The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve (...) sample quizzes and solutions. The Symbolic Logic Study Guide is essential for all instructors and students who use LPL in their symbolic logic classes. (shrink)

"This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with (...) basic syllogisms and deductions." CHOICE connect "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with basic syllogisms and deductions." CHOICE Connect For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results. Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents. Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy. (shrink)

Historical studies convincingly demonstrate that the knowledge process [Erkenntnis] in natural science consists of the gradual adaptation of the thoughts to the facts. This adaptation happens through happy circumstances, which increasingly reveal the more general similarities and subtle differences of the facts. By this, the precision of the representation of the facts by the thoughts grows, so that the latter finally become an image of the former, which for certain intellectual purposes may completely substitute for them. The one who admits (...) this sober view of the meaning of natural science will assign to natural science teaching no other purpose, but to promote the aspired adaptation of thoughts with highest economy of work on shortcuts, by artificially bringing about those favorable circumstances avoiding the unfavorable historical coincidences and delays.One should in teaching first and foremost proceed psychologically; only secondarily and as much logically, as this is enabled through the psychological preparation so that it becomes a need. New concepts, theories, hypotheses, solutions of problems should only be introduced, when the need for this is felt in order to be able to master the topic. For each sentence, which appears during teaching, clarity and explicitness, but in general not indefeasibility from the point of view of the goal of teaching, should be required. (shrink)

This guide accompanies the following article: ‘Logic and Divine Simplicity’. Philosophy Compass 6/4 : pp. 282–294, doi: Author’s IntroductionFirst‐order formalizations of classical theistic doctrines are increasingly used in contemporary work in philosophy of religion and philosophical theology, as a means for clarifying the conceptual structure of the doctrines and their role in inferential procedures. But there are a variety of different ways in which such doctrines have been formalized, each representing the doctrines as having different conceptual structures. Moreover, the (...) adequacy of such formalizations as such has, at least with respect to some classes of doctrines, been disputed. One reason for disputing their adequacy derives from the conceptual impact of classical theism’s doctrine of divine simplicity.Author RecommendsFrege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. The preface contains interesting remarks about the purpose of formalization as understood by the chief pioneer of modern formal logic. These remarks are also connected by Frege to his views on the relation between thought and language more generally.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press.The preface and first section of the long introduction contain remarks on the purpose and advantages of formalization. Chapter 1 of the introduction contains what is probably one of the first formalizations ever of a theistic doctrine, and is given in terms of a definite description analysis.Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Clear and concise discussion of some of the advantages of formalization in philosophical inquiry, written by a prominent contemporary American philosopher‐logician.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9.A valuable paper that narrates, among other things, the programme of formalizing theistic doctrines that emerged in Poland in the 1920s under the influence of the Lvov‐Warsaw School. Various examples of formalizations are also given.Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press.In Section 27 of this classic study, Quine offers a formalization of theistic doctrines which seeks to avoid the difficulties of earlier formalizations by means of a subtle extensional singleton set analysis. The proposal has not won many adherents, but is worthy of careful study nonetheless.Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.A concise but lucid survey of some attempts to formalize theistic doctrines and some problems besetting these attempts. Woleński also proposes his own method of formalization, which could be described as a simplified version of Quine’s method in Mathematical Logic.Bocheński, Joseph The Logic of Religion. New York: New York University Press.The first book‐length treatment of the relation between modern logic and theism. It covers much ground, and remains very readable.Alston, William P. ‘Religious Language and Verificationism,’ in The Rationality of Theism, eds. Paul Moser and Paul Copan. London: Routledge, pp. 17–34.Identifies some problems with attempts at articulating theistic doctrines by means of subject‐predicate language. Highly relevant to formalizations of theistic doctrines, even though this topic is not dealt with explicitly.Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass.Offers a survey of three main methods of formalizing theistic doctrines, and of some variants of these methods. Argues that certain formalizations of theistic doctrines are bound to be rejected as conceptually inadequate by all who understand the doctrines at hand within the framework provided by the traditional doctrine of divine simplicity.Sample Syllabus Week I: The Idea of Formalization and the Project of Formalizing Theistic Doctrines Reading:Frege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9. Week II: Formalizing Theistic Doctrines: Three Alternative Methods Reading:Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press. Week III: Arguments for and Against Some Formalizations of Theistic Doctrines Reading:Bocheński, Joseph The Logic of Religion. New York: New York University Press. Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass, Vol. 6, No. 4, pp. 282–94.Focus Questions1 What do Frege, Russell and Whitehead, and Suppes understand the purpose or purposes of logical formalization to be, and why do they think formalization can achieve these purposes?2 Woleński sketches some simple ways of formalizing theistic doctrines such as ‘God exists’ or ‘God is almighty’ in terms of 1‐place predicates which he subsequently abandons in favour of other methods. What reasons lead him to abandon these more simple methods of formalization?3 What are the advantages of the definite description formalization of theistic doctrines offered by Russell and Whitehead?4 Quine offers a subtle formalization of the theistic doctrine ‘God exists’ in terms of singleton sets. What problems are Quine’s formalization intended to accommodate, and how does it seek to accommodate them?5 Which relative merits or demerits are there in Bocheński’s and Kraal’s respective arguments for and against the adequacy of certain formalizations of theistic doctrines? (shrink)

A text that would find a place for the realistic formalism of Aristotle, the scientific penetration of Peirce, the pedagogical soundness of Dewey, and the ...

