Introduction: Course Philosobophy XX1 Critical Thinking Peter Horban Diamond Building 5606 778 782 4806 Email: [e-mail] www.sfu.ca/~horban Course Requirement: 10% 6 parts 1st Midterm (week 8) 20% 2nd midterm (week 11) 30% Final exam 40% Wednesday April 16th @ 12 noon Office Hour: Tuesday, Thursday 10.30-11.20 Wednesday 12.30-1.20
What is Critical thinking? Critical thinking:: the careful and deliberate determination of whether to accept, reject or suspends judgment about a statement, and the determination of what level of confidence is appropriate if we accept or reject it. Reason and Argument: The title of our text links arguments with the use of reason. What should I believe in now? Whenever we are trying to determine what's true and what's false, we are reasoning. We are using arguments. Understanding how arguments work can help us reason better. Argument: a set of proposition (claims or statements), one of which, the conclusion, is supposed to be supported by the others, the remises (or reasons) Argument evaluation is the process of determining how good an argument is. Argument interpretation: is the process of identifying the premises and conclusion of an argument. Argument analysis is the process of interpreting (reconstructing) and evaluation an argument. Our overall aim is to improve our ability to analyze arguments, with the result that we will reason better. Argument can be analyzed in terms of their rhetorical power literary merit rational (logical) strength
Some Obstacles to Argument Analysis lack of an adequate vocabulary or background the desire to be tolerant confusing the argument with its presentation the use of "argument stoppers" An argument stopper is a response to an argument that has the effect of cutting off discussion and preventing careful argument analysis. Examples include: "That's just a matter of opinion." "That's a subjective judgment" "Who's to say that that's true?" Remarks such as these never amount to substantive criticism of arguments. Instead, they typically indicate that the speaker is ignoring the question of whether the premises of the argument are true, or whether they provide significant support for the conclusion. Consider "who's to say" questions More often than not, people utter these word to make a statement, rather than to ask for information. Example Who's to say whether or not God exist? Who's to say whether capital punishment is morally right or wrong?" There are three types of situations where this is a legitimate question. 1. Who can determine (decide) this matter just by virtue of their say-so?
Example: Who's to say whether this material will be on the exam? Answer: the instructor --often this is a matter of authority. Who has the authority to say (decide)...?
2.
Who is in the best position to determine (i.e. find out) how things are
Examples: Who's to say what smith died of? Answer: the coroner Example: Who's to say whether these steel beams will support the roadbed? Answer: the structural engineer. 3. How does anyone determine (find out) how things are? What's the methodology? What are the criteria? Example. Who's to say what's right and what's wrong? Note: This is not a request for anyone's name or position. Instead, it amounts to the following: How does one tell what's right and what's wrong?
Language and Truth Old title for XX1: "In pursuit of truth" What is truth? What sorts of things are true or false? propositions, statements, claims Propositions vs Sentences Sentences are linguistic entities. "It is raining" "Il pleut." These are two different sentences yet they assert the same thing. They convey the same information. They are used to express the same proposition (statement). Generally, a proposition is what is expressed or asserted by a declarative sentence. Two different sentences might express the same proposition. And the same sentence, uttered on different occasions, or by different individuals, might express different propositions. Before we can determine whether what someone says is true or false, we have to determine just hat the person is claiming with the sentence he or she utters. What proposition is being expressed? What make a true proposition true? Note the important difference between a proposition's being true, and it being believed to be true. The correspondence principle: a proposition is true just in case it describes things as they actually are. It corresponds to the facts.
Simple theory of truth Real theory of truth
The Myth of Degrees of Truth "Peter has one hundred dollars in his wallet." In fact, I have fifty dollars in my wallet. "Well, it's half-true that Peter has one hundred dollars in his wallet." OR "It is 50% true that Peter has one hundred dollars in his wallet." But it is just plain false that I have one hundred dollars... What is true is that I have one-half (or 50%) of one hundred dollars in my wallet. There are, strictly speaking, no half truths. The one truth value principle: Every proposition has exactly one truth value, It is either true or false, but not both Note: Sometimes we may not be able to determine the truth value of a given proposition.
