Chapter 1: Basic Concepts
Chapter 1: Basic Concepts Section 1: Arguments, Premises, and Conclusions Logic Argument Statement Truth Value Premises Conclusion Conclusion Indicators Premise Indicators Inference Proposition Syllogistic Logic Modal Logic
the science that evaluates arguments group of statements with one or more premises and one conclusion where the premises purport to prove the conclusion sentence that is either true or false whether a statement is true or false Statements that set forth the reason or evidence The statement that the evidence claims to support or imply therefore, thus, entails that, as a result, etc. Since, as indicated by, owing to, etc. Reasoning process expressed by an argument Meaning or information content of a statement Fundamental elements are terms; evaluated as good or bad depending on how the terms are arranged; Aristotle Involves possibility, necessity, belief, and doubt; Aristotle
**identify the premises and conclusion Section 2: Recognizing Arguments Factual Claim Inferential Claim Simple Noninferential Passage Warning
A claim that presents evidence or reason Claim that the alleged evidence supports or implies something Unproblematic passages that lack a claim that anything is being proven Simple noninferential passage; form of expression that is intended to put someone on guard against a dangerous
Piece of Advice
Statement of Belief / Opinion
Loosely Associated Statements
Report
Expository Passage
Illustration Argument from Example Explanation
Explanandum Explanans Conditional Statement Sufficient Condition Necessary Condition
or detrimental situation Simple noninferential passage; form of expression that makes a recommendation about some future decision or course of conduct Simple noninferential passage; expression about what someone happens to believe or think about something Simple noninferential passage; may be about the same general subject, but they lack a claim that one of them is proved by the others Simple noninferential passage; group of statements that convey information about some topic or event Kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence; the objective is not to prove the topic sentence, but to expand or elaborate on it Expression involving one or more examples that is intended to show what something means or how it is done; the example is not meant to prove anything Basically an illustration where the examples purport to prove something Expression that purports to shed light on an event or phenomenon; the event/phenomenon is usually accepted as a matter of fact statement of an explanation that describes the event/phenomenon being explained; the fact statement of an explanation that actually does the explaining; the explanation “if (antecedent), then (consequent)” A if the occurrence of A is all that is needed for the occurrence of B B if A cannot occur without the
occurrence of B **determine if it is an argument **where is the conclusion **if not an argument, what kind of nonargument **determine whether a condition is necessary or efficient Section 3: Deduction and Induction
Deductive Argument
Inductive Argument
Deciding b/w Deductive and Inductive Argument Based on Math
Argument from Definition
Categorical Syllogism Hypothetical Syllogism Disjunctive Syllogism Prediction
Argument incorporating that claim that it is impossible for the conclusion be false given that the premises are true; involve necessary reasoning; general to particular Argument incorporating that claim that it is improbable that the conclusion be false given that the premises are true; involves probabilistic reasoning; particular to general (1) occurrence of indicator words (2) actual strength of the inferential link between premises and conclusion (3) form or style of argumentation Deductive; the conclusion depends on some purely arithmetic or geometric computation or measurement Deductive; the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion Deductive; consists of 2 premises and 1 conclusion; each statement begins with “all”, “no”, or “some” Deductive; consists of 2 premises and 1 conclusion; “if…, then…” for one or both of its premises Deductive; consists of 1 premises and 1 conclusion; “either…or…” Inductive; proceeds from our knowledge of the past to a claim about the future
Argument from Analogy Generalization Argument from Authority Argument Based on Signs
Causal Inference Particular Statement General Statement
Inductive; depends on the existence of an analogy or similarity between 2 things or states of affairs Inductive; proceeds on the knowledge of a selected sample to some claim about the whole group Inductive; concludes that something is true because a presumed expert or witness has said that it is Inductive; proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes Inductive; proceeds from the knowledge of a cause to a claim about an effect, or conversely, from the knowledge of an effect to a claim about a cause Makes a claim about one or more particular members of a class Makes a claim about all of the members of a class
**determine whether it is deductive or inductive **what type of deductive argument **what type of inductive argument Section 4: Validity, Truth, Soundness, Strength, Cogency
Valid Argument
Invalid Argument
Sound Argument
Deductive arguments; impossibility of a false conclusion given true premises; the conclusion follows with necessity from the premises; **can have a valid argument with false premises Deductive arguments; possibility of a false conclusion given all true premises; conclusion does not follow necessarily from the premises; **can have an invalid argument with true premises and a true conclusion Deductive arguments; valid argument with all true premises
Unsound Argument Strong Argument Weak Argument Cogent Argument
Uncogent Argument
Deductive arguments; invalid argument, has one or more false premises, or both; Inductive argument; conclusion follows probably from the premises Inductive argument; conclusion does not follow probably from the premises Inductive argument; strong with all true premises that meet the total evidence requirement Inductive argument; weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these
**determine whether the deductive argument is (a) valid or invalid and (b) sound or unsound **determine whether the inductive argument is (a) strong or weak and (b) cogent or uncogent
Chapter 6: Propositional Logic Section 1: Symbols and Translation Operators/Connectives Propositional Logic Simple Statement Compound Statement Negation Conjunction Disjunction Implication