Having studied mathematics, in particular foundations and philosophy of mathematics, it happened that I was asked to teach logic to the students in the Faculty of Philosophy of the Radboud University Nijmegen. It was there that I discovered that logic is much more than just a mathematical discipline consisting of definitions, theorems and proofs, and that logic can and should be embedded in a philosophical context. After ten years of teaching logic at the Faculty of (...) Philosophy at the Radboud University Nijmegen, thirty years at the Faculty of Philosophy of Tilburg University and nine years at the Faculty of Philosophy of the Erasmus University Rotterdam, I got many ideas how to improve my LOGIC book which was published twenty five years ago in 1993 by Verlag Peter Lang. Although the amount of work was enormous, I felt I should do it. It is like working on a large painting where you put some extra color in one corner, add a little detail at another place, shed some more light on a particular face, etc. (shrink)

The sources for this volume are the unpublished papers of Reid contained in the Birkwood Colletion. As the title of the volume indicates, Reid’s teaching as a Regent included Logic, Rhetoric, and the Fine Arts. The regenting system assigned cadres of students to a specific teacher who would pace them through the entire curriculum of study. Broadie cites Reid’s own defenses of this system and the important educational and civic aims achieved by it, at the relatively slight (...) cost of unavoidable superficiality. Today’s academic world might benefit from a consideration of current practices as informed by Reid’s ideas on just this point. (shrink)

Moving education to Zoom, Microsoft Teams, and the many alternatives during the COVID19-pandemic raised the question of pedagogical form. In a sense, pandemic education in its two-dimensionality was a frictionless, sanitized reduction of education to pure form; it offered a more efficient transfer of knowledge and was marked by a heightened means-to-an-end logic. This has made the informal, unforming and deformational activity that Stefano Harney and Fred Moten call study even more difficult, if not impossible during pandemic education. (...) In this article, we consider the pitfalls of thinking in terms of pedagogical form and the formalization of education by engaging with Emile Bojesen’s work on education as (de)formation. Via Harney and Moten, we reflect on what the concept/practice of study by way of formless formation teaches us about (pre-)pandemic education and about pedagogical forms that might be in keeping with study in post-pandemic education. (shrink)

This paper presents three lessons designed to alert students to the setting in which they are learning (the classroom) and the ways in which this setting provides the context for a discourse which is different than everyday discourse. In the first lesson, students examine empirical studies that illustrate how being in a classroom significantly changes how one reasons about even the most basic logical relationships. In the second lesson, Levi critiques an imaginative way of teaching logic that, while (...) appearing to call on students to use critical reasoning skills they already possess, still fails to take into account its setting. In the final lesson, students translate an editorial into the form of declarative sentences, ordered as premises and a conclusion. Students are prompted to consider what is lost in this rendering and how it distorts the original argument, after which a more successful strategy for paraphrasing and evaluating arguments is attempted. These lessons aim to teach students to think for themselves by encouraging them not to learn logic by wrote, but to see its lessons as tools whose very applicability to real life is something they must critically evaluate. (shrink)

Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help ...

Teaching research methods is especially challenging because we not only wish to convey formal knowledge and encourage critical thinking, as with any course, but also to enable our students dream up meaningful research projects, translate them into logical steps, conduct the research in a professional manner, analyze the data, and write up the project in APA style. We also wish to spark interest in the topics of research papers, and in the intellectual challenge of creating a research report, but (...) we have learned just how difficult these goals can be from teaching undergraduates and from serving as journal reviewers: many submissions contain flaws such as elementary errors of logic (e.g., using a null control condition instead of a placebo or dummy treatment), tangled statistics, a lack of graphs, and ungrammatical, unclear writing that violates APA rules. Yet these manuscripts are written by university faculty, often with doctorates and years of experience. Even published papers may contain egregious faults (Standing & McKelvie, 1986). And although we have both published widely, we still hone our skills. It requires optimism to expect that a typical undergraduate will do better, on the basis of just a year or two of studies in psychology. In this paper, we describe a systematic set of methodology courses and two specific practices that we think can help. Methodology Courses as the Backbone of our Psychology Program How can methodology courses promote undergraduate involvem... (shrink)

Basic course of study of Buddhist logic and dialectrical studies prescribed for Rato Datsang, a monastery at Nyetang in Tibet, China.

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) logic texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

In this important work, Dr. Felipe Fierro offers a comprehensive view on the subject of Introduction to the Study of Law, in which he revives the use of Gnoseology, Philosophy, History and Logic as Auxiliary Sciences; and exposes how the abandonment of such has contributed to the exponential growth of Skepticism and Relativism, currently prevailing in the legal world. The above, through extensive experience in teaching Law from the Aristotelian-Thomistic platform, based on the elementary assumption that we (...) must first prove the existence of the object of study, and contrast main legal branches in topics such as: what is Law?, why is Science?, what are Law, Justice, Facultative rights and the Common Good?; supported by extensive and select bibliography. In addition, the being, nature, concept, essence and properties of the sources, fundamentals and classification are described. But important elements such as knowledge, order, principles, Jurisprudence, and Natural law, fundamental legal concepts, the legislative process, the Constitution, interpretation and others are not absent. Morality and Legal Law are obligatory markers, which although considered in their own field, are not excluded, but different as to object and method. Predominantly, Justice is exposed as one of the great values of the Law, and main theories in order to offer future lawyers the basis regarding the current Science of Law and its significance. (shrink)

