Advice for Choosing Philosophy Courses for Math & Science Students
Philosophy courses can provide students with skills necessary to excel in professions related to mathematics and computer science. In addition, philosophy courses can engage the interests and concerns of majors in those areas.
[The following are extracts from Robert L. Causey, “Why Logic is Important for Computer Science and Mathematics:”
Logic is concerned with forms of reasoning. Since reasoning is involved in most intellectual activities, logic is relevant to a broad range of pursuits. The study of logic is essential for students of computer science, and very valuable for mathematics students. Logic includes the study of deductive inferences, in which the conclusion must be true if the premises are. Recall elementary geometry: Assuming that the postulates are true, we prove that other statements, such as the Pythagorean Theorem, must also be true. Geometric proofs, and other mathematical proofs, typically use many deductive inferences.
‘Logic and reasoning’ introduce some special symbols in what are called ``formal languages,'' but logic is not symbol manipulation. The general concepts and methods taught in logic are useful independently of formal languages. Students learn how to construct proofs in English, as well as in a formal language, so the concepts and methods learned can be used in a variety of contexts.
The idea of a general purpose computer, the Turing Machine, was invented in the course of research in logic. Computer programs are written in special, symbolic languages, e.g., Fortran, C++, Lisp, Prolog. These languages contain features of logical symbolism, and Lisp and Prolog are derived from formal languages for logic. Through such connections, the study of logic can help one in the design of programs.
Mathematicians reason about abstract concepts, for example, continuous functions, algebraic systems such as ``rings,'' and topological spaces. Most math students learn to write proofs about such things by following examples in their classes. This is part of learning math, but it is slow, and often leads to confusions. Math majors who study logic find that it helps them in their mathematical thinking. It is helpful in avoiding confusions and helpful in constructing clear, convincing proofs. The study of logic is essential for work in the foundations of mathematics, which is largely concerned with the nature of mathematical truth and with justifying proofs about mathematical objects, such as integers, complex numbers, and infinite sets.
The skills conferred by philosophy courses include:
Critical thinking and problem solving:
- extracting the main points from difficult material.
- following and reconstructing arguments.
- and thinking questions through.
- learning to analyze and solve problems.
- considering them from many points of view.
- assessing the pros and cons of different proposals.
- learning to express yourself clearly and persuasively.
- skills in making decisions and then justifying your position in a clear, logical, and compelling way.
Creativity, research, and investigation:
- proficiency at conducting investigations.
- learning to ask the right questions.
- and to develop and assess methods and standards for answering those questions.
- solving problems using careful but innovative techniques and basing your conclusions on reliable evidence.
- appreciation of logical and philosophical issues and their importance, and the ability to recognize philosophical problems and considerations in many contexts.
- the ability to recall, articulate and apply various approaches to philosophical problems, and to appraise for yourself the routes for dealing with important issues.
- the ability to reproduce and compare various approaches to solving common human problems that have philosophical and logical dimensions.
- applying philosophical thinking to the “real world” – to everyday living, specific problems and puzzles, social issues, challenges in your career, and so forth.
Although all philosophy courses offer opportunities for math and computer science students, the following courses are most strongly recommended:
- PHIL 107: Logic and Reasoning
- PHIL 308: Metaphysics and Mind
- PHIL 207: 18th-Century Philosophy
- PHIL 208: 19th-Century Philosophy
By taking philosophy courses, math and science students will encounter questions such as the follows:
- How can we analyze arguments as they occur in ordinary, informal contexts?
- How can English-language statements and arguments be symbolized in terms of formalized languages?
- What are the biggest logical pitfalls in reasoning and deduction?
- Are minds like software running on the hardware of the brain?
- What constitutes consciousness, and is it the kind of thing artificial minds could have?
- What is free will?
- How is it related to the cognitive processing? Are we any more free than a computer program?