppressed in favour of heaven, and – though I cannot sufficiently address this in the following sections – women in favour of men. These are the dualisms that Plumwood specifies in all her works; there are, of course, others. Plumwood’s ecological spirituality would be nothing less than a concrete change in practice that takes up and celebrates the fact that a) I am my body, not spirit, b) my body is material, but not dead, inert matter, c) material is the basis for the generation and continuity of life, and d) the Earth has intrinsic value as that place where material is the cycle of life. To briefly illustrate one facet of Plumwood’s account, I’ll turn to the food/death imaginary. The heavenist narrative of western canon assures us that after our ‘gross and fleshy bodies’ perish, our ‘true selves’ – our spirits – will depart the Earth for that place of ‘true’ value. The modernist-reductionist narrative cuts out the happy ending, assuring us that we are no more than gross, fleshy bodies made of atoms flying around in accordance with sheer luck. These narratives have ‘structured out’ a key aspect of our lives as material beings: we are made of matter that other living things appropriate in order to live. “Attention to human foodiness is tasteless,” Plumwood writes (Eye of the Crocodile 93). The notion of humans being eaten by another being is a topic reserved for horror movies. A fair illustration of this phenomenon comes to us from the season seven Simpsons episode, “Lisa the Vegetarian,” wherein a chart of the “food chain” shows animals from every phylum as inexorable prey for human predators. Recognizing our role as food for “earth-others” is not only recognition of a basic fact that philosophy knew, but chose to forget – the notion that the matter organized to form my body will someday be matter belonging to another body necessarily involves a decentering of the self: Seen in this embedded way, the ‘personal’ is not to be equated with the solipsistic hyperbolised individual whose essential self identity can be maintained beyond death in a separate realm, but acknowledges essential links to nations and communities of earth others, including the more-than-human ancestors of the human. Since these communities of nature live on after an individual’s death, a satisfying form of continuity for the fully embedded person may be found in the mutually life-giving flow of the self upon death back into the larger life-giving other that is nature, the earth and its communities of life. (Environmental Culture 227) “We are not set apart,” Plumwood reminds us (226). A new ecological ethics cannot simply be an extension of human ethics to the non-human. The decentering effect of ecological materialism means that we can enter into a dialogical ethics with “more-than-human others.” What is significant – that is, what forms a signification – for other species ought to inform our ecological ethics. When Plumwood was pulled into three deathrolls by a saltwater crocodile in the Outback, she recognized that her presence signified food to the croc – the crocodile cannot simply be considered a Disney-style antagonist (Eye of the Crocodile 5). These prejudices that inform western culture resist our ability to think ecologically. As Plumwood points out, the ability to recognize matter and place as sacred is not something that will just fall into our laps: Because its dominant traditions have been hostile to or remote from nature and place, locating the sacred in a transcendent higher world beyond the fallen earth, the development of a non-superficial spirituality of place that locates the sacred
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as immanent in particular places is highly problematic for western culture, and requires major rethinking and re-imagining. (Ecological Mastery 231) The appeal to indigenous animism is a recognition of several cultures that are present to some degree in our lives (here in the ‘colonies’), but it is at the same time met with the same resistance accountable for the ecological crisis. I appeal to Merleau-Ponty, therefore, as an illustration of a source within the western canon that readily lends itself to Plumwood’s argument and problematizes reductionistmaterialism. The Structure of Behaviour is meant to be an account of nature’s relation to consciousness given from the outside – that is, this is an account offered by initially adopting the role of the experimenter and examining various case studies. It was a direct response to the then fashionable behaviourism of the 1940s; one that is nothing other than a modernist-reductionist account of our “earthothers” offered entirely “from the outside.” What is a structure for Merleau-Ponty? It does not refer to the definition of “structure” as found in structuralism (though the fact that these definitions share a word should be interesting, especially to structuralists). His understanding of a structure has its origin in the “Gestalt” of Gestalt psychology: a structure is a system comprising multiple orders such that one order is founded upon and integrates another, but cannot be reduced to it. It is not a question of risking one hypothesis among others, but of introducing a new category, the category of ‘form,’ which, having its application in the inorganic as well as the organic domain, would permit bringing to light the ‘transverse functions’ in the nervous system … For the ‘forms,’ and in particular the physical systems, are defined as total processes whose properties are not the sum of those which the isolated parts would possess. (The Structure of Behaviour, 47) A solid patch of colour on a homogeneous surface forms a figure-background structure that cannot be reduced merely to the constituent colours. If I superimpose a second patch of colour on top of the first, a “hole” is produced in the foregrounded figure:
A structure in this sense can be applied to any observation, theory, or law with some kind of evidence – for the structure belongs to perception. As an example, … the law of falling bodies expresses the constitution of a field of relatively stable forces in the neighborhood of the earth and will remain valid only as long as the cosmological structure on which it is founded endures. Cavendish's experiment gives us an independent (en soi) law only if it is supported by the
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Newtonian conception of gravitation. But if the notion of gravitational field is introduced and if, instead of being an individual and absolute property of heavy bodies, gravitation is tied to certain regions of qualitatively distinct space as the theory of generalized relativity holds, the law could not express an absolute property of the world; it represents a certain state of equilibrium of the forces which determine the history of the solar system. (138) Gravity is a physical structure. It is foregrounded against a background of various conditions of the universe that it is not reducible to. “The university” expresses the constitution of a field of relatively oppressive forces in the neighborhood of the earth and will remain viable only as long as those upon whose backs we tread – human and more-than-human – endure. Now this is in one sense how Merleau-Ponty applies structure to animal behaviour. Animal behaviour must be considered the result of the situation as a whole – a situation that is not reducible to its constituent parts, namely stimulus, reflex, and whatever physicochemical reactions to which we try to reduce them. An animal, incapable of seizing its food with its right member after the partial excision of the appropriate cerebral region, recovers the use of it after amputation of the left member which had been substituted for the first. If at this time the excision of the centers which govern the right member is