This anthology opens new perspectives in the domain of history, philosophy, and science teaching research. Its four sections are: first, science, culture and education; second, the teaching and learning of science; third, curriculum development and justification; and fourth, indoctrination. The first group of essays deal with the neglected topic of science education and the Enlightenment tradition. These essays show that many core commitments of modern science education have their roots in this tradition, and consequently all can benefit from (...) a more informed awareness of its strengths and weaknesses. Other essays address research on leaning and teaching from the perspectives of social epistemology and educational psychology. Included here is the first ever English translation of Ernst Mach’s most influential 1890 paper on ‘The Psychological and Logical Moment in Natural Science Teaching’. This paper launched the influential Machian tradition in education. Other essays address concrete cases of the utilisation of history and philosophy in the development and justification of school science curricula. These are instances of the supportive relation of HPS&ST research to curriculum theorising. Finally, two essays address the topic of Indoctrination in science education; a subject long-discussed in philosophy of education, but inadequately in science education. This book is a timely reminder of why history and philosophy of science are urgently needed to support understanding of science. From major traditions such as the Enlightenment to the tensions around cultural studies of science, the book provides a comprehensive context for the scientific endeavour, drawing on curriculum and instructional examples. Sibel Erduran, University of Oxford, UK The scholarship that each of the authors in this volume offers deepens our understanding of what we teach in science and why that understanding matters. This is an important book exploring a wide set of issues and should be read by anyone with an interest in science or science education. Jonathan Osborne, Stanford University, USA This volume presents new and updated perspectives in the field, such as the Enlightenment Tradition, Cultural Studies, Indoctrination in Science Education, and Nature of Science. Highly recommended. Mansoor Niaz, Universidad de Oriente, Venezuela This volume provides an extremely valuable set of insights into educational issues related to the history and philosophy of science. Michael J Reiss, University College London, UK. (shrink)

Charles Sanders Peirce’s first rule of logic (EP 2.48, 1898) identifies the inception point of human inquiry. Taking a closer look at this principle, we find at its core a necessary relationship between emptiness and desire that underlies all genuine instances of human learning and adaptation. This composite relationship plays a critical role in the function or failure of learning but has received scant attention in the literature. As a result, the complexities of the first rule of logic (...) are not well understood, often being mistakenly conflated with the rule’s famous corollary, ‘do not block the way of inquiry’, or passed over with cursory definitions, including ‘wonder’, ‘doubt’ and ‘the will to learn’. Following a background discussion highlighting the nature of reflexive inquiry and fallibilism that situate human consciousness both within and beyond animal being, I draw on multiple layers of evidence from a range of disciplines to better reveal the complex dynamics intrinsic to the first rule of logic. These layers include a closer reading and exegesis of the original passage and surrounding text; a semiotic reanalysis of this reading in light of recent advances in the semiotic theory of learning; a resituation of these distinctions within broader contemporary discussions of emptiness ontology to which I contribute in part via an original semantic/rhetorical analysis of a linguistic construction in Laozi; the introduction of a closely related pedagogical tool under development in the context of my own university-level teaching in ethnography and research methods; and the dialogic situation of this diagram within discourses of psychotherapy, philosophy and literature. Building on these principles and distinctions, the paper closes with a perspective shift on obstacles and desire in human learning and an expanded reformulation of the first rule of logic. (shrink)

This paper considers the nature of the changes that took place in logic teaching at the University of Oxford from the beginning of the sixteenth century, when students attended university lectures on Aristotle’s texts as well as studying short works dealing with specifically medieval developments, to the beginning of the eighteenth century when teaching was centred in the colleges, the medieval developments had largely disappeared, and manuals summarizing Aristotelian logic were used. The paper also considers the (...) reasons for these changes, including changes in English society, and the effect of humanism and the more scholarly Aristotelianism that it produced. (shrink)

