Introductory Logic Research Articles

One Logical Lacuna

The effectiveness of place-based education in inspiring care for natural and local environments, improving academic performance, dispelling with artificial dichotomies, and grounding philosophic discourse is supported by research whose results have been published not only concerning elementary and alternative settings, but collegiate ones as well. However, very little if any reporting has been done on its effectiveness in formal logic. Given the foundational nature of logic and its tendency to fulfill general education requirements, this is unfortunate. Though I am persuaded it takes more than pedagogical magic wands to inspire self-driven student success, reflections on and examples of the actual constructions of a collegiate level introductory logic course that uses place-based curricula that also boasts some general statistical reassurance seems worth sharing. And, much to my own enjoyment, “sharing” provides me with an opportunity to describe a well-received extra credit opportunity involving a nationally recognized on campus tree tour.

Logik und Geschlecht? Empirische Daten zu Logikeinführungen im Philosophiestudium an deutschen Universitäten1

Although the underrepresentation of women in academic philosophy is well-known and hard to overlook, philosophers started to pay more attention to the actual data on and potential explanations of the underrepresentation of women in philosophy only in the last decade and predominately in anglophone countries. The data I present in this paper deal with introductory logic courses at German universities (gender of textbook authors, gender of logic course instructors, student grades by gender at one university). Two results are particularly noteworthy: For one, logic teaching in Germany is currently predominantly male and even more male than philosophy teaching as a whole. For another, there is no evidence for any differences between grades of female and male students. The student grade data, however, illustrate how statistical phenomena like Simpson's paradox can explain how male students can appear to achieve better grades than female students even if there is no underlying difference: When correcting for students’ major (philosophy vs. STEM), logic grades of male and female students are remarkably similar. Although the scope of the data presented here is limited, they allow to add further details to an emerging map of the profession. I close with some suggestions for avoiding stereotyping logic as “male”.

Teaching an Introductory Logic Course in High Schools and Colleges

In order to improve the challenging situation in teaching an introductory logic course as a part of a curriculum in high schools and colleges, this paper aims to answer the following two questions. First, what should an introductory logic course teach? Second, what would be an effective teaching plan for an introductory logic course? An answer can be found at the 2022 High School Logic and Thinking Curriculum. It emphasizes first, to teach contemporary logic, second, to teach deductive logic and inductive logic evenly, and third, to introduce the connection between logic and contemporary science technologies such as coding and machine learning. In addition, this paper proposes that an urgent practical matter to be dealt with is a reference book for such an introductory logic course and re-education programs for teachers of this sort in high schools and colleges.

Blended Instruction in Symbolic Logic

This study examines through action research whether blended instruction in an upper-level philosophy course in introductory symbolic logic can help undergraduate philosophy students to achieve better learning outcomes than undergraduate philosophy students in a traditional, face-to-face version of the same course. The authors conclude that the change from traditional instruction to blended instruction did have a positive and significant effect on student learning as measured in course grades and student assessment scores for one course learning objective, as well as a positive but non-significant effect on student assessment scores for two additional course learning objectives.

DYNAMIC SEPARATION LOGIC AND ITS USE IN EDUCATION

Mathematical logic is widely used in hardware and software verification. Hoare logic is particularly suitable for reasoning about imperative programs. Its extension, separation logic, introduces the separating conjunction, which makes it possible to reason about programs working with pointers and mutable data structures. Dynamic logic, an ex-ample of modal logic, is yet another formalism used for verification. This article introduces propositional dynamic separation logic, which adds separating conjunction to dynamic logic. We describe syntax, semantics and Hilbert-style deductive system for propositional dynamic separation logic and prove its soundness. The definition of the logic is rather abstract. Thus, the programming language consists of so-called regular programs rather than while-programs, and the set of atomic commands can be arbitrary as long as they correspond to local actions. Special attention is devoted to the soundness of the frame rule, which allows writing program specification using a small footprint, i.e., specifying exactly the portion of the heap that the program reads or writes. Programs that perform tests are also treated differently from regular dynamic logic. The article also argues for the use of separation logic in computer science curriculum. It is more intuitive that other substructural logics and can be taught even in introductory logic courses. At the same time, it is an active research area with numerous verification tools built on its foundation. Therefore, it serves an excellent introduction to formal methods.

