Presents a self-contained introduction to logic suitable for majors and nonmajors, and can be covered entirely in a one-semester course. Natural deduction systems of sentential logic and of first-order logic, truth tables, and the basic ideas of model theory are presented without superfluous discussion.

This a review of Logic Primer, written by Colin Allen and Michael Hand and published by MIT Press in 1992.

This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable (...) for advanced undergraduates or graduates, but also of interest to professional philosophers. There are well-thought-out exercises, and a number of advanced topics treated in appendices, while some are brought up in exercises and some are alluded to only in footnotes. By this means, it is hoped that the reader will at least be made aware of most of the important ramifications of the subject and its tie-ins with current research, and will have some indications concerning recent and relevant literature. (shrink)

Excerpt from Primer of Logical Analysis: For the Use of Composition Students To be sure, then, that we understand a sentence, we must be able to say, when any new and equally well-understood sentence is put beside the first, whether the new sentence is in meaning equivalent to the first, or consistent with the first, or deducible from the first, or opposed to the first. Yet other questions may be asked about the relative force of two sentences; but these (...) are enough for the present. Let us explain what we mean by them. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

This text is a short introduction to logic that was primarily used for accompanying an introductory course in Logic for Linguists held at the New University of Lisbon (UNL) in fall 2010. The main idea of this course was to give students the formal background and skills in order to later assess literature in logic, semantics, and related fields and perhaps even use logic on their own for the purpose of doing truth-conditional semantics. This course in (...) logic does not replace a proper introduction to semantics and is not intended as such, although parts of Chapter 1 and 4 could be used to supplement an introductory course in semantics. In contrast to other introductions it has a certain focus on ‘writing things down correctly.’ Proofs of metatheorems are omitted, though. -/- This is work in progress. Please send suggestions and corrigenda to [email protected]. Have fun! (shrink)

In 1672 John Eliot, English Puritan educator and missionary to New England, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof (Eliot 1672) The Logick Primer: Some Logical Notions to Initiate the INDIANS in the Knowledge of the Rule of Reason; and to Know How to Make Use Thereof, Cambridge, MA: Marmaduke Johnson]. This roughly 80 page pamphlet introduces syllogistic vocabulary (...) and reasoning so that syllogisms can be created from Biblical texts. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot's book is that it is bilingual, written in both English and Massachusett (Wôpanâak), an Algonquian language spoken in eastern coastal and southeastern Massachusetts. It is one of the earliest bilingual logic textbooks and it is the first, and perhaps only, textbook in an indigenous American language.In this paper, we (1) introduce John Eliot and the linguistic context he was working in; (2) introduce the contents of the Logick Primer – vocabulary, inference patterns, and applications; (3) discuss notions of ‘Puritan’ logic that inform this primer; and (4) address the importance of his work in documenting and expanding the Massachusett language and the problems that accompany his colonial approach to this work. (shrink)

In 1672 John Eliot, English Puritan educator and missionary to New England, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof (Eliot 1672) The Logick Primer: Some Logical Notions to Initiate the INDIANS in the Knowledge of the Rule of Reason; and to Know How to Make Use Thereof, Cambridge, MA: Marmaduke Johnson]. This roughly 80 page pamphlet introduces syllogistic vocabulary (...) and reasoning so that syllogisms can be created from Biblical texts. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot's book is that it is bilingual, written in both English and Massachusett (Wôpanâak), an Algonquian language spoken in eastern coastal and southeastern Massachusetts. It is one of the earliest bilingual logic textbooks and it is the first, and perhaps only, textbook in an indigenous American language.In this paper, we (1) introduce John Eliot and the linguistic context he was working in; (2) introduce the contents of the Logick Primer – vocabulary, inference patterns, and applications; (3) discuss notions of ‘Puritan’ logic that inform this primer; and (4) address the importance of his work in documenting and expanding the Massachusett language and the problems that accompany his colonial approach to this work. (shrink)

