Computer-based “Introduction to Formal Logic” A Review of Logic Textbooks and Software Michael Byron Department of Philosophy Kent State University [email protected] http://mbyron.philosophy.kent.edu 330/672.02 Introduction Kent State University comprises an eight-campus network throughout northeast Ohio. It draws students to its programs regionally, nationally, and internationally. A staple of the University’s Liberal Education Requirement is the Philosophy Department’s course, “Introduction to Formal Logic,” which bears the course number Philosophy 21002. Unfortunately, the Philosophy Department has so far been unable to deliver this course to all eight of the University’s campuses. The course is regularly taught only at the Kent campus and two of the regional campuses. The advent of distance learning technologies provides the Philosophy Department with an opportunity to offer this course more widely than it currently can, given the available staff. In reflecting on this opportunity, the department recognized a concern that none of the content be lost in the shuffle to distance learning. A pilot project of some sort seemed to be in order. This report describes the initial phases of that project. In order to assess the feasibility of migrating “Introduction to Formal Logic” to a distance learning format, I proposed a three stage project. With the generous support of a Summer Teaching Development Award from the College of Arts and Sciences, the first two stages of the project have been accomplished. The first phase aimed to develop a curriculum, instructional materials, and an approach to teaching Philosophy 21002, Introduction to Formal Logic, in the 1

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Philosophy Department’s computer classroom. The second phase of the project aimed to develop the same course for presentation in a distance learning format. The final stage of the project, which would involve implementing the course in distance learning format with the help of the university’s Media Services team, was not part of this project but is scheduled for development in Summer, 2001. The first step, developing the formal logic course for our computer classroom, seemed to be a good half-measure toward assessing the feasibility of teaching the course in a distance learning format. Teaching logic in the computer classroom would allow instructors to develop a course that was already computer-based, so that the transition to distance learning would do minimal violence to the course curriculum. And, since the course would be taught initially in a classroom, technology issues could be resolved in the background while instruction proceeded in a more traditional classroom mode. Of all the courses taught by faculty in the Philosophy Department, Introduction to Formal Logic is among the best suited for distance learning instruction. As currently taught, however, the course would not easily fit into distance learning format. Instructors rely predominantly on lectures and in-class problem solving, use the chalkboard extensively, and make minimal use of instructional technologies. Many members of the department—including especially faculty who teach Philosophy 21002—have an interest in developing this course for distance learning format. Hence, the overall aim of the project was to discover how best to effect the migration of the course to distance learning and to begin that process. The project divides into two phases.

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Phase I: Computer-based classroom instruction This phase of the project developed the instructional and curricular materials to teach Introduction to Formal Logic in the Philosophy Department computer classroom. Most instructors now teach the course much as it has been taught for decades: the instructor lectures, the students take notes, and together they go over sample and homework problems from the textbook. This mode of instruction has worked fairly well in the past, but it does not take advantage of some of the instructional technologies now available. It seems likely that the course could serve students even better through the thoughtful integration of those technologies with standard instructional modes. Philosophy 21002 taught in the computer classroom would still likely be a lecture course, in which class meetings involved discussing logical concepts and working problems. But instead of doing homework and exams on paper and turning them in, students would do their assignments on the computer. One advantage of software-based assignments for the students is immediate feedback: they no longer need to wait to have their answers evaluated by the instructor. An advantage for instructors would be the automated grading of homework and exams. Although some sections of the course might still need to be graded manually (translation problems, or some proofs), the use of software to grade and track student progress could contribute significantly to faculty effectiveness in this course. A major step toward teaching the course in the computer classroom would be an assessment of available textbook/software packages. Currently, six main textbook/software packages seem promising (complete bibliographic information appears below in the reviews): 1. Hurley, A Concise Introduction to Logic (Prentice Hall) 2. Barwise & Etchemendy, Language, Proof, and Logic (Seven Bridges) 3. Bergmann et al., The Logic Book (McGraw Hill)

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4. Copi, Introduction to Logic (Prentice Hall) 5. DeHaven, The Logic Course (Broadview) 6. The LogicWorks (Philosophy Documentation Center; software for use with any text) Phase I of the project was dedicated mainly to testing, evaluating, and writing reviews of each textbook/software package. In addition, this part of the project involved assessing the web-based resources of each publisher, including facilities for hosting web-based problem sessions and web-based exams. An evaluation of the instructional materials provided the basis for developing a sample syllabus and an approach to teaching the course in the computer classroom. The questions to be addressed included: * How should students be introduced to the instructional technologies employed in the course, given their different backgrounds and levels of facility with computers? * What considerations will help shape the best mix of lecture, discussion, and problem solving in the computer classroom? * How can lectures and computer-based problem solving reinforce each other in the classroom? * How will students be able to do homework for the course without access to a computer at home? * What accommodations may be required for disabled students and others who are unable or unwilling to use the computer-based instructional materials? * What other challenges to successful learning might arise when this course is migrated to a web-based medium? These questions are addressed in the “Classroom Strategies” section below.

