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Animal Cognition, Species Invariantism, and Mathematical Realism

In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61 (2019)

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  1. Methods of Ethics and the Descent of Man: Darwin and Sidgwick on Ethics and Evolution.Hallvard Lillehammer - 2010 - Biology and Philosophy 25 (3):361-378.
    Darwin’s treatment of morality in The Descent of Man has generated a wide variety of responses among moral philosophers. Among these is the dismissal of evolution as irrelevant to ethics by Darwin’s contemporary Henry Sidgwick; the last, and arguably the greatest, of the Nineteenth Century British Utilitarians. This paper offers a re-examination of Sidgwick’s response to evolutionary considerations as irrelevant to ethics and the absence of any engagement with Darwin’s work in Sidgwick’s main ethical treatise, The Methods of Ethics . (...)
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  • Knowledge Under Threat.Tomas Bogardus - 2014 - Philosophy and Phenomenological Research 88 (2):289-313.
    Many contemporary epistemologists hold that a subject S’s true belief that p counts as knowledge only if S’s belief that p is also, in some important sense, safe. I describe accounts of this safety condition from John Hawthorne, Duncan Pritchard, and Ernest Sosa. There have been three counterexamples to safety proposed in the recent literature, from Comesaña, Neta and Rohrbaugh, and Kelp. I explain why all three proposals fail: each moves fallaciously from the fact that S was at epistemic risk (...)
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  • Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
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  • Frege, Mill, and the Foundations of Arithmetic.Glenn Kessler - 1980 - Journal of Philosophy 77 (2):65-79.
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  • An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Stucture.James Franklin - 2014 - Palgrave MacMillan.
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...)
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  • Moral Epistemology: The Mathematics Analogy.Justin Clarke-Doane - 2014 - Noûs 48 (2):238-255.
    There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...)
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  • On the Limits of Infants' Quantification of Small Object Arrays.Lisa Feigenson & Susan Carey - 2005 - Cognition 97 (3):295-313.
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  • Exact and Approximate Arithmetic in an Amazonian Indigene Group.Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene - 2004 - Science 306 (5695):499-503.
    Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...)
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  • Numerical Cognition and Mathematical Realism.Helen De Cruz - 2016 - Philosophers' Imprint 16.
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...)
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  • Testimony and Children’s Acquisition of Number Concepts.Helen De Cruz - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. London, UK: pp. 172-186.
    An enduring puzzle in philosophy and developmental psychology is how young children acquire number concepts, in particular the concept of natural number. Most solutions to this problem conceptualize young learners as lone mathematicians who individually reconstruct the successor function and other sophisticated mathematical ideas. In this chapter, I argue for a crucial role of testimony in children’s acquisition of number concepts, both in the transfer of propositional knowledge (e.g., the cardinality concept), and in knowledge-how (e.g., the counting routine).
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  • What is the Benacerraf Problem?Justin Clarke-Doane - 2017 - In Fabrice Pataut (ed.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity. Springer Verlag.
    In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem (...)
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  • Non-Symbolic Arithmetic in Adults and Young Children.Hilary Barth, Kristen La Mont, Jennifer Lipton, Stanislas Dehaene, Nancy Kanwisher & Elizabeth Spelke - 2006 - Cognition 98 (3):199-222.
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  • From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
    Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...)
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  • Natural Goodness.Philippa Foot & Thomas Hurka - 2001 - Mind 112 (445):130-139.
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  • Natural Goodness.Philippa Foot - 2001 - Tijdschrift Voor Filosofie 64 (3):604-606.
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  • Have Elephant Seals Refuted Aristotle? Nature, Function, and Moral Goodness.Micah Lott - 2012 - Journal of Moral Philosophy 9 (3):353-375.
    An influential strand of neo-Aristotelianism, represented by writers such as Philippa Foot, holds that moral virtue is a form of natural goodness in human beings, analogous to deep roots in oak trees or keen vision in hawks. Critics, however, have argued that such a view cannot get off the ground, because the neo-Aristotelian account of natural normativity is untenable in light of a Darwinian account of living things. This criticism has been developed most fully by William Fitzpatrick in his book (...)
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  • Metaethics and the Empirical Sciences.Richard Joyce - 2006 - Philosophical Explorations 9 (1):133 – 148.
    What contribution can the empirical sciences make to metaethics? This paper outlines an argument to a particular metaethical conclusion - that moral judgments are epistemically unjustified - that depends in large part on a posteriori premises.