Objectivity and Truth In general, whether a proposition is true is an entirely different question from whether you or anyone else believes it. There may be truth that no one believes, and there may be false propositions that everyone thinks are true. The concept of truth that we are working with assumes a fundamental distinction between the way things really are and the way they may seem to be to this or that individual mind. In the final analysis, whether what we say (or believe is true is determined by the way things are the things we are talking about. In that sense, truth (being true) is an objective property of all those propositions (and only those propositions) that accord with reality that specify what is in fact the case. Some people say that truth is always a subjective matter fostered by sloppy thinking and speaking. Example: Smith: Black olives taste good. Jones: No, black olives do not taste good. Does this show that the same proposition can be both true and false? Smith: It's true for me that black olives taste good Jones: It's false for me that black olives taste good. Does this show that truth is objective, at least in matters, such as taste? Smith: I, Smith, like the taste of black olives. Jones: I, Jones, do not like that taste of black olives. Once we are clear about what Smith and Jones are saying, it becomes obvious that truth (or falsity) mush be an objective property of their remarks.
Smith's and Jones's remarks are true, if and only if they accurately describe reality. Suppose someone just say that black olives taste good. Is the proposition that this person expresses true or false? Here (again we must remember that before we can determine whether that someone says is true or false, we have to figure out just what proposition is being expressed by that person's remark. If someone merely say, "Black olives taste food", then I should talk further with the person to find out what proposition is intended. Is the person claiming that he or she like the taste of black olives? If so, what would make that true. Is the person claiming that everyone enjoys the taste of black olives? If so, what would make that true?
An objection to the objectivity of truth Consider the proposition that the height of Mt Everest is 8847.7 meters. It is claimed that this is true. However, height is measured by certain procedures that human being have invented. And the size of a meter is merely a social construct a human convention. We could have used a different symbol to refer to this length, or we could have used the word "meter" to refer to some other length. If we had adopted some other conventions, and used the term "meter" to refer to a length that is double the one that we have settled on. then we would say that the height of Mt. Everest is 4423.85 meters. Similarly, the reference point that we use for measuring the height of mountains is a matter of human convention. We have chosen sea level, but we could have chose some other baseline. Of course, the names, and even the boundaries of mountains reflect human conventions ones that could easily have been different. And so on. Both mountains and height, therefore, are social constructs. Hence, human begins to create their own reality. It follows that so-called truths about the height of mountains are also social constructs. Rather than being an objective property of certain propositions, truth, like reality, is a product of human conventions and linguistic practice. -------------------------------------------------------------------------------------What shall we say about that above reasoning? In summary, all that the above considerations indicate is that the sentences that we use to express proposition are the result of social and linguistic
conventions. This does not in the least show that truth is not an objective property of those propositions that describer things as they actually are.
Rational belief "Beliefs for which we have good reason are rational beliefs." R.Feldman Strictly speaking, a rational belief of mine is a proposition a) that I belief, b) that it is rational for me to believe. It is a proposition that I believe, such that my believing is in accordance with the dictates of reason. I believe it, and I am warranted or justified in believing it. Belief, Disbelief, and Suspension of Judgment You must take exactly one of three attitudes towards any proposition that you consider. To believe a proposition is to believe that it is true. mental consent to believe agreement To disbelieve a proposition is to believe that it is false. To suspend judgment about a proposition is to consider it but be unable to decide whether it is true or false. It is to consider the proposition but neither believes nor disbelieves it. Note the difference between not believing and disbelieving. Examples: 1. Bertrand Russell did not believe that God exists. 2. Bertrand Russell believed that God does not exist. That is, he disbelieved that God exist. The expression "does not believe" often results in ambiguity. 3. 3a. 3b. Diane does not believe that there are diamonds on Mars. Diane disbelieves (thinks it false) that there are diamonds on Mars. Diane is not convinced that there are diamonds on Mars.
Perhaps she suspends judgment. Perhaps she has never even thought about the matter.