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Phase II: Distance-learning instruction Philosophy 21002 is not currently offered or accessible to students at all regional campuses. The course is offered regularly only at the Stark and Trumbull campuses. The first phase of the project might be implemented at any time by faculty members in the Philosophy Department at the Kent campus, since all of the required technology (though not the software) is already available in the department’s computer classroom. To teach the course in distance learning format, however, several further issues would need to be addressed. For example, the customary instruction of the course using lectures would be more difficult and time-consuming in a distance learning setting. A more profitable use of time might include focusing more on individual exercises, using web-based software, that allowed students to proceed at their own pace and provided immediate feedback. The development of web-based homework and exam systems would also facilitate a distance learning version of 21002, provided that the systems provided adequate mechanisms for students to ask questions and instructors to monitor student progress. A less obvious but perhaps more vexing issue concerns symbols. Most computer systems have no difficulty transmitting ASCII (standard keyboard) symbols over the internet. But logic symbols are not in the standard set (of mainly letters and numerals), and therefore create a unique challenge. Each of the web-based solutions mentioned in Phase I has some way of addressing this issue. The question in Phase II was: what is the best solution for not only homework and exams, but for web-based distance learning interaction? The objective of Phase II, then, was to prepare a model distance learning course for Introduction to Formal Logic, including syllabus, textbook, software, web-based resources, weekly curriculum, homework assignments, and exams. Questions to be addressed in this phase of the project, then, included:

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* What considerations govern the best use of class time for lectures, discussion, and problems? * What software solutions currently available would be most feasible for a distance learning version of Philosophy 21002, given the emphasis on individual learning that this modality encourages? * What software solutions enable exams and quizzes in a distance learning setting? * How can the symbols issue best be addressed for distance learning? * What considerations will help determine whether synchronous or asynchronous modes are better for teaching Philosophy 21002 via distance learning? These questions are addressed in the “Distance Learning Strategies” section below.

Textbook Reviews Although for the purposes of migrating Philosophy 21002 to computer-based instruction the available software will be a paramount consideration, the quality of textbook is also important. The following criteria govern the assessment of textbooks for Introduction to Formal Logic. 1. Basic Data Sheet: The Kent State University Basic Data Sheet for Philosophy 21002 requires that 3 distinct topic areas be covered by the course. Although the course itself need not be structured to follow this order, the three topic areas are: (1) Categorical Logic, including Venn diagrams, (2) Propositional or Sentential Logic, and (3) Predicate Logic. It is understood that students will do proofs in the second and third sections of the course. A textbook that fails to cover any of these topic areas would be a less than ideal choice. 2. Quality of Text: The best choice will include explanatory text that is clear and complete, neither too long nor too short, include many examples, and integrate exercises adequately.

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3. Quantity and Quality of Exercises: Flexibility is important here. A text needs to include a range of exercises of varying difficulty, and a sufficient number at each level of difficulty. Most students in Philosophy 21002 will be able to do difficult exercises in Categorical Logic, but will have trouble with even relatively easy exercises on relational predicates in Predicate Logic. 4. Cost: although not an overriding concern, if other things are equal, a less expensive textbook is better.

Jon Barwise & John Etchemendy, Language, Proof and Logic, (Seven Bridges, 1999). Resources include: CD-ROM.

Barwise and Etchemendy offer an interesting and challenging text, together with innovative and useful software (see “Software Reviews” below). The three parts of the book address propositional logic, predicate logic, and metalogic, which suggests that this package might be more suited to the Philosophy Department’s formal logic (31045) and metalogic (41045) courses. 1.Basic Data Sheet: Barwise & Etchemendy do not address categorical logic as such, and so adopting this text would entail using supplementary material to teach the categorical logic section of the course. 2. Quality of Text: Barwise & Etchemendy develop their own system and notation and present it as intuitively as possible. The level of the material is fairly high, but their explanations are mostly clear. * Categorical Logic: Barwise & Etchemendy do not address this topic as such. * Propositional Logic: The presentation of propositional logic takes the students through atomic sentences and the construction of complex sentences with connectives. Each

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section includes exercises with the software, which employs a system of manipulating the truth conditions of sentences and evaluating the impact on validity and soundness. The software package also includes a proof builder. Fitch-style proofs are introduced early on as a way of learning about arguments. Proof techniques are developed in tandem with the introduction of logical connectives. * Predicate Logic: The quantifiers are explained, along with the proof rules, and relational predicates have been in use from the beginning, so the introduction of multiple quantifiers makes sense. The language of the text has also used identity right along, and so the applications within predicate logic are fairly intuitive. Unlike Hurley (which is the standard text of the department; see the review below), whose logical system is quite formal and makes students struggle to translate, Barwise and Etchemendy use only a few predicates of varying arity. But they use them right along, introducing connectives and, later, quantifiers in a natural way. Although they do teach propositional logic, they continue to use predicates throughout the part on propositional logic to flesh out examples. This pedagogical technique seems likely to reinforce the connections between propositional and predicate logic. 3. Quantity and Quality of Exercises: The exercises in this text are numerous and interspersed in the text. They are of three sorts: * “You try it”: as the name implies, these are practice exercises, generally not to be turned in, usually using the software. * “Submit”: using the proprietary “Submit” program, these exercises are uploaded over the internet to the “Grade Grinder,” which evaluates the student’s responses and reports them to the student and instructor.

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* “Turn in”: these exercises are not amenable to mechanical evaluation; students write out their answers and turn them in to the instructor on paper. 4. Cost: at $43.95, Barwise & Etchemendy is reasonably priced. Overall assessment: This text has many attractive features, and the authors aim to develop an extremely intuitive system. That system is very different from the Copi/Hurley system, and it would be interesting to try it with students at Kent State University. Each chapter has additional “optional” material that an introductory class would omit; probably some of the exercises would be omitted as well. The one grave drawback of the text from the perspective of Philosophy 21002 is the lack of significant material on categorical logic. Of course, of the three sections of the course, that would be the easiest to cover using handouts or a packet.

Merrie Bergmann, James Moor, Jack Nelson, The Logic Book (McGraw-Hill, 1998). Resources include: solutions to some exercises.

