Philosophy can be structured and practiced in a top-down manner
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Philosophical reference sources document that top-down methodologies and approaches have historical precedent in analytical traditions and the philosophy of science.
methodology, they tend to endorse a bottom-up rather than a top - down approach. In other words, they tend to draw ... central effort in the literature is to establish that diagrams can be highly structured and systematic, particularly ... inference. In practice, mathematicians generally expect that if a step in a proof is correct, it can be spelled ...
--> The Philosophy of Mathematical Practice (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy Menu Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Navigation Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top The Philosophy of Mathematical Practice First published Tue Apr 7, 2026 “Philosophy of Mathematical Practice” (PMP) refers to a broad cluster of approaches in the philosophy of mathematics.
This siren song has held the philosophy of mathematics in thrall, leaving it to drift into the rocky shores. (2018a, 6) Philosophers of mathematical practice tend to get their hands dirty with all sorts of different mathematics. They recognize that mathematics is not monolithic but multiform. The common thought is that focusing on a few areas such as arithmetic and set theory results in a lost opportunity for philosophical analyses of mathematics.
In the introduction to the volume The Philosophy of Mathematical Practice , Paolo Mancosu explains: The authors in this collection believe that the single-minded focus on the problem of ‘access’ has reduced the epistemology of mathematics to a torso.
They also commonly rely on results without proving them for themselves. Focusing on the social dimension of mathematics has shown that themes that are gaining traction in social epistemology could be fruitfully applied to the philosophy of mathematics, and scholars working in PMP have been especially sensitive to incorporating these developments.
Summarizing the above, we can say that, in addition to contributions that address problems of mathematical practice with a more traditional methodology of conceptual analysis, a more detailed attention to mathematical practice and the subjects practicing it has led several scholars engaged in PMP to take into account the cognitive architecture of the subjects and the social dimension of the epistemic activities in which mathematicians are engaged in, at times in consonance with parallel developments in mainstream analytic philosophy. 1.3 Methodology Although most results within PMP deploy traditional philosophical methodology, they tend to endorse a bottom-up rather than a top-down approach.
Top-down approaches were typical of the earlier analytic tradition (even when motivated by the desire to include more attention to mathematical practice) and offered general characterizations of mathematical explanation. Influential proposals are Steiner’s (1978) account of explanation in terms of a “characteristic property” and Kitcher’s (1981) unificationist account. While important in having brought the attention of philosophers to mathematical explanation, these proposals have been criticized by scholars looking at detailed case studies from the practice of mathematics, thus adopting a bottom-up approach.
See Hamami and Morris 2020 and Weber and Inglis 2024 for two overviews from mathematics educators and philosophers of mathematical practice. See also the Special Issue of the Journal of Mathematical Behavior edited by De Toffoli, Inglis, Hamami, and Mejia-Ramos (forthcoming). We should also add that analytic philosophy of mathematics has also been faced with similar boundary issues.
Of course, proponents of PMP would go on to point out that one cannot limit attention to only these aspects of the mathematical
For example, Lakatos (1976) explicitly argued against a ‘deductivist’ view of mathematics, while Tymoczko (1986) and Aspray and Kitcher (1988) saw in foundationalist approaches their primary target. To emphasize the radical nature of their view, the latter presented themselves as part of the “maverick tradition” in philosophy of mathematics.
On the contrary, the anti-foundationalist stance directly opposes foundationalist efforts. A contribution adopting this stance is Corfield 2003. Even within the analytic framework, one can perceive anti-foundationalist features in the work of Maddy (1997), at least to the extent that her naturalism rejects a philosophy-first approach and she embraces a methodology that sits uncomfortably with the traditional foundationalist programs.
While the ecumenical stance sees the developments in the philosophy of mathematics as an extension of the topics and the perspectives which fall under the purview of philosophy of mathematics, the anti-foundationalist stance sees it as an irreconcilable split between different approaches and traditions.
The latter is made explicit in the “brief and biased history” of philosophy of mathematics by Aspray and Kitcher (1988), who identify two traditions that are centered around two general research programs: (1) the mainstream , which started with Frege and is centered around questions regarding the foundations of mathematics; and (2) a much less developed, maverick tradition that began with Lakatos.
Mathematicians appeal to this phenomenon often enough. While early work in the area (see Sandborg 1997 and Hafner and Mancosu 2005) had attempted to sample the variety of mathematical explanations and the extent of their recognition in mathematical practice by limited search tools, a combination of experimental philosophy (Pease, Aberdein, and Martin 2019) and application of AI using large language models (D’Alessandro forthcoming; Meja-Ramos et al.
... philosophy of science that opposed the top-down methodology associated with Carnap and the logical empiricists. This ... manner, Structure offered a novel method for ana- lyzing science that significantly departed from the logical ...
In 1962, the publication of Thomas Kuhn’s Structure ‘revolutionized’ the way one conducts philosophical and historical studies of science. Through the introduction of both memorable and controversial notions, such as paradigms, scientific revolutions, and incommensurability, Kuhn argued against the traditionally accepted notion of scientific change as a progression towards the truth about nature, and instead substituted the idea that science is a puzzle solving activity, operating under paradigms, which become discarded after it fails to respond accordingly to anomalous challenges and a rival paradigm. Kuhn’s Structure has sold over 1.4 million copies and the Times Literary Supplement named it one of the “Hundred Most Influential Books since the Second World War.” Now, fifty years after th
Through the introduction of both memorable and controversial notions, such as paradigms, scientific revolutions, and incommensurability, Kuhn argued against t... See more about this book Science & math William J. Devlin is Associate Professor of Philosophy at Bridgewater State University and Summer Lecturer at University of Wyoming. His areas of research include philosophy of science, 19th century philosophy, and existentialism. He has written on issues related to the philosophies of time travel, causality, truth, Thomas Kuhn, and Friedrich Nietzsche.