The creation and application of a question bank for an Introductory Logic module

The creation and application of a question bank for an Introductory Logic module

Who Benefits From a Foundational Logic Course? Effects on Undergraduate Course Performance

Being able to understand and evaluate arguments in different modalities and in different disciplines is thought to be a key component of students’ academic success in college. However, many students do not receive explicit instruction in the basic concepts and rules of argumentation. Using a difference-in-differences approach with a multicohort longitudinal data set of almost 15,000 undergraduates beginning in health and science, technology, engineering, and mathematics (STEM)-related fields at a research university, we examined changes in relative performance of students after enrolling in an introductory logic course. We find that students improved their grade point average (GPA) after taking the course, especially if they begin college with low academic achievement (Cohen’s d = 0.18). Our results are consistent with the idea that acquiring foundational skills, in particular general skills in argumentation, prepares STEM students for future learning.

Two-Sided Trees for Sentential Logic, Predicate Logic, and Sentential Modal Logic

This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.

Burn all your textbooks

The standard propositional exposition of necessary and sufficient conditions, as available in introductory logic texts, leads to a contradiction. It should be abolished.

Teaching to the Test: A Pragmatic Approach to Teaching Logic

The proper goal of an introductory logic course, teaching critical thinking, is best achieved by maintaining the principle of continuity between student experiences and the curriculum. To demonstrate this I explain Dewey’s naturalistic approach to logic and the process of inquiry, one which presents the elements of traditional logic in the context of student experiences. I offer an example of a logic textbook which models the maintenance of the principle of continuity I advocate. Last, I advocate a pluralistic and experimental approach to accomplish this, including methods that rely on the role of the body in learning and reasoning.

Medieval Logic Diagrams

This article describes the finding, documentation and significance of the set of medieval logic diagrams and associated text, all in highly abbreviated Latin minuscule, sketched on an inside wall of the Romanesque tower of the parish church in Bro, near Visby. The diagrams depict the Square of Opposition, the basic concept to be mastered in introductory logic as taught at medieval schools and universities. A date c.1200-1225 is suggested by their being executed in the earliest plaster when wet (tower built c.1200), while up to 1350 is suggested by palaeography. Dating by textual content is still in progress. Either way the Bro diagrams are among the earliest logic texts written in Scandinavia, and this is the first time for such texts to be found outside a manuscript. They are also the earliest known physical evidence of a teaching session or a discourse in logic. Furthermore they contribute to a growing body of evidence of the high standard of learning that existed in medieval Gotland.

Introduction

This article describes the finding, documentation and significance of the set of medieval logic diagrams and associated text, all in highly abbreviated Latin minuscule, sketched on an inside wall of the Romanesque tower of the parish church in Bro, near Visby. The diagrams depict the Square of Opposition, the basic concept to be mastered in introductory logic as taught at medieval schools and universities. A date c.1200-1225 is suggested by their being executed in the earliest plaster when wet (tower built c.1200), while up to 1350 is suggested by palaeography. Dating by textual content is still in progress. Either way the Bro diagrams are among the earliest logic texts written in Scandinavia, and this is the first time for such texts to be found outside a manuscript. They are also the earliest known physical evidence of a teaching session or a discourse in logic. Furthermore they contribute to a growing body of evidence of the high standard of learning that existed in medieval Gotland.

Defining Deduction, Induction, and Validity

In this paper I focus on two contrasting concepts of deduction and induction that have appeared in introductory (formal) logic texts over the past 75 years or so. According to the one, deductive and inductive arguments are defined solely by reference to what arguers claim about the relation between the premises and the conclusions. According to the other, they are defined solely by reference to that relation itself. Arguing that these definitions have defects that are due to their simplicity, I develop definitions that remove these defects by assigning a combination of roles to both arguers’ claims concerning the premises/conclusion relation and the relation itself. Along the way I also present and briefly defend definitions of both deductive and inductive validity that are significantly different from the norm.

