Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to t...
Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the...
Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application...
Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to t...
Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy." Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second Philosopher." mhis Second Philosopher begins from...
Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philos...
Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In this book, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy." Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly - "trust only the methods of science " or some such thing - so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second Philosopher." This Second Philosopher begins from...
Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In this book, Pe...
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay s conjecture, and on...
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings i...
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly...
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have...
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay s conjecture, and on...
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings i...
The Logical Must is an examination of Ludwig Wittgenstein's philosophy of logic, early and late, undertaken from an austere naturalistic perspective Penelope Maddy has called "Second Philosophy." The Second Philosopher is a humble but tireless inquirer who begins her investigation of the world with ordinary perceptual beliefs, moves from there to empirical generalizations, then to deliberate experimentation, and eventually to theory formation and confirmation. She takes this same approach to logical truth, locating its ground in simple worldly structures and our knowledge of it in...
The Logical Must is an examination of Ludwig Wittgenstein's philosophy of logic, early and late, undertaken from an austere naturalistic pers...
How do you know the world around you isn't just an elaborate dream, or the creation of an evil neuroscientist? If all you have to go on are various lights, sounds, smells, tastes and tickles, how can you know what the world is really like, or even whether there is a world beyond your own mind? Questions like these -- familiar from science fiction and dorm room debates -- lie at the core of venerable philosophical arguments for radical skepticism: the stark contention that we in fact know nothing at all about the world, that we have no more reason to believe any claim -- that there are trees,...
How do you know the world around you isn't just an elaborate dream, or the creation of an evil neuroscientist? If all you have to go on are various li...