1. Basic Data Sheet: Bergmann, like Barwise and Etchemendy, omits categorical logic, and so the text would have to be supplemented to meet the requirements of the Basic Data Sheet. 2. Quality of Text: * Categorical Logic: the only material on categorical logic is folded into the treatment of quantifiers in the chapter on categorical logic. No material on syllogisms is included. * Propositional Logic: After an introductory chapter on basic notions of logic, Bergmann moves directly into propositional (sentential) logic. Propositional logic is broken down into syntax and semantics, and the semantics are introduced via truth tables and truth trees. The book uses a modified Fitch-style proof system.

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* Predicate Logic: Bergmann carefully lays out the syntax and semantics of predicate logic, and extends the use of truth trees to that system. The Fitch-style proof system is also extended to handle predicate logic, including conditional and indirect proof. 3. Quantity and Quality of Exercises: Bergmann scores well here. The book has many exercises of varying difficulty and is extremely flexible. 4. Cost: At about $48, the book is reasonably priced; it includes, however, no software, and the free software available for download is quite inadequate. Overall assessment: Lack of material on categorical logic, and lack of quality software, take this text out of contention for our purposes.

Irving Copi & Carl Cohen, Introduction to Logic, 10th edition (Prentice Hall, 1998). Resources include: CD-ROM, instructional website (which is reviewed in “Software Reviews” below).

Copi has become the standard for many introductory logic courses outside Kent State. The fact that it is in its 10th edition testifies to its enormous popularity. Copi is, moreover, the model for Hurley’s book, which is the standard at Kent State University. 1. Basic Data Sheet: Copi covers all three topic areas, Categorical Logic, Propositional Logic, and Predicate Logic. By this criterion, it is a satisfactory text for the course. 2. Quality of Text: Copi is comprehensive and covers all of the needed material, usually at a satisfactory level of detail. The text seems longer than Hurley’s, with more explanation and fewer diagrams and illustrations. The four parts of the book cover reasoning, language, deduction, and induction. For Philosophy 21002, mainly the third part is useful.

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* Categorical Logic: Three chapters in Copi address categorical logic, one on categorical propositions, one on syllogisms, and one on translation. Venn diagrams are not introduced until the second of these chapters, while the first focuses on immediate inferences and the square of opposition. A chapter focusing on ordinary language arguments rounds out this section. * Propositional Logic: Copi’s treatment of propositional logic begins with a 50-page chapter explaining connectives and equivalence (including de Morgan’s theorems). A briefer chapter on proofs follows, which develops the 9 inference rules and 10 rules of replacement of the Copi proof system. * Predicate Logic: A single chapter introduces predicate logic and extends the proof techniques to them. The introduction of the ideas of predicate logic and quantification is good, but there is no discussion of relational predicates. 3. Quantity and Quality of Exercises: Copi contains many problems of differing sorts and levels of difficulty. Another nice feature of the exercises is that frequently Copi will include an example problem and the solution to it. The quantity and quality of exercises makes Copi a flexible and useful text. 4. Cost: at $64.95, Copi is an expensive option. Overall assessment: Copi is in some ways preferable to Hurley and in most ways comparable to it, but the somewhat shallow treatment of predicate logic is unattractive.

Steven DeHaven, The Logic Course, 2nd edition (Broadview, 1998). Resources include: workbook.

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1. Basic Data Sheet: DeHaven covers all three topics, and so this text would require no supplement to meet the demands of the Basic Data Sheet. 2. Quality of Text: DeHaven spends the first 5 of 14 chapters on basic concepts and informal logic. The treatment of categorical logic comprises a single chapter placed between propositional logic and predicate logic. The text generally goes by quickly, with sparse explanations and only a few examples. No exercises are included in the text; all are in the workbook, which includes chapter summaries, examples, exercises, and quizzes. * Categorical Logic: DeHaven’s treatment of categorical logic includes introduction of quantifiers, translation into standard form, and Venn diagrams. The discussion of Venn diagrams incorporates some treatment of syllogisms, but the treatment is not extensive or explained in much detail. * Propositional Logic: The text uses a modified Copi proof system, together with a symbol system designed to integrate with the software (e.g., using an arrow, ->, for conditional instead of a horseshoe, ⊃, and a double arrow, <->, for biconditional instead of triple bar, ≡). The strategy throughout the text seems to be to introduce the basic concepts as clearly and briefly as possible, and then to have students do exercises, quizzes, and web-based problems until they master the material. The chapter on proofs covers indirect and conditional proof. * Predicate Logic: The chapter introducing quantificational theory covers both one-place and relational predicates, as well as identity. Little emphasis is placed on translation. The proof system is extended to incorporate predicate logic. Again, the treatment is sketchy, relying on exercises to teach the material. 3. Quantity and Quality of Exercises: There are only a few exercises for each section, and these are of intermediate difficulty for the most part (some are easy). The quizzes at the end of each

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chapter are useful, but don’t compensate for the lack of exercises. Many more exercises are included in the BlueStorm software (reviewed below in the software reviews). 4. Cost: Text: $28, workbook: $19, software: $17. Package: $64. Overall assessment: The material is introduced at the right level, but the explanations are too brief, and the exercises aren’t sufficiently flexible to teach the material well.

Patrick Hurley, A Concise Introduction to Logic, 7th ed. (Wadsworth, 2000). Resources include: Study Guide booklet, Instructor’s Manual, and CD-ROM.

