Penelope Maddy is a UCI Distinguished Professor of
LogicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
and
Philosophy of ScienceThe philosophy of science is concerned with the assumptions, foundations, and implications of science. The field is defined by an interest in one of a set of "traditional" problems or an interest in central or foundational concerns in science...
and of
MathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
at the
University of California, IrvineThe University of California, Irvine is a public coeducational research university founded in 1965, located in Irvine, California....
. She is well-known for her influential work in the
philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
, where she has worked on realism and naturalism.
Maddy received her Ph.D. from
Princeton UniversityPrinceton University a private university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League and is considered one of the Colonial Colleges....
in 1979.
Her early work, culminating in
Realism in Mathematics, she tried to defend
Kurt GödelKurt Gödel was an Austrian-American logician, mathematician and philosopher. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N...
's position that mathematics is a true description of a mind-independent realm that we can access through our intuition.
Penelope Maddy is a UCI Distinguished Professor of
LogicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
and
Philosophy of ScienceThe philosophy of science is concerned with the assumptions, foundations, and implications of science. The field is defined by an interest in one of a set of "traditional" problems or an interest in central or foundational concerns in science...
and of
MathematicsMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
at the
University of California, IrvineThe University of California, Irvine is a public coeducational research university founded in 1965, located in Irvine, California....
. She is well-known for her influential work in the
philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
, where she has worked on realism and naturalism.
Maddy received her Ph.D. from
Princeton UniversityPrinceton University a private university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League and is considered one of the Colonial Colleges....
in 1979.
Her early work, culminating in
Realism in Mathematics, she tried to defend
Kurt GödelKurt Gödel was an Austrian-American logician, mathematician and philosopher. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N...
'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 I see the three cups on the table in front of me, I also see the set as well. 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
QuineWillard Van Orman Quine was an American philosopher and logician in the analytic tradition...
'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. However, rather than a unified picture of the sciences like Quine's, she has a picture on which mathematics is separate. This way, 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
metaphysicalMetaphysics investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world...
and
epistemologicalEpistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope of knowledge...
concerns of the
philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
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.
Throughout her career, she has been dedicated to understanding and explaining the methods that
set theoristsThe modern study of set theory was initiated by Cantor and Dedekind in the 1870s. After the discovery of paradoxes in informal set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.The...
use in agreeing on
axiomIn traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision...
s, especially those that go beyond ZFC.
Selected publications
- Second Philosophy, Oxford University Press, 2007. ISBN 0-19-927366-9
- Naturalism in Mathematics, Oxford University Press, 1997. ISBN 0-19-825075-4
- Realism in Mathematics, Oxford University Press, 1990. ISBN 0-19-824035-X
External links