Topic One: Basic Logic Concepts for Critical Thinkers and Writers
1. Logic is the formal study of necessary inferences in our reasoning, when these inferences are done correctly, when they go wrong, and how to distinguish between the two. When Logic yields 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 in that particular discipline.
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 authors purpose in order to distinguish between real arguments and explanatory passages.
3. Some arguments are deductive, some inductive and others are analogical. This course will study all three categories of argument. Deductive arguments claim conclusions which follow from their premises with absolute necessity; they are valid when, assuming the premises to be true,the conclusion would have to be true by necessity.We call this necessity 'entailment'. If such necessity fails to happen in a deductive argument, then that deductive argument is invalid. Similar to pregnancy, logical validity of arguments is an either/or condition. A deductive argument is either valid or it is invalid. There is no such thing as a deductive argument being more valid or less valid. 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. Analogical arguments attempt to convince us of their conclusion by suggesting the line of reasoning is similar to another well accepted line of reasoning. Thus, they are a variation of inductive arguments since they cannot demonstrate by absolute necessity that the conclusion follows from the premises with absolute certainty.
4. Solving 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.
Reading Assignment from REASON ARGUE REFUTE e-Textbook: Pages 16-26
Key Terms - An Essential understanding:
Truth: Any coherent, consistent claim that something is the case or something is not the case.
Proposition: Any sentence or sentence fragment that claims that something is the case or is not the case
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 propositions fail to deductively entail a conclusion proposition by logical necessity, then and only then is the argument invalid.
Recommended Basic Logic Links for Personal Research:
PhilosphyPages.com on Arguments and Inference
PhilosphyPages.com on Language and Logic
Lander.edu(Quizzes on Introduction to Logic Topics)
Copi Chapter and Sample Test on Basic Logic Objectives
Logic Puzzles of the kind that will show up as BONUS questions on our exams!
Some More Helpful Sites