Hurley’s book has become the standard for most instructors of Philosophy 21002 at the Kent Campus (one of us uses Lemmon, which does not come with software and so is not reviewed in this project). 1. Basic Data Sheet: Hurley covers all three topic areas, Categorical Logic, Propositional Logic, and Predicate Logic. By this criterion, it remains a satisfactory text for the course. 2. Quality of Text: Hurley is comprehensive and covers all of the material, usually at a satisfactory level of detail. * Categorical Logic: Two chapters in Hurley address categorical logic, the first introducing the basic notions of quantity, quality and distribution, together with basic Venn diagram techniques and immediate inferences, and the second explaining categorical syllogisms. The first chapter also explains translations from ordinary language into standard form categorical statements, while the second chapter extends this skill to syllogisms. * Propositional Logic: As with categorical logic, Hurley devotes two chapters to introducing propositional logic. The first explains symbolic notation and translation, and

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introduces propositional operators via truth functions and truth tables. The second develops the rules for natural deduction, using a modified Copi-style proof system that includes 8 inference rules and 10 rules of replacement. The chapter on natural deduction also introduces strategies of conditional and indirect proof. * Predicate Logic: Hurley’s single chapter on predicate logic explains the connection between it and categorical and propositional logic. It moves directly to proofs and extends the skills learned in propositional logic by introducing the required symbolic notation and corresponding (Copi-style) introduction and elimination rules. The chapter concludes with a brief treatment of relational predicates. A more extended treatment of relational predicates would be more rigorous. Some of the explanatory text goes by fast—particularly in predicate logic—and Hurley’s treatment of translations into propositional and predicate logic could be improved by including more intuitive shortcuts and rules. 3. Quantity and Quality of Exercises: The exercises in Hurley are numerous (usually 4-5 sections of 10 or more exercises each). The exercises build up a range of skills, focusing on easier tasks at each level first, then demanding more of the students. The exercises also include different levels of difficulty. The proofs include both fill-in-the-blank type exercises, whole proofs, and story problems (which require translation before the proof can be completed). Hurley uses a modified Copi-style proof system. The number, level of difficulty, and variety of exercises are all useful, as the students have plenty of extra problems (some of which are answered in the back of the book) should they need extra practice. 4. Cost: at $67.95, Hurley is not cheap. Overall assessment: Hurley is a good, comprehensive text, and it sets the standard for Philosophy 21002.

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Software Reviews As mentioned in the Introduction, this project completed two phases of what is ultimately a three-phase program. The final phase, which comprises migrating the course to distance learning format, is not part of this project. Nevertheless, it is partly with an eye to the ultimate feasibility of that migration that software was to be evaluated. The most immediate criteria concern the format and content of the software.

Format Instructional software generally, and logic software in particular, falls into two categories, web-based and proprietary. * Web-based software will run on any browser, and can be accessed either by LAN or over the internet. * Proprietary software, in contrast, usually comes on a CD-ROM and must be run on a client machine running some particular operating system (usually some version of Microsoft Windows, sometimes Macintosh). Each format has advantages and disadvantages. For distance learning and computer classroom instruction, web-based software (usually programmed in java) has clear advantages: it can be accessed from anywhere by any browser and requires no additional software. A major drawback of web-based programs concerns symbols. The most current versions of Internet Explorer and Netscape (v. 6 is in preview release, as of 8/00) do support an extended math symbol set (including the horseshoe, ⊃, the wedge, ∨, and the existential quantifier, ∃). But these symbols are not accessible directly from the keyboard, and so students cannot type them when doing homework, quizzes, or exams. Moreover, web-based exercises that can be machine graded are

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limited to objective-type questions, including multiple choice, true/false, and matching. That’s a limitation for Philosophy 21002, which involves working a lot of proofs. Proprietary software is frequently more professionally done, may have a friendlier user interface, and sometimes has sophisticated grading tools (though see the reviews for some exceptions). Proprietary software also can overcome the symbolization problem, usually by incorporating push buttons to insert symbols (though someone will eventually use java to do this for web-based software, too). A drawback of proprietary software is that it must run under a particular operating system (Windows or Mac OS), and so students who have computers that use the other OS cannot use the software at home.

Content The content of a software package typically tracks its textbook, and will be judged by roughly the same criteria. For example, the ideal software package for Philosophy 21002 will cover all of the three main areas of the course, including categorical, propositional, and predicate logics. It will have sufficient flexibility of exercises to encourage, develop, and challenge the skills of the typical student. And it will have sufficient functionality to permit online quizzes and exams. Homework: One function of software will be to provide a medium for doing homework exercises. Ideally, the homework will be done, turned in, graded, and returned all over the internet. A goal is paperless homework (unless the student chooses to print homework out, which should also be an option). Quizzes: Students should be able to take quizzes online, with either automatic grading and reporting or online grading by the instructor.

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Exams: As with quizzes, students should be able to take their exams online, with automatic grading and reporting of results. The best software package would include options for immediate feedback and reporting to the instructor, provide automatic grading of homework assignments, quizzes, and exams, and integrate tightly with the text.