completed, the animal remains capable of utilizing it when the situation makes it imperative, for example, when the food is located outside of the cage. It is scarcely possible to posit a new emergency device corresponding to each of the phases of this experiment, for which devices the situation of the moment would be the adequate stimulus; the hypothesis that there is an entirely novel distribution of innervations for each phase, governed by the situation itself, is in much better agreement with the character of the phenomenon. (Trendelenburg cited in SB) This wall of text is one of the various case studies Merleau-Ponty analyzes in the Structure of Behaviour. The point here is that nothing stops the organism from creating and operating within a situation. Remove part of the monkey’s brain so it can’t use its right hand? It’ll use its left hand. Cut off the left hand? It’ll use its right hand when the situation calls for it. The organism lives within a milieu – or Umwelt for any Uexkellians readers out there – with which it forms a structure of behaviour. This isn’t vitalism or anything magical, but rather – We mean only that the reactions of an organism are understandable and predictable only if we conceive of them, not as muscular contractions which unfold in the body, but as acts which are addressed to a certain milieu, present or virtual: the act of taking a bait, of walking toward a goal, of running away from danger. The object of biology is evidently not to study all the reactions which can be obtained with a living body in any conditions whatsoever, but only those which are its reactions or, as one says, ‘adequate’ reactions. (151) This understanding of structure, however, breaks from that of a Gestalt in that classical Gestalt psychology treats the Gestalt as a physical entity, subject to the same reductionism that both Plumwood and Merleau-Ponty reject. The object of biology is to grasp that which makes a living being a living being, that is, not – according to the realist postulate common to both mechanism and
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vitalism – the superposition of elementary reflexes or the intervention of a ‘vital force,’ but an indecomposable structure of behavior. (43) Physicochemical reactions, to which some people are so eager to reduce the world (and I will address who “some people” are later), are only intelligible in an organism when that organism is conceived as a whole. The organism’s behaviour – its reflexes and reactions – themselves constitute a whole that is not reducible to stimulus-reflex response. And on top of all of this, we give narratives and accounts that are predicated on these reductionist explanations but not reducible to them. We have orders of structure that build upon each other, with higher structures altering lower ones in such a way that they cannot be reduced to them. Can we represent the world as these various structures? I think we can.
We have what Merleau-Ponty calls the “physical order,” which is governed by quantity. This is what reductionism aims for. The other day I was listening to another grad student here remark on the stupidity of our poster for this event (pictured above). At one point he noted, “Oh good, there are chemicals in the poster. Because there are chemicals in the environment. That’s relevant, I guess.” He’s absolutely right – chemicals qua chemistry is totally irrelevant to the environment. They make absolutely no sense unless they’re explained by the next order up.
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The vital order: those structures that operate within a situation, within a milieu. It could be plants growing to follow the light of the sun, or we could refer to the animals that react to these leaves as a source of food or a poison to avoid. The vital order is where we encounter the residue that is Plumwood’s animism. We don’t want to inject a separate living causality into matter; we need to recognize that matter, or quantity, forms a structure that is not reducible to matter qua matter or qua quantity. Matter, in the form of living things, generates situations and behaviour. It authors values – things to pursue and avoid – even if these authors are not human. Now this may sound like a gross oversimplification, and to clarify, there is indeed the human order of structure, which refers to humans as those creatures that can recognize physical and vital structures and subordinate them to even larger wholes that are not reducible to their parts.
This is where sense, or signification, dominates. Individual components come together to form a whole that makes sense. This is where, in my opinion, we may intersect with structuralism. Language, after all, is difficult to reduce: The meaning of any phrase is not reducible to its constituent words as individuals, but rather is derived from the phrase as a potato. As Merleau-Ponty notes: It is here that the notion of form would permit a truly new solution. Equally applicable to the three fields which have just been defined, it would integrate them as three types of structures by surpassing the antimonies of materialism and mentalism, of materialism and vitalism. (SB 131) Bear in mind we’re not doing away with materialism in general, but we’re getting rid of materialism conceived as dead, inert corpuscles bouncing off of each other unable to generate meaning. Matter
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generates meaning all the time, and if this meaning is not reducible to matter qua matter, it’s because matter as the basis of our perceptual organs forms miraculous internal connections that generate structures of meaning. Matter makes sense, in every way possible. This is, in a sense, the question that continued to occupy Merleau-Ponty until his death in 1961. The “being” of matter, however matter is conceived, is to form structures. Structure, while not animism itself, co-exists with the animism that Plumwood’s new spirituality calls upon; it is the spirituality, or the source of meaning, that we need to refer to in order to concretize changes in our practices that allow us to be more civil with our “more-than-human-others.”: Place loses agency along with salience, and places themselves become interchangeable, irrelevant and instrumentalisable, neutral surfaces upon which ‘rational’ human projects can be inscribed. The dullness and dislocation that is associated with placelessness has been remarked as an impoverishing feature of rationalist culture. From inside a culture that destroys such narratives, space and time are silent, the province of experts equipped with charts and theories.” (Environmental Culture, 231) Place is a structure; space is place reduced to the physical order. During Dr. Glazebrook’s Q&A session (Concordia University, Montreal), we brought up the distinction between the scientists we know personally – people who seem genuinely passionate about the environment – and “science,” which claims to be complete and impartial. For Plumwood, this is the distinction between what I’ll refer to as narrators (human or otherwise) and “the province of experts”; for Merleau-Ponty, this is the distinction between being-in-the-world and the pensée de survol (which is essentially a view from nowhere). Heideggerians may also recognize this as the distinction between Dasein and das Mann. Plumwood’s call to spirituality is a call to narrative; a call to partial knowledge – or rather, the recognition that all knowledge is partial. Practicing Plumwood’s account of the Earth as a structure opens up her ecological thought to the Merleau-Pontian corpus: a body of thought that not only resonates Plumwood’s work – with themes of embodiment, the decentring of the subject, and the careful interrogation of dualisms – but already has its own concrete style and ontology.
