Critical Thinking: Identifying Arguments, Premises, and Conclusions, Exercises of Logic

Download Critical Thinking: Identifying Arguments, Premises, and Conclusions and more Exercises Logic in PDF only on Docsity! inquiry J generalizations aed 4 g re yA lif oT Cet tt 8] Tol UF) ote} Critical Thinking tests rationales, ! i.e., reasons connected to conclusions by justifying or explaining principles ! Why do CT?! Answer: Opinions without logical or evidential support are worthless.! An argument is a collection of claims intended to establish the truth of a specific claim ! 1. How to define a good argument! •  “An argument is GOOD if and only if it is either SOUND or COGENT.”! •  Thus, an argument is good if and only if it is either deductively valid plus all of its premises are true, i.e., SOUND, or, it is inductively strong plus all of its premises are true, i.e., COGENT.! •  an argument is VALID if and only if it is impossible for the conclusion to be false when all of its assumptions are true! •  an argument is STRONG if and only if is improbable that the conclusion is false when all of its assumptions are true! •  Understand, memorize, apply this definition - it will help you every day … ! How the text relates to the skills! Section 1.1: Identify arguments, premises and conclusions! Section 1.2: Recognizing arguments and explanations! Section 1.3: Discern deductive from inductive arguments! Section 1.4: Validity, soundness, strength and cogency! Section 1.5: Argument forms, proving invalidity! •  You should complete all exercises assigned from each of these sections according to the syllabus schedule.! Overview True Statements << False Groups of statements Deductive arguments Inductive arguments Arguments Nonarguments Valid _ Invalid (all are unsound) Strong Weak (all are uncogent) Deductive Inductive Sound Unsound Cogent Uncogent 2. How to recognize an argument! •  arguments present rational reasons for belief (rational = reasonable, non-emotional, non-personal, non-historical)! •  argument ≠ disagreement! •  argument = proof, some arguments are good and some are bad, but all arguments must cite evidence! •  does the set of claims aim to justify/prove a conclusion about a specific issue (the main subject of controversy)? if not, it is a non-argument, e.g., these are not arguments: an exposition, a report, an illustration, an explanation, a conditional statement, or any statement of belief …! •  the conclusion is the one precise claim which all other claims (premises) support – there can only be one conclusion! •  premises (evidence) must present reasons which justify accepting the conclusion! 3. How to identify premises and conclusions! •  look for indicator words – because, since, for, therefore, so, given that, we may infer that, it follows that … ! •  check support relations – which claim needs the most support, which claims seem to be supporting another! •  eliminate alternatives – when you can’t distinguish premises from the conclusion, just choose one claim at a time as the conclusion and decide whether the rest support it, if not, keep reconstructing these until you get the most charitable reconstruction! •  reconstruct using a charitable interpretation – presume that other people, like yourself, are lovers of the good and believers of truths, so when more than one interpretation of an argument is possible, interpret the argument so that the premises provide the strongest support for the conclusion! Section 1.2: Recognizing arguments and explanations! 4. How to distinguish an argument from an explanation! •  what are the reasons doing? – use the diagram –! •  notice arguments and explanations both have conclusions and reasons ... but only explanations describe what causes a conclusion to be true! •  justifying ≠ explaining! •  if reasons are justifying belief in the conclusion, then it's an argument ! •  if reasons are specifying cause(s) of truth of the conclusion, then it's an explanation! Arguments vs. Explanations Argument Premises {}— Conclusion Accepted facts Claimed to Explanation Explanans {}— Explanandum Claimed to shed light on ___ Accepted fact Section 1.3: Discern deductive from inductive arguments! 5. How to distinguish deduction from induction! •  reconstruct using a charitable interpretation - when more than one interpretation of an argument is possible, interpret the argument so that the premises provide the strongest support for the conclusion! •  if the conclusion seems necessary, then it is deduction! •  if the conclusion seems probable, then it is induction! •  conclusions of inductive arguments assert more than what is contained in the premises, but conclusions of deductive arguments do not - the conclusion of a deductive argument is not supposed to contain more information than the premises! •  if the conclusion of an argument could be false when all of the premises are true, then the argument is not deductive! All entertainers are extroverts. David Letterman is an entertainer. Therefore, David Letterman is an extrovert. The vast majority of entertainers are extroverts. David Letterman is an entertainer. Therefore, David Letterman is an extrovert. 