Barwise & Etchemendy Description of software: Barwise & Etchemendy have developed an extraordinarily sophisticated system of instructional software for use with Language, Proof, and Logic. The system comprises four proprietary application programs: Boole, Fitch, Submit, and Tarski’s World. All programs run on either Macintosh or PC computers. Moreover, a server administered by the authors runs an application called Grade Grinder that, used in conjunction with Submit, will grade students’ assignments and report the scores to student and instructor. Although the package offers no way for students to take quizzes or exams, the quality and comprehensiveness of the software make the package extremely attractive. Boole: This application allows the student to create truth tables and to assess statements. It incorporates tools for verifying the correctness of columns and of the student’s assessment of a particular statement (that it is a tautology, contradiction, equivalent to another statement, etc.). The application allows the student to save and print the truth tables thus created, and thereby to upload the assignment using Submit (see below). Most of the instructors of Philosophy 21002 spend only a small amount of time on truth tables, but this application would be useful during that section. Fitch: This application is a proof checker, using a modified Fitch-style proof system. It allows students to build and then evaluate proofs, both in propositional and predicate

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logic. The application allows nested conditional and indirect proofs, and incorporates an extremely powerful proof engine that verifies individual steps and entire proofs. Students may save and print their proofs. The program includes an authoring mode that would be useful for constructing quizzes and exams (though authored problems cannot be submitted by Submit). Submit: An ingenious application that allows students to submit their homework files from any of the other three applications over the internet to the Grade Grinder, a server programmed to evaluate the answers submitted and report the scores (at the student’s option) to the student, instructor, or GA. The Grade Grinder is fast, and typically reports scores within seconds. The Grade Grinder is programmed to grade only the homework assignments that come preloaded with Fitch, Boole, and Tarski’s World, so it is not available to grade quizzes, exams, or other custom content. Tarski’s World: This innovative application allows students to manipulate the elements of a “world” that contains 3-dimensional geometric shapes of varying sizes and positions. By moving and changing these elements, the students learn to assess the truth conditions of the sentences describing the world. The application also includes a “game” that demonstrates the logical decomposition of complex sentences and the semantic dependence of the complex sentence on its parts. Overall assessment: In general, the software for Language, Proof, and Logic is the best proprietary package available. The interface is friendly, the system is intuitive, and (judging by its success) it works. It is available for both Macintosh and PC. Like the textbook it accompanies, it has no material on categorical logic, and that’s a serious shortcoming, but one that could be remedied with supplementary material (which would also, of course, add cost for

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the student). Lack of functionality for handling quizzes and exams is also a drawback and makes the package less attractive for our purposes.

Bergmann et al. Description of software: The Logic Book comes with no software and no instructional website. The publisher’s website for the book is merely informational, though it does have a link to a page offering two pieces of instructional software for use with the book. These programs, Bertie and Twootie, are rudimentary DOS programs (proprietary software). Bertie is a proof checker, using the system of The Logic Book. It offers students immediate feedback about whether a rule has been applied correctly, and thus whether a proof is step-wise correct. That is its only functionality; it checks proofs and gives students feedback. Twootie is a tool for checking semantic tableaux, or truth trees, in propositional and predicate logic. Again, the software offers the students immediate feedback on a range of exercises, but that is all. The interfaces of these programs are clunky but stable. The software comes preloaded with a range of exercises comparable to what is contained in The Logic Book. There is no provision for quizzes or exams, or any material pertaining to categorical logic. Overall assessment: Bertie and Twootie are instructional software that help students with proofs and truth trees. They do not have the scope or features needed for Philosophy 21002.

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Copi & Cohen Description of software: Copi ships with a CD that contains the “Logic Review,” which is proprietary software that runs under DOS or Windows. It is a DOS-based program with an ancient interface that poses multiple-choice questions to students. Students get immediate feedback about their answers, which means the software will not be useful for homework, quizzes, or exams. More interestingly, Prentice Hall has created an instructional website (http://cw.prenhall.com/copi/) to accompany the Copi textbook. Each chapter is covered by a section in the website. Each section includes a statement of objectives and offers three types of question—multiple choice, true/false, and “exercises” that typically require longer written responses (short answers, proofs, etc.). Students submit their answers to the server, which grades the responses and reports them to the students. The students then have the opportunity to redo the exercises or submit their scores to the instructor via email. The website questions are numerous and are fairly flexible (many are challenging). The scoring application on the server indicates how many questions a student left blank, how many responses were correct, and how many incorrect. So that would allow for the selective assignment of questions. Like the Copi text, the website covers all three essential components of Philosophy 21002: categorical, propositional, and predicate logics. One drawback in categorical logic is that students cannot draw Venn diagrams. Multiple choice questions test the concepts around Venn diagrams, and some of the short-answer exercises ask students to describe the diagramming techniques. But students don’t actually diagram any syllogisms. The short-answer exercises cannot be machine graded (i.e., proofs are not checked by the server but are transferred to the instructor via email).

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A further drawback of the instructional website concerns symbols. The site itself employs the symbolic notation of the Copi text (which are standard). But when students do proofs, they cannot generate those symbols using a standard ASCII character set (i.e., from their keyboards). As a result, they must use substitutes that don’t match the symbols in the exercises (e.g. for • students must type &, for ∃ they must use E, for ⊃ they must use ->). These substitutions might be confusing. The instructional website has no facility for giving quizzes or exams. Overall assessment: The proprietary Logic Review software is outdated and not terribly useful. The instructional website incorporates all of the functionality of the Logic Review and adds more, while presenting it more accessibly over the internet. The website is useful, but it is limited by its inability to check proofs (which make up more than half of the homework for Philosophy 21002) and its inability to host quizzes or exams. The Copi text/software package holds some promise, but it is far from ideal.

DeHaven Description of software: The companion software to the DeHaven text is called BlueStorm. It is a web-based java program that is extremely elaborate and covers most of the same material as DeHaven’s text. The software offers three different types of resource. 1. Explanatory text: the “manual” reviews material presented in the text. 2. Tutorial: used in the chapter on propositional logic and natural deduction, the “tutorial” introduces students to the workings of the java-based proof checker. 3. Exercises: used in every chapter, the exercises allow students to do problems in categorical, propositional, and predicate logic.

