This is a clarification of and development upon my previous work. It includes a rework of "Concerning the weakest coherent formalization of methodological skepticism as a Bayesian updater" and "On the finitist Wolfram physics model", then there is an outline of finite content theory and mathematical notes in various areas. Digital phenomenology itself is the study of a finitist (and therefore discrete) phenomenalism. It also includes my work on predictive liquid democracy, where liquid democracy is combined with prediction markets. The system allows for local satisfaction of Condorcet's jury theorem extended to multiple alternatives. See the part about predictive liquid democracy.
Collected papers of Digital Phenomenology is a clarification of and development upon Digital Phenomenology. It includes "Concerning the weakest coherent formalization of methodological skepticism as a Bayesian updater" and "On the finitst Wolfram physics model", then there is an outline of finite content theory and mathematical notes in various areas. Digital Phenomenology itself is the study of a finitist (and therefore discrete) phenomenalism.
This is a clarification of and development upon my previous work. It includes a rework of "Concerning the weakest coherent formalization of methodological skepticism as a Bayesian updater" and "On the finitist Wolfram physics model", then there is an outline of finite content theory and mathematical notes in various areas. Digital phenomenology itself is the study of a finitist (and therefore discrete) phenomenalism. It also includes my work on predictive liquid democracy, where liquid democracy is combined with prediction markets. The system allows for local satisfaction of Condorcet's jury theorem extended to multiple alternatives. See the part about predictive liquid democracy.
This is a clarification of and development upon my previous work. It includes a rework of "Concerning the weakest coherent formalization of methodological skepticism as a Bayesian updater" and "On the finitist Wolfram physics model", then there is an outline of finite content theory and mathematical notes in various areas. Digital phenomenology itself is the study of a finitist (and therefore discrete) phenomenalism. It also includes my work on predictive liquid democracy, where liquid democracy is combined with prediction markets. The system allows for local satisfaction of Condorcet's jury theorem extended to multiple alternatives. See the part about predictive liquid democracy. [Elib].
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
Digital Phenomenology is a report on the philosophical theory of everything. From the first principle, digital philosophy and post-Keynesian economics are proved. The report is technical and aimed toward philosophers, mathematicians, computer scientists, physicists, economists, and political scientists.
Paolo Mancosu presents an innovative set of studies of logic and the foundations of mathematics in the first half of the 20th century. He sheds new light on important topics such as the relationship between phenomenology and the exact sciences, the nature of truth and logical consequence, and the nature of mathematical intuition.
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