Some of the most interesting recent work in philosophy of language and metaphysics is focused on questions about propositions, the abstract, truth-bearing contents of sentences and beliefs. The aim of this guide is to give instructors and students a road map for some significant work on propositions since the mid-1990s. This work falls roughly into two areas: challenges to the existence of propositions and theories about the nature and structure of propositions. The former includes both a widely discussed puzzle about (...) propositional designators as well as direct and indirect arguments against the existence of propositions. The latter is dominated by what is currently the central debate about the metaphysics of propositions, i.e. whether they are structured, composite entities or unstructured ontological simples. This issue has eclipsed older debates about whether propositions can be identified with sets of possible worlds or other kinds of sentence intensions. Author Recommends 1. Soames, Scott. 'Direct Reference, Propositional Attitudes, and Semantic Content.' Philosophical Topics 15 (1987): 47–87. Reprinted in Propositions and Attitudes . Eds. N. Salmon and S. Soames. Oxford: Oxford University Press, 1988. 197–239. Essential groundwork for more recent work on propositions. Soames gives a careful and exacting presentation of the case against identifying propositions with sets of possible worlds or other truth-supporting circumstances. Also contains a detailed statement of the Russellian conception of propositions on which propositions are ordered sets of objects, properties and relations. 2. King, Jeffrey. 'Designating Propositions.' The Philosophical Review 111 (2002): 341–71. Sometimes substituting a definite description for a corresponding 'that'-clause can lead to bizarre changes in truth-conditions: compare 'Bill fears that Hillary will be president' with 'Bill fears the proposition that Hillary will be president'. This puzzle about propositional designators threatens the relational analysis of propositional attitude reports, the view that 'believes' expresses a relation to the proposition designated by its 'that'-clause, and thereby poses an indirect threat to the existence of propositions. King's solution posits an ambiguity in verbs like 'fear' that embed both 'that'-clauses and definite descriptions. 3. Jubien, Michael. 'Propositions and the Objects of Thought.' Philosophical Studies 104 (2001): 47–62. A direct attack on the existence of propositions. Jubien deploys an analogue of the problem that Paul Benacerraf raised for set-theoretical reductions of numbers against metaphysical reductions of propositions. Just as numbers can be reduced to sets in many different ways, any reduction of propositions brings with it equally good variants, thus making any such reduction arbitrary and unmotivated. The only alternative is to treat propositions as abstract metaphysical primitives. As Jubien argues, however, abstract primitive entities are incapable of doing what propositions must do, i.e. represent objects and states of affairs on their own, without the input of thinking subjects. The upshot is the propositions cannot be reduced and they cannot be primitive, and so they must not exist. 4. Hanks, Peter. 'How Wittgenstein Defeated Russell's Multiple Relation Theory of Judgment.' Synthese 154 (2007): 121–46. Scepticism about propositions has recently led some philosophers, Jubien included, to resuscitate Russell's multiple relation theory of judgment, the idea that judgment is a many-place relation to objects, properties and relations. This paper explains why Russell himself abandoned that theory, and why the theory is still refuted by an objection due to Wittgenstein. 5. Hofweber, Thomas. 'Inexpressible Properties and Propositions.' Oxford Studies in Metaphysics . 2 vols. Ed. D. Zimmerman. Oxford: Oxford University Press, 2006. 155–206. An indirect attack on the existence of propositions. Hofweber argues that sentences like 'Bill believes something that Hillary asserted' do not commit us to the existence of propositions. His view is that propositional quantification is an instance of what he calls 'internal' or 'inferential role' quantification, a kind of quantification that carries no ontological implications. 6. Schiffer, Stephen. The Things We Mean . Oxford: Oxford University Press, 2003. esp. chs 1–2. Schiffer defends his theory of pleonastic propositions, on which propositions are unstructured, have no parts, and are very finely grained. 7. Bealer, George. 'Propositions.' Mind 107 (1998): 1–32. Bealer defends his algebraic theory of propositions, which, like Schiffer's pleonastic account, treats propositions as unstructured metaphysical simples. 8. King, Jeffrey. The Nature of and Structure of Content . Oxford: Oxford University Press, 2007. The best developed current theory of the structure in structured propositions. King identifies propositions with certain kinds of facts in which objects, properties and relations are bound together by amalgams of syntactic and semantic relations. 9. Hanks, Peter. 'Recent Work on Propositions.' Philosophy Compass 4 (2009): 1–18. A survey of work on propositions since the mid-1990s that complements this teaching and learning guide. Contains responses to Jubien's and Hofweber's arguments against propositions and critical discussions of Schiffer's pleonastic propositions and King's theory of propositional structure. Online Resources 1. http://plato.stanford.edu/entries/propositions/ Propositions (Matthew McGrath) 2. http://plato.stanford.edu/entries/propositions-structured/ Structured Propositions (Jeffrey King) 3. http://plato.stanford.edu/entries/propositions-singular/ Singular Propositions (Greg Fitch) Sample Partial Syllabus The following partial syllabus can be used as a unit on recent work on propositions in graduate level courses in philosophy of language or metaphysics. Week 1: A Substitution Puzzle About Propositional Designators King, Jeffrey. 'Designating Propositions'. Moltmann, Friederike. 'Propositional Attitudes Without Propositions.' Synthese 135 (2003): 77–118. Week 2: The Benacerraf Problem and Propositional Representation Benacerraf, Paul. 'What Numbers Could Not Be.' Philosophical Review 74 (1965): 47–73. Jubien, Michael. 'Propositions and the Objects of Thought.' Week 3: Propositional Quantification Hofweber, Thomas. 'Inexpressible Properties and Propositions'. Hofweber, Thomas. 'A Puzzle about Ontology.' Noûs 39 (2005): 256–83. Week 4: Schiffer on Pleonastic Propositions Schiffer, Stephen. 'Language-Created Language-Independent Entities.' Philosophical Topics 24 (1996): 149–67. Schiffer, Stephen. The Things We Mean , chs 1–2. Week 5: King on Structured Propositions King, Jeffrey. 'Structured Propositions and Complex Predicates.' Noûs , 29 (1995): 516–35. King, Jeffrey. The Nature and Structure of Content , chs 1–3. Focus Questions 1. Why does identifying propositions with sentence intensions, e.g. sets of possible worlds, 'require the attitudes to have a particular sort of closure under logical consequence, which they clearly don't have' (Mark Richard)? 2. How does the difference between (a) and (b) pose a threat to the existence of propositions? (a) Bill fears that Hillary will be president. (b) Bill fears the proposition that Hillary will be president. 3. What is the Benacerraf problem for metaphysical reductions of propositions? 4. Why must a proposition represent 'on its own cuff' (Michael Jubien)? Why is this a problem for the view that propositions are primitive abstract entities? 5. What does it mean to say that propositions are structured ? Give two different accounts of what propositional structure might be. (shrink)