All Propositions propositions that I believe proposition that I disbelieve proposition that I suspend judgment about proposition that I do not even consider
Propositions that I consider
proposition that I do not believe
Rational Belief and Evidence If a person's evidence concerning a proposition supports that proposition, then it is rational for that person to believe the proposition. If the person's evidence goes against the proposition, then it is rational for that person to disbelieve the proposition. If the person's evidence is neutral, then it is rational for that person to suspend judgment concerning the proposition. The above constitutes the rational belief principle. The rationality of belief (believing) is determined entirely by the evidence available to the believer. Might it be rational for a person to believe a proposition even though that proposition is false? Fallibilism: it may be rational to believe a proposition even though that proposition turns out to be false. A person's evidence might justify his or her acceptance of a proposition even if that evidence is less than conclusive and, as a result, fails to guarantee its truth.
Evidence Evidence is that which provides warrant to justification for belief. Evidence is routinely expressed in the form of propositions indicating the truth (or falsity) of some other proposition. In these cases, evidence is used to prove or support a proposition. Sources of Evidence sensory experience memory testimony Some propositions are self-evident, or self-evidently true. Example: No spinster is married. All triangles have three sides. Many self-evident truths are analytic truth. An analytic proposition is one whose truth or falsity is determined simply by virtue of the meanings of its terms. Example of analytic proposition: All triangles have three sides. Some spinsters are married. Analytic propositions are frequently contrasted with synthetic ones. Examples of synthetic propositions: Some movie stars are wealthy. Peter Horban is more than 2 feet tall. Peter Horban is less than 2 feet tall.
Conflicting proposition Genuine disagreement involves conflicting and beliefs hence conflicting propositions. Conflicting propositions are inconsistent with each other. It is logically impossible that they both be true (together). 2 species (contradictories and contraries): Two propositions are contradictories if and only if a) they cannot both be true, and b) they cannot both be false Example: "There are more than 25 people in this room. and "There are fewer than 26 people in this room." Two propositions are contraries if and only if a) they cannot both be true, but b) they can both be false. Example: "There are more than 30 people in this room." and "There are fewer than 20 people in this room." To determine the relationship between two propositions, ask the following two questions in this order. 1. Is it possible that there 2 propositions both be true (together)?
If "yes", then they are not in conflict. They are consistent. You can stop. If "no", then they are inconsistent and you must ask question 2. 2. Is it possible that these 2 propositions both be false (together)?
If "yes", then they are contraries. If "no", then they are contradictories.
Examples: 1. There is an elephant in this room now." 2. There is a giraffe in this room now 3. Peter Horban is more than 12 feet tall 4. There are no animals in this room now 5. Peter Horban is less than 12 feet tall. a. b. c. consistent (ie not conflicting) contraries contradictories a b b
1 and 2 1 and 4 3 and 5
Examples: Smith believes that 2+3=5 Jones believes that 2+3=6 A All triangles have three sides. Some spinsters are married. C Peter Horban does not exist (ever). Peter Horban teaches Philosophy XX1. B
Argument Analysis There are two basic ways in which an argument can be defective. Internal: having to do with the relationship between premises and conclusion. External: having to do with truth-values of the premises. Arguments in which the conclusion is rightly related to the premises are well-formed arguments. There are two types of well-formed arguments: deductively valid, and deductively cogent. A valid argument is one in which the premises and conclusion are related to each other in such a way that it is impossible that the premises all be true and the conclusion be false. In any valid argument, the truth of the premises would guarantee the truth of the conclusion. Any argument that is not valid is invalid. Which of the following arguments are valid? 1. The president of SFU earns more than $200,000 per year. 2. Anyone who earns more than $200,000 per year owns at least 15 pairs of shoes. 3. The president of SFU owns at least 15 pairs of shoes. Valid 1. 2. 3. Valid All pigs can fly. All cats are pigs. All cats can fly.
What's so special about valid arguments? They never let you reason from true premises to a false conclusion.
