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Penelope Maddy
Penelope Maddy
Penelope Maddy
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Penelope Maddy (born 4 July 1950) is an American philosopher. Maddy is Distinguished Professor Emerita of Logic and Philosophy of Science and of Mathematics at the University of California, Irvine. She is well known for her influential work in the philosophy of mathematics, where she has worked on mathematical realism (especially set-theoretic realism) and mathematical naturalism.

Key Information

Education and career

[edit]
Maddy standing in front of her Science Talent Search exhibit, March 1968

Maddy first became interested in mathematics in her first algebra class in middle school.[2] After being given a book on abstract algebra by her teacher, she entered the 1968 Westinghouse Science Talent Search, becoming a finalist and placing seventh overall.[3] She went on to study mathematics at University of California, Berkeley and received her bachelor's degree in 1972.[2]

Maddy's interest in the continuum hypothesis—which she had initially learned of during high school—and the fact that it could not be proved without introducing a new axiom, led her to question what could count as evidence for one axiom over another.[3] According to Maddy, at this point she was "already well down the slippery slope from mathematics to philosophy"[4] and she went to pursue a PhD in philosophy at Princeton University.[3] She received her PhD in 1979. Her dissertation, Set Theoretical Realism, was supervised by John P. Burgess.[5]

She taught at the University of Notre Dame and University of Illinois, Chicago before joining University of California, Irvine in 1987.[2] There she held positions as the chair of the philosophy department and later as the founding chair of the department of logic and philosophy of science. She was named Chancellor's Professor in 2002 and Distinguished Professor in 2007. She retired in 2020.[6] She is Distinguished Professor Emeritus.[7]

She was elected a Fellow of the American Academy of Arts and Sciences in 1998.[8][9] She won the 2002 Lakatos Award for her 1997 book Naturalism in Mathematics.[10] The German Mathematical Society awarded her a Gauss Lectureship in 2006. She was the president of the Association for Symbolic Logic from 2007 to 2009, during which time she oversaw the launch of the Review of Symbolic Logic.[6] She was president of the Pacific division of the American Philosophical Association from 2019-2020.[11]

Philosophical work

[edit]
Main articles: Set-theoretic realism and Naturalized epistemology

Maddy's early work, culminating in Realism in Mathematics, defended Kurt Gödel's position that mathematics is a true description of a mind-independent realm that we can access through our intuition. However, she suggested that some mathematical entities are in fact concrete, unlike, notably, Gödel, who assumed all mathematical objects are abstract. She suggested that sets can be causally efficacious, and in fact share all the causal and spatiotemporal properties of their elements. Thus, when one sees three cups on a table, one also sees the set. She used contemporary work in cognitive science and psychology to support this position, pointing out that just as at a certain age we begin to see objects rather than mere sense perceptions, there is also a certain age at which we begin to see sets rather than just objects.

In the 1990s, she moved away from this position, towards a position described in Naturalism in Mathematics. Her "naturalist" position, like Quine's, suggests that since science is our most successful project so far for knowing about the world, philosophers should adopt the methods of science in their own discipline, and especially when discussing science. As Maddy stated in an interview, "If you're a 'naturalist', you think that science shouldn't be held to extra-scientific standards, that it doesn't require extra-scientific ratification."[12] However, rather than a unified picture of the sciences like Quine's, her picture has mathematics as separate. That is, mathematics is neither supported nor undermined by the needs and goals of science but is allowed to obey its own criteria. This means that traditional metaphysical and epistemological concerns of the philosophy of mathematics are misplaced. Like Wittgenstein, she suggests that many of these puzzles arise merely because of the application of language outside its proper domain of significance.

She has been dedicated to understanding and explaining the methods that set theorists use in agreeing on axioms, especially those that go beyond ZFC.