Bibliography Merleau-Ponty, Maurice. The Structure of Behaviour. Trans. Alden L. Fisher. Pittsburgh: Duquesne University Press, 1963. Plumwood, Val. Environmental Culture: The Ecological Crisis of Reason. New York: Routledge, 2002. The Eye of the Crocodile. Ed. Lorraine Shannon. Canberra: ANU E Press, 2012.
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The Inevitability of Care in a Posthuman World Marie-Anne Casselot
This presentation is part of my ongoing research on connections and tensions between ecofeminism and new materialism. I will focus this presentation on Sherilyn MacGregor and Rosi Braidotti: the former as a representative of “political ecofeminism” and the latter a representative of “posthuman feminism”. I argue that MacGregor’s ecofeminist approach is political and ethical, but remains anthropocentrically centered on the human issues of sex, gender and work. MacGregor’s inspiring insight into the inevitability of care, however, could be connected to Braidotti’s posthuman stance on the agency of the more-thanhuman world (ecosystems) and the nonhuman world (animals and living beings). First, I will present MacGregor’s “ecofeminist citizenship” approach, and then I will proceed to delineate Braidotti’s posthuman view of agency. I believe reading MacGregor’s political account of caregiving work with Braidotti’s posthumanist feminism can lead us to consider climate change, the environment, and the ‘Anthropocene’, by bridging the political and the ontological together. Although two different approaches, ecofeminism and new materialism can inform each other of what and who we should care for. MacGregor’s Ecofeminist Citizenship Approach Care work, traditionally associated with women and femininity, must be taken into account when we envision new ecological alternatives to capitalism. That is why Sherilyn MacGregor calls for an ecofeminist citizenship that politicizes care work by making it inevitable work-- work that has to be done, that is necessary because it allows political communities to be sustained; she thus questions the sexual/gendered division of labour and the public-private divide. MacGregor is wary and critical of (cultural) ecofeminism’s praise of mothering and caregiving as feminine dispositions. By disconnecting caregiving activities from gender roles, MacGregor aims to frame care work as inevitable and necessary, contrasting de facto with some ecofeminists’ glorification of care work as either a “mothering” for others or a “mothering” of nature. MacGregor usefully distinguishes between “caring as a set of material practices (i.e., to take care of something or someone as a form of labour) and caring as an ethical disposition (values or ethics)”. (MacGregor: 58) When some ecofeminists want to revalue women's material contribution to work, they are positing a universal ethical disposition supposedly shared by all women.1 This highly gendered conflation between caring as a praxis and caring as an ethics is rooted in patriarchal dualisms that exacerbate the traditional maternal role. While praising women's “special connection” to other human beings and to nature, some ecofeminists uncritically reinforce the association of women to motherhood and to care, and women’s subsequent relegation to the private sphere within a patriarchal and a capitalist order. To deconstruct cultural ecofeminism's problematic stance on care, MacGregor outlines three 1
“For many ecofeminists (e.g., Mies and Shiva 1993; Merchant 1996; Salleh 1997; Mellor 1997), the two are closely interrelated. Because it is women (as mothers) who do the caring, nurturing, and subsistence work that sustains human life, women care about (assume a sense of compassion, responsibility, and connection towards) their environments which in turn leads them to take action to preserve and repair them. This relationship is to be celebrated, they argue, because caring for people and environments produces special insights about the interrelated processes of life that are different from the individualistic and exploitative (read: masculine) approach to these processes that has led to environmental degradation.” (MacGregor: 58)
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practical notions to identify how it can be harmful: feminization, privatization, and externalization cast care as apolitical work. First, feminization refers to the process of socialization and the division of labour: women are taught to develop a compassionate set of values that leads them to take on caregiving roles and jobs in society (especially by overvaluing the maternal role). The feminization of care relies on “essentializing” women's supposedly more compassionate nature (their ethical disposition to caring), but it refers also to the unequal distribution of caregiving work on women, especially migrant women and women of colour. Caregiving activities (the material set of practices of caring) are thus enforced on these women, making their social positions invisible in the public realm. Second, privatization means the withdrawal of care activities from the public domain and its transfer onto individual responsibility. It is the way that states dismantle social programs and reassign caregiving work to private corporations or families; hence the responsibility of caring is displaced from the public to the private. Privatization thus intensifies women's domestic labour while reaffirming a strict public-private divide that controls the division of labour. Caregivers thus work for free, at their own economical and emotional expense. And as we know, women pay the highest price for this exploitative process. Finally, externalization is the capitalist refusal to address the social consequences of the privatization of care. Instead of being recognized as socially or collectively beneficial, as a work that sustains the political sphere, care work is dismissed as ‘private concerns’. Externalization means a removal of political discussion of care out of the public sphere. It means that states avoid taking responsibility and accountability for care practices in political discussions and practices. In other words, care must be considered a relevant political contribution to society, not merely a private and feminine task. Hence, ecofeminism’s uncritical celebration of women’s roles as caregivers is dangerous since it risks reinforcing - rather than challenging - the feminization, privatization, and externalization of care work. MacGregor’s “ecofeminist citizenship approach” separates the set of practices from the ethical attitude, but it does not ‘drop’ either of them. The material practices of caring and the ethical attitude are important; the former is inevitable and necessary (and everyone should equally contribute to it), and the latter is informed by one's upbringing and values. Ideally, in order to politicize care, we ought to separate them from gendered connotations and roles. To summarize, this “ecofeminist approach to citizenship” implies: a) that we question the publicprivate divide within cultural ecofeminism, through ecopolitical alternatives to capitalism, b) that we “degender” caring activities, and c) that we make care a crucial and inevitable part of work. Blurring the private-public distinction can allow care to become a political issue inscribed within our definition of citizenship.2 In her words, “an ecofeminist approach demands that care is not only an ethic that can inform citizenship but as a set of time consuming practices that make citizenship possible.” (MacGregor: 79) Care activities should be valued as an important yet inevitable contribution to society regardless of gender. MacGregor casts care work as “inevitable” because it has to be done: it cannot be totally removed from the private sphere. For instance, caregiving work like food transformation, healing psychological or physical wounds, cleaning a household, are all examples of work that is done within what we call the ‘private sphere’, but it has a real political impact in the sense that it allows one to go about her life, professionally and/or politically. Importantly, seeing care as necessary work also acknowledges our