Argument Patterns Example: If Smith applied for a scholarship, then she'll get one. Furthermore, Smith did apply for a scholarship; therefore, she'll get one. Note the form or pattern here. 1. 2. 3. If --- then ... _--...
modus ponens (or affirming the antecedent) We can express the same pattern using the propositional variables "P" and "Q". 1. 2. 3. If P then Q. P Q
The above argument is valid because of its form or pattern. Any argument having this pattern is valid. There are many valid argument patterns. In this valid argument pattern, one of the premises asserts a conditional of the form if P then Q. The other premise asserts the antecedent P of the conditional. The conclusion is the consequent Q of the conditional. modus tollens (or denying the consequent) 1. 2. 3. If P then Q. Not-Q Not-P
disjunctive syllogism (or argument by elimination)
1. 2. 3.
(Either) P or (else) Q Not-P Q
hypothetical syllogism 1. If P then Q 2, If Q then R 3. If P then R. simplification 1. P and Q 2. Q contraposition 1. If P then Q. 2. If not Q then non-P equivalence 1. P if and only if Q. 2. Not-P 3. Not-Q WARNING! Two invalid argument patterns: The fallacy of affirming the consequent 1. If P then Q. 2. Q 3. P The fallacy of denying the antecedent 1. 2. 3. If P then Q Not-P Not-Q
In general, one can show that an argument pattern is invalid if one can show that there is even one case of an argument having that specific pattern in which the premises are (all) true yet the conclusion is false.
Doing the amounts to showing that with that pattern, it is possible that the premises all be true and the conclusion false.
An example using the above pattern: 1. If Peter Horban is more than twenty feet tall, then he's more than two feet tall. 2. Peter Horban is not more than twenty feet tall. 3. Peter Horban is not more than two feet tall. invalid Compare the above example with the following one. 1. If Peter Horban is more than twenty feet tall, then he's more than eighteen feet tall. 2. Peter Horban is not more than twenty feet tall. 3. Peter Horban is not ore than eighteen feet tall. This argument is also invalid
Argument Patterns in Predicate Logic This set of patterns involves groups, classes, or sets of things. Many propositions of predicate logic are known as categorical propositions. Four types: A. All A are B. E. No A are B. I. Some A are B. O. Some A are not B. "A" and "B" functions as class variables. They designate groups of things having certain properties (or predicates). Conversion of these propositions involves switching the A class with the B class. Conversions Valid Conversions: 1 Every proposition of the form "No A are B" is equivalent to its converse, "No B are A". 2. Every propositions of the form "Some A are B" is equivalent to its converse, "Some B are A." Invalid Conversions: 1. From a proposition of the form "All A are B", nothing follows about the truth values of its converse. "All B are A" so the inference is not valid. 2. From a proposition of the form "Some A are not B", nothing follows about the truth value of its converse, "Some B are not A." so the inference is not valid.
Categorical Propositions ad Syllogism A E I O All S are P. universal No S are P. Some S are P. Some S are not P. particular
"A" and "I" propositions are affirmative. "E" and "O" propositions are negative. Distribution is a technical notion that you need not understand at all. For the purpose of the course, simply note the following: In any universal proposition, the subject term is distributed. In any negative proposition, the predicate term is distributed. All others are undistributed. USNP
Categorical Syllogisms Class Variables: A,B,C (each occurs twice) 1. 2. 3. All/No/Some ... are (perhaps are not) ... . All/No/Some ... are (perhaps are not) ... . All/No/Some ... are (perhaps are not) ... . end term The term that does not appear in the conclusions is the middle term. It appears once in each premise. The above describes any categorical syllogism (valid or invalid) expressed in standard form. The Four Rules 1. The number of negative premises must equal the number of negative conclusions (for O). 2. The middle term must be distributed at least once. 3. Every term distributed in the conclusion must be distributed in the premises. 4. If the conclusion is a particular proposition, then at least one premise must be particular. Test the following syllogism for validity. 1. 2. 3. All Canadians are consumers. Some consumers are not liberals. Some Canadians are not liberals.