Selected publications

[edit]
  • Maddy, Penelope (June 1988). "Believing the Axioms, I". Journal of Symbolic Logic. 53 (2): 481–511. doi:10.2307/2274520. JSTOR 2274520. (a copy with corrections is available at the author's web page)
  • Maddy, Penelope (September 1988). "Believing the Axioms, II". Journal of Symbolic Logic. 53 (3): 736–764. doi:10.2307/2274569. JSTOR 2274569. S2CID 16544090.
  • Realism in Mathematics, Oxford University Press, 1990. ISBN 0-19-824035-X[13]
  • Naturalism in Mathematics, Oxford University Press, 1997. ISBN 0-19-825075-4[14]
  • Second Philosophy, Oxford University Press, 2007. ISBN 0-19-927366-9
  • Defending the Axioms, Oxford University Press, 2011. ISBN 0-19-959618-2
  • The Logical Must, Oxford University Press, 2014.
  • What do Philosophers Do? Skepticism and the Practice of Philosophy, Oxford University Press, 2017. ISBN 9-78-019061869-8
  • A Plea for Natural Philosophy and Other Essays, Oxford University Press, 2022.

See also

[edit]

References

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Penelope Maddy

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Penelope Maddy is an American philosopher renowned for her contributions to the philosophy of mathematics, particularly the foundations of set theory, naturalism, and the methodology of philosophical inquiry in relation to science. She serves as Distinguished Professor Emerita of Logic and Philosophy of Science at the University of California, Irvine, where she also held joint appointments in the Department of Mathematics. Born in , Maddy showed an early aptitude for , earning seventh place as a finalist in the 1968 Westinghouse Talent Search for a project on the algebraic properties of sets. She received a B.A. in from the in 1972 and a Ph.D. in from in 1979, with her dissertation examining the in . Maddy began her academic career as an assistant professor at the University of Illinois at Chicago from 1979 to 1983, before joining UCI as an associate professor in 1983, advancing to full professor in logic, , and , and achieving distinguished status in 2007 until her emerita appointment in 2020. Her scholarly work has evolved from realism about mathematical objects—positing that sets can be spatiotemporally perceived—to a naturalistic framework called "second philosophy," which integrates with empirical and critiques traditional axiomatic justifications in . Key publications include Naturalism in Mathematics (1997), which earned the 2002 Lakatos Award; Second Philosophy (2007); Defending the Axioms (2011); The Logical Must (2014); What Do Philosophers Do? (2017); and A Plea for Natural Philosophy and Other Essays (2022), alongside her to the American Academy of Arts and Sciences in 1998 and the Phi Beta Kappa-Romanell Professorship in 2014–2015.

Early Life and Education

Birth and Early Influences

Penelope Maddy was born on July 4, 1950, in , . She grew up in , where she attended local schools, including Dana Middle School. Maddy's interest in began during her early teenage years, specifically in ninth-grade algebra class, where she was struck by the power of translating word problems into equations to solve them. "It amazed me that you could take those little bits of information in a word problem, translate them into an equation or two, and find out the answer," she later recalled. Her teacher further fueled this curiosity by lending her a book on , which introduced her to the concept of sets treated as a form of numbers, inspiring her to explore these ideas independently. This early exposure led to her earning seventh place as a finalist in the 1968 Westinghouse Science Talent Search, with a project on the algebraic properties of sets. In high school, Maddy's fascination deepened when she discovered that much of classical could be reduced to , and that foundational questions like the remained open and unsettled. She was part of the school math team and accessed from her teacher's book cabinet, which introduced her to the foundations of . These experiences, though limited in documented family or environmental details, clearly directed her toward analytical pursuits, setting the stage for her undergraduate studies in at the .

Academic Training

Penelope Maddy earned her degree in from the , in June 1972. She then pursued graduate studies in at , where she completed her degree in January 1979. Her doctoral thesis, titled "Set Theoretical Realism," addressed foundational issues in the , particularly the ontological status of sets. The work was supervised by John P. Burgess.

Academic Career

Initial Appointments

Following her Ph.D. in philosophy from Princeton University in 1979, Penelope Maddy commenced her academic career as Assistant Professor in the Department of Philosophy at the University of Illinois at Chicago (UIC), holding the position from 1979 to 1983. This appointment underscored her interdisciplinary expertise bridging philosophy and mathematics, with an emphasis on foundational issues in these fields. At UIC, Maddy's responsibilities included teaching undergraduate and graduate courses in logic, , and related areas within the , while developing her early research on mathematical realism and foundations. Her work during this period contributed to emerging discussions in , particularly how empirical and scientific considerations inform mathematical practice. In 1983, Maddy transitioned to the (UCI), where she was appointed Associate Professor in the Department of Philosophy, marking a significant step in her career toward a long-term affiliation with the institution. This move allowed her to expand her teaching and research in logic and within a supportive environment for interdisciplinary studies.

