Mathematics textbooks teach logical reasoning by example, a practice started by Euclid; while logic textbooks treat logic as a subject in its own right without practical application to mathematics. Stuck in the middle are students seeking mathematical proficiency and educators seeking to provide it. To assist them, the article explains in practical detail how to teach logic-based skills such as: making mathematical reasoning fully explicit; moving from step to step in a mathematical proof in logically correct ways; (...) and checking to make sure inferences are logically correct. The methodology can easily be extended beyond the four examples analyzed. (shrink)

In medieval writers an important distinction was drawn between two applications of the term ‘logica’: there was logica utens, the practice of thinking logically about this or that subject-matter, and there was logica docens, the construction of logical theory. Of course the English word ‘logic’ and its derivative ‘logical’ have a corresponding twofold meaning, and we ignore the distinction at the risk of serious confusion. ‘Logical thought’ may mean thinking that is being commended as orderly, consistent, and consequent, whatever (...) its subject-matter; or it may mean the thinking of logicians about logic, which alas has not always exhibited these virtues. Similarly for ‘teaching logic’: there is trying to get people, by precept and example, to be orderly, consistent, and consequent in their thinking, and there is the endeavour to train logicians for the next generation. In any respectable philosophy department there will be someone teaching logic in the first sense; in my own university there are very many first-year undergraduates who do a course called Reason and Argument with this aim. But we hold that the teacher of such logica utens must himself have a sufficient skill in logica docens if he is to do his job properly; and we undertake the further task of training people in logical theory so that some of them, who have sufficient native ability and motivation, may take up the torch from their teachers. (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)

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)

This paper is about teaching elementary logic to blind or visually impaired students. The targeted audience are teachers who all of sudden have a blind or visually impaired student in their introduction to logic class, find limited help from disability centers in their institution, and have no idea what to do. We provide simple techniques that allow direct communication between a teacher and a visually impaired student. We show how the use of what is known as Polish (...) notation simplifies communication, and pedagogically is a great notation for a Braille reader. (shrink)

In medieval writers an important distinction was drawn between two applications of the term ‘logica’: there was logica utens, the practice of thinking logically about this or that subject-matter, and there was logica docens, the construction of logical theory. Of course the English word ‘logic’ and its derivative ‘logical’ have a corresponding twofold meaning, and we ignore the distinction at the risk of serious confusion. ‘Logical thought’ may mean thinking that is being commended as orderly, consistent, and consequent, whatever (...) its subject-matter; or it may mean the thinking of logicians about logic, which alas has not always exhibited these virtues. Similarly for ‘teaching logic’: there is trying to get people, by precept and example, to be orderly, consistent, and consequent in their thinking, and there is the endeavour to train logicians for the next generation. In any respectable philosophy department there will be someone teaching logic in the first sense; in my own university there are very many first-year undergraduates who do a course called Reason and Argument with this aim. But we hold that the teacher of such logica utens must himself have a sufficient skill in logica docens if he is to do his job properly; and we undertake the further task of training people in logical theory so that some of them, who have sufficient native ability and motivation, may take up the torch from their teachers. (shrink)

Similar to learning the grammatical structures of a foreign language, one problem that students face in learning logic is that many of the operations and concepts they need to learn require more practice to fully master. To solve this problem, the author proposes the use of “repetitive exercises”, exercises that aim to develop a familiarity with a concept or operation through repeatedly focusing on that concept or operation. According to the author, the best method for implementing these exercises is (...) the use of on-line teaching environments, specifically WebCT, which allows instructors to develop exercises that they deem appropriate and allows for mechanical grading. Finally, the paper provides an overview of why WebCT is preferable to the use of Blackboard, and notes that the major drawback to the online solution is its poor support for the symbols used in propositional and predicate logic. (shrink)

