Introduction to Formal Logic

The aim of this course is to provide systematic overview and introduction to formal logic and its applications in deductive reasoning in general, with a particular focus placed on inferences in social science research. By the end of the course the participants will be able to recognize deductive inferences, analyze their structure and identify the appropriate formal tools, and subsequently apply those tools in order to make the inferences more streamlined and precise.

The course is best suited for students of social sciences who wish to develop or improve their use of the tools of formal logic in their general and academic reasoning. Moreover, the course will provide a useful preparation for students looking to attend Set-Theoretic Methods introductory and advanced courses.

The course will start from applications of general deductive ability and then expand it with the addition of formal tools. It will combine lecture and demonstration by the course instructor with collaborative problem-solving and discussion of examples from social sciences practice. Given that logic is a scientific discipline comparable to mathematics, in which a relatively small formal apparatus can yield an unlimited amount of novel and intriguing results, familiarity which logic is inseparable from the skill at using it. Only through repeated use is one able to quickly and effectively identify, and then reliably apply, the tools that logic provides. Therefore, it is important for course participants to receive as much hands-on experience with using the said apparatus and so the students are expected and encouraged to actively participate in the classes. Moreover, throughout the course optional homework assignments will be offered to provide further opportunities to broaden and establish the goals of the lesson.

Three major topics to be covered in the course are: (1) the introduction to the field of logic and its role both in the history of thought and in the contemporary world, with particular focus on the academic sphere, (2) the concepts of truth and proof and formal tools for testing both, as well the field of related concepts and terminology and (3) predicate calculus and the basic set theory.

Introduction. In introducing logic, we will work towards a way of precisely defining what it is. To do so, we will offer an overview of the history of logic, in order to begin understanding what logic is and how it can, and has been, used. We will discuss the applications of deductive thinking to general and academic reasoning. At least as important, if not more so, we will discuss what it is not and how it can not be used through the examination of some commonly encountered fallacies. Moreover, we will introduce, discuss and try to justify the use of formalism in doing modern logic. As every formal notation has its advantages and drawbacks, at this point the decision on which to use for the remainder of the course will be agreed upon through discussion with course participants.

Truth and proof. One of the central concepts of logic is truth. We will define the meaning of the word ‘truth’ as it is used in logic and examine the relations of truth values, i.e. truth and falsity, of sentences. Most importantly, we will get to know how the truth values of some sentences can be used to infer those of others. In other words, we will see how some sentences prove or disprove others, and we will learn to connect chains of such inferences to construct proofs. Again, it will be at least as important to likewise understand how, when and why the construction of such chains fails, which will allow the participants to either improve or refute proofs in any form of a debate, scientific or otherwise.

Predicate calculus and set theory. In addition to the introduction of the basic apparatus of logic, in this course we will also expand it to other, more complex and correspondingly more powerful, tools. The advantage here is that while the expansion is relatively minor and straightforward, the resulting system is very useful, and consequently ubiquitous. Namely, we will introduce the predicate calculus, and it will in turn be used to explain and understand set theory.

Although any background in formal logic participants might posses will facilitate the course, it assumes no previous familiarity with either informal or formal logic.