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This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The basic theme here is the analysis of formal logic in terms of what metaphysical assumptions we need when we develop the formal systems we use. The essays together give a perspective of formal logic as part of the art of reasoning well.

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Reasoning And Formal Logic

This book presents a new perspective on ways we encounter the world with our languages. There are two kinds of languages.Some direct speakers to encounter the world as made up of things. Others direct speakers to encounter the world as the flow of all with no idea of change, for there is no thing to change, only differing descriptions of the flow.The essays by Richard L. Epstein set out this division of languages and explore its significance for linguistics, metaphysics, thought, meaning, logic, and ethics.The other essays, by Dorothy Lee, Benjamin Lee Whorf, M. Dale Kinkade, Friedrich Nietzsche, and Benson Mates, extend, or contradict, or support those ideas, leading to a large view of how we talk and understand, and how that affects how we live.

Language And The World

The BARK of DOG is a collection of the stories and wisdom of the way of DOG.It is published and distributed by The BARK of DOG Foundation, dedicated to helping homeless people and homeless dogs, to promoting peace, to teaching how to reason so people can think clearly from the heart, all through the way of DOG.

The Bark Of Dog

The classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel''s incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church''s Thesis and readings on the foundations of mathematics. This third edition contains the timeline "Computability and Undecidability" as well as the essay "On Mathematics".

Computability

This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The essays overlap, forming a unified analysis of logic as the art of reasoning well, yet each essay is designed so that it may be read independently. The topic of this volume is prescriptive reasoning. Descriptive claims say how the world is, was, or will be; prescriptive claims say how the world should be. We have fairly clear rules for reasoning with descriptive claims. The goal of the first essay, "Reasoning with Prescriptive Claims," is to clarify how to reason with prescriptive ones. The first step in doing so is to justify our viewing prescriptions as true or false. That justification is part of a general approach to reasoning in which many kinds of personal evaluations are taken to be true-false divisions. That view has been implicit if not explicit in analyses of reasoning from formal logic through argument analysis. in "Truth and Reasoning" I set out reasons for adopting that methodology. Theories, too, seem to be descriptive or prescriptive. Some say how the world is, others how the world should be. Yet, as shown in "Prescriptive Theories?", on close examination the distinction evaporates. Unless, that is, one says that certain theories about values use an entirely different notion of truth than is used in science and is codified in our usual methods of reasoning. Absent that, there seems to be no justification for constructing and evaluating what are typically thought of as prescriptive theories differently from descriptive ones. Many discussions of how to evaluate prescriptive claims are given in terms of what is rational or irrational to do. In the final essay, "Rationality," what we mean by the idea of someone being rational is investigated and the limitations of that label in evaluating reasoning or actions is shown.

Prescriptive reasoning

This series of volumes is meant to extend the scope of what we can formalize in classical predicate logic, and in doing so see the real limitations of what can be done.In the first section the standard of modern formal logic, classical predicate logic with equality, is set out, drawing on the full development in An Introduction to Formal Logic.In the second section classical predicate logic is extended to formalize reasoning that involves adverbs and relative adjectives by viewing those as modifiers of simpler predicates. What is normally taken to be atomic predicates, such as barking loudly, can then have internal structure. Reasoning that involves conjunctions of terms, as in Tom and Dick lifted the table, conjunctions of modifiers, conjunctions of predicates, and disjunctions of predicates can also be formalized by viewing them as part of the internal structure of atomic predicates.The internal structure of names is the topic of the third and last section. Names for functions are used in classical predicate logic to form complex names are presented first. In our ordinary reasoning we use descriptions to form functions, such as the wife of, and descriptions to form names, such as the cat that scratched Zoe. To reason with those we can take account of their internal structure by dropping the assumption that every name must refer to a specific thing.The formal systems that are developed here are not just formalisms but are meant to help us understand how to reason well. Many worked examples show how to use them. They also uncover limitations of the formal work. The analyses in the examples are tentative, presented with the hope of stimulating you to deeper and clearer analyses.The work here proceeds by abstracting and creating formal models to formalize reasoning. By paying attention to the process of abstracting we gain insight into why we consider some reasoning to be good and some reasoning bad, and insight also into the deeper assumptions we make about the world on which our judgments rely. Questions about the metaphysics we assume for modern formal logic and the nature of formalizing have to be faced, most particularly the assumption that the world is made up of objects that we can name.This work extends the scope of classical predicate logic by showing how to formalize reasoning that involves adverbs, relative adjectives, conjunctions of terms, conjunctions of modifiers, and conjunctions of predicates as part of the internal structure of atomic predicates. Descriptive names functions and non-referring names are also analyzed.