Philosophy is the study of the most general and fundamental problems of human life. The main areas of study in philosophy includes metaphysics, epistemology, logic, ethics and aesthetics etc. there are other several branches of philosophy which characterize different branches of knowledge. Philosophy being a very abstract branch of study, has not much scope of using equipment on a large scale to supplement the normal lecture schedules. However, in some papers/areas there are comparatively better scope to (...) make the lectures more concrete and interesting through proper use of various teaching aids and modes. We include logic, philosophy of science, applied philosophy, applied ethics, social and political philosophy, philosophy of mind, philosophy of cognitive science and history of philosophy etc., we can use various modern aids. In this article my attempt is to draw out an outlines of aids and modes for effective philosophy teaching. (shrink)

This chapter focuses on John Locke's relation to scholasticism. It explores who the schoolmen referred to by Locke were, and what he might have learned from them, particularly with respect to topics in metaphysics, logic, and language. The chapter considers the Oxford curriculum which provided the framework for Locke's years of study and teaching there, as there is little reason to believe that he enriched his acquaintance with the schoolmen in his later career. The topic of substance (...) was raised both in metaphysics textbooks and in logic textbooks, but the material in both was largely similar. The chapter considers some of Locke's remarks and focuses on what the scholastics had to say. Locke goes on to claim that the very use of syllogistic depends on the prior ability to see the connections between ideas. The area in which Locke showed the most obvious influence of scholasticism is that of language. (shrink)

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was (...) essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the formulation of group theory; and geometry, transformed by Riemann, lay at the heart of topology, which in turn transformed much of modern mathematics. Using complex numbers as my case study, I argue that the best way to teach students mathematics is through a repertoire of modes of representation, which is also the best way to make mathematical discoveries. (shrink)

What is argumentation? -- Building a classroom culture of argumentation -- Structuring classroom discussions to focus on argumentation -- Infusing all instruction with argumentation -- Argumentation for all students -- Argumentation and the mathematical practices -- Technology in teaching and learning argumentation -- Assessing argumentation and proof -- Conclusion.

The article discusses the formation of the philosophical concept of Leonid Evgenievich Gabrilovich (1878–1953), a Russian thinker of the first half of the 20th century. In the Rus­sian period of creativity, i.e. until 1918, as it is shown in the article, in his philosophi­cal development Gabrilovich experienced the influence of such fundamental theories as the philosophy of normative, immanent philosophy of W. Schuppe and phenomenology of E. Husserl. The article studies the following articles by L.E. Gabrilovich of the first, “Russian” (...) period: “On the concepts of truth and reliability in the theory of knowledge” 1908, “On two scientific concepts of thinking (to justify one dativist logic)” 1909, “On the meaning and essence of elementary concepts (an attempt at a new development of the problem of universal concepts)” 1910, as well as some others. It is shown that in his philosophical work L.E. Gabrilovich consistently and purposefully followed the de­velopment of his own concept, the nature of which makes it possible to attribute his phi­losophy to the logical and epistemological direction in Russian philosophy of the 20th cen­tury. The article proves that according to their ideas and structure, the analyzed texts of Gabrilovich revealed the themes of mathematical formalism, dativist logic, at the same time they were the main stages in the development of his own logical and epistemological concept as mathematical thinking and the actual form. L.E. Gabrilovich outlined the re­sults of these developments in the book “On Mathematical Thinking and the Concept of the Actual Form”, a 1914 essay written by him in German. It is concluded that the con­cept of “dativist logic”, developed by Gabrilovich in articles of 1909 and 1910, will later result in his theory of “actual forms”. (shrink)