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MacGregor addresses this criticism to both ecofeminists and ecological political theorists : “At a minimum, an ecofeminist approach to citizenship needs to call into question the public-private divide that is taken for granted in both green political theories and in ecofeminist narratives that celebrate care.” (MacGregor: 78)
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inherently interdependent nature. It is impossible not to do care work for ourselves and for others, and we reciprocally need care from others.3 MacGregor thus highlights how the distribution of care work is an issue related to a global transformation of economy in general. In striving for new ecological ways to rethink cities and communities, we must take into account the distribution of necessary work such as caregiving activities.45 In order to maximize diversity in decision-making processes, MacGregor points out the importance of a thoughtful non-gendered (and non-racialized) distribution of necessary work in sustainable ecological alternatives to capitalism. To avoid the feminization of care work, an ecofeminist approach to citizenship would make care practice(s) a crucial part of political engagement. If everyone partakes in care practice(s), ideally its gendered burden would decrease. Hence the active participation of women in political and environmental change would be encouraged.6 I agree with MacGregor that we ought to have “a public debate over who does what, when, how and under what conditions [and that this] ought to be built in to the very definition of environmental citizenship.” (MacGregor, 2007, 10) Necessary labor is a crucial part of our political discussions and practices on sustainability and environmental change. Sustainability is a feminist issue.7 Braidotti’s Posthumanist Feminism Yet if care is inevitable, within such a political ecofeminist approach, we are actually caring specifically for human beings. In the face of climate change and the ecological crisis, should we not extend care to the more-than-human world?8 Should we not seek different ways to think about nature? 3
“Also central to feminist citizenship theory is an acknowledgement that as embodied human beings, all citizens are inevitably dependent on others for care and nurturance.” (MacGregor, 2007: 8) 4 “For example, without an analysis of the gendered division of necessary labor, green notions of self-reliance, sustainable communities, and “doing one’s bit” at home and in the public domain threaten to intensify women’s already unsustainable burden of responsibility for care. (MacGregor: 77) Notions of “self-reliance”, “self-discipline” and “sustainability”, if disregarding care and gender, obscure our dependent nature and women's unequal burden in care work …“sustainability”, if disregarding care and gender, obscure our dependent nature and women's unequal burden in care work. 5 “The nature of household or family relationships is not considered relevant to democratic public debate even though changing the practices and behaviour of individual citizens in the private sphere is becoming an important part of many visions of an ecological society. Moreover, when environmental citizenship is said to include a sense of personal responsibility for actions in the private sphere, the private sphere seems to be synonymous with (unsustainable) consumption or it is a place where people procreate (too much). Only in rare cases is it considered to be a space of productive and reproductive work as feminists have been arguing since the 1970s. And in all cases, self-discipline and self-reliance are ecological virtues.” (MacGregor, 2007 : 8) 6 “Citizenship, understood as being about active participation in the public sphere, is by definition a practice that depends on ‘free time’; it is thus not designed for people with multiple roles and heavy loads of responsibility for productive and reproductive work. As Carole Pateman (1988) and Anne Phillips (1993) have argued, modern theories of citizenship fail to take into account the sexual division of labour that not only sustains democracy but also makes it extremely difficult for women (and others with time scarcity) to participate as equal members of a political community.” (MacGregor, 2007:8) 7 “Few ecopolitical theorists have addressed the question of how necessary labour [...] will be distributed in a sustainable society. [...] Yet few greens call, [...] for the democratization of the household that would allow for a more equitable distribution of this necessary work. In fact, the question of how green practices in the private sphere are to be initiated, distributed, and sustained is seldom, if ever, asked.” (MacGregor, 2007: 8) 8 By “more-than-human”, I understand natural elements such as air, soil, water, temperature that affects living beings, but also human-made forces that surrounds us and are part of our way of life (communication systems, waste, etc.). They all impact the environment in various ways.
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Posthuman feminists argue that we ought to seek both interspecies and intergenerational justice if we are to live through the ecological crisis that we are already experiencing. For example, Rosi Braidotti focuses her work on ontologies and epistemologies of nature, rather than examining alternative economies or environmental policies; I think her posthumanist stance could decenter MacGregor’s anthropocentric perspective on gender and work and even possibly extend care to the more-than-human world. MacGregor addresses her critique to ecofeminists and to ecologists: we must rethink the distribution of care work if we want to be sustainable. However, her framework limits care work within the delineations of human societies. MacGregor thinks about human relationality and intrinsic dependency within ‘our’ communities. Posthumanist feminists, on the other hand extend agency to (other living) nonhuman beings, and to the more-than-human world because it is on them that we rely also. Framing care as inevitable could go along with a posthuman account of agency because we have to be attuned to the world - its flux and its multiple “becomings”, as per Braidotti’s account. Braidotti’s nomadic account of the “becoming-” aims at decentering the subject from the dualistic grip of oppositional consciousness that is traditional in identity politics.9 Her Deleuzian understanding of becoming takes into account embodiment as it is internally differentiated, or in other words, every being that ‘becomes’ does so because of some specificities10 proper to its species, its gender or its race. Indeed, Braidotti posits three axes of differences: sexualization, racialization and naturalization (sometimes she also adds animalization) that will determine one’s process of becoming. Braidotti’s becomings are multiple paths of being that change according to one’s positioning: “These point of asymmetrical and differentiated paths of becoming, which unfold from dissymmetrical and ultimately irreconcilable starting-off subject positions.” (Braidotti: 49) What is particularly difficult to grasp about her account of becomings is that it’s radically anti-essentialist while being neo-materialist:specific embodied subjectivities are the starting point of her thought, but (crucially) these embodied locations do not fix/determine identity. Furthermore, all embodied agents are “surfaces of intensities and an affective field in interaction with others”11 (Braidotti 2011: 50), which means that we are always affected and affecting each other, whatever species we are. Subjects are never, for Braidotti, fixed and determined; rather, a subject, for example ‘woman’, is always multiple, complex, and constituted by a number of variables.12 Braidotti believes that those referents of otherness such as gender, race, and species can be useful to politically organize sometimes, but ideally we should move away from identity politics because of the intrinsic risk of essentialism. Subjectivity is closely related to agency and for Braidotti and other posthuman feminists, agency is always ‘co-emergent’ with the world: biology, nature, organisms, objects and sociohistorical contexts all shape one another. In an Aristotelian vein, Braidotti argues that we ought to rethink the current tendency to conceive of life as bios - centering itself around human needs and rights - in favour of a concept of life as zoe - a “generative vitality”, “a transversal force cutting across previously separated domains” (Braidotti 2011: 92). Zoe is the “endless vitality of life as a continuous becoming” where the “subject is dissolved and regrounded in an eco-philosophy of multiple belongings” (Braidotti 2006: 41). 9