Positions at UC Irvine

Penelope Maddy joined the (UCI) in 1983 as an in the Department of . She held the position of in the Department of from 1983 to 1987, followed by joint appointments as in the Departments of and from 1987 to 1989. In 1989, Maddy advanced to full Professor of , a position she maintained until her retirement in 2020. She also served as Professor of from 1989 to 1998 and again from 2014 to 2020. From 1998 to 2020, she held the role of Professor of Logic and Philosophy of Science, reflecting her interdisciplinary expertise. She was appointed Chancellor's Professor from April 2002 to November 2007. In 2007, she was appointed , a prestigious designation recognizing her contributions across logic, philosophy, and mathematics, which she held until 2020. Maddy assumed several administrative roles at UCI, including Chair of the Department of from 1991 to 1995 and founding Chair of the Department of Logic and from 1998 to 2001. She also served as Departmental Director of Graduate Admissions from 1997 to 1999. Throughout her tenure, Maddy supervised 12 doctoral students, including Jeffrey Schatz, who completed his PhD in 2019. Upon her retirement on July 1, 2020, Maddy was honored as Emerita, a title she continues to hold.

Philosophical Contributions

Mathematical Realism

Penelope Maddy's advocacy for mathematical realism centers on the acceptance of mathematical objects as genuinely real entities, a position she developed in the late 1980s and early 1990s, heavily influenced by the indispensability arguments advanced by W.V.O. Quine and . According to this argument, mathematical entities must exist because they are indispensable to our best scientific theories, which we accept as empirically successful descriptions of the world. Maddy builds on this by positing that the ontological commitment to follows directly from our commitment to , thereby grounding realism in the practical efficacy of mathematical applications in empirical inquiry. In her seminal 1990 book Realism in Mathematics, Maddy articulates the core thesis that mathematical realism is justified precisely by the empirical success of , where mathematics plays an irreplaceable role in formulating and confirming scientific hypotheses. She argues that this indispensability extends beyond mere instrumental utility, compelling belief in the objective existence of mathematical objects such as numbers and sets, much like our belief in unobservable physical entities like electrons. Maddy further contends that knowledge of these objects arises through a form of , akin to sensory experience but tuned to abstract structures, allowing mathematicians to "see" mathematical truths in a reliable, if non-traditional, manner. Maddy's defense of realism includes pointed critiques of prominent anti-realist alternatives, such as and formalism, which she views as inadequate to the actual practice of . , which treats mathematical statements as useful fictions without truth values, fails in her estimation to account for the discoverative nature of mathematical work, where practitioners treat theorems as objective discoveries rather than inventions. Similarly, formalism, with its emphasis on symbols and rules devoid of extrinsic meaning, strikes Maddy as nihilistic and disconnected from the provides in science, rendering it unable to justify the indispensability that realism accommodates so naturally. This early realist framework laid the groundwork for Maddy's subsequent philosophical evolution toward a naturalistic approach, though her core commitment to the reality of mathematics persisted.

Naturalism and Second Philosophy

In Naturalism in Mathematics (1997), Penelope Maddy transitioned from her earlier realist commitments to a naturalistic framework, arguing that philosophical inquiries into mathematics should be continuous with empirical scientific practice rather than relying on a priori justifications for its foundational assumptions. She contended that mathematical axioms and proofs, traditionally viewed as self-evident or metaphysically grounded, are better understood through the lens of how scientists and mathematicians actually employ them in ongoing investigations, thereby integrating philosophy of mathematics into the broader naturalistic enterprise. This naturalistic turn culminated in Maddy's development of "Second Philosophy," introduced in her 2007 book Second Philosophy: A Naturalistic Method, which posits an idealized inquirer who approaches foundational questions empirically and without preconceived metaphysical commitments. The Second Philosopher, as Maddy describes this figure, relies solely on the tools and methods available within the physical world—such as observation, experimentation, and mathematical reasoning—to evaluate philosophical claims, eschewing any external or transcendental vantage point. This method emphasizes a practice-based assessment of concepts like truth, knowledge, and existence, grounded in the actual workings of science and mathematics. Maddy contrasts Second Philosophy with "First Philosophy," the traditional metaphysical approach exemplified by Descartes, which seeks absolute foundations through a priori reasoning detached from empirical constraints. She argues that First Philosophy's quest for unassailable certainties is untenable under naturalism, as it imposes artificial boundaries on inquiry that ignore the provisional, evidence-driven nature of human knowledge. Instead, Second Philosophy favors an empirical, iterative process that aligns philosophy with scientific progress, rejecting dogmatic authority and prioritizing the outcomes of naturalistic investigation.