This paper constitutes my philosophy of teaching. I aim to model self-examination of teaching practice with the use of philosophical actionresearch. I use the method of triangulation and a mix of qualitative and quantitative data to validate and to strengthen my assertions. The analysis was grounded on empirical information, relevant current literature, and reflection. I argue that self-examination of practice is a worthy exercise for educators. When conducted systematically, self-examination efforts should not be regarded as merely subjective. It (...) can be harnessed as a tool to improve an educator's academic performance and personal wellbeing. It should rather be viewed as a basic or foundational discipline to sustain one's growth and love for teaching. The reflections on experience, insights, and the external validation one gathers in the process are worth the challenge. An examined life becomes worth living. (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)

Logic is one of the most male-dominated areas within the already hugely male-dominated subject of philosophy. Popular hypotheses for this disparity include a preponderance of confident, mathematically-minded male students in the classroom, the historical association between logic and maleness, and the lack of female role-models for students, though to date none of these have been empirically tested. In this paper I discuss the effects of various attempts to address these potential causes whilst teaching second-year formal and philosophical (...) logic courses at different universities in the UK. I found the most noticeable positive effect came from assigning a good proportion of reading by female authors presenting an original point of view. I go on to suggest some implementations for incorporating more texts by female authors into our arsenal of tools for teaching logic. (shrink)

During the nineteenth century, German philosophy developed from a type of general knowledge to an academic discipline at the university. Changes across disciplines to the philosophy of science and psychological surveys created new challenges for the place and purpose of philosophy in the educational system. The content of logic courses for secondary schools (Gymnasiums) was centred on the dissociation of nature and the scale of logic. In this paper, I will examine a number of projects for teaching (...) philosophy at the secondary school level from new humanism to reduce philosophical to philological concerns about different projects offered by Niethammer, Hegel and Herbart. Then, I will focus on the most successful – Adolf Trendelenburg’s Elements of Aristotle’s Logic (1st edition of 1836). This work is a compilation of the logical texts of Aristotle, and for as long as sixty years, it was an official textbook in Prussian secondary schools. The aim of the paper is to show how the rethinking of Aristotle’s heritage affected the theoretical and ideological expectations of propaedeutic courses and transformed the image of logic as a philosophical discipline. (shrink)

Like many philosophy instructors throughout the academy, one of my primary services to the university is teaching 100-level logic, a required course for all undergraduate students. In many ways I relish the responsibility and consider teaching the course one of my more valuable roles at the university. Furthermore, that the university requires logic makes me hopeful that higher education still values the cultivation of critical thinking, which should be a primary function of a logic class. (...) However, required courses at the university follow a mandated assessment process that involves the administration of entry and exit exams, and a comparison of the test results to track teaching effectiveness. Passing the exit .. (shrink)

Is it possible for one and the same person to be a feminist and a logician, or does this entail a psychic rift of such proportions that one is plunged into an endless cycle of self-contradiction? Andrea Nye's book, Words of Power (1990), is an eloquent affirmation of the psychic rift position. Although eloquent, I believe it is mistaken in certain serious ways, which I shall address in this paper.Nye advances this position in her concluding essay to Words of Power (...) (Ibid.). In brief, her position is that the logical enterprise is inherently self-contradictory for feminist thinkers. Feminists who attempt to use logic to demonstrate its shortcomings are doomed to failure; arguing against logical claims is self-defeating, for the critic will be sucked into the maelstrom of logical tradition. Hydra-headed, the logical monster will thrive rather than perish under the sharpened edge of argument; hence the critic succeeds only in strengthening the very endeavour whose shortcomings she attempts to expose. This is guaranteed to happen, according to Nye, because in entering the debate, one is thereby committed to the terms of the debate. The critic herself will be devoured in the process, for logic was constructed to eliminate the voices and concerns of women. ‘The feminist logician speaks from a script in which the master always wins' (Ibid., p. 180).If feminists cannot use logic itself to attack the arrogant and unsupportable assumptions of logic, what are our alternatives? Nye sketches two alternatives - one is to simply turn our backs on logic, ignoring it in all of its masculine arrogance, and talk among ourselves in our own women's language about our own concerns. Nye does not recommend this alternative, for although it escapes the criticism of arrogance, it does so at the price of impotence. What she does recommend is the second alternative, that as feminists we direct our energy towards reading other people's work, including that of the logicians, and responding to it in ways ‘that can mortally wound’ (Ibid., p. 184) the authors; women, Nye believes, are particularly adept at reading. ‘It is a skill we have perfected’ (Ibid.) in the course of our oppression.In what follows, I shall discuss Nye's proscription of logic as well as her perceived alternatives of a woman's language and reading. This will be followed by a discussion more sharply focused on Nye's feminist response to logic, namely, her claim that feminism and logic are incompatible. I will end by offering a sketch of a class in the life of a feminist teaching logic, a sketch which is both a response to Nye (in Nye's sense of the word) and a counter-example to her thesis that logic is necessarily destructive to any genuine feminist enterprise. (shrink)