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BlueStorm is new software, and it has some of the problems of new software. Many of the homework exercises provide answers that are incorrect. The section on proofs in predicate logic does not yet exist. (That is a major drawback for implementing the software in Philosophy 21002.) And the integration with the text is not as tight as it might be. Another shortcoming for our purposes is the lack of material on Venn diagrams. Although the textbook and workbook cover Venn diagrams briefly, BlueStorm offers no coverage at all. Moreover, the treatment of categorical logic focuses primarily on the terms and their correct application rather than on developing the tools for evaluating validity, which is more the focus in Philosophy 21002. A third area of difficulty concerns the proof builder. BlueStorm incorporates an elaborate java proof builder that works well. The problem with it is that it uses a proof system alien to the DeHaven text. The textbook uses a modified Copi system, whereas the proof builder uses a Gentzen system of introduction and elimination rules. So students would have to learn 2 proof systems: one to read the textbook and do the exercises in the workbook, and another to use the proof builder software. And, like the rest of BlueStorm, the proof builder is limited to propositional logic and has no capacity for predicate logic. Overall assessment: BlueStorm holds tremendous promise. It is flexible and can be reprogrammed with other exercises or another system. The developer promises functionality for a server that will grade homework and track scores, but that software has yet to be released (as of 8/00). But it is not right for Philosophy 21002 until it covers predicate logic and includes Venn diagrams. Also, some functionality for giving tests would be useful.

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Hurley Description of software: Hurley’s text arrives with a CD that includes 4 pieces of software: the LogicCoach, a program called Learning Logic that covers Venn diagrams and informal fallacies, an application that discusses truth trees (semantic tableaux), and a Critical Thinking and Writing Guide. The latter two would be less useful for Philosophy 21002. Learning Logic is a web-based (Shockwave) tutorial and practice problem set for doing Venn diagrams. It supplements but does not replace the material in the Hurley textbook, and it includes no homework exercises or testing functionality. The LogicCoach is proprietary software that includes most of the homework problems in the Hurley textbook. Students work the problems and get immediate feedback about whether they have correctly answered the problem. Although the interface is somewhat dated, the program is fairly stable and is comprehensive (it is more stable under Windows than its Macintosh port). LogicCoach includes no functionality for grading homework or giving quizzes or exams. LogicCoach covers categorical logic, including Venn diagrams. The interface for this part of the course is a “dial” type that future versions promise to replace. Propositional and predicate logic are handled with a proof builder that is fairly intuitive and uses Hurley’s modified Copi-style system. Overall assessment: LogicCoach is minimal, but it is tightly integrated with the text. The software in this package comes with the textbook at no additional cost. By itself, the program does not include all the features that the ideal package would have, but it could be integrated in the computer classroom with LogicWorks.

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LogicWorks Description of software: The LogicWorks is a proprietary, stand-alone package that comes in a plain version and versions supporting the Hurley, Copi, and other textbooks. I have evaluated the version supporting Hurley. The package includes three disks. 1. The student disk includes exercises from the Hurley textbook (most of them) as well as some practice tests. The exercises are not organized according to Hurley’s chapters, but rather by sections: basic concepts, Venn diagrams, categorical syllogisms, natural deduction, etc. This arrangement makes matching up the homework to the Hurley text a chore, but it can be done. 2. The instructor package includes the Grader, which is a program for keeping a gradebook for each section of logic one teaches. The Grader program records grades for each homework assignment, each quiz, and each exam. It also grades all of these kinds of assignment. The Grader interface is not intuitive (it uses a menu-driven, DOS-style interface rather than the more common graphical user interface common in Windows and the Mac OS), but once mastered it promises to be a huge time-saver. 3. The instructor package also includes the Editor, which is an application that allows the instructor to add exercises for homework, quizzes, or exams. This application makes the package very flexible and allows instructors to migrate content from non-computer based versions of the course into a computer-based version. Using the LogicWorks is a real step backwards, technologically. The interface is menudriven and single-color, rather than incorporating the graphical user interface from Windows or Mac. This change will require some adjustment from the students. The software is available for either platform and for site-licensing as well.

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The package covers the entire range of the Hurley book, including the three areas of the Basic Data Sheet for Philosophy 21002, namely categorical, propositional, and predicate logic. The only variation I noticed between the exercises in the LogicWorks and those in Hurley was in the proofs: whereas Hurley uses “ACP” to indicate “assumption for conditional proof,” and “AIP” to indicate “assumption for indirect proof,” LogicWorks merely uses “AP” to indicate an assumption. The indented sequence is discharged in the same way for both systems. One other discrepancy: LogicWorks includes none of the translation exercises from Hurley’s chapters on propositional and predicate logic. These could, however, be done using the LogicCoach software that comes bundled with the Hurley textbook and turned in on paper. Overall assessment: Although the interface is a drawback, the functionality of this system and its tight integration with a text already in wide use in the department make it the best choice for computer-based instruction. No other package I have seen combines the flexibility, extendibility, and grading features of the LogicWorks.

Classroom Strategies This section proposes some answers to questions relevant to teaching Philosophy 21002 in the computer classroom, using instructional software.