Set Theory and Axioms

Penelope Maddy's work in the philosophy of prominently features her exploration of large cardinals and the principle of axiom maximization, as detailed in her 2011 book Defending the Axioms. In this text, she argues that large cardinals, such as measurable cardinals, contribute to the depth and fruitfulness of by generating stable consequences that enhance mathematical understanding, thereby justifying their inclusion as beyond the standard ZFC framework. Maddy examines how the hierarchy of large cardinals supports a robust structure for , emphasizing that maximization—selecting that maximize and consistency—provides a pragmatic basis for axiom choice without relying on intrinsic truth. This approach contrasts minimalist views by prioritizing the empirical success and theoretical richness that large cardinals afford in resolving open problems like the . Central to Maddy's contributions is her advocacy for the set-theoretic multiverse, which she presents as a naturalistic alternative to the traditional "universe of sets" view embodied in the ultimate . In her 2012 article "The Set-Theoretic Multiverse," Maddy posits that encompasses a plurality of distinct universes, each governed by different axioms and forcing extensions, reflecting the diverse possibilities arising from mathematical practice. This multiverse perspective accommodates the undecidability of key conjectures, such as the , by viewing them as varying across universes rather than seeking a singular resolution in one absolute . She argues that this framework aligns with a naturalistic , allowing set theorists to evaluate axioms based on their intra-theoretic virtues like fruitfulness and coherence. Maddy further advances the multiverse idea through philosophical reconstructions of related projects, notably in her 2020 co-authored article "A Reconstruction of Steel's Project" with Toby Meadows. Here, they systematically reconstruct John Steel's multiverse approach from his 2014 work Gödel's Program, defining "" theories and axioms while introducing a function to relate models across the multiverse. The reconstruction assesses the status of the within this structure, identifying and addressing potential defects in Steel's original framework to ensure coherence. By comparing Steel's project to those of Joel David Hamkins and , Maddy and Meadows highlight how such multiverse constructions provide a unified yet flexible foundation for set-theoretic . Building on these themes, Maddy co-authored the 2023 monograph Philosophical Uses of Categoricity Arguments with Jouko Väänänen, which investigates the role of categoricity arguments in justifying set-theoretic axioms and structures. Applying her Second Philosophy approach, the work evaluates how such arguments contribute to foundational debates in , emphasizing their empirical and practice-based validation over a priori appeals.