(becoming-woman, -nomadic, -minoritarian, -animal, -posthuman) “A nomadic becoming-woman starts from the recognition of the dissymmetry between the sexes and the emphasis on female specificity as the starting point for the process of redefining subjectivity. […] It moves toward a broadening of the traditional feminist political agenda to include a larger spectrum of options […] issues that seem to have nothing to do with women at first sight.” (Braidotti: 41) 11 Hence Braidotti argues that her nomadic theory is anti-essentialist. “In other words, feminist emphasis on embodiment goes hand-in- hand with a radical rejection of essentialism.”(Braidotti 2011: 50). 12 “One of the key points is not so much that sexualized, racialized and naturalized differences don’t matter, but rather that they no longer coincide with sexually, racially and naturally differentiated bodies. Advanced capitalism has delinked the empirical referents of otherness (woman/native/earth other) from the imaginary institutions of sexuality/race/nature, which traditionally framed them. […] The sexualized, racialized and naturalized others are no longer the boundary markers of categorical distinctions.” (Braidotti: 51) 10
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Moving from bios to zoe entails a change of position and a change of ontological status of the subject/agent: “The zoe-centered subject is shot through with relational linkages of the symbiotic contaminating/viral kind that interconnect it to a variety of others, starting with the environmental or ecoothers.” (Braidotti 2011: 95) How we think about life itself should be decentered from humanity, and it should have a strong emphasis on what Braidotti calls the “prehuman” and “nonhuman” elements that “compose a web of forces, intensities and encounters” that ground subjectivities (Braidotti 2006: 41). For example, thinking about the becoming-animal, she states that animals express their own kind of immanence while in the same material world; they are in zoe just as we are. They are embodied subjects with a consciousness completely immersed in their habitat/environments, unlike human beings who have created a distance between them and their environments. Braidotti thus posits a radical interdependence between various subjects (various becomings) in this material world we inhabit all together. Her ontological nomadic philosophy presents this multiple belongings of various subjects as affectively interconnected. Finally, she says that her nomadic theory implies a “bio-centered”/“trans-species” egalitarianism deeply rooted in ecological thinking as it “strikes an alliance with the productive force of zoe – or life in its inhuman aspects.” (Braidotti 2006: 97). Braidotti advocates for this “bio-centered egalitarianism” by recognizing the generative and positive account of the non-human, the more-thanhuman, and inorganic life. Given her view of life as zoe, Braidotti is adamant to expand our care beyond humanity itself in order to counteract ecological degradation. In her book Transpositions, Braidotti affirms being wary of the liberal subject constructed in traditional moral ethics of care. As such, she sees the ethics of care as an accountable and situated practice – a moral variation of feminist standpoint theory. Although she acknowledges that “care entails qualities of attentiveness, responsibility, competence and responsiveness that can help construct better citizens as well as making better agents.” (Braidotti 2006: 119), she remains critical of the liberal subject embedded in a care theory that is construed as anthropocentric or humanist. Rather, Braidotti believes that interconnectedness (on her account of the multiple becomings) constitutes us as active ‘caring’/affective subjects. Analyzing the power dynamics of the gendered division of labor (as per MacGregor’s account) and the distribution of care work would be one practical step for Braidotti, but it would not be sufficient to explain how caring subjects come to be. She strives for an ontological change in our categories of subjects and agents that would lead us away from a “humanist impasse”. Interestingly, then, her view of sustainability is closely linked with subjectivity: What sustainability stands for, then, is a regrounding of the subject in a materially embedded sense of responsibility and ethical accountability for the environments she or he inhabits. What is at stake is the very possibility of future, of duration or continuity. Becomings are the sustainable shifts or changes undergone by nomadic subjects in their active resistance against being subsumed in the commodification of their own diversity. (Braidotti 2006: 137). Here, then, Braidotti’s ontological version of sustainability can enhance MacGregor’s political/practical view of the inevitability of care within sustainable communities. There are multiplicities of becomings in the world, and if we really aim for sustainability, we ought to integrate a variety of beings and forces (beyond our human collectivities) that we affect and by whom we are affected. I think that Braidotti’s definition of agents as “affective entities” is compatible with MacGregor’s stance on the importance of caring as an ethical disposition. MacGregor’s ‘ecofeminist citizenship’ considers important the set of caring practices and the ethical attitude of caring, although she wants to separate one from the other, and more importantly disconnect them from gender roles. I push this line even further by saying that it is all affective agents who deserve care to some degree. We also need to be sensitive to how non-human affective agents, such as animals, demonstrate care in ways that are hard for our human minds to grasp.
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MacGregor’s ecofeminist citizenship recasts care as a crucial political practice for ecological organising, and Braidotti’s account of becomings and affects, in its assertion that affective entities are all interconnected, further pressures such an ecofeminist political view. I do not think Braidotti’s viewpoint undermines MacGregor’s; rather I am positive that they can inform and complement each other. In conclusion, if “caring” (as a humanist concept) for rocks or mountains or the effects of garbage disposals on climate, or the change in air currents, seems irrelevant, then being attuned or responsive could work instead for this Anthropocene era that is ours, already here. It is inevitable that we will have to be attuned and responsive to other beings and forces that inhabit and evolve in this shared world and I believe a strong feminist commitment, be it a political ecofeminist or a posthumanist one, is necessary to overcome our destructive anthropocentric worldview.