The Internal Structure Of Predicates And Names

This series of books is meant to present the fundamentals of reasoning well in a clear manner accessible to both scholars and students. The body of each essay gives the main development of the subject, while the footnotes and appendices place the research within a larger scholarly context. The topic of this volume is the nature and evaluation of reasoning in science and mathematics. Science and mathematics can both be understood as proceeding by a method of abstraction from experience. Mathematics is distinguished from other sciences only in its greater abstraction and its demand for necessity in its inferences. That methodology of abstraction is the main focus here. The study of these subjects is not just of academic interest. First comes clear thinking, then comes clear research and clear writing. The essays:  Background  Models and Theories  Experiments  Mathematics as the Art of Abstraction

Reasoning In Science And Mathematics

The forms and scope of logic rest on assumptions of how language and reasoning connect to experience.In this volume an analysis of meaning and truth provides a foundation for studying modern propositional and predicate logics.Chapters on propositional logic, parsing propositions, and meaning, truth and reference give a basis for criteria that can be used to judge formalizations of ordinary language arguments.Over 120 worked examples of formalizations of propositions and arguments illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, functions, and second-order logic.The chapter on second-order logic illustrates how different conceptions of predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things.Notable for its clarity of presentation, and supplemented by many exercises, this volume is suitable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formalizing "The forms and scope of logic rest on assumptions of how language and reasoning connect to experience.In this volume an analysis of meaning and truth provides a foundation for studying modern propositional and predicate logics.Predicate Logic was originally published by Oxford University Press.

Predicate logic

This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The essays overlap, forming a unified analysis of logic as the art of reasoning well, yet each essay is designed so that it may be read independently. The question addressed in this volume is how we can justify our beliefs through reasoning. The first essay, "Arguments," investigates what it is that we call true or false and how we reason toward truths through arguments. A general theory of argument analysis is set out on the basis of what we can assume about those with whom we reason. The next essay, "Fallacies," explains how the classification of an argument as a fallacy can be used within that general approach. In contrast, there is no agreement on what the terms "induction" and "deduction" mean, and they are not useful in evaluating arguments, as shown in "Induction and Deduction." In reasoning to truths, in the end we must take some claims as basic, not requiring any justification for accepting them. How we choose those claims and how they affect our reasoning is examined in "Base Claims." The essay "Analogies" considers how comparisons can be used as the basis of arguments, arguing from similar situations to similar conclusions. An important use of analogies is in reasoning about the mental life of other people and things, which is examined in "Subjective Claims," written with Fred Kroon and William S. Robinson. "Generalizing" examines how to argue from part of a collection or mass to the whole or a larger part. The question there is whether we are ever justified in accepting such an argument as good. "Probabilities" sets out the three main ways probability statements have been interpreted: the logical relation view, the frequency view, and the subjective degree of belief view. Each of those is shown to be inadequate to make precise the scale of plausibility of claims and the scale of the likelihood of a possibility. Many discussions of how to reason well and what counts as good reason are given in terms of who or what is rational. In the final essay, "Rationality," it''s shown that what we mean by the idea of someone being rational is of very little use in evaluating reasoning or actions. This volume is meant to give a clearer idea of how to reason well, setting out methods of evaluation that are motivated in terms of our abilities and interests. At the ground of our reasoning, though, are metaphysical assumptions, too basic and too much needed in our reasoning for us to justify them through reasoning. But we can try to uncover those assumptions to see how they are important and what depends on them, which is a major them of this volume.

The Fundamentals Of Argument Analysis

Time and Space in Formal Logic begins with an analysis of assumptions about how logic and language relate.Then in the first section, times are taken to be established by true propositions, and those are related as before and after with temporal propositional connectives.In the second section, times are treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over times.In the third section, locations in space are also treated as things that can be picked out and counted, leading to a predicate logic that allows for quantification over both times and locations.Many applications of the formal systems to formalizing ordinary language propositions and inferences clarify better the assumptions we make in reasoning taking account of time and space by making those precise in the formal systems.Appendices on events, branching times, intentions, and descriptive names add to the scope of the work.

Time And Space In Formal Logic

 Intended for a course for beginning students in philosophy, mathematics, linguistics, or computer science.  Motivation for each formal concept and each step in building a formal logic in terms of formalizing reasoning. Provides a conception of formal logic and not just a collection of results. Summaries at important junctures in the book keep students aware of what they''re doing and where they''re going.  Hundreds of exercises that teach.  Criteria of formalization with many examples of formalizing ordinary language reasoning in an example-analysis format.  A complete course: syntax, semantics, and completeness theorems for classical propositional logic and classical predicate logic, and syntax and semantics for second-order classical predicate logic.

An introduction to formal logic: Second edition

This is an attempt to give a systematic analysis of how to reason that is not tied to our European languages, to step out of our language conceptions and habits. Consider then this work as a bridge, a chance for us as speakers of languages that focus primarily on the world as made up of things to begin to see the richness and complexity of encountering the world as the flow of all, the one and not many. The contrasts, often unsettling, can lead us to understand better how we encounter and reason about the world as made up of things.

Reasoning And Formal Logic (2015)

Language And The World (2021)

The Bark Of Dog (2013)

Computability (2008)

Prescriptive reasoning (2013)

The Internal Structure Of Predicates And Names (2016)

Reasoning In Science And Mathematics (2011)

Predicate logic (1994)

The Fundamentals Of Argument Analysis (2013)

Time And Space In Formal Logic (2022)

An introduction to formal logic: Second edition (2020)

Reasoning About The World As The Flow Of All (2024)