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers (...) explore the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:502 Feminist Studies 46, no. 2. © 2020 by Feminist Studies, Inc. Jaime Madden Teaching Online: Issues of Equity and Access in Writing-centric Formats The COVID-19 pandemic has turned us all into online teachers. In the context of this crisis, we have quickly learned new technologies and the affordances of asynchronous and synchronous delivery. We have grappled with the challenges of building community and supporting active engagement, and (...) we have turned to adapting our assessment methods for the remote environment. We have done this work at traditional colleges and universities, where online teaching was formerly the purview of graduate students and adjunct instructors. Online learning can no longer be associated with those who struggle to access traditional classrooms, such as disabled students and those who attend for-profit colleges. Instead, access to online learning can now be associated with access to wealth and to health—specifically as relates to avoiding contact with the virus. In K-12 education, we have seen districts that largely enroll white students make the decision to continue online or go hybrid for the fall 2020 semester, whereas those that largely enroll students of color are returning to the classroom.1 Inequalities pervade the teaching landscape as well. Teaching is not a job usually marked as high risk, but within this environment, some 1. The work of activist and artist @bmore_radical shows how these decisions are being made in Baltimore, Maryland. See https://www.instagram.com /bmore_radical/?hl=en. Jaime Madden 503 bodies suffer at higher rates. In a recent article published in this journal, coauthors writing as the Brocher Foundation Feminist Collective describe their experience and knowledge “of the ways that academia produces sickness.”2 The authors are white and cisgender women at Anglo-American and European universities, and even though they acknowledge that they did not experience high levels of racism, classism, linguistic marginalization, and/or illness, they still found themselves—at different stages of their careers—“worn thin” in a system where “bodies are disposable.”3 Commenting on this problem in another context, disability studies scholar Alison Kafer notes that disability is “more fundamental, more inevitable, for some than others.”4 The pandemic has made this much clear: able-bodied people are “temporarily able-bodied,” and those who experience racism and classism are among the most frequently and intensely sickened. In attending to how teachers and students transition online en masse, we need to consider how we are differently positioned within institutions governed by the logics of racialized capitalism. It is important to recognize not only which students can access these online spaces but also which skills such spaces tend to reward. It is also important to ask which teachers are disproportionately impacted by the transition online. In this piece, I describe the challenges of assessment and then wrestle with broader questions of access as a scholar invested in feminist studies and disability studies. The tension in online education between its promise of access and its methods of assessment is, I argue, worthy of urgent attention. The Challenges of Assessment I have taught online courses at four institutions: two private colleges and two public universities. Good teaching and learning can undoubtedly happen across a range of spaces. In online environments, I have found that my best teaching happens in the feedback I give students. 2. Laura Bisaillon, Alana Cattapan, Annelieke Driessen, Esther van Duin, Shannon Spruit, Lorena Anton, and Nancy S. Jecker, “Doing Academia Differently: ‘I Needed Self-Help Less Than I Needed a Fair Society,” Feminist Studies 46, no. 1 (2020): 132. 3. Bisaillon, et al., “Doing Academia Differently,” 136, 140. 4. Alison Kafer, Feminist, Queer, Crip (Bloomington: Indiana University Press, 2013), 26. 504 Jaime Madden This is understandable since assessment practices are important teaching opportunities in all contexts. In online environments, and particularly in asynchronous teaching, I have found that it is while carrying out assessments of student work that my most intense teaching occurs. It is through grading and offering comments on papers and assignments that I am most directly in communication with students as their teacher. When I mark student work, I ask questions of students, I prompt them to consider how our course materials may be placed... (shrink)

Ordinary textbooks for such a course are purely mathematical in their nature, and students usually find the course difficult, boring and very technical. Our approach motivates the students through reading the classic novel Alice's Adventures in Wonderland, written by Lewis Caroll who was not only one of the best storytellers but also a logician.

In lieu of an abstract, here is a brief excerpt of the content:Toward a Theoretical Framework for the Study of Humor in Literature and the Other ArtsJerry Farber (bio)With a clearer understanding of the way humor works, we might be better able to give it the attention it deserves when we study and teach the arts. But where do we turn to find a theoretical framework for the study of humor—one that will help to clarify the role (...) that humor plays in the arts and that will help us as well to understand differences in the way individual perceivers respond to humor in art?A superiority theory of humor emerged in classical times and more or less held the stage through the seventeenth century; now, however, though an occasional attempt to revive it is still made,1 superiority theory is usually regarded as far too narrow in scope to be useful as a general account of humor. What are commonly referred to as "release" (or, occasionally, "relief") theories— and associated with Spencer and Freud—were for a time very influential, but are somewhat narrow too in their own way, and furthermore, as Noël Carroll puts it, "have the liability of presupposing hydraulic views of the mind that are highly dubious."2 Incongruity theory, which has been around in one form or another since at least the eighteenth century, dominates contemporary humor theory but is still widely regarded as not quite there yet. And so humor remains somewhat mysterious and elusive. Or not even that. It may be that most people, even teachers in the arts, bypass theory entirely and simply accept humor as a given: an unanalyzable fact of human life. I've sometimes wondered if it may be that we don't want to understand humor, either because we're afraid that this understanding will spoil the game or, just possibly, because we sense that, as a consequence of it, we may discover things about ourselves that we would prefer not to know.Is a well-founded, broadly inclusive theoretical framework for the study and teaching of humor in the arts achievable? I want to propose that it is if [End Page 67] we take incongruity theory a few steps further, integrating an analysis of the humorous situation (that is, what we perceive: the caricature, the witty dialogue, the bit of stage business) with an analysis of what goes on in the perceiver (the humor experience itself).A General Theory of HumorIncongruity theory, though clearly the front-runner these days, continues to be problematic, making too much sense for us to discard it, but not quite enough sense to get us where we need to go. Thus, Carroll concludes his recent overview of this theoretical tradition: "Though promising, the Incongruity Theory of Humor remains a project in need of further research."3 Reading this we may find ourselves wondering, just as we might about some writer or performer who's been on the scene for a good long time, how much longer this centuries-old theoretical approach gets to remain "promising."What have been the major problems associated with incongruity theory? For one thing, it doesn't tell us much about the affective dimension of humor.4 Neither does it satisfactorily explain differences in the way individual perceivers respond. The major weakness of incongruity theory, however, has been a failure to account adequately for all of those instances of incongruity that are not funny: for example, brainteasers, logic problems, and puzzles. One way of dealing with this problem has been to keep adding on exclusionary clauses until the category has been pared down satisfactorily. In other words, humor is based on incongruity, provided that we exclude situations that inspire fear, or are disgusting, or are perceived instrumentally, or are regarded primarily as a puzzle, and so on. But, of course, this is patchwork. What we need is a humor theory where stipulations such as these don't have to be added on, because they follow logically from the theory itself.It's been proposed repeatedly that the incongruous elements in humor are likely to be connected in some way, though some of the terms that have been advanced to identify this connection are unnecessarily limiting if... (shrink)