Logic and Meta-Philosophy

In her 2014 book The Logical Must: Wittgenstein on Logic, Penelope Maddy examines the nature of and necessity through a naturalistic lens inspired by Wittgenstein's early and late philosophies, arguing that logical necessity arises from the structure of rather than any transcendental or a priori foundation. Drawing on her Second Philosophy framework, which underpins these inquiries by prioritizing empirical investigation over armchair speculation, Maddy naturalizes Kantian and Wittgensteinian ideas by collapsing the distinction between transcendental and empirical realms into a single empirical level. She interprets the "logical must" as tied to rule-following and the picturing function of , grounded in how our discursive engages the , while distinguishing this naturalized modality from traditional metaphysical necessity, which she views as an outdated remnant of non-empirical traditions. For instance, Maddy contends that the validity of logical laws stems from physical contingencies, not abstract essences, allowing logic to be revisable in light of scientific progress. Building on this naturalistic orientation, Maddy's 2017 book What Do Philosophers Do? Skepticism and the Practice of Philosophy expresses toward traditional philosophical methods, particularly conceptual analysis and a priori reasoning, which she argues often lead to unproductive standoffs in addressing about the external world. Instead, she advocates a naturalistic meta-philosophy that integrates scientific naturalism and common sense, evaluating philosophical practices through empirical lenses such as how ordinary people acquire reliable beliefs despite uncertainties like the "" scenario. Maddy critiques methods like for their insularity and favors those aligned with , such as investigating cognitive processes empirically, concluding that philosophy's value lies in clarifying how we navigate in a contingent reality rather than seeking indubitable foundations. This approach reinforces her view that philosophical inquiry should emulate scientific humility, acknowledging limitations without descending into defeatism. Maddy extends these themes in her 2022 collection A Plea for Natural Philosophy: And Other Essays, issuing a call to revive "" as an integrated practice where and mutually inform each other, eschewing the modern disciplinary divide that privileges a priori over empirical . Through the Second Philosophy method, she describes an ideal inquirer who begins with common-sense perceptions, refined by scientific observation and experimentation, to tackle longstanding questions in , , and logic without relying on transcendental arguments. For example, Maddy applies this to reassess realism and truth, arguing that philosophical claims must be tested against , such as developmental psychology's insights into mathematical understanding, to avoid the pitfalls of isolated conceptual work. This plea underscores her broader meta-philosophical commitment to a science-first stance, where serves as a reflective tool within the natural world rather than an autonomous arbiter of it. In her 2024 article "Wittgenstein on Mathematics," Maddy further develops her naturalistic interpretation of Wittgenstein's philosophy of mathematics, examining how his views on mathematical practice align with empirical inquiry and Second Philosophy, extending the themes from The Logical Must.

Major Publications

Books

Penelope Maddy's first major monograph, Realism in Mathematics (1990), defends a form of mathematical realism by appealing to the indispensability argument, positing that mathematical entities exist because they are indispensable to our best scientific theories. In Naturalism in Mathematics (1997), Maddy introduces a naturalistic approach to the , arguing that mathematical practice and justification should be understood through empirical and scientific lenses rather than a priori reasoning. Her book Second Philosophy: A Naturalistic Method (2007) elaborates on methodological naturalism under the framework of "Second Philosophy," which treats philosophical inquiry as continuous with scientific investigation from the perspective of an idealized empirical scientist. Defending the Axioms: On the Philosophical Foundations of (2011) applies a naturalistic perspective to the acceptance of set-theoretic axioms, evaluating them based on their role in mathematical practice and empirical adequacy rather than traditional philosophical criteria. In The Logical Must: Wittgenstein on Logic (2014), Maddy explores the nature of logical necessity through a naturalistic reading of Ludwig Wittgenstein's early and late philosophies of logic. What Do Philosophers Do? Skepticism and the Practice of Philosophy (2017) critiques traditional philosophical methods and advocates for a naturalistic meta-philosophy that confronts by aligning philosophical practice with scientific naturalism. Maddy's most recent , A Plea for : And Other Essays (2022), collects essays advocating for an integrated that revives the pre-modern tradition of natural inquiry under her Second Philosophy framework.