Volume 45, Issue 3, August 2024, Page 278-301.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS El Primer Principia del Obrar Moral y las Normas Especificas en el Pensamiento de G. Grisez y!. Finnis. By AURELIO A.NSALDO. Roma: Pontificia Universita Lateranense, 1990. Pp. xiii+ 255. This unusually excellent and important doctoral dissertation was written in Rome at the Istituto Giovanni Paolo II per Studi su Matrimonio e Famiglia, a component of the Lateran University. The author currently teaches at the Ateneo Romano (...) della Santa Croce in Rome. The volume is of special importance for three reasons: (1) it provides a comprehensive, detailed, and accurate account of the moral theory developed by Germain Grisez and John Finnis over the past quarter century (Joseph Boyle has also made important contributions to this theory, and Ansaldo has noted these); (2) it defends Grisez and Finnis against many of the criticisms which have been unjustly leveled against their thought; and (3) it raises some critically import· ant issues by way of constructive criticism. In what follows I will briefly comment on the first and second features of Ansaldo's work and discuss more fully the third important component of his scholarly study. In the first part of his work (pp. 3-100), Ansaldo offers readers a splendid synthesis of the thought of Grisez and Finnis. He has carefully studied everything written by these authors from 1964 to 1988. He has included important material from Finnis that had escaped even my attention, and I have tried to study everything these authors have written. He has also succeeded in presenting their thought comprehensively and faithfully. He understands what they think, appreciates it, and presents it accurately. In short, he does justice to their thought. In this respect his study is quite superior to another doctoral dissertation, Russell Hittinger's A Critique of the New Natural Law Theory. Hittinger's work has been severely criticized, and rightly so, not only by Grisez but by others (e.g., Robert George and William Marshner) ; it seriously misrepresents the work of Grisez and Finnis. A criticism of this sort cannot be levelled against Ansaldo's work; it provides an accurate and very scholarly account of their thought. In the second part of his study (pp. 103-229) Ansaldo offers a critical assessment of the work of Grisez and Finnis. Here he first shows that many of the criticisms leveled against their thought are unjust and unfounded, particularly those offered by such writers as Veatch, Rittinger, Flicken, Bourke, et al. These writers charge that Grisez and Finnis fail to show how moral principles are rooted in metaphysics and anthropology, that they completely separate ethics from metaphysics, natural law from human nature, etc. Ansaldo, by a patient and thorough BOOK REVIEWS 888 examination of their thought and the thought of St. Thomas, defends Grisez and Finnis from these misguided criticisms. He shows, first of all,,that Grisez and Finnis are correct (and fully in accord with St. Thomas) in holding that our krwwledge of the primary principles of natural law is not derived from our knowledge of metaphysics or of human nature. By referring to appropriate texts of Grisez and Finnis, Ansaldo shows conclusively that these authors explicitly recognize the intimate rela· tionship between ethics and metaphysics, between natural law and human nature. They fully and explicitly recognize that, were our na· ture other than it is, namely, the nature of human beings, the goods pedective of us would be other than what they actually are. When these goods are grasped by practical reason, they serve as starting points or principles of purposeful human action. Nonetheless, our practical krwwledge of these goods, is not epistemologically derived from or dependent upon prior knowledge, speculative in character, of human nature. In short, in contrast to their critics and in conformity with St. Thomas, Grisez and Finnis are correct in holding that our practical understanding of the primary principles of natural law is not dependent upon our prior understanding of metaphysics or human nature. At the same time they explicitly acknowledge and defend the truth that onto· logically ethics is grounded in metaphysics and anthropology. "Our authors," Ansaldo writes, " have always sought not only to respect but even more to defend and explain the fact that the basis... (shrink)

In this chapter, I’ll provide an introduction to the mathematics of probability theory.1 The philosophy of probability doesn’t require much mathematical sophistication, at least not to get a good grip on the main problems and views. Nothing in this chapter is particularly complicated, and even the mathematically shy should, with a little effort, find it easy to follow. I do assume familiarity with the basics of an elementary logic course, and some basic facility with the notion of a set.

Rational consequence relations and Popper functions provide logics for reasoning under uncertainty, the former purely qualitative, the latter probabilistic. But few researchers seem to be aware of the close connection between these two logics. I’ll show that Popper functions are probabilistic versions of rational consequence relations. I’ll not assume that the reader is familiar with either logic. I present them, and explicate the relationship between them, from the ground up. I’ll also present alternative axiomatizations for each logic, showing (...) them to depend on weaker axioms than usually recognized. (shrink)

Study of Navyanyāyabhāṣāpradīpa of Maheśacandranyāyaratna on Navya Nyāya philosophy; includes Sankrit text with English translation.