본 연구의 목적은 최근 20여 년 동안 진행되어 온 학습이론에 대한 피아제의 명제논리학적 학습이론과 베이즈주의의 확률론적 학습이론의 융합에 근거하는 새로운 융합교수학습모형을 개발하는 것이다. 연구자는 이 새로운 교수학습모델을 “베이지안 구조구성주의 교수학습모형”(Bayesian structure-constructivist Model of Teaching-learning: 이하 약칭 BMT)이라 명명한다. 본고는 역사-비판적 관점 및 형식화적 관점에서 피아제의 명제논리학적 학습모형에서 해석된 학습이론과 베이즈주의의 확률론적 추론모형에서 해석된 학습이론을 일차적으로 분석하고, 논문의 후반부에서는 이를 근거로 교수법의 관점에서 양자의 학습이론을 통합하는 새로운 교수학습모델, 즉 BMT의 중요한 특성들을 세부적으로 제시한다. 몇 가지 핵심만 언급하면, 첫째로, BMT는 개념 (...) 학습이든 이론 학습이든 모든 학습은 표상과 샘플링의 상호작용임을 강조한다. 매우 이른 나이에서부터 아동은 학습하기 이전에 자기에게 주어진 예시들이 약한 샘플링인지 강한 샘플링인지, 특히 교육학적 샘플링인지 비교육학적 샘플링인지를 구분한다. 둘째로, 따라서 학습을 촉진시킬 수 있는 샘플을 선택하기 위해서 교사는 교육학적 추론을 위한 베이지안 모델을 활용하면서 직접적인 강의식 수업과 발견학습 수업을 병행해야 한다. 셋째로, 아동은 때때로 구체적인 규칙들보다는 추상적인 규칙들을 먼저 학습하기도 하지만, 대부분의 영역에서 추상적인 지식의 학습은 구체적인 지식의 학습에 의존한다. 따라서 성공적인 학습을 위해서는 피아제가 강조한 보편적 언어로서 논리적 문법과 그들 사이의 위계성을 고려하는 샘플을 개발하고 제시해야 한다. (shrink)

This paper looks at what David Kaplan's work on indexicals can teach us about logic and the philosophy of logic, and also what Kaplan's logic (i.e. the Logic of Demonstratives) can teach us about indexicals. The lessons are i) that logical consequence is not necessary truth-preservation, ii) that that the linguistic doctrine of necessary truth (also called conventionalism about modality) fails, and iii) that there is a kind of barrier to entailment between non-context-sensitive and context-sensitive claims.

Introductory-level undergraduate classes in Logic or Critical Thinking are a staple in the portfolio of many Philosophy programs. A standard approach to these classes is to include teaching and learning activities focused on formal deductive and inductive logic, sometimes accompanied by teaching and learning activities focused on informal fallacies or argument construction. In this article, I discuss a proposal to include an additional element within these classes—namely, teaching and learning activities focused on intellectual virtues. After (...) clarifying the proposal, I identify three reasons in favor of implementing it and I discuss how to implement it, focusing on questions about pedagogical strategies and pedagogical resources. (shrink)

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, (...) humility, clarity, observationalism, contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. This lecture expands points which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic 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)