Bibliography Braidotti, Rosi. Nomadic Subjects: Embodiment and Sexual Difference in Contemporary Feminist Theory. New York: Columbia University Press, 2011. Transpositions: On Nomadic Ethics. Cambridge: Polity Press, 2006. MacGregor, Sherilyn. “From care to citizenship: Calling ecofeminism back to politics.” Ethics & the Environment 9.1 (2004):56-84. Beyond mothering earth: ecological citizenship and the politics of care. Vancouver: UBC Press, 2007.
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Skeptical Symmetry: A Wittgensteinian Approach to Scientific Reasoning Erik Nelson In a 1926 review of Russell and Whitehead’s Principia Mathematica, the logician Harry Sheffer argues, “the attempt to formulate the foundations of logic is rendered arduous by a...‘logocentric’ predicament. In order to give an account of logic, we must presuppose and employ logic” (228). The logocentric predicament has spilled very little ink when compared to its older sibling, Hume’s problem of induction. The major reason for this seems to be that most philosophers simply assume that deductive inferences are prima facie justified. For example, Peter Lipton has written that inductive inferences are “underdetermined by evidence and the rules of deduction…”, while valid deductive arguments are “perfect truth conduit[s]” and their justification is achieved simply by “show[ing] that arguments we judge valid are in fact so” (392). In this paper I will argue that the philosophers have wrongly assumed that there is an asymmetry between the problem of induction and the logocentric predicament, and that the exposure of this symmetry will reveal that skepticism is unavoidable when demanding justification for the structure of reasoning. Using a Wittgensteinian approach, I will argue that justification has an internal relation with deductive and inductive inferences. Separating the concepts so that one can be applied to the other is, then, a misunderstanding of the role that these words play within scientific reasoning. 1. Induction Karl Popper defines inductive inferences as ones that pass “from singular statements…such as accounts of the results of observations or experiments, to universal statements, such as hypothesis or theories” (406). But the finite capabilities of the observer means that there is always the possibility of an exception that the observer has failed to perceive. If one has never seen an albino raven, then the inference that all ravens are black will move from true particular observations to a false generalized conclusion. Popper argues that justification for induction will have to be found either through analytic statements or synthetic statements. Popper’s reason for denying justification through analyticity is that such a justification would have to be formulated in purely logical terms, collapsing induction into a form of deduction. He writes, “the principle of induction must be a synthetic statement; that is a statement whose negation is not self-contradictory but logically possible” (407). But valid deductive arguments preserve truth, which means that a deductive proof for induction would end up showing a relation between the premises and the conclusion that always holds. Since synthetic statements are particular observations, using them to prove a universal statement would be an inductive form of inference, thereby justifying induction by induction. This leads inevitably to an infinite regress, since every inductive principle would require a further principle of induction. Popper deals with the problem of induction by arguing that science is actually a deductive process. He argues that testable predictions can be derived from a hypothesis. The derived predictions are then compared with the results of scientific experiments and if the predictions are shown to be false, “their falsification also falsifies the theory from which they were logically deduced” (411). If the process does not show the predictions to be false, then one can say that they have “proved [their] mettle”, or that they are “corroborated” (411). A theory or hypothesis is never actually proven to be true; it is only shown to not be false. For Popper, this solves the problem of induction because he has removed the need for an unjustified form of inference from the scientific method. Popper’s proposal turns entirely on the assumption that deductive inferences do not face the same justificatory problems that are faced by induction.
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2. The Logocentric Predicament But deduction does have problems that are symmetrical to those faced by induction. Wittgenstein noticed this problem in both Russell’s and Frege’s works, pointing out in the Tractatus: If p follows from q, I can conclude from q to p ; infer p from q. The method of inference is to be understood from the two propositions alone. Only they themselves can justify the inference. Laws of inference, which – as in Frege and Russell – are to justify the conclusions, are senseless and would be superfluous (§ 5.132). Ricketts argues that this passage is similar to Lewis Carroll’s skepticism in his paper “What the Tortoise Said to Achilles” (11-12). Carroll imagines a dialogue between the tortoise and Achilles in which Achilles tries to convince the tortoise that Modus Ponens is a valid argument. The tortoise accepts that the premises are true and that the conclusion follows if the premises are accepted as true, but then refuses to accept the conclusion. Achilles’ answer to this infuriating dilemma is to introduce an inference rule as a premise itself. The new premise says that the tortoise has to accept the conclusion if he accepts the premises and accepts that the conclusion follows from the premises. The tortoise is able to maintain his skepticism even in the face of the new premise by demanding a further premise for the justification of the new inference. This leads the bewildered Achilles into an infinite multiplication of premises, since for each new inference the tortoise is able demand another premise. If this is the type of dilemma that Wittgenstein is referring to, then one would expect that Frege and Russell have made the same mistake as Achilles. Ian Proops argues that one would have to read Frege and Russell uncharitably to find this mistake in their work, especially since they were both aware of Carroll style problems and explicitly avoided them. Proops points to a passage in the Principia Mathematica in which Russell writes: The principle of deduction gives the general rule according to which the inference is made, but is not itself a premise in the inference. If we treated it as a premise, we should need either it or some other general rule to enable us to infer the desired conclusion, and thus we should gradually acquire an increasing accumulation of premises without ever being able to make any inference... (Russell and Whitehead qtd. in Proops 285). Russell is referring to tortoise style problems and then avoids them by giving inference rules the “status of informal principles that are employed in making inferences but not recorded as lines in the proofs” (Proops 286). Carroll is often viewed as failing to notice the difference between inference rules and suppressed premises (Smiley 727). Proops and Smiley both argue that these early incarnations of the logocentric predicament are easily dissolved once this distinction has been made. Smiley argues that inference rules, unlike suppressed premises, exist in an external relationship to the structure of arguments, meaning that the original structure of the argument does not have to change in order to justify the inference (731). Inference rules can be interpreted as kind of general permission that exists in the metalanguage instead of the object language (Hanna 57). Once Achilles is able to point out this distinction, the Tortoise will be unable to get his infinite regress going. To demand a further premise that asserts the validity of the previous inference means that the tortoise has failed to understand that validity is generated by following rules, not by hidden premises.
