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A new approach to the metaphysics, background logic, and semantics of ontological debate, Ontology Without Borders offers new solutions to perennial philosophical puzzles about constitution and the nonexistent. Book jacket.
Ordinary language and scientific language enable us to speak about, in a singular way (using demonstratives and names), what we recognize not to exist: fictions, the contents of our hallucinations, abstract objects, and various idealized but nonexistent objects that our scientific theories are often couched in terms of. Indeed, references to such nonexistent items-especially in the case of the application of mathematics to the sciences-are indispensable. We cannot avoid talking about such things. Scientific and ordinary languages thus enable us to say things about Pegasus or about hallucinated objects that are true (or false), such as "Pegasus was believed by the ancient Greeks to be a flyin...
Humans involuntarily experience physical items as having meaning-properties. Semantic Perception explores this experience--the phenomenology of the understanding of language--in depth. Jody Azzouni shows the many ways that we experience the meaning-properties of language artifacts as independent of the intentions of their makers.
If we take mathematical statements to be true, must we also believe in the existence of abstract invisible mathematical objects? This text claims that the way to escape such a commitment is to accept true statements which are about objects that don't exist in any sense at all.
This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things at all. Jody Azzouni argues that mathematical knowledge is a special kind of knowledge that must be gathered in its own unique way. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics sensitive both to mathematical practice and to the ontological and epistemological issues that concern philosophers. The book will be of special interest to philosophers of science, mathematics, logic, and language. It should also interest mathematicians themselves.
In this book Jody Azzouni challenges existing epistemological conventions about knowledge: what it means to know something, who or what is seen as knowing, and how we talk about it. He argues that the classic restrictive conditions philosophers routinely place on knowers only hold in special cases, and suggests that knowledge can be equally attributed to children, sophisticated animals (great apes, orcas), unsophisticated animals (bees), and machinery or devices (driverless cars). Through this perspective and a close examination of its relation to linguistics and psychology, Azzouni freshly approaches longstanding epistemological puzzles including the dogmatism paradox, Gettier puzzles, Agrippa's trilemma, and the surprise-exam paradox.
In Attributing Knowledge, Jody Azzouni challenges philosophical conventions about what it means to know something. He argues that the restrictive conditions philosophers place on knowers only hold in special cases; knowledge can be attributed to babies, sophisticated animals (great apes, orcas), unsophisticated animals (bees), and machinery (drones, driverless cars). Azzouni also gives a fresh defense of fallibilism. Relying on lexical semantics and ordinary usage, he shows that there are no knowledge norms for assertion or action. He examines everyday cases of knowledge challenge and attribution to show many recent and popular epistemological positions are wrong. By providing a long-sought ...
A new approach to the metaphysics, background logic, and semantics of ontological debate, Ontology Without Borders offers new solutions to perennial philosophical puzzles about constitution and the nonexistent. Book jacket.
When ordinary people--mathematicians among them--take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, of our reasoning. This point is illustrated with a close analysis of a paradigmatic case of ordinary reasoning: mathematical proof.
The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume: Jeremy Avigad Jody Azzouni David H. Bailey David Berlinski Jonathan M. Borwein Ernest Davis Philip J. Davis Donald Gillies Jeremy Gray Jesper Lützen Ursula Martin Kay O’Halloran Alison Pease Steven Piantadosi Lance Rips Micah T. Ross Nathalie Sinclair John Stillwell Hellen Verran