We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.

Table of Contents Volume I Preface to Volumes I and II: A Guide to the Primer Chapter 1, Basic Ideas and Tools Chapter 2, Transcription between English and Sentence Logic Chapter 3, Logical Equivalence, Logical Truths, and Contradictions Chapter 4, Validity and Conditionals Chapter 5, Natural Deduction for Sentence Logic: Fundamentals Chapter 6, Natural Deduction for Sentence Logic: Strategies Chapter 7, Natural Deduction for Sentence Logic: Derived Rules and Derivations without Premises Chapter 8, Truth Tree (...) for Sentence Logic: Fundamentals Chapter 9, Truth Trees for Sentence Logic: Applications Index for Volume 1 Solutions Manual for Volume 1 Table of Contents to Volume II Introduction to Predicate Logic Notes Chapter 1, Predicate Logic: Syntax Chapter 2, Predicate Logic: Semantics and Validity Chapter 3, More about Quantifiers Chapter 4, Transcription Chapter 5, Natural Deduction for Predicate Logic: Fundamentals Chapter 6, More on Natural Deduction for Predicate Logic Chapter 7, Truth Tress for Predicate Logic: Fundamentals Chapter 8, More on Truth Tress for Predicate Logic Chapter 9, Identity, Functions, and Definite Descriptions Chapter 10, Metatheory: The Basic Concepts Chapter 11, Mathematical Induction Chapter 12, Soundness and Completeness for Sentence Logic Trees Chapter 13, Soundness and Completeness for Sentence Logic Derivations Chapter 14, Koenig’s Lemma, Compactness, and Generalization to Infinite Sets of Premises Chapter 15, Interpretations, Soundness, and Completeness for Predicate Logic Index for Volume II Solutions Manual for Volume II Diagrammatic Summary of Rules Corrections to the Text. (shrink)

Setting out to understand Frege, the scholar confronts a roadblock at the outset: We just have little to go on. Much of the unpublished work and correspondence is lost, probably forever. Even the most basic task of imagining Frege's intellectual life is a challenge. The people he studied with and those he spent daily time with are little known to historians of philosophy and logic. To be sure, this makes it hard to answer broad questions like: 'Who influenced Frege?' (...) But the information vacuum also creates local problems of textual interpretation. Say we encounter a sentence that may be read as alluding to a scientific dispute. Should it be read that way? To answer, we'd need to address prior questions. Is it .. (shrink)

이 책자는 형식 논리의 일종인 양상논리에 입문하고 싶으신 분들을 위한 짧은 교재입니다. “양상논리 맛보기” 라는 말마따나, 이 책자는 양상논리에 관심은 있지만 아직 본격적으로 공부를 시작하진 않은 분들께서 ‘맛보기’를 하기에 적합한 안내 책자입니다. 아무쪼록 이 책자가 양상논리를 공부해나가시는데 유용한 첫 발판이 될 수 있기를 바랍니다. / This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert (...) Trueman's A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and also includes material from forall x: Lorain County Remix by Cathal Woods and J. Robert Loftis.) This booklet is licensed under a Creative Commons Attribution 4.0 license. (shrink)

Al-Abharī’s Isagoge is an introductory primer in logic which has received numerous commentaries, each geared towards students of various levels of familiarity with this instrumental science. Al-Fanārī’s advanced commentary on the Isagoge, called al-Fawāʾid al-Fanāriyya, has confounded students of logic for centuries due to its terse and dense style as well as the presumption that the reader knows well the science of disputation along with the subtle interpretive disagreements discussed in other texts and commentaries. Sājaqlīzādah’s primer (...) on disputation entitled al-Waladiyya, written nearly 300 years after al-Fanārī’s commentary, provides useful examples of the possible claims, objections, and defenses available to one making scholarly claims in the form of definitions, classifications, and propositional assents or syllogistic reasoning. In this article, I explore several instances of al-Fanārī’s use of the terms and methods of disputation in order to defend definitions or classifications found al-Abharī’s Isagoge. I aim to identify the specific disputational moves used by al-Fanārī, drawing from those described by Sājaqlīzādah. In doing so, I demonstrate that this important advanced commentary on a popular logic primer is best understood through the lens of disputation. I also argue that Sājaqlīzādah’s suggested methods of making claims, objections, and defenses can be transposed in whole or in part from one category of claim—definitions, classifications, assents—to another, indicating a greater complexity of disputational possibilities than his introductory handbook provides. (shrink)

Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic and Temporal (...) class='Hi'>Logic are consequently related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language. (shrink)

Set theory -- Logic -- Proofs -- Functions -- Group theory -- Linear algebra.

Epistemic Aphorisms is a wide-ranging consideration of issues in epistemology, from the classical and familiar (knowledge and justified true belief, and the problem of induction) to the unusual and often neglected (what alien science might look like, the ethics of epistemology, and the limits of conceptualization). In particular, it addresses questions in epistemology that are not generally asked, including questions regarding the ethics of secrets, the costs of inquiry, the factual trajectory of amassed information and its philosophical implications, and the (...) prospect of science based on radically different categories. These inquiries are accompanied by suggestions for formal treatment in epistemic logic, again in directions that have not been previously pursued. This book will be of use for undergraduate and graduate courses on epistemology and systems of knowledge and will also appeal to those undertaking advanced research in the field. (shrink)

'Live and die in Aristotle’s works.' - Christopher Marlowe, _Faustus_ Aristotle is without doubt one of the most influential people in history. His belief that philosophy should be grounded in observation laid the foundation for the scientific method. His moral philosophy exerted a profound influence on religious thinking and has recently returned to prominence with the resurgence of virtue ethics. His works are so thorough and wide-ranging as to constitute a quasi encyclopaedia of Greek knowledge. Amongst the most important are (...) Physics, Metaphysics, Nicomachean Ethics, Politics, On the Soul, Poetics, and the Organon, with which he created the field of logic and dominated it so thoroughly and for so long that even Kant thought that he had said the last word upon it. This book aims to provide the student and general reader with a comprehensive overview of Aristotle’s thought. It includes an introduction to the life of Aristotle, and – for the first time – a précis of each of his works, including the Organon, Physics, Metaphysics, Nicomachean Ethics, Politics, On the Soul, Poetics, and several others. _Author description:_ Dr Neel Burton is a philosopher and psychiatrist and prize-winning author who lives and teaches in Oxford, England. His other books include Plato’s Shadow, The Art of Failure, and The Meaning of Madness, all also with Acheron Press. (shrink)

_A Pocket Guide to Formal Logic_ is a succinct primer meant especially for those without any prior background in logic. Its brevity makes it well-suited to introductory courses in critical thinking or introductory philosophy with a formal logic component, and its friendly tone offers a welcoming introduction to this often-intimidating subject. The book provides a focused presentation of common methods used in statement logic, including translations, truth tables, and proofs. Supplemental materials—including more detailed treatments of select (...) methods and concepts as well as additional sample questions and answers—are available on a companion website. (shrink)

A key ingredient of the metaphysical doctrine of dual-aspect monism is a psychophysically neutral domain, of which mental and physical aspects arise as epistemic descendants that manifest themselves by decomposition. This primer first introduces some elementary notions to define the basic concepts needed to understand the approach, such as those of states, state spaces, observables, partitions and correlations. Using these notions, the concepts of decomposition and manifestation are explained, and a differentiated view of the mereological distinction of wholes and (...) parts is outlined. Next, a number of historical and contemporary accounts of psychophysical neutrality with philosophical (Plato, Spinoza, Schelling, Kant), scientific (Bohm, Pauli, Jung, Connes, Gibson), and artistic (sculpture, music) flavor are given as illustrative examples. Finally, correlations between the psychophysically neutral, the mental, and the physical domain of reality are discussed, in which these correlations are substantiated by meaning. (shrink)

This is a brief primer on elementary logic originally developed for an Applied Ethics course. I offer it here for any who might find it worthwhile or useful.