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  • Numerical Competence in Animals: Definitional Issues, Current Evidence, and a New Research Agenda.Hank Davis & Rachelle Pérusse - 1988 - Behavioral and Brain Sciences 11 (4):561-579.
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  • Are There Genuine Mathematical Explanations of Physical Phenomena?Alan Baker - 2005 - Mind 114 (454):223-238.
    Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...)
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  • Core Systems of Number.Stanislas Dehaene, Elizabeth Spelke & Lisa Feigenson - 2004 - Trends in Cognitive Sciences 8 (7):307-314.
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  • Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
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  • Morality and Mathematics: The Evolutionary Challenge.Justin Clarke-Doane - 2012 - Ethics 122 (2):313-340.
    It is commonly suggested that evolutionary considerations generate an epistemological challenge for moral realism. At first approximation, the challenge for the moral realist is to explain our having many true moral beliefs, given that those beliefs are the products of evolutionary forces that would be indifferent to the moral truth. An important question surrounding this challenge is the extent to which it generalizes. In particular, it is of interest whether the Evolutionary Challenge for moral realism is equally a challenge for (...)
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  • Giving the Boot to the Bootstrap: How Not to Learn the Natural Numbers.Lance J. Rips, Jennifer Asmuth & Amber Bloomfield - 2006 - Cognition 101 (3):B51-B60.
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  • Spontaneous Number Representation in Mosquitofish.Marco Dadda, Laura Piffer, Christian Agrillo & Angelo Bisazza - 2009 - Cognition 112 (2):343-348.
    While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated that in fish the same set of signature limits that characterize non-verbal numerical systems in primates is present but yet to provide any demonstration that fish can really represent number rather than basing their (...)
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  • A Darwinian Dilemma for Realist Theories of Value.Sharon Street - 2006 - Philosophical Studies 127 (1):109-166.
    Contemporary realist theories of value claim to be compatible with natural science. In this paper, I call this claim into question by arguing that Darwinian considerations pose a dilemma for these theories. The main thrust of my argument is this. Evolutionary forces have played a tremendous role in shaping the content of human evaluative attitudes. The challenge for realist theories of value is to explain the relation between these evolutionary influences on our evaluative attitudes, on the one hand, and the (...)
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  • The Nature of Mathematical Knowledge.Philip Kitcher - 1985 - Philosophical Quarterly 35 (138):104-107.
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  • Warrant and Proper Function.Alvin Plantinga - 1993 - Oxford University Press.
    In this companion volume to Warrant: The Current Debate, Plantinga develops an original approach to the question of epistemic warrant; that is what turns true belief into knowledge. He argues that what is crucial to warrant is the proper functioning of one's cognitive faculties in the right kind of cognitive environment.
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  • A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation.John Stuart Mill (ed.) - 1843 - Cambridge University Press.
    This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work constitutes (...)
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  • Reply to Copp: Naturalism, Normativity, and the Varieties of Realism Worth Worrying About.Sharon Street - 2008 - Philosophical Issues 18 (1):207-228.
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  • The Descent of Man, and Selection in Relation to Sex.Charles Darwin - 1898 - Plume.
    The most accessible edition ever published of Darwin’s incendiary classic, edited by “as fine a science essayist as we have” ( New York Times ) The Descent of Man , Darwin’s second landmark work on evolutionary theory (following The Origin of the Species ), marked a turning point in the history of science with its modern vision of human nature as the product of evolution. Darwin argued that the noblest features of humans, such as language and morality, were the result (...)
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  • Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
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  • Core Knowledge.Elizabeth S. Spelke - unknown
    Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a fifth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human primates, children and adults in diverse cultures can aid both understanding of these systems and attempts to overcome their limits.
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  • The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.
    Only human beings have a rich conceptual repertoire with concepts like tort, entropy, Abelian group, mannerism, icon and deconstruction. How have humans constructed these concepts? And once they have been constructed by adults, how do children acquire them? While primarily focusing on the second question, in The Origin of Concepts , Susan Carey shows that the answers to both overlap substantially. Carey begins by characterizing the innate starting point for conceptual development, namely systems of core cognition. Representations of core cognition (...)
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  • Teleology and the Norms of Nature.William J. FitzPatrick - 2000 - Routledge.
    This work is an examination of teleological attributions i.e. ascriptions of proper functions and natural ends) to the features and behavior of living things with a view to understanding their application to human life.
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  • Addition and Subtraction by Human Infants. 358 (6389), 749-750. Xu, F., & Spelke, ES (2000). Large Number Discrimination in 6-Month-Old Infants. [REVIEW]K. Wynn - 1992 - Cognition 74 (1).
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