The seven virtues of simple type theory

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.

Essentialism, Consistency and Islam: A Critique of Edward Said's Orientalism

Since 9/11, and obviously for some considerable time before it, a question has arisen about the relationship between Islam and terrorism. Is it legitimate to prefix the term ‘terrorism’ with the ad...

From if to iff: Conditional perfection as pragmatic strengthening

Geis and Zwicky's squib on “conditional perfection” (1971) released a hornet's nest of rebuttal and counter-rebuttal into the pragmatic atmosphere, with many scholars in the area playing alternately the roles of stinger and stingee. Geis and Zwicky's goal was to explain the notorious tendency among introductory logic students and ordinary speakers to ‘perfect’ an if-then conditional of the form of If you mow the lawn, I'll give you five dollars into the corresponding iff biconditional of the form if and only if you mow the lawn, I'll give you five dollars. In an overlapping pair of studies, van der Auwera (1997a,b) has recently contributed a comprehensive survey of the literature on conditional perfection before and since Geis and Zwicky as a microcosm of the development of post-Gricean pragmatic theory. While agreeing with van der Auwera on the centrality of the if → iff move for contemporary pragmatics, I will critique his treatment and offer my own perspective on the data and their ramifications, along with an expanded history that touches on the manifestations of conditional perfection and related inferential fallacies addressed in philosophical treatises, empirical psycholinguistic studies, and self-help primers. By extending the data base to include counterfactuals and other non-predictive conditionals, I will also present problems for Dancygier and Sweetser's (1997) alternative recent account of the CP phenomenon within the mental-spaces framework. The overall focus will be on the implications for the theory of conversational implicature, and in particular of R-based pragmatic strengthening, that can be drawn from the conditions on - and motivation for - conditional perfection.

Necessary Assumptions

In Evaluating Critical Thinking Stephen Norris and Robert Ennis say: "Although it is tempting to think that certain [unstated] assumptions are logically necessary for an argument or position, they are not. So do not ask for them." Numerous introductory logic text authors and various highly visible standardized tests (e.g., the LSAT and GRE) presume that Norris and Ennis are wrong; the presumption is that many arguments have (unstated) necessary assumptions and readers and test takers can reasonably be expected to identify them. This paper proposes and defends criteria for determining necessary assumptions of arguments. Both theoretical and empirical considerations are brought to bear.

Teaching Legal Theory with Venn Diagrams

Venn diagrams, which are widely used in introductory logic courses, provide a convenient and illuminating way of presenting the various theories concerning the nature of law. When combined with the Aristotelian square of opposition, these diagrams show not only how the theories are related to one another, logically, which is essential to understanding them, but also which theories are compossible. One surprising result of this approach is that it shows the substantive compatibility of the theories of law set forth by H. L. A. Hart and Ronald Dworkin, who are usually pitted against one another. I show, through quotation and visual representation, that there is no essential disagreement between these jurisprudential stalwarts concerning the relation of law and morality.

Can We Teach Introductory Logic?

Can We Teach Introductory Logic?

The Verilog hardware description language

Thomas & Moorbys The Verilog Hardware Description Language has become the standard reference text for Verilog. This edition presents the new IEEE 1364-2001 standard of the language. The examples have all been updated to illustrate the new features of the language. A cross referenced guide to the new and old features is provided. Thus, designers already familiar with Verilog can quickly learn the new features. Newcomers to the language can use it as a guide for reading old specifications. The Verilog Hardware Description Language, Fifth Edition, is a valuable resource for engineers and students interested in describing, simulating, and synthesizing digital systems; the extensive number of simulatable examples and wide range of representation styles covered ensure its quick use in design. The book is also ready for use in university courses, having been used for introductory logic design and simulation through advanced VLSI design courses. An appendix with tutorial help and a work-along style is keyed into the introduction for new students. Material supporting a computer-aided design course on the inner working of simulators is also included.