Selected Articles

Penelope Maddy has produced a series of influential peer-reviewed articles that advance her philosophical views on , with a focus on realism, naturalism, , and meta-philosophical issues. These works, often published in leading journals such as the Journal of Symbolic Logic and Philosophia Mathematica, exemplify her commitment to rigorous analysis grounded in mathematical practice. The selection here emphasizes her early contributions to realism and set-theoretic foundations before the 1990s, alongside later articles that explore historical shifts, conceptions, and Wittgensteinian interpretations. Maddy's pre-1990s articles established her as a key voice in mathematical realism and the epistemology of set theory. In "Perception and Mathematical Intuition" (1980), she defends a perceptual model of set-theoretic intuition, positing that very small finite sets can be perceived directly, which supports a modest realism about mathematical objects without relying on abstract platonism. This piece bridges philosophy of mind and mathematics, influencing subsequent debates on the empirical basis of mathematical knowledge. Building on this, her two-part series "Believing the Axioms. I" and "Believing the Axioms. II" (both 1988) investigates the justification for set-theoretic axioms like the Axiom of Choice and large cardinal principles. In the first installment, Maddy argues that belief in these axioms arises from their indispensability to science and a naturalistic intuition, rejecting purely a priori rationales. The second extends this to axioms implying determinacy for sets of reals, emphasizing empirical and practical warrants over intrinsic necessity. Published in the Journal of Symbolic Logic, these articles have shaped discussions on axiom choice in set theory by integrating philosophical analysis with working mathematicians' methods. Turning to her later scholarship, "How Applied Mathematics Became Pure" (2008) offers a historical examination of 's disciplinary evolution. Maddy traces how early modern views of mathematics as tied to physical applications gave way to a conception of as autonomous and foundational, drawing on figures from Descartes to Hilbert. She contends that this shift, published in the Review of Symbolic Logic, has profound implications for understanding mathematical ontology today, particularly in distinguishing "pure" from "applied" domains without rigid boundaries. In a more recent contribution, "A Reconstruction of Steel’s Multiverse Project" (2020, co-authored with Toby Meadows), Maddy philosophically clarifies John Steel's set-theoretic framework from his 2014 work Gödel's Program. The article contrasts Steel's approach—which emphasizes a core with evidential constraints—with multiverse views by Joel Hamkins and , arguing for its compatibility with naturalistic while highlighting its role in resolving inner debates; it appeared in the Bulletin of Symbolic Logic. Finally, "Wittgenstein on " (2024) applies Ludwig Wittgenstein's later therapeutic method to core mathematical domains. Maddy demonstrates how this yields fresh insights into arithmetic and , portraying as a rule-governed practice rather than a quest for ultimate foundations, in line with Wittgenstein's emphasis on ordinary language and conceptual clarification. Published in Philosophical Investigations, this work extends Maddy's second by engaging Wittgenstein to critique traditional meta- of . More recently, in "On multiversism" (2024), a chapter in The Philosophy of Penelope Maddy (Springer), Maddy examines approaches in from a naturalistic perspective. Additionally, "What can (or can't) do for " (2025, Journal of Philosophical Logic) explores the limits of philosophical contributions to set-theoretic foundations. And "Strawson on naturalism and skepticism" (2025), a chapter in Scepticism and Naturalism (Brill), discusses Peter Strawson's views in relation to her naturalistic framework. These articles were selected for their enduring impact, as measured by their placement in high-profile venues like Philosophia Mathematica—where Maddy has also contributed pieces such as "Naturalism and Ontology" (1995), which links naturalistic methodology to mathematical realism—and their role in advancing key debates across her career.

Awards and Honors

Professional Awards

In 2002, Penelope Maddy was awarded the Lakatos Prize for her book Naturalism in Mathematics (1997), which examines the naturalistic justification of mathematical axioms, particularly in set theory. The Lakatos Award, established by the London School of Economics in memory of philosopher Imre Lakatos, recognizes outstanding contributions to the philosophy of science—broadly construed—through a book published in English within the preceding six years; it is widely regarded as one of the highest honors in the field, often highlighting innovative approaches to foundational questions in mathematics and science. Maddy's receipt of the prize, announced in November 2002, underscored the impact of her work in bridging philosophical naturalism with mathematical practice during her established career as a professor at the University of California, Irvine. In 2013–2014, Maddy was selected as the Romanell Professor, an annual honor from the Phi Beta Kappa Society that celebrates distinguished philosophical scholarship and contributions to public understanding of , without restriction to any particular . The , endowed in of Patrick Romanell and supported by a $7,500 stipend, requires the recipient to deliver three public lectures at or near their home institution, fostering broader engagement with philosophical ideas. Maddy's lectures, given at UC Irvine in 2014–2015 and later published as What Do Philosophers Do? Skepticism and the Practice of (, 2017), addressed and the role of in scientific inquiry, amplifying her influence on meta-philosophical debates. This recognition came midway through her tenure as a UCI Distinguished Professor, affirming her ongoing leadership in and logic.

Academic Recognitions

Penelope Maddy was elected to the American Academy of Arts and Sciences in April 1998, recognizing her distinguished contributions to philosophical scholarship in the humanities and arts, particularly in the philosophy of mathematics. During her long-term career at the University of California, Irvine, Maddy was appointed UCI Distinguished Professor from 2007 to 2020, a title awarded to faculty exemplifying exceptional institutional excellence in research, teaching, and service. Maddy served as President of the Association for Symbolic Logic from 2007 to 2009, providing leadership to the international organization dedicated to advancing research in and its applications. She served as President of the American Philosophical Association's Pacific Division from 2019 to 2020. She has held ongoing editorial roles that underscore her influence in the field, including membership on the of Philosophia Mathematica since 1993 and of the Review of Symbolic Logic since 2014.

