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| Author | : John Leslie Mackie |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 322 |
| Release | : 1973 |
| Genre | : Philosophy |
| ISBN | : 0198244029 |
Classic work by one of the most brilliant figures in post-war analytic philosophy.
| Author | : Yudi Pawitan |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2024 |
| Genre | : Mathematics |
| ISBN | : 9781003341659 |
Mathematics is focused on formal manipulation of abstract concepts, while statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, biases, assumptions or preconceptions of the interpreter, leading to a variety of potential interpretations of concepts as well as results. This book thoroughly examines the distinct philosophical approaches to statistics - Bayesian, frequentist, and likelihood - arising from different interpretations of probability and uncertainty. These differences are highlighted through a variety of puzzles and paradoxes. Features: Exploration of the philosophy of knowledge and truth and how they relate to deductive and inductive reasoning, and ultimately scientific and statistical thinking. Discussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist views. Exposition and examination of Savage's axioms as the basis of subjective probability and Bayesian statistics. Explanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principle. Discussion of fiducial probability and its evolution to confidence procedure. Introduction of extended and hierarchical likelihood for handling random parameters, with the recognition of confidence as extended likelihood, leading to epistemic confidence as an objective measure of uncertainty for single events. Detailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, etc. Substantive yet non-technical, catering to readers with only introductory exposure to the theory probability and statistics. This book primarily targets statisticians, including both undergraduate and graduate students, as well as researchers interested in the philosophical basis of probability and statistics. It is also suitable for philosophers of science and general readers intrigued by puzzles and paradoxes.
| Author | : Yudi Pawitan |
| Publisher | : CRC Press |
| Total Pages | : 352 |
| Release | : 2024-03-21 |
| Genre | : Philosophy |
| ISBN | : 1003849032 |
Unlike mathematics, statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, preferences, assumptions and preconceptions of the interpreter, leading to a variety of interpretations of concepts as well as results. Philosophies, Puzzles and Paradoxes: A Statistician’s Search for Truth thoroughly examines the distinct philosophical approaches to statistics – Bayesian, frequentist and likelihood – arising from different interpretations of probability and uncertainty. These differences are highlighted through numerous puzzles and paradoxes and illuminated by extensive discussions of the background philosophy of science. Features: Exploration of the philosophy of knowledge and truth and how they relate to deductive and inductive reasoning, and ultimately scientific and statistical thinking Discussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist views Exposition and examination of Savage’s axioms as the basis of subjective probability and Bayesian statistics Explanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principle Discussion of fiducial probability and its evolution to confidence procedure Introduction of extended and hierarchical likelihood for random parameters, with the recognition of confidence as extended likelihood, leading to epistemic confidence as an objective measure of uncertainty for single events Detailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, and more Substantive yet non-technical, catering to readers with only introductory exposure to the theory of probability and statistics This book primarily targets statisticians in general, including both undergraduate and graduate students, as well as researchers interested in the philosophical basis of probability and statistics. It is also suitable for philosophers of science and general readers intrigued by puzzles and paradoxes.
| Author | : Lee Walters |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 279 |
| Release | : 2021-02-04 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 0198712731 |
Conditionals, Paradox, and Probability comprises fifteen original essays on themes from the work of Dorothy Edgington, the first woman to hold a chair in philosophy at Oxford. Eminent contributors from philosophy and linguistics discuss a range of topics including conditionals, vagueness, knowledge, reasoning, and probability.
| Author | : Robert L. Martin |
| Publisher | : |
| Total Pages | : 334 |
| Release | : 1984 |
| Genre | : Language Arts & Disciplines |
| ISBN | : |
This collection of recent essays includes important and influential work on the concept of truth and the semantic pardoxes. Using techniques of mathematical logic, these philosophers tackle this age-old problem to offer new insights and widely varying analyses.
| Author | : I. Niiniluoto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 542 |
| Release | : 2012-12-06 |
| Genre | : Philosophy |
| ISBN | : 9400937393 |
The modern discussion on the concept of truthlikeness was started in 1960. In his influential Word and Object, W. V. O. Quine argued that Charles Peirce's definition of truth as the limit of inquiry is faulty for the reason that the notion 'nearer than' is only "defined for numbers and not for theories". In his contribution to the 1960 International Congress for Logic, Methodology, and Philosophy of Science at Stan ford, Karl Popper defended the opposite view by defining a compara tive notion of verisimilitude for theories. was originally introduced by the The concept of verisimilitude Ancient sceptics to moderate their radical thesis of the inaccessibility of truth. But soon verisimilitudo, indicating likeness to the truth, was confused with probabilitas, which expresses an opiniotative attitude weaker than full certainty. The idea of truthlikeness fell in disrepute also as a result of the careless, often confused and metaphysically loaded way in which many philosophers used - and still use - such concepts as 'degree of truth', 'approximate truth', 'partial truth', and 'approach to the truth'. Popper's great achievement was his insight that the criticism against truthlikeness - by those who urge that it is meaningless to speak about 'closeness to truth' - is more based on prejudice than argument.
| Author | : Hartry Field |
| Publisher | : Oxford University Press |
| Total Pages | : 423 |
| Release | : 2008-03-06 |
| Genre | : Philosophy |
| ISBN | : 0199230757 |
Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke>'s, and Lukasiewicz>'s theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists>' claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.
| Author | : Eric Christian Barnes |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 2012-07-19 |
| Genre | : Science |
| ISBN | : 9781107405165 |
An enduring question in the philosophy of science is the question of whether a scientific theory deserves more credit for its successful predictions than it does for accommodating data that was already known when the theory was developed. In The Paradox of Predictivism, Eric Barnes argues that the successful prediction of evidence testifies to the general credibility of the predictor in a way that evidence does not when the evidence is used in the process of endorsing the theory. He illustrates his argument with an important episode from nineteenth-century chemistry, Mendeleev's Periodic Law and its successful predictions of the existence of various elements. The consequences of this account of predictivism for the realist/anti-realist debate are considerable, and strengthen the status of the 'no miracle' argument for scientific realism. Barnes's important and original contribution to the debate will interest a wide range of readers in philosophy of science.
| Author | : Vann McGee |
| Publisher | : |
| Total Pages | : 236 |
| Release | : 1990 |
| Genre | : Liar paradox |
| ISBN | : 9780872200869 |
| Author | : Agustin Rayo |
| Publisher | : MIT Press |
| Total Pages | : 321 |
| Release | : 2019-04-02 |
| Genre | : Mathematics |
| ISBN | : 0262039419 |
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.
