Chapter One: The Logic in Critical Thinking

Essentials of Logic, the required class text, is not normally used as a class text for undergraduate courses in 'Critical Thinking.' That's unfortunate, because no where on the planet can a student better learn the necessary and sufficient conditions of becoming a critical thinker and writer than in Essentials of Logic.

Students with marginal acquaintance in the functions of language in formal argumentation can easily make up their deficit by mastery of Chapters 1-4. Just studying these chapters alone would equip any serious student with insights into how language ought to work and the informal mistakes most of us make in our attempts at 'reasoning' to the truth of any debatable topic.

Not only are the key concepts of classical Categorical Logic rigorously laid out, but a thorough presentation of modern Propositional Logic is comprehensively found.. Not content by only providing a student with a robust understanding of DEDUCTIVE VALIDITY, but authors: Copi and Cohen pull a 'hat-trick' by rounding out a students understanding of the relation between Deductive and Inductive reasoning. Here, the intricacies of Analogical Reasoning, Argument Refutation, Scientific Method and Probability Theory are exhausted. If the goal of 'Critical Thinking' courses is to educate students to become masters of VALID and SOUND reasoning, then surely Essentials of Logic provides a sufficient set of conditions for that outcome.

It's not uncommon, therefore, to meet successful judges, lawyers, doctors, executives, professors, members of the general public that have all studied 'the art of reasoning' from some edition of Copi, Cohen.

One recent student, Anthony Brett Bezsylko, at U.C. Berkley returned to visit me so I asked him "Did our course in Copi, Cohen do a good job for you?" "Yes," he said, "It was like 'boot-camp-for-the brain'."

But the study of formal logic does not necessarily make a "Critical Thinker", since Logic is not concerned with the factual truth or falsity of premises used to derive conclusions. Logic is only concerned with the process of deriving conclusions from premises through VALID inferences. It is up the critical thinker to examine valid arguments and test the factual truth of the premises through experimental verification. If successful, then the critical thinker has produced SOUND inferences and not merely VALID ones.

So, a student can merely study Logic in Essentials of Logic or a student can both study Logic and actually become a critical thinker by mastering the concepts, methods and insights presented in this course.

The OPTIONAL class text, in addition to the required Essentials of Logic, is my own textbook now in pre-release as a Limited Edition: Reason, Argue, Refute: Are We Drinking Paint? has all the same content as Essentials of Logic but is more narrative in presentation with different sequence designed to cultivate students skills to Reason, Argue and Refute arguments on any topic in their courses of study.

~ Mark McIntire


Logic as Art and Science

1. Logic is the formal study of necessary inferences in our reasoning; when they are done correctly, when they go wrong, and how to distinguish between the two. When Logic yeilds verifiable principles of valid reasoning, then it is a 'science'. When Logic reveals how to formulate valid and sound reasoning, or refute invalid, unsound reasoning, then it is an 'art'. The first requirement in the study is being able to recognize arguments, which are made up of propositions (one of which is the conclusion, and the others which are the premises that support it by 'inference'). Viewed this way, Logic is the common tool for all academic arts and sciences that seek to discover what is real, true, good and beautiful.

2. Arguments can be analyzed, once recognized, by paraphrasing them or by diagramming them. Recognition involves identifying conclusion indicators and premise indicators, and also being aware of the different ways that arguments can be stated (such as with non-declarative premises, or with premises that are not directly stated). In addition, some clusters of propositions are merely explanations, though they at first may appear to be arguments. Students will sometimes need to be sensitive to context and the author’s purpose in order to distinguish between real arguments and explanatory passages.

3. Some arguments are deductive, and some inductive—and all arguments are either one or the other. Deductive arguments have conclusions which follow from their premises with absolute necessity; they are valid when their conclusions are necessarily true if the premises are true. The relationship between true (or false) propositions and valid (or invalid) arguments is sometimes quite complex. Inductive arguments, on the other hand, are never valid or certain; they can be better or worse, more or less probable, but they can never be valid or invalid.

4. Problems of reasoning are interesting and effective ways to strengthen reasoning skills. Often, the solution to such problems can be made clearer with the use of a matrix. Another type of problem involves retrograde analysis, where we must reason from what exists to what the original state of affairs must have been at some point in the past. Even though real-world problems are more complex—and less tidy—than such artificial problems of reasoning, they are nevertheless valuable, even fun activities.


Key Terms - An Essential understanding:

Truth: Any claim that can be publicly verified to correspond to reality

Proposition: Any sentence that claims that something is factually true or factually false

Premise: Any proposition that is used to infer the truth of another proposition

Conclusion: Any proposition that is inferred from a premise or premises

Deduction: Any inference of drawing out one proposition (conclusion) from other propositions (premise or premises). Latin; deduco, to lead out of or from

Induction: Any inference of leading up to a probable general conclusion based on sufficient individual experiments being verified. Latin: induco to lead up to

Explanation: Any statements that answer the who, what, when, where, or even why something is either factually true or factually false

Argument: Any series of propositions that give reasons to accept the truth or falsity of some other proposition.

Validity: When premise propositions deductively entail a conclusion proposition by logical necessity then and only then is the argument valid.

Invalidity: When premise proposition fail to deductively entail a conclusion proposition by logical necessity, then and only then is the argument invalid.