1. How should students be introduced to the instructional technologies employed in the course, given their different backgrounds and levels of facility with computers? This is a central question for this project. I think several considerations are relevant to answering it. First, the students who sign up to take this section of Philosophy 21002 are a selfselected group of people who wish to take the class in the computer classroom. The Spring 2001 Kent Campus Schedule of Classes will clearly indicate that this section is to be taught in the

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computer classroom, will use instructional technology, and may require lab hours beyond scheduled class times. So it seems likely that virtually all of the students who choose this section of Introduction to Formal Logic will want to be in it. Second, given the general background of such students, probably the level of facility with computers will be fairly high. It seems reasonable to expect that they will be able to load a floppy disk and launch an application without difficulty. I will assume no prior experience with the particular applications that we will use for the course. With those points in view, it seems natural to approach the question of introducing the students to the software by practical experience. They will, of course, have the manuals that come with their software. But the most crucial time will be the first week of class, when they will encounter the software for the first time. During that first week, the best approach may be to work as a class through the setup of each student's data file on the server. This will establish a unique file for each student where all scores—homework, quizzes, and exams—will be recorded. Any general software issues can be addressed at this time. (It is also to be expected that there will be problems configuring the network and server, and time must be allocated for resolving those issues.) In addition, since each kind of exercise is somewhat different in the LogicWorks, it will be necessary to spend some time during each new unit introducing the software for that unit. So, for example, answering on the computer true/false questions about validity should be very easy for the students. Drawing Venn diagrams may not be as easy, and learning the proof system may be more complex still. In order to save time, it makes sense to be teaching content along with the skills of using the software. So, for example, we could do sample exercises on the computer to illustrate the

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lesson at hand. That would prevent instruction on the use of software from inordinately interfering with the schedule. Finally, it might make sense for me to spend an office hour each week in the computer classroom helping people with software issues. That would allow those who need more help with the technology to have some focused assistance outside of class.

2. What considerations will help shape the best mix of lecture, discussion, and problem solving in the computer classroom? The most important consideration will be the ease with which the students take to the software. Initially, I expect to have to spend several classes familiarizing them with the general features of the software and the functionality for grading (how to run the application, how to call up one's data file from the server, how to submit homework, etc.) A special session will also be needed prior to the first exam in order to explain how to take exams. It's virtually impossible to know in advance how much time these explanations will take—preparation will be important, but there is no substitute for hands-on experience. Like many faculty teaching Philosophy 21002, I have generally used class time for lecture or going over homework. The lecture time I expect to remain roughly constant. Since the software will help students understand why they have made mistakes, I expect to recover some of the time spent going over homework. That time could be fruitfully used to work on software issues. It might make sense to begin each class with questions about the software, at least at the beginning. Some of that recovered time could also be used to discuss problems that students have found especially difficult, even having worked the problem using the software. As students become more familiar with the software and the way the course is running—say, after the first exam—it should be possible to incorporate the software more and

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more into the discussion. For instance, many of the sample problems in the text are included as exercises in the software. The students could work these out, step by step, during lecture. That could be a much better learning experience than simply copying down my proof or work on the board, since the students would need to think through it themselves. It might also stimulate more questions than are often asked. In the past, I have held class from time to time in the computer classroom in order that the students could do homework on the computer. During this time, students who had trouble could receive one-on-one assistance from me. I anticipate using this system again, since it seemed to help the students who most needed assistance, and the better students had an opportunity to use class time for homework. Moreover, I saw many of the better students helping other students during this class time in the computer classroom. This sort of peer assistance could be encouraged, especially concerning software issues.

3. How can lectures and computer-based problem solving reinforce each other in the classroom? One way for lectures and problem solving to reinforce each other I have already mentioned: students can work out sample problems on their computers during lecture. As I go through a proof, say, students can try various “next steps,” and report one that works. Also, when time allows working problems in class after lecture, students will have an opportunity to apply what they've learned while it's still fresh in their minds and while the instructor is available to answer questions. Finally, having the exercises from the text available in the software should facilitate quizzes in class. (The LogicWorks handles quizzes just like exams—they're treated like short exams.)

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4. How will students be able to do homework for the course without access to a computer at home? This questions raises a more general question: how will students do the homework for the course? Several points are relevant here: 1. All of the homework assigned for the course is from the Hurley textbook. It is possible to do any or all of the assignments on paper. Due to the fact that the course is taught in the computer classroom, however, it is expected that students will take their exams and quizzes on the computer, and usually turn in homework by computer. The fact that the exercises are all in the textbook allows for a hard-copy backup in case the computer is broken the night before an assignment is due. 2. Students who have computers at home can do their homework there and store their homework files on a floppy disk (or email the files to themselves at school). The homework files can be transferred to the server for grading at the next class. 3. Students who have no computer at home can do their homework in any of the Academic Computing labs, including the Philosophy Department computer classroom (which operates as a lab when no class is using it). They should have access to the server to store their homework files, and with their floppy disks they can run the program anywhere. One important point about the floppy disks: the software manual emphasizes, and I will reiterate in class, that frequent backups are essential. Using the server to store student homework should prevent many instances of data-loss. Some policy concerning loss of data (homework, exams, etc.) will be required.

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5. What accommodations may be required for disabled students and others who are unable or unwilling to use the computer-based instructional materials? Where feasible, I would urge such students to take Philosophy 21002 in the traditional classroom setting. Typically, the department offers multiple sections in any given semester. If, however, all other sections are full, it would be possible for students to complete this section of the course without using the instructional technology. They would have to submit their homework and exams on paper, but this is feasible. The LogicWorks application makes printing exams possible.