References

  1. https://faculty.sites.uci.edu/pjmaddy/
  2. https://sites.socsci.uci.edu/~pjmaddy/cv.pdf
  3. https://www.scientificamerican.com/article/penelope-maddy-philosopher-westinghouse/
  4. https://www.idref.fr/031266215
  5. https://sites.socsci.uci.edu/~pjmaddy/bio/DualistVol15_Maddy.pdf
  6. https://www.the-workbench.ca/interviews/penelope-maddys-workbench/
  7. https://www.socsci.uci.edu/newsevents/news/2020/2020-07-01-maddy.php
  8. https://www.lib.uci.edu/library/publications/philosophy/maddy.html
  9. https://philpapers.org/rec/MADSTR
  10. https://history.princeton.edu/graduate/alumni/hos-alumni/doctoral-degrees-awarded
  11. https://iep.utm.edu/indimath/
  12. https://global.oup.com/academic/product/realism-in-mathematics-9780198240358
  13. https://www.researchgate.net/publication/268035956_Realism_in_Mathematics
  14. https://philpapers.org/rec/MADRIM
  15. https://global.oup.com/academic/product/naturalism-in-mathematics-9780198235736
  16. https://www.colyvan.com/papers/Maddy.pdf
  17. https://global.oup.com/academic/product/second-philosophy-9780199273669
  18. https://philarchive.org/rec/MADSP
  19. https://www.logicmatters.net/2009/02/28/maddys-second-philosophy-introduction/
  20. https://ndpr.nd.edu/reviews/second-philosophy-a-naturalistic-method/
  21. https://global.oup.com/academic/product/defending-the-axioms-9780199596188
  22. https://www.logicmatters.net/resources/pdfs/MaddyReview.pdf
  23. https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/settheoretic-multiverse/B27885BC5F1D9860585F070B5DE1D53A
  24. https://www.cambridge.org/core/journals/bulletin-of-symbolic-logic/article/reconstruction-of-steels-multiverse-project/4309A83D64CFE43F0EF2544DAD301F60
  25. https://www.cambridge.org/core/books/philosophical-uses-of-categoricity-arguments/DD5FF451F6FB1BB46255EC35B6710292
  26. https://global.oup.com/academic/product/the-logical-must-9780199391752
  27. https://ndpr.nd.edu/reviews/the-logical-must-wittgenstein-on-logic/
  28. https://global.oup.com/academic/product/what-do-philosophers-do-9780190618698
  29. https://ndpr.nd.edu/reviews/what-do-philosophers-do-skepticism-and-the-practice-of-philosophy/
  30. https://global.oup.com/academic/product/a-plea-for-natural-philosophy-9780197508855
  31. https://ndpr.nd.edu/reviews/a-plea-for-natural-philosophy-and-other-essays/
  32. https://onlinelibrary.wiley.com/doi/full/10.1111/phin.12441
  33. https://global.oup.com/academic/product/defending-the-axioms-9780199596118
  34. https://global.oup.com/academic/product/the-logical-must-9780197511787
  35. https://www.jstor.org/stable/2274520
  36. https://www.jstor.org/stable/2274569
  37. https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/how-applied-mathematics-became-pure/C8D15ED909275B3334E60FFE1411C496
  38. https://link.springer.com/book/9783031584244
  39. https://link.springer.com/article/10.1007/s10992-025-09805-7
  40. https://brill.com/view/title/9789004697215
  41. https://www.lse.ac.uk/philosophy/research/imre-lakatos
  42. https://www.pbk.org/awards/romanell-professorship
  43. https://www.socsci.uci.edu/newsevents/news/2014/2014-05-06-maddy-named-phi-beta-kappa-romanell-professor.php
  44. https://news.uci.edu/2007/11/07/uci-philosopher-of-mathematics-named-distinguished-professor/
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