Recent reflection on the professional knowledge of teachers has been marked by a shift away from more reductive competence and skill-focused models of teaching towards a view of teacher expertise as involving complex context-sensitive deliberation and judgement. Much of this shift has been inspired by an Aristotelian conception of practical wisdom (phronesis) also linked by Aristotle to the development of virtue and character. This has in turn led recent educational philosophers and theorists – inspired by latter-day developments in virtue (...) ethics and virtue epistemology – to investigate the contribution of various forms of virtue to the effective practice of teaching. In this light, the present paper undertakes further exploration of the logical geography of virtue, character and practical deliberation in teaching. (shrink)

In this clearly written and impressive volume, Giorgio Pini has provided the first systematic book-length study of Duns Scotus’s doctrine of the categories and an extremely useful sketch of his views on logic generally. Divided into six chapters, the work covers the gamut of interpretations of Aristotle’s Categories over the course of the thirteenth century, ranging from the views of Robert Kilwardby and Albertus Magnus in the 1240s to the leading opinions of the 1280s and 1290s, those held (...) by Radulphus Brito, Simon of Faversham, and Peter of Auvergne. Through this survey of historical background to Scotus’s logical, metaphysical, and theological works, the reader becomes readily acquainted with the systematic options for understanding categories, both in logic and in metaphysics, while appreciating all the more keenly the full bearing of Scotus’s own teaching. (shrink)

The paper discusses the place and the status of fallacies in Arnauld and Nicole’s Port-Royal Logic, which seems to be the first book to introduce a radical change from the traditional Aristotelian account of fallacies. The most striking innovation is not in the definition of a fallacy but in the publication of a new list of fallacies, dropping some Aristotelian ones and adding more than ten new ones. The first part of the paper deals with the context of the (...) book’s publication. We then show the influence of Cartesian and Augustinian/Pascalian philosophy on the whole book, especially their common critical views about logic, dialectic and their traditional academic teaching. The third part of the paper discusses the two chapters on fallacies. It focuses on their place in the book and their relation with its general orientation, before turning to their content, closely connected with some major concerns of the time. (shrink)

A critical study of McPeck's recent book, in which he strengthens and develops his arguments against teaching critical thinking (CT). Accepting McPeck's basic claim that there is no unitary skill of reasoning or thinking, I argue that his strictures on CT courses or programs do not follow. I set out what I consider the proper justification that programs in CT have to meet, and argue both that McPeck demands much more than is required, and also that it is (...) plausible that this deflated justification can be met. Specitically, I argue that it is reasonable to expect transfer of learning for basic logical skills. Additional topics covered include: the relation ofliberal education to critical thinking, argument analysis, testing for CT, and the value of conceptual or linguistic analysis. (shrink)

Stories of Philosophy is an introduction to philosophy textbook that combines both fiction and philosophical discussion. It combines compelling stories devoted to particular philosophical problems followed by clear and detailed guided discussions of the topics and ideas explored within the fictional stories. The text includes chapters on Logic, Appearance and Reality, The Nature of Mind, Freedom and Responsibility, The Existence of God, and Morality. Each chapter has several highly praised pedagogical features, including chapter-opening learning objectives, boldfaced key terms, questions (...) for discussion, definitions of terms, and suggested further readings. It will be accompanied by online support material for the instructor and the student. (shrink)

The era in which Abū Naṣr al-Fārābī emerged as a canonical scientist significantly contributed to his education and shaped his scientific worldview. The formation of al-Farabi’s spiritual worldview and his ideas is directly associated with embracing the ancient philosophical tradition, more precisely, Aristotle’s philosophy and logic. The focus of the article is alFarabi’s analysis of Aristotle’s principles in the study of logic and their further development. Al-Farabi’s worldwide reputation as the Second Teacher after Aristotle, the First Teacher, (...) in the East is directly rooted in his mastery and advancement of the science of logic. In simple terms, the philosopher states that logic leads a person to a straight path to being capable of radically discerning between good and bad, truth and lies, and honesty and deceit. This, in turn, steers humanity away from succumbing to mistakes or getting into trouble. Al-Farabi constructs a comprehensive scientific analysis of the socio-cultural foundations of Aristotle’s doctrine of logic and the ability to adapt it in his unique way to society. The study of the theoretical basis of al-Farabi’s teachings on logic and its significance involves employing hermeneutic, comparative, and stylistic methods in the research of the texts. (shrink)

Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students (...) in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library. (shrink)

Adding instructional time and holding teachers accountable for teaching social studies are touted as practical, logical steps toward reforming the age-old tradition of marginalization. This qualitative case study of an urban elementary school, examines how nine teachers and one administrator enacted district reforms that added 45 min to the instructional day and implemented a series of formative and summative assessments. Through classroom observations, interviews, time journals, and official school documents, this article describes underlying perceptions and priorities that were (...) barriers to any positive impact time or testing might have afforded social studies. Two recommendations emerge from results: 1) time structures need to provide space for the teaching of and planning for social studies; and 2) testing can have positive outcomes, but these are limited when assessments structures are hierarchical, misaligned, and poorly communicated. (shrink)