6. What other challenges to successful learning might arise when this course is migrated to a web-based medium? Two issues arise. 1. Instructional technology can be a distraction. The interface of the LogicWorks is lowtech and menu driven, and that will take some students a while to become accustomed to. The concern is that students may spend more time figuring out the software than they spend using it to learn. Since all of the LogicWorks exercises use the same style of interface, however, students can be expected to master the system fairly quickly and have no trouble from then on. 2. The possibility of cheating exists, as always. Just as students can copy homework from each other, they can copy and rename data files from each other. The software is not designed with security in mind, and copying data files is easy. When the software people at Academic Computing install the system for next spring, I will consult with them about this issue. For homework, there's probably little that can be done. For exams, it should be easier to prevent cheating.

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Distance Learning Strategies This section proposes some answers to questions relevant to teaching Philosophy 21002 via distance learning, using instructional software.

1. What considerations govern the best use of class time for lectures, discussion, and problems? Compared to the classroom presentation of computer-based Introduction to Formal Logic, the distance learning version raises issues for lecture presentation. It simply is not as easy to lecture, even using iLink and other sophisticated distance learning modalities. For one thing, it is difficult for a lecturer to gauge how well the class as a whole is grasping the material under discussion. One nice feature of iLink allows instructors to use their computer screens as a kind of electronic chalkboard. This feature enables instructors to work problems for the students and to ask for questions. It will be useful to schedule some class time for students to use the software and work homework problems in class, especially early on, in order to troubleshoot and answer problems as a class. Chances are that if one student has a certain sort of problem with the software, other students will also. The e-chalkboard feature may be configurable to turn the students' screens over to another student. This feature would be useful for going over homework problems in class. A student could explain his or her reasoning to the class, much as students now do at the chalkboard in 21002.

2. What software solutions currently available would be most feasible for a distance learning version of Philosophy 21002, given the emphasis on individual learning that this modality encourages?

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The best solution seems to be LogicWorks. In response to the particular concern of this question, LogicWorks includes a number of features that enhance individual learning. First, it enables students to work at their own pace. For homework problems there is no time limit. The software is flexible enough, however, to impose time limits where necessary, for instance when students take exams or quizzes. Second, LogicWorks provides the students with feedback immediately upon their answering homework questions. Particularly in the sections on basic logical concepts, the students are told not only whether they have the correct answer, but why their answer was correct or incorrect. That kind of feedback often exceeds what instructors are able to write on homework papers. LogicWorks is preferable to other available software packages on other grounds, and it seems no worse than the others with respect to fostering individual learning through the distance learning modalities.

3. What software solutions enable exams and quizzes in a distance learning setting? As far as I have been able to determine, LogicWorks is the only software package capable of hosting exams and quizzes of sufficient complexity for use in Philosophy 21002. The Copi and Thompson Learning (the publisher of Hurley; the publisher has an instructional website, but not one specifically for Hurley) instructional websites can host quizzes and exams. But they can grade only multiple choice, true/false, and matching type exercises. Most of the work in Philosophy 21002 involves evaluating proofs, and software that cannot check proofs is of only limited usefulness for this course. This is one of the areas in which LogicWorks seems clearly superior, despite its interface and archaic programming. A version of LogicWorks programmed in Java would be preferable, but as far as I know, no such project is forthcoming.

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4. How can the symbols issue best be addressed for distance learning? The problem is that it is impossible to enter logical symbols directly using a computer (ASCII) keyboard. This issue is especially pressing when students are building proofs. Keyboard shortcuts are possible, but they must be incorporated into the software. Some software uses buttons, which works fine. LogicWorks uses keyboard shortcuts (typing '&' enters the dot for conjunction, '>' yields a horseshoe for conditional, '=' produces a triple bar, 'E' produces an existential quantifier, etc.). This system is satisfactory and is easy to use once mastered.

5. What considerations will help determine whether synchronous or asynchronous mode is better for teaching Philosophy 21002 via distance learning? In synchronous presentation, the instructor is “live” before the students on the screen and can answer questions in real time. In asynchronous presentation, the instructor is “recorded,” and students view the lesson at their own pace on their own schedule. The choice between the two is a vexed question, and I cannot hope to provide a decisive answer here. Instead, I will merely express my preference for synchronous presentation and provide my rationale for that preference. I think three primary considerations support a preference for synchronous delivery. First, logic is hard. Most students need extra help of some kind beyond simply doing homework problems, and the most straightforward way for them to interact with the instructor to get that help is to ask questions in class. Only in synchronous mode is direct question and answer possible.

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Second, it is common for students to have the same questions—so when one asks the question, many may benefit from hearing the instructor's answer. In asynchronous mode that benefit is lost. Third, although it would be possible for experienced instructors to anticipate many student questions in a recorded lecture, it is extremely valuable for instructors to be able to see the students and form a general impression of how well they understand a particular concept or topic. Synchronous presentation makes this assessment more difficult than a traditional classroom setting; asynchronous mode makes it impossible.

Results For a complete report of the material in this article, together with the course materials developed for computer classroom and distance learning presentations of Philosophy 21002 at Kent State University, see my website, http://mbyron.philosophy.kent.edu. The best combination of text and software for Philosophy 21002 in the computer classroom seems to be the Hurley text together with the LogicWorks software. Students will be able to work on the computers in class and save their work to the server. Alternatively, they can do homework on any computer, save their work to a floppy, and upload it to the server in class. Exams will be given and graded on the computer. The facility in LogicWorks to maintain student work files and records on the server should allow a fairly seamless transition to distance learning instruction when the department moves forward with that project. Specific issues with maintaining the server will have to be worked out with Academic Computing in advance of teaching the class in the computer classroom in Spring, 2001.