In this article, I seek to shed new light on a lesser-known stage of the development of Hans Reichenbach’s thought, namely his research, output and teaching activities at Istanbul University. I argue that the experience of Turkish exile was decisive in the elaboration of Reichenbach’s probability theory of meaning and knowledge. His work Experience and Prediction, produced while in Istanbul, should therefore be put in its Turkish context of elaboration and reception. To this end, I will take into consideration (...) not only Reichenbach’s efforts to popularize and extend the Berlin Group’s program of scientific philosophy in Turkey and throughout Europe in the 1930s, but also the forgotten work of Reichenbach’s students—most of them women—at Istanbul University. (shrink)

This article advances the view that propositional logic can and should be taught within general education logic courses in ways that emphasizes its practical usefulness, much beyond what commonly occurs in logic textbooks. Discussion and examples of this relevance include database searching, understanding structured documents, and integrating concepts of proof construction with argument analysis. The underlying rationale for this approach is shown to have import for questions concerning the design of logic courses, textbooks, and the general (...) education curriculum, particularly the sequencing of formal and informal logic courses. (shrink)

Teaching and learning in a virtual learning environment poses some difficulties, but also challenges and opportunities to rethink the whole learning process, particularly in abstract subjects like logic or high level mathematics. On the other hand, resources and ways to work, now available in VLEs, might soon extend to all kinds of environments. In this paper, we will present experiences at the Open University of Catalonia , a particular VLE, concerning the whole process of teaching logic (...) and mathematics. In addition, we will discuss some challenges and we will present some innovation projects allowed by the present and near future technologies. (shrink)

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, (...) humility, clarity, observationalism, contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. One rather conspicuous example is that the process of refining logical terminology has been productive. Future logic students will no longer be burdened by obscure terminology and they will be able to read, think, talk, and write about logic in a more careful and more rewarding manner. Closely related is increased use and study of variable-enhanced natural language as in “Every proposition x that implies some proposition y that is false also implies some proposition z that is true”. Another welcome development is the culmination of the slow demise of logicism. No longer is the teacher blocked from using examples from arithmetic and algebra fearing that the students had been indoctrinated into thinking that every mathematical truth was a tautology and that every mathematical falsehood was a contradiction. A fifth welcome development is the separation of laws of logic from so-called logical truths, i.e., tautologies. Now we can teach the logical independence of the laws of excluded middle and non-contradiction without fear that students had been indoctrinated into thinking that every logical law was a tautology and that every falsehood of logic was a contradiction. This separation permits the logic teacher to apply logic in the clarification of laws of logic. This lecture expands the above points, which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

happens, how it happens, and why it happens. Our assumption ought to be that this is as true in education as it is in atomic physics. But this leaves many other questions to answer. The crucial ones: What kind of science is proper or appropriate to education? How does it differ from physics? What is wrong with the prevai1~ ing, virtually unopposed research tradition in education? What could or should be done to replace it with a more adequate tradi tion? (...) What concepts are necessary to describe and explain what we find there? It is in this realm that we find ourselves. Where to start? One place - our place, needless to say - is with one limited but central concept in education, teaching. A long philosophical tradition concerned with the nature of teaching goes back (along with everything else) to Plato, divulging most recent ly in the work of such philosophers as B. O. Smith, Scheffler, Hirst, Komisar, Green, McClellan, Soltis, Kerr, Fenstermacher, et al. An empirical tradition runs parallelto the philosophers -it has its most notable modern proponents in Gage, the Soars, Berliner, Rosen shine, but its roots can be traced to the Sophists. These two tradi tions have been at loggerheads over the centuries. (shrink)

The article aims at (1) organizing the theoretical ideas of critical thinking on the basis of an overall and systematic conception of education, (2) exposing tensions and contradictions in the various conceptions of critical thinking and (3) suggesting a directing principle for the teaching of critical thinking. In order to achieve these far-reaching aims, the author projects “The Cognitive Map of Instruction” developed by Zvi Lamm on the discourse of critical thinking. Through this “map” it seems that all sub-trends (...) of teaching critical thinking may be divided into three defined “logics,” and that these sub-trends harbor two kinds of internal contradictions: between the different “logics” of teaching, and between their pattern of teaching and the idea of critical thinking. Since none of the three “logics” suggested by Lamm (1976) in “The Cognitive Map of Instruction” suits the purpose of teaching critical thinking, the article turns away from this “map,” that served it so well to locate and expose the various trends of critical thinking. This turn is made on behalf of another idea of Lamm—that of undermining pedagogy. This well-rooted idea may direct the pedagogy of critical thinking toward a coherent and effective instruction. (shrink)