Evolution and Religion in American Education shines a light into one of America’s dark educational corners, exposing the regressive pedagogy that can invade science classrooms when school boards and state overseers take their eyes off the ball. It sets out to examine the development of college students’ attitudes towards biological evolution through their lives. The fascinating insights provided by interviewing students about their world views adds up to a compelling case for additional scrutiny of the way young people’s educational experiences (...) unfold as they consider—and indeed in some cases reject—one of science’s strongest and most cogent theoretical constructs. Inevitably, open discussion and consideration of the theory of evolution can chip away at the mental framework constructed by Creationists, eroding the foundations of their faith. The conceptual battleground is so fraught with logical challenges to Creationist dogma that in a number of cases students’ exposure to such dangerous ideas is actively prevented. This book provides a detailed map of this astonishing struggle in today’s America—a struggle many had thought was done and dusted with the onset of the Enlightenment. (shrink)

hese notes don’t reach any conclusions. Their purpose is to point to issues one needs to think through seriously when thinking about logic teaching. They indicate some of the relevant literature where some of these issues are addressed, but they also raise points that seem to have been overlooked. They aim to promote informed discussion. That indeed was their origin: they are descended from an internal discussion document prepared a few years ago when the then Department of Philosophy (...) at the University of Edinburgh was reviewing its logic teaching. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Logic Pamphlets of Charles Lutwidge Dodgson and Related PiecesIrving H. AnellisFrancine F. Abeles, editor. The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. The Pamphlets of Lewis Carroll, 4. New York-Charlottesville-London: Lewis Carroll Society of North America-University Press of Virginia, 2010. Pp. xx + 271. Cloth, $75.00.Until William Bartley’s rediscovery and reconstruction of Dodgson’s lost Part II of Symbolic Logic, Lewis Carroll’s reputation (...) in logic, when taken seriously, rested upon his few published articles on logical paradoxes and puzzles, while his published books, The Game of Logic and Symbolic Logic, were regarded as suitable perhaps as pedagogical tools, but dismissed otherwise as amusements, on a par with the Alice works. Richard Braithwaite asserted (“Lewis Carroll as Logician”) that “Carroll regarded formal and symbolic logic not as a corpus of systematic knowledge about valid thought nor yet as an art for teaching a person to think correctly.” He suggested that Dodgson used his pseudonym for his popular and whimsical writings, reserving his legal name only for his serious mathematical products. Philosophers practicing linguistic analysis in their assault on nonsense deriving from misuse of language meanwhile developed an interest in Carroll (e.g. George Pitcher, “Wittgenstein, Nonsense, and Lewis Carroll”). Abeles, on the contrary, stresses the seriousness of Dodgson’s pedagogical and popularizing mission (195–99).Bartley’s discovery opened the door for reevaluating Dodgson as a serious logician, and Abeles has been in the forefront of that reevaluation. Her general introduction and introductions to the main divisions of this collection of Carroll’s publications (and additional material from his Nachlass and a handful of publications of others, composed in response to Carroll’s published articles) place his serious logical work and its significance in historical perspective, providing a deeper, more sophisticated view than found in Bartley’s “Editor’s Introduction” to Lewis Carroll’s Symbolic Logic. Abeles also offers brief introductions to the individual entries, which describe their physical characteristics and circumstances of composition.Dodgson aligned with the majority of those British logicians of his day, starting with George Boole, who understood formal logic to be Aristotelian syllogistic, and symbolic logic to be syllogistic logic expressed algebraically. His notational innovation was employing indices to terms so that, independently of the arrangement of terms, propositions could easily be read; thus, “xy0” can be read as “no x are y” or “no y are x” and “x1y0” as “all x are not y” or “no x are y”. In dealing with the classical elimination problem in the class calculus—to determine the maximum information, without duplications, obtainable from a given set of premises—Dodgson in his later work and unpublished letters anticipated several concepts of automated theorem proving.Central to both geometry and to formal logic are the rules of logical inference that establish the validity of arguments and guarantee that conclusions inferred from true [End Page 506] premises are true. The modern analytic tableaux, or tree method, is a fundamental tool in this regard, both for deriving theorems and for determining the validity or invalidity of the proofs for propositional calculus and first-order predicate calculus.Introducing his reconstruction of Part II of Symbolic Logic, Bartley noted that, along with the logic diagrams that Carroll devised, he also devised a tableau method that strongly resembled Beth’s semantic tableaux. Abeles went more deeply and convincingly into that resemblance in her earlier research. Beth’s tableaux, together with Hintikka’s model sets, were the direct ancestors of Smullyan’s analytic tableaux, which in turn are the theoretical basis for the Robinson resolution method that continues to be central to much work in programming logic.Abeles has also shown that the work in Studies in Logic by Charles Peirce and his logic students at Johns Hopkins University served as a source of inspiration for Dodgson. More critically, she demonstrated that Dodgson devised and employed the tree method for carrying out proofs of syllogisms and chains of syllogisms, or soriteses, in Part II of Symbolic Logic (see her “Lewis Carroll’s Method of Trees: Its Origins in Studies in Logic,” Modern Logic 1 [1990]: 25–34). The tree... (shrink)