6. How to understand (and test) logical implication! •  implication = conditional = hypothetical! •  To say that "P implies Q" means that whenever P is true Q is also true. ! •  P implies Q = if P then Q = all P are Q = the only P are Q = P only if Q! •  “P does not imply Q” when P is true and Q is not.! •  “P only if Q” is the best way to read “if P then Q” or ! “P implies Q” statements. Why? “P only if Q” is logically equivalent to “P implies Q” and makes our brains see two things: (1) that P is only sufficient for Q – it is not necessary, and (2) that Q is necessary for P – P can’t be true without Q also being true.! Every conditional has two components! – the antecedent condition implies the consequent condition! How to test logical implications! •  implication = conditional = hypothetical! •  Conditionals are false only when their antecedents are true and their consequent is false. We test a conditional for truth by thinking of a counter-example to it which shows that it is false.! •  The implication fails when P does not imply Q,! i.e., when P is true and Q is not.! Suppose someone says: ! •  “If you love me, then you buy me a diamond ring.”! When is this clearly false?! •  Answer: Whenever the antecedent is true and the consequent is false. That is, in any case where it is plausible that one both loves someone and one does not buy that someone a diamond ring. ! A syllogism, in general, is an argument consisting of exactly two premises and one conclusion. Categorical syllogisms will be treated in greater depth in Chapter 5, but for now we will say that a categorical syllogism is a syllogism in which each statement begins with one of the words “all,” “no,” or “some.” Example: All ancient forests are sources of wonder. Some ancient forests are targets of the timber industry. Therefore, some sources of wonder are targets of the timber industry. Arguments such as these are nearly always best treated as deductive. A hypothetical syllogism is a syllogism having a conditional (“if ... then”) state- ment for one or both of its premises. Examples: If estate taxes are abolished, then wealth will accumulate disproportionately. If wealth accumulates disproportionately, then democracy will be threatened. Therefore, if estate taxes are abolished, then democracy will be threatened. If Fox News is a propaganda machine, then it misleads its viewers. Fox News is a propaganda machine. Therefore, Fox News misleads its viewers. Later in this book, the first of these arguments will be given the more specific name of pure hypothetical syllogism because it is composed exclusively of conditional (hypo- thetical) statements. The second argument is called a mixed hypothetical syllogism because only one of its component statements is a conditional. Later in this book, the second argument will be given the more specific Latin name modus ponens. A disjunctive syllogism is a syllogism having a disjunctive (“either ... or ...”) statement. Example: Either global warming will be arrested, or hurricanes will become more intense. Global warming will not be arrested. Therefore, hurricanes will become more intense. Section 1.5: Argument forms, proving invalidity! 8. How to show that a deductive argument is invalid! •  show it is NOT valid by showing how conclusion can be true when all assumptions false! •  reveal the pattern, then consider counter-examples to the logical form itself …! •  construct a substitution instance (using all true premises and a false conclusion) with the counter-example method to test whether a form is valid or invalid ! •  How to do this: (1) STATE the argument. (2) EXTRACT its logical form. (3) SUBSTITUTE terms. (4) EVALUATE - does your example show that the conclusion could be false when all of the premises are true? If yes, the argument is invalid. If no, try again, but at some point you have to consider that it might be valid, or you are unable to think of a counter-example but it really is invalid. ! •  every substitution instance of a valid form is a valid argument but it is not the case that every substitution instance of an invalid form is an invalid argument - this is rare! 10. How to prove that any argument is bad! •  Show that its form is illogical, because it is either not truth- preserving (deductively valid) or not truth-generating (inductively strong). Call this the form test or the logic check.! •  Or, show that its content - at least one of its assumptions - is incredible, because it is either demonstrably false or improbable. ! •  Good arguments, by comparison, are less vulnerable to these problems than are bad arguments. Call this the fact check or reality check. This is a test of soundness for deductive arguments, and a test of cogency for inductive arguments.! •  An argument is bad, i.e., fails to justify its conclusion, if and only if it fails either the logic check or the reality check.! •  In other words, an argument is bad it is neither sound nor cogent. Such arguments fail either the logic check or the reality check.! Sound Valid All true argument argument premises Cogent Strong All true argument argument premises So, a BAD argument is one which is not sound and not cogent.!