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This critique of Carroll’s paper has a certain amount of initial appeal, but it is hard not to feel as if this interpretation has failed to understand the full weight of the problem. While metalogic may be able to remove the problem from the object language, it is not clear how a similar problem will not arise in the metalanguage. Quine points out that if logic is to come from generalized conventions, the “derivation of the truth of any specific statement from the general convention thus requires a logical inference, and this involves us in an infinite regress...” (103). In other words, moving from general conventions or rules to particular instances requires or presupposes a further logic that must also come from further conventions or rules and so on. This means that the deductive move from generalised rules to particular instances invites just as much skepticism as the inductive move from particular instances to generalised rules. Smiley’s solution also invites skepticism about rule following in a manner that is similar to Kripke’s reading of the later Wittgenstein. Kripke points out that while rules may be general, one can only ever apply them to a finite number of cases and therefore one can never really know if the rule one thought they or another was following only applied to the past cases and not to future ones (Hymers 2010, 132). For example, a student could have thought they were following the rule +2, but when exposed to an extremely large number they discover that they are actually following the rule +2 only until a certain number is reached - at that point, the rule becomes +4. In the case of general logical rules, one may think that one is following a certain metalogical rule. But when faced with a particular instance, one may find that one is following something quite different than initially perceived. If there is an infinite amount of cases to which a general rule can be applied, and the rule can only be read off a finite amount of previous applications, then Kripke has argued that there is no way to know what rule is actually being followed (Hymers 2010, 132). By taking Russell’s suggestion and creating a hierarchy of languages, we have just allowed tortoises to multiply. 3. Is Wittgenstein a Tortoise? Instead of interpreting Wittgenstein’s remarks on inference as a tortoise style critique, there is good reason to see Wittgenstein waving away unnecessary conceptual machinery. In other words, Wittgenstein is pointing out that both Frege and Russell have spent a lot of time guarding against problems that do not exist. In examining the nature of logical relations, Wittgenstein writes that if God “creates a world in which certain propositions are true, he creates thereby also a world in which all propositions consequent on them are true” (§5.132) While this line and the ones following it could be interpreted as Wittgenstein arguing that even God cannot escape logic, Wittgenstein’s main point is that logical relations are internal to the propositions themselves. He writes that a “proposition asserts every proposition which follows from it” (§5.124), meaning that a logical relation is not something that is separate from the proposition itself. In other words, logical relations are a part of the structure of the proposition. If it is not obvious that one proposition follows from another, then it is a failure of the symbolism. The logician’s job is to symbolize the structure of propositions as perspicuously as possible. If one proposition follows from another, this relation does not come about by being connected in another proposition; rather,“these relations are internal, and exist as soon as, and by the very fact that the propositions exist” (§5.131). For Wittgenstein, “a property is internal if it is unthinkable that its object does not possess it” (§4.123). Internal relations are similar: a relation is internal if it is unthinkable that this relationship does not hold. He uses the example of two shades of blue, one brighter and one darker than the other. The two shades exist in an internal relationship with each other because their very identity is at least partly composed of the relation in which they stand (Hymers 1996, 593). Part of the identity of the shade dark blue is parasitic on lighter shades of blue and vice versa. This relation does not exist because one has held up two shades of blue beside each other; instead the relation is a part of the structure of each. In other words, God could not create a world with lighter and darker shades of blue whose identity - of being lighter or darker - was independent of the relation between those shades of blue. In logic, if p follows from q, then it is unthinkable that they do not stand in the relation. If q is true, then everything that
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follows from q must also be true: the structure of the propositions means that even God cannot deny this fact. This means that the fault might not be with the tortoise for denying the logical inference, but with Achilles or the logician, for not creating a notation that is perspicuous enough to lay bare the structure of the propositions. If they had, the tortoise would have to cover his ears in order to continue denying the logical inference. Wittgenstein writes, “the proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand” (§4.022). Achilles has made the mistake of thinking that he can say what the inference rule is, he thinks that by adding a further premise it is possible to force the tortoise into accepting the conclusion if he accepts the premises. The mistake is not that Achilles could have avoided the infinite regress if he presented his inference rule as a metalogical rule instead of a premise within the object language; the mistake is to think that he could say anything about the rule. The rule needs to be shown, and what needs showing is in the propositions themselves, not in an external logical structure. Wittgenstein thinks that if the internal structure can be properly shown through some logical notation, the tortoise would have to also deny reality in order to continue denying the inference. In § 4.023 Wittgenstein writes that while descriptions are about the external features of an object, “propositions describe reality by its internal properties.” Propositions are able to represent the world because they share a logical structure with the world, so when the logical structure of the proposition is exposed, the logical structure of the world is also exposed. Therefore, the tortoise’s denial becomes a different type of skepticism, one that is similar to traditional Cartesian skepticism. 4. Language Games and Tortoises While Wittgenstein does provide the tools to the answer the tortoise in the Tractatus, it still might not seem very persuasive, mostly because there are few philosophers who find the metaphysics of the Tractatus all that compelling, including the later Wittgenstein himself. But Wittgenstein’s answer to the tortoise is actually strengthened once the metaphysics of the Tractatus are left behind. The idea of internal relations survives Wittgenstein’s move to language games and exists in their grammar (the structure). For the later Wittgenstein, the meaning of a word is no longer determined by the logical relation it shares with reality but by “its use in the language” (2009, §43). Two concepts are internally related if “in order to understand one I must also understand the other” (Hymers 1996, 597). If we are teaching concepts to a child, and the only way for the child to understand the meaning of one concept is to also teach them another concept, then we can say that those concepts are internally related. Wittgenstein once again uses colours as an example. He notes that when one says “white is lighter than black” it seems like it is expressing something about the essence of the two colours...” (1972, §105). But this does not make very much sense because essence makes one think that there is something “inside” or in the “constitution” of a thing; it is hard to imagine what it would mean for there to be something inside black. This leads Wittgenstein to ask “Whom do we tell ‘White is lighter than black’? What information does it give?” (§105). The idea that “white is lighter than black” seems to be already given if one understands the concepts in the proposition. This shows that white and black are internally related. If one uses the words ‘white’ and ‘black’ without understanding this relation between them, then it is unlikely that one will be able to use these words in a communicative or non-confused way. The process of justification has an internal relationship with deductive and inductive inference rules. Wittgenstein notes that it is tempting to try to justify the “rules of grammar” by saying, “But there really are four primary colours” (1967, §331). The assertion of this fact, however, cannot justify: the colour words one uses, that some are primary and others are not, the number of colours that are primary, or even that one has divided up the world in such a way. Any attempt to do so will use the very rules and structures one is trying to justify (O’Neill 8). We are now in a position to diagnose why the justification of deduction and induction has been such an abysmal failure.