Alisa Bokulich is Professor of Philosophy and Director of the Center for Philosophy and History of Science at Boston University, where she also organizes the Boston Colloquium for Philosophy of Science. She is a series editor for Boston Studies in the Philosophy and History of Science and an Associate Member of Harvard University’s History of Science Department. In addition to several edited books she is author of Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism with Cambridge University Press. William J. Devlin is Associate Professor of Philosophy at Bridgewater State University and Summer Lecturer at University of Wyoming.
His areas of research include philosophy of science, 19th century philosophy, and existentialism. He has written on issues related to the philosophies of time trave... See more about this author Write a review Smartphones and tablets Install the Google Play Books app for Android and iPad/iPhone . It syncs automatically with your account and allows you to read online or offline wherever you are. Laptops and computers You can listen to audiobooks purchased on Google Play using your computer's web browser. eReaders and other devices To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device.
influenced by top - down processes. Zhuangzi can retort that different systems of names can result in differently ... preserve awareness of a world as we “know” it. Our conceptual scheme exerts a top - down organization of the ... brothers. In 2 A 7 Mengzi says that no one can cause us not to be ren—failure in this derives from a lack of ...
--> Mind (Heart-Mind) in Chinese Philosophy (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy Menu Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Navigation Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top Mind (Heart-Mind) in Chinese Philosophy First published Mon Jul 10, 2023 This entry covers major views of mind in the period of classical Chinese philosophy (from about the 6 th to the end of the 3 rd century BCE).
As discussed below, different conceptions of the heart-mind in the Chinese philosophical tradition motivate important distinctions in the account of its role in the body (the Mengzi and the Xunzi ), in knowing and skills or crafts (the Mozi ), and in relation to other natural creatures (the Daodejing and the Zhuangzi ). 1. The heart-mind and its ontological relation to the body in classical Chinese philosophy 1.1 Holistic interpretations of the relationship between heart-mind and body 1.2 Critical discussion of holistic interpretations 2.
The later Mohists kept the basic outlines of the consequentialist ethic that Mozi and the early followers developed, but further developed and revised that ethic along with their methodology of argument, philosophy of language and epistemology. In addition, they wrote on metaphysical topics such as causality and space and time, and in a number of the sciences such as geometry and mechanics. Their writings comprise six chapters of the Mozi (see CTP: chapters 40–45 [trans. 2020: part IV]).
Compare, he asks the king, a soldier who throws down his weapon and flees from the enemy for one hundred paces to one who flees for fifty paces. Is not the second still fleeing? The King agrees by saying that “this” is also fleeing. Mengzi then points out that the King lets dogs and swine eat food meant for human beings while his people die of famine. The implication is that the king’s policies still fall far short of being human-hearted, even if metaphorically they go fifty paces less in the wrong direction.
Mengzi’s horizontal reasoning coming from comparing particular cases stands in significant contrast with vertical, top-down reasoning from general principles. It holds superior appeal if one thinks that one’s moral intuitions are more solid when rooted in the particular, and it allows for building up to general principles through noting recurrent patterns of similarities and dissimilarities (Wong 2002). In 1A3, as seen above, Mengzi uses analogies to get King Hui to see that he has to do more to keep his people from starving. Since the duan include emotions, however, growth of the sprouts also depends on growth or maturation of the sprouts of emotion.
This cheng xin 成心, the fully-structured heart-mind then “shoots out” “this-right!” and “not that-wrong!” suggests that the piping of human beings is formed on the basis of selecting from some this’ s and rejecting others. We acquire a conception of “right” and “wrong” from our past practice. The passage goes on to say, “Courses are formed by walking them. Things are so by being called so” ( Qi Wu Lun , 6 [trans. 2009: 13]).
Scientists have discovered that perception is both bottom-up and top-down. We receive sensory input, but the mind fills in gaps (e.g., the famous “blind spot” to preserve awareness of a world as we “know” it. Our conceptual scheme exerts a top-down organization of the sensory input. Some of the classifications we get are inborn, but most are learned from infancy partly from our culture and from our exploring our environment, seeing which of our guesses as to what is bringing sensory input to us are correct.
Acuity of perception in Xunzi’s terms, the range of distinctions our senses can distinguish may be something given to us by Tian but the world we see is profoundly influenced by top-down processes. Zhuangzi can retort that different systems of names can result in differently populated and structured worlds. Contemporary conclusions about the relation between nature and nurture may support Mengzi’s conception of the inborn capacity as like a sprout that develops under the right environment conditions as well as Xunzi’s emphasis on nurture.
Secondary Sources Ames, Roger T., 2015, “‘Bodyheartminding’ ( Xin 心): Reconceiving the Inner Self and the Outer World in the Language of Holographic Focus and Field”, Frontiers of Philosophy in China , 10(2): 167–180. Barrett, Louise, 2011, Beyond the Brain: How Body and Environment Shape Animal and Human Minds , Princeton, NJ: Princeton University Press. Cahn, B. Rael and John Polich, 2006, “Meditation States and Traits: EEG, ERP, and Neuroimaging Studies.”, Psychological Bulletin , 132(2): 180–211.
doi:10.1353/pew.2003.0009 Stephens, Daniel J., 2021, “Later Mohist Ethics and Philosophical Progress in Ancient China”, British Journal for the History of Philosophy , 29(3): 394–414. doi:10.1080/09608788.2020.1816528 Tan, Sor-Hoon, 2005, “Imagining Confucius: Paradigmatic Characters and Virtue Ethics”, Journal of Chinese Philosophy , 32(3): 409–426. doi:10.1111/j.1540-6253.2005.00201.x Tiwald, Justin, 2017, “Punishment and Autonomous
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