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PHIL512 - 1/13/26

Agenda

  1. Syllabus
  2. Assignments
  3. What is Logic?
  4. Why Care?

What is Logic?

It is helpful to get a working definition of "logic?" (we can revise it). We can graft what we learn onto this general and vague conception. Take a look at some definitions of "logic" below and try either craft your own definition or pick the definition you like the best.

  1. Dictionary definition: "reasoning conducted or assessed according to strict principles of validity"
  2. Smith (An Introduction to Formal Logic): "The business of logic is the systematic evaluation of arguments for internal cogency. And the kind of internal cogency that will especially concern us is deductive validity*."
  3. L.T.F. Gamut (LLM, v1): "Logic, one might say, is the science of reasoning. Reasoning is something which has various applications, and important among these traditionally is argumentation. The trains of reasoning studied in logic are still called arguments, or argument schemata, and it is the business of logic to find out what it is that makes a valid argument (or a valid inference) valid."
  4. Loveland, Hodel, Sterrett (Three View, p.3): "What is deductive logic? It has two major components, a formal language and a notion of deduction."
  5. Agler: "Logic is a science that aims to separate good and bad arguments."
  6. Quine (Elem. Logic, p.1): "Logic [...] [is] the science of necessary inference."
  7. Gensler (Intro to Logic, 2nd ed., p.1): "Logic is about reasoning -- about going from premises to a conclusion. [...] Logic is the analysis and appraisal of arguments. When you do logic, you try to clarify reasoning and separate good from bad reasoning."
  8. Peirce ("Logic", Baldwin Dictionary): "Nearly a hundred definitions of it have been given. It will, however, generally be conceded that its central problem is the classification of arguments, so that all those that are bad are thrown into one division, and those which are good into another, these divisions being defined by marks recognizable even if it be not known whether the arguments are good or bad."

Why care?

People and students want to know "Why study logic?" Take a look at some reasons below and answer the following: (1) which do you find most compelling (or come up with your own), (2) which do you think students would find most compelling, and (3) which do you think might be bs?

  1. Seems interesting / cool / fun.
  2. There is a section on the Law School Admission Test (LSAT) called "logical reasoning" and this can help me do well on it.
  3. Because it is required: major / graduation (math) requirement
  4. Improve critical thinking skills (some minimal experimental evidence)
  5. Desirable by employers (based on surveys)
  6. Decreases anxiety (based on study of elementary math teachers)
  7. Increases autonomy / rational self-control. I wish to govern myself but often act against myself because I act based on temporary emotions or fleeting desires. Logic will help me increase my autonomy.
  8. Self-knowledge / improvement: Part of who I am is a rational being and I want to know, improve, explore that part of me.
  9. Read philosophical papers that make use of logic
  10. I want to criticize the rational / analytical method that dominates analytic philosophy so I need to know about logic.
  11. Increased resistance to consumer scams: People today develop scams (e.g., letter scams, ponzi schemes, Airbnb scams) and learning logic will help me evaluate the premises of these scams more critically.
  12. Avoid exploitation: corporations, universities, and a variety of organizations make use of sophistry (bad arguments) to exploit workers. Being able to identify bad arguments will either (1) allow you to avoid exploitation or (2) at least allow you to know you are being exploited.
  13. Important for a healthy democracy: People today are influenced by propaganda and bad arguments. A working democracy assumes "the people" are the ultimate source of authority of the government. But, if decisions people make are not "their decisions", then there is no working democracy.
  14. Be more rational: I want my beliefs to be rational. Rational beliefs are those that are supported by the best arguments. Logic is the study of good / bad arguments. Therefore, if I want to be rational, I should study logic.
  15. Anti-authority: People naturally accept what is true based on authorities (famous people, role models, tradition, politicians) or their intuitions (gut feels). This is wrong; it should be based on reasons / good arguments.
  16. Draw conclusions from legal cases: Take a 2026 case involving oral arguments before the Supreme Course. A justice asked one of the lawyers: "If you accept that the regulation, by its own terms, permit sex-based, separate sports. [...] What in Title IX explicitly, or even logically, says you have to give transgender girls the same opportunity?"

Next Time

  1. Read Ch1, pp.3-38
  2. Quiz: 01 - Basics - Logic Concepts
  3. Quiz: 01 Identifying Propositions
  4. Think of an argument that "seems good" but is not good.
  5. Think of what makes an argument good or bad, e.g., intuition? consensus? science? God? Truth? Relevance? Form? Practical results?