Negative premise \Rule 1 Negative conclusion /
Rule 3,4 satisfied. Invalid (rule 2) 1. 2. 3. Some neurotics are not well-adjusted people. Some well adjusted people are not ambitious people Some neurotics are not ambitious people
2 negative premise -> 1 negative conclusion 1. 2. 3 All liberal are pacifists. No generals are liberals. No generals are pacifists.
invalid (rule 1)
Invalid (rule 3) Cogent Argument In a cogent argument, it is unlikely (but still possible) that the premises all be true, and the conclusion false. Note: with cogent arguments, as with valid ones, the premises need not actually be true. An argument that is neither valid nor cogent is ill-formed. Degrees of cogency Some patterns of cogent arguments See the examples found in the text. 1. 2. 3. Most A are B. X is an A. X is a B.
Singular statements propositions Cogent argument pattern A cogent argument pattern (CAP) is an argument pattern all of whose substitution instances are cogent arguments. A valid argument pattern (VAP) is an argument pattern all of whose substitution instances are valid arguments.
What about the following pattern? 1. 2. 3. VAP 1. 2. 3, Most A are B. Most B are C. Most A are C. Most A are B. All B are C. Most A are C.
neither VAP nor CAP
Example: 1. Most men are right-handed people. 2. Most right-handed people are females. 3. Most men are females. 1. 2. 3. All A are B. Most B are C. Most A are C.
neither VAP or CAP Example: 1. All mice are mammals. 2. Most mammals weigh more than five pounds. 3. Most mice weigh more than five pounds. Not all cogent arguments are easily recognized simply by their form or pattern. And it may be that some are "not" substitution instances of a CAP (contrary to what Feldman says in definition D3.2b on pages 85 and 91) We lack a well-developed formal (syntactic) notion of cogency. For this reason, we'll be more concerned with VAPs than with CAPs. Cogency and Background Information 1. The chair of the Philosophy Department drives her car to work each day. 2. The chair of the Philosophy Department has had a driver license at some time (or other). Is this argument valid, cogent, or ill-formed. Knowing just the information contained in this argument, we would not be entitled to say it is well-formed.
As it stands, the argument is ill-formed; but because it can be rendered well-formed in a fairly obvious and simple way, we will say that it is an incomplete argument.
Strong Argument An argument is "deductively strong" for a person if and only if both of the following conditions are met. 1. it is valid, and 2. it is reasonable for the person to believe all of the argument's premises. Any argument that is deductively strong for you is one whose conclusion you ought to accept. Inductively strong arguments 1. Some public transit buses come up the mountain to SFU almost every day that is not a holiday. 2. Tomorrow is a day that is not a holiday. 3. Some public transit buses will come up the mountain to SFU tomorrow. The above argument is invalid but cogent. Furthermore, since its premises are reasonable to believe, it is probably an inductively strong argument. However, the fact that it is cogent, together with the fact that it is reasonable for us to accept its premises, does not imply that it is reasonable for us to accept the conclusion. We might know that there is a transit strike planned for tomorrow, say, and that bus service to SFU will almost certainly be suspended. That is, out total evidence might be such that wile we recognize that this argument is cogent, and that it is reasonable for us to believe its premises, it is unreasonable for us to accept its conclusion. In this case, the argument would be defeated (or undetermined) by our total evidence. An argument is defeated by a person's total evidence if and only if all of the following conditions are met:
1. the argument is cogent 2. the premises are reasonable for the person to believe, BUT 3. the person's total evidence does not support the conclusion of the argument. In other words, there is at least one other proposition that the person reasonably believes; but if it were added to the original premise set, the new argument would not be cogent (though the original one the defeated one still is) An argument is inductively strong for a person if and only if all of the following conditions are met: 1. 2. and 3. The argument is cogent, and the person is justified in believing all the premises of the argument, the argument is not defeated by the person's total evidence
Cogent arguments, unlike valid ones, can be defeated by a person's total evidence. Notice that the strength of an argument admits of degrees. The strength of a valid argument depends upon how reasonable it is to believe its premises. The strength of a cogent argument depends upon how reasonable it is to believe its premises, how cogent the argument is, and the extent to which one's total evidence weakens (without defeating) the argument. Note: Deductively strong and inductively strong are out best guide to true conclusions. However, these are not infallible. Even an argument that is deductively strong for you may turn out to have a false conclusion. How's that?