Symbols that express the relationships between two letters that represent statements Fundamental elements are whole statements (propositions) Does not contain any other statement as a component Contains at least one simple statement as a component ~ (tilde) not, it is not the case that (dot) and, also, moreover V (wedge) Ore, unless > (horseshoe)
Equivalence Biconditional Statement Main Operator WellFormed Formula
if…then…, only if… use “SUN” Ξ (triple bar) If and only if Expresses the relationship of material equivalence Operator that has as its scope everything else in the statement Syntactically correct arrangement of symbols
**translate into symbolic form Section 2: Truth Functions Truth Function Statement Variables Statement Form
Truth Table
Any compound proposition whose truth value is completely determined by the truth value of its components Lowercase letters that can stand for any statement Arrangement of statement variables and operators where substitution of statements in place of variables results in a statement Arrangement of truth values that shows every possible case of the truth value of the compound proposition
**identify the main operator **determine the truth values of statements Section 3: Truth Tables for Propositions Logically True / Tautologous Logically False / SelfContradictory Contingent
Classification of compound statements with all true values under the main operator Classification of compound statements with all false values under the main operator Classification of compound statements
Logically Equivalent Contradictory Consistent Inconsistent
with at least one true and one false value under the main operator Comparison of compound statements where both have the same truth value on each line Comparison of compound statements where they have opposite truth values on each line Comparison of compound statements where there is at least one line where they both have true truth values Comparison of compound statements where there is no line on which the truth values are both true
**classify the statement **compare the statements Section 4: Truth Tables for Arguments **a line in which all premises are true and there is a false conclusion indicates an invalid argument. **if there is no line where the above exists, then it is valid. Section 5: Indirect Truth Tables **working backwards from the truth value of the main operator, only looking at the lines where the conclusion is false, then among those only looking at lines where the premises are true. Section 6: Argument Forms and Fallacies
Argument Form
Disjunctive Syllogism Hypothetical Syllogism
Arrangement of statement variables and operators such that the uniform replacement of the variables by statements results in an argument P V Q ~P Q P>Q
Modus Ponens Modus Tollens
Affirming the Consequent
Denying the Antecedent
Constructive Dilemma Destructive Dilemma Grasping by the Horns Escaping between the Horns
Q>R P>R P>Q P . Q P>Q ~Q ~P Invalid P>Q Q . P Invalid P>Q ~P ~Q (N>I) (C>A) N V C I V A (P > Q) (R > S) ~Q V ~S ~P V ~R Prove the conjunctive premise false by proving either conjunct false Prove the disjunctive premise false
**identify the argument forms **difference between constructive and destructive dilemma **difference between grasping/escaping horns
Chapter 7: Natural Deduction in Propositional Logic Section 1: Rules of Implication I Rules of Implication I
Consist of basic arguments from whose premises imply their conclusion (1) modus ponens (2) modus tollens (3) hypothetical syllogism
(4)
disjunctive syllogism
**use the rules of inference to derive the conclusion Section 2: Rules of Implication II
Rules of Implication II
Conjunction Simplification Addition
constructive dilemma conjunction simplification addition Any two lines can be combined on one line with a conjunction as the main operator A conjunction can be separated into 2 lines if it is the main operator Another variable can be added to a line separated by a wedge as the main operator (1) (2) (3) (4)
**use the rules of implication to derive the conclusion Section 3: Rules of Replacement I Rules of Replacement DeMorgan’s Rule Commutativity Associativity Distribution Double Negation **use the rules to derive the conclusion
Pairs of logically equivalent statements can be substituted for eachother regardless of the main operator ~(P Q) = (~P v ~Q) ~(P v Q) = (~P ~Q) (P v Q) = (Q v P) (P Q) = (Q P) [ P (Q R) ] = [ (P Q) R ] [ P v (Q v R) ] = [ (P v Q) v R ] [P (Q v R)] = [(P Q) v (P R)] [P v (Q R)] = [(P v Q) (P v R)] P = ~~P
Section 4: Rules of Replacement II Transposition Implication Equivalence Exportation Tautology
(P > Q) = (~Q > ~P) (P > Q) = (~P v Q) (P Ξ Q) = [( P > Q) (Q > P)] (P Ξ Q) = [(P Q) v (~P ~Q) [(P Q) > R] = [P > (Q > R)] P = (P v P) P = (P P)
**use the rules to derive the conclusion
Chapter 3:Informal Fallacies
Section 1: Fallacies in General Fallacy Formal Fallacy Informal Fallacy
Defect in an argument that consists of something other than false premises alone One that can be identified merely by examining the form or structure of an argument One that can be identified only by examining the content of the argument
**distinguish between formal and informal fallacies, or if none exists at all Section 2: Fallacies of Relevance Fallacy of Relevance Appeal to Force
Premises are logically irrelevant to the conclusion; ay appear psychologically relevant “Argumentum ad Bacculum” appeal to the stick arguer poses a conclusion to the audience and tells them either explicitly or implicitly that some harm will come
Appeal to Pity Argument from Compassion Appeal to the People
Direct Approach
Indirect Approach
Bandwagon Appeal to Vanity Appeal to Snobbery
Argument Against the Person
Ad Hominem Circumstantial Ad Hominem Abusive
to him/her if they do not accept the conclusion “Argumentum ad Misericordiam” arguer attempts to support a conclusion merely by evoking pity from the audience argument from compassion The pity actually applies to a victim “Argumentum ad Populum” uses the desires of the reader or listener to accept a conclusion Direct and Indirect Approach Appeal to the people; arguer addresses a large crowd and uses emotions and enthusiasm to get them to support him/her Appeal to the people; arguer aims his appeal at individuals in a crowd bandwagon appeal to vanity appeal to snobbery Appeal to the peopleindirect you will be left behind if you do not use the product Appeal to the people indirect associated with admiration Appeal to the peopleindirect you will be elite or exclusive if you use the product “Argumentum as Hominem” occurs between 2 people one arguer attacks the person himself and not the actual argument ad hominem circumstantial ad hominem abusive tu quoque Argument against the person The opponent is affected by the outcome of the situation Argument against the person
Tu Quoque Accident Straw Man Missing the Point
Red Herring
One arguer is verