LOGIC AND CRITICAL THINKING

1. LOGIC AND CRITICAL THINKING Jonathan Dolhenty, Ph.D.Logic and Critical Thinking. Available at http://www.radicalacademy.com/logiccritthinking.htm

2. TRUTH AND THINKING • Truth is the object of thinking. • Some truths are obvious; others are difficult to acquire. • Some judgments we make are simple; some judgments are complicated. • Some arguments, whether made by us or others, may be straightforward and easily understood; other arguments may be complex and consist of a series of smaller arguments, each needing to be critically examined and evaluated.

3. CRITICAL THINKING AND LOGIC • Every object of knowledge has a branch of knowledge which studies it. • EXAMPLES: • Planets, stars, and galaxies are studied by astronomy. • Chemistry studies the structure, composition, and properties of material substances and the transformations they undergo. • The origin, evolution, and development of human society is the object studied by sociology. • Economics, biology, geography, and grammar all have objects of knowledge which they investigate, describe, and try to explain. • WHAT ABOUT CRITICAL? • Critical thinking involves knowledge of the science of logic, including the skills of logical analysis, correct reasoning, and understanding statistical methods. • Critical thinking, however, involves more than just an understanding of logical procedures. • A good critical thinker must also understand the sources of knowledge, the nature of knowledge, and the nature of truth.

4. THE SCIENCE OF LOGIC • The object of knowledge involved in the science of logic is "thinking," but it is "thinking" approached in a special way. • Generally speaking, logic is that branch of knowledge which reflects upon the nature of "thinking" itself. • But this may confuse logic with other branches of knowledge which also have the nature of "thinking" as a part of their specific object of investigation.

5. “THINKING” AND LOGIC • Logic doesn't just deal with "thinking" in general. Logic deals with "correct thinking." • Training in logic should enable us to develop the skills necessary to think correctly, that is, logically. • A very simple definition would be: • Logic is the subject which teaches you the rules for correct and proper reasoning. • A more complete and "sophisticated" definition of logic, you can define it this way: • Logic is the science of those principles, laws, and methods, which the mind of man in its thinking must follow for the accurate and secure attainment of truth.

6. A KIND OF LOGIC: NATURAL LOGIC • “Natural Logic" or Common Sense • We all have an internal sense of what is logical and what is not, which we generally refer to as "common sense." • This "natural" logic we have learned from the moment of birth, through our personal experiences in the world and through our acquisition of language.

7. A KIND OF LOGIC: SCIENTIFIC LOGIC • Scientific logic is simply our natural logic trained and developed to expertness by means of well-established knowledge of the principles, laws, and methods which underlie the various operations of the mind in the pursuit of and attainment of truth.

8. LOGIC AS A SCIENCE AND AN ART • Logic as a science: • The science part is the knowledge of the principles, laws, and methods of logic itself. • Logic as an art: • Logic must be put into action or else the knowledge provided within the science of logic is of little use. • We can speak of the "art" of logic, that is, the practical application of the science of logic to our everyday affairs. • Logic as a science and an art • Logic is not intended merely to inform or instruct. • It is also a directive and aims at assisting us in the proper use of our power of reasoning. • In this sense, we can speak of logic as both a science and an art, a practical art meant to be applied in our ordinary affairs.

9. Why Study Logic? • Aim: To develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. • Benefits: an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.

10. THREE OPERATIONS OF THE MIND

11. Simple Apprehension, Judgment, Reason • Simple Apprehension: an operation of the mind whereby we abstract from the non-essential elements of a thing and recognize those essential elements which make it to be precisely that particular thing. • Judgment: an operation of the mind which unites two ideas by affirmation or separates by negation. • Reasoning / Mediate Inference: an operation of the mind that involves a process whereby from certain truths already known, we proceed to another which is different from those that are given but necessarily following from them.

12. Basic Concept: ARGUMENTS • Argument: a group of statements, one of which (the conclusion) is claimed to follow from the other or others (the premises). • Good arguments: those in which the conclusion really does follow from the premises • Bad arguments: those in which does not, even though it is claimed to

13. Basic Concept: Statement • Basis: Argument as a group of statement • Statement: a sentence that is either true or false; typically a declarative sentence. • Examples: • Hydrogen is combustible. • World War II began in 1939. • Some ducks are fish. • Abraham Lincoln was beheaded.

14. Basic Concept: Truth - Value • Truth value of the statement: the attribute by which a statement is either true or false. • Examples: • Hydrogen is combustible. (true) • World War II began in 1939. (true) • Some ducks are fish. (false) • Abraham Lincoln was beheaded. (false)

15. Basic Concept: Non-Statements • Sentences which cannot be said to be either true or false. • What is the atomic weight of carbon? (question) • Let’s go to the park today. (proposal) • We suggest that you travel by bus. (suggestion) • Turn to the left at the next corner. (command) • Ouch! (exclamation)

16. Components of an Argument: Premise(s) and conclusion • Premises: the statement that set forth the evidence. • Conclusion: the statement that is claimed to follow from the evidence. • Example: • All cats are animals. • Felix is a cat. • Therefore, Felix is an animal. • N.B. the first two statements are the premises; the third is the conclusion. • The claim that the conclusion follows from the premises is indicated by the word “therefore”.

17. Schema of an Argument:

18. Recognizing Arguments • One of the most important tasks in the analysis of arguments is being able to distinguish premises from conclusion. • If what is thought to be a conclusion is really a premise, and vice versa, the subsequent analysis cannot possibly be correct. • Frequently, arguments contain certain indicator words that provide clues in identifying premises and conclusion.

19. Conclusion Indicator • A word that provides a clue to identifying a conclusion. • Examples • Therefore hence whence • Wherefore thus consequently • Accordingly so it follows that • Entails that as a result We may conclude • Implies that it must be that We may infer • Whenever a statement follows one of these indicators, it can usually be identified as the conclusion. • By process of elimination the other statements in the argument are the premises. • Example: This is pen is out of ink. Consequently, it will not write.

20. Premise Indicator • A word that provides a clue to identifying a premise. • If an argument does not contain a conclusion indicator, it may contain a premise indicator. • Examples: • for the reason that in that seeing that • As indicate by for since • Because as inasmuch as • may be inferred from given that owing to • Any statement following one of these indicators can usually be identified as a premise. • Example: This locket is worth a lot of money, since it is made of platinum.

21. Basic Concept: Inference & Proposition • An inference, in the technical sense of the term, is the reasoning process used to produce an argument. • A proposition, in the technical sense, is the meaning or information content of a statement.

22. Passages lacking an inferential claim (1) • Passages lacking an inferential claim contain statements that could be premises or conclusions (or both) but what is missing is a claim that a reasoning process is being expressed. • Warnings/ pieces of advice: kinds of discourse aimed at modifying someone’s behavior. • Ex. “Watch out that you don’t slip on the floor.” • Ex. “I suggest you take philosophy in the first semester.” • Each of these could serve as the conclusion of an argument; but in their present context, there is no claim that they supported or implied by reasons of evidence. • Statements of beliefs or opinion: expressions of what someone happen to believe or think at a certain time. • Ex. I think a nation such as ours, with its high moral traditions and commitments, has a further responsibility to know how to became drawn into this conflict, and to learn the lessons it has to teach us for the future. • Alfred Hassler, Saigon, U.S,A.

23. Passages lacking an inferential claim (2) • Loosely associated statements: may be about the same general subject, but they lack a claim that one of them is proved by the others. • Ex. Not to honor men of worth will keep the people from contention; not to value goods that are hard to come by will keep them from theft; not to display what is desirable will keep them from being unsettled of mind. • Lao-Tzu, Thoughts from the Tao Te Ching • Report: consists of a group of statements that convey information about some situation or event. Ex. News Report • Expository passage: a kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence. • Illustration: consists of a statement about certain subject combined with a reference to one or more specific instances intended to exemplify that statement. • Ex. Chemical elements, as well as compounds, can be represented by molecular formulas. Thus, oxygen is represented by “O2”, sodium chloride by “NaCl”, and sulfuric acid by “H2SO4”.

24. Conditional Statements • A conditional statement is an “if… then…” statement. • Ex. If it rains, the soil is wet. • It is made up of two component statements: if = antecedent; then = consequent • Occasionally, “then” is left out • Conditional statements are not arguments because there is no claim that either the antecedent or the consequent presents evidence. • In other words, there is no assertion that either the antecedent or the consequent is true. Rather, there is only the assertion that if the antecedent is true, then so is the consequent. • A conditional statement may serve as premise or the conclusion of an argument.

25. Explanations • An explanation consists of a statement or a group of statements intended to shed light on some phenomenon that is usually accepted as a matter of fact. • Ex. Cows can digest grass, while humans cannot, because their digestive systems contain enzymes not found in humans. • 2 parts: • Explanandum: the statement that describes the event or phenomenon to be explained. • Explanans: the statement or group of statements that purports to do the explaining. • Explanations are sometimes mistaken for arguments because they often contain the indicator word “because”. Yet explanations are not arguments for the following reason: In an explanation, the explanans is intended to show why something is the case, whereas in an argument the premises are intended to prove that something is the case.

26. SCHEMATIC DIAGRAM Premises Explanans Conclusion Explanandum