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Deductive and inductive inferences play an internal role in the process of justification: in order to understand justification, one must (at least, implicitly) understand the processes of deduction and induction and vice versa. This internal relationship is clear when one tries to imagine what justificatory practices would look like without deduction or induction, or when one tries to imagine explaining deduction to someone who has no understanding of the concept of justification. Wittgenstein’s early idea of a relation being internal if it is unthinkable that the relation does not hold is also relevant – these scenarios are unimaginable. Since the process of deduction is internal to the practice of justification, to ask for its justification is ultimately confused. From this perspective, it makes complete sense that trying to justify deduction through deduction does not work. Like the grammar of colours, the process has to presuppose itself if one attempts to justify it in this way. Induction fails to justify deduction because this is an attempt to step outside the language game of justification itself. A justification for deduction by induction seems to cannibalize deduction. An inductive proof for deduction can only ever say: Since every valid deductive inference from true premises used thus far has also had a true conclusion, the relation between the premises and the conclusion will probably continue to hold. Deductive proofs can only be, at best, inductively true. But such a ‘proof’ seems to make every deductive inference just a form of induction. O`Neill writes that using a different conceptual grammar to the grammar that one is trying to justify cannot work, because the “justification will employ concepts different from our own, and will thereby be irrelevant to the justification of our grammar”, and since the “rules of grammar determine meaning...the employment of a different conceptual grammar will involve the use of different concepts” (8). While induction and deduction are both internal to justificatory practices, they are different concepts, and therefore they play different roles in the process of justification. Using one to justify the other is the attempt to use something completely irrelevant to its justification. An inductive proof cannot justify deduction, instead it can only show itself. The fact that deduction and induction are internal to justificatory language games does not make them prima facie justified. Instead, this relation points out the way in which the tortoise’s demand is inappropriate— he is asking Achilles to do something unthinkable. The later Wittgenstein does not give a solution to the logocentric predicament. Instead, Wittgenstein offers a therapeutic approach, whose aim is to dissolve the problem by utilizing the tools of internal relations, grammar, and language games. 5. Conclusion In this paper I have argued that Wittgenstein’s understanding of internal relations is central to both his early and later responses to the logocentric predicament. In the Tractatus he asserted that internal relations are those in which it would be unthinkable if the relation did not hold and that those relations are a part of the propositions themselves. In his later work, Wittgenstein’s understanding of internal relations changes slightly, as he sees an internal relation as holding if, and only if, in order to understand one concept, one must understand another. I have argued that an internal relation holds between the concept of justification and the concepts of deduction and induction. Both Popper and the tortoise’s request for a justificatory inference rules is ultimately confused.
Bibliography Carroll, Lewis. "What the Tortoise said to Achilles." Mind. 4.14 (1895): 278-280. Hanna, Robert. Rationality and Logic. Cambridge: MIT, 2006.
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Hymers, Michael. "Internal Relations and Analyticity: Wittgenstein and Quine."Canadian Journal of Philosophy 26.4 (1996): 591-612. Wittgenstein and the Practice of Philosophy. Peterborough: Broadview, 2010. Lipton, Peter. “Introduction.” Philosophy of Science: The Central Issues. Ed. Martin Curd et al. 2 Ed. New York: Norton, 2013. 390-405. nd
O'Neill, Martin. "Explaining ‘The Hardness of the Logical Must’: Wittgenstein on Grammar, Arbitrariness and Logical Necessity." Philosophical Investigations 24.1 (2001): 1-29. Popper, Karl. “The Problem of Induction.” Philosophy of Science: The Central Issues. Ed. Martin Curd et al. 2 Ed. New York: Norton, 2013. 406-411. nd
Proops, Ian. “The Tractatus on Inference and Entailment.” From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Ed. Erich H. Reck. New York: Oxford, 2002. 283-307. Quine, W. V. “Truth by Convention.” The Ways of Paradox and Other Essays. Cambridge: Harvard, 1976. 77-106. Ricketts, Thomas G. "Frege, the Tractatus, and the Logocentric Predicament."Nous 19.1 (1985): 3-15. Sheffer, Henry M. “Review of Principia Mathematica.” Isis 8.1 (1926): 226-231. Smiley, Timothy. "A Tale of Two Tortoises." Mind 104.416 (1995): 725-736. Wittgenstein, Ludwig. Philosophical Investigations. Trans. and Ed. G. E. M. Anscombe, et al. Singapore: Blackwell, 2009. Remarks on the Foundations of Mathematics. Trans. and Ed. G. H. von Wright, et al. Cambridge: MIT, 1972. Tractatus-Logico-Philosophicus. Trans. and Ed. C. K. Ogden. New York: Cosimo, 2007. Zettel. Ed. and Trans. G. E. M. Anscombe, et al. Oxford: Blackwell, 1967.