In elementary logic textbooks, Venn diagrams are used to analyze and evaluate the validity of syllogistic arguments. Although the method of Venn diagrams is shown to be a powerful analytical tool in these textbooks, it still has limitations. On the one hand, such method fails to represent singular statements of the form, “a is F.” On other hand, it also fails to represent identity statements of the form, “a is b.” Because of this, it also fails to give an (...) account of the validity of some obviously valid arguments that contain these types of statements as constituents. In this paper, owing to the developments in the literature on Venn diagrams, we offer a way of supplementing the rules of the Venn diagram found in textbooks, and show how this retooled Venn diagram technique could account for the problem cases. (shrink)

I share my experiences teaching Practical Logic with a focus on good reasoning as eliminating alternative conclusions. This unites the various topics traditionally taught in such courses in a way that I have found to be extremely effective.

This article examines the attempted reform of education within an emerging audit culture in Australia that has led to the implementation of a high-stakes testing regime known as NAPLAN. NAPLAN represents a machine of auditing, which creates and accounts for data that are used to measure, amongst other things, good teaching. In particular, we address the logics of a policy intervention that aims to improve the quality of education through returning ‘good teaching’. Using Deleuze’s concepts of series, events, (...) copies and simulacra, we suggest that an attempt to return past commonsense logics of ‘good teaching’ as a result of NAPLAN is not possible. In an audit culture as exemplified by NAPLAN, ‘good teaching’ is being reconceptualized through those practices and becomes unrecognizable. Whilst policy claims to improved equity and quality are admirable, this article suggests that the simulacral change to logics of good teaching may actualize something very different. (shrink)

Over the past century, there has been considerable debate over whether and how anything changes with respect to existence. Most A‐theorists of time (presentists, growing block theorists, and branch theorists) think things come to exist or cease to exist. B‐theorists of time (four‐dimensionalists, in particular) think objects do not change with respect to existence. In my Compass article, I outline a serious difficulty that A‐theorists face in trying to reason about temporary existents. The most straightforward logics for time and existence (...) entail that nothing exists merely temporarily. The problem arises from a set of theorems of the simplest temporal logic – the converse Barcan formulas. But attempts to fix the logic to get rid of the Barcan formulas pressure A‐theorists to abandon an intuitive and widespread assumption about existence. I survey the logical and metaphysical options for solving the problem. (shrink)

In the paper, I have presented a portrait of Jerzy Pelc as a teacher. He followed in the footsteps of Kazimierz Twardowski and his direct disciples and tried to develop his students’ skills of critical thinking and clear speaking—the basics of good work in philosophy. These skills are connected with methodological postulates of criticism and precision which were shared by all the members of the Lvov-Warsaw School. Jerzy Pelc treated these postulates also as didactic postulates arising out of the conceptions (...) of logical culture and general logic. In my article, I have sketched a general picture of the relation between logic and didactics, I have presented the aforementioned postulates, the concepts of logical culture and general logic and its curriculum. (shrink)

Recent students of late medieval intellectual history have treated Oxford theologians' Sentences lectures from the 1320s to 1330s as revealing the interface of the theological, logical, and scientific thinking characteristic of a historically momentous ‘New English Theology’. Its conceptual achievement, historians generally concur, was the casting off of the speculative metaphysics of such thirteenth-century authors as Robert Grosseteste and Roger Bacon; its methodological novelty made it akin to twentieth-century analytic philosophy and seminal for the early Scientific Revolution. Yet the metaphysically (...) cast thirteenth-century sciences of perspectiva and astrologia persisted among scholars long into the early modern period. To show how this apparent paradox may be dissolved, this article details the intersection of thirteenth-century metaphysics and fourteenth-century analysis in the lectures of a controversial and influential proponent of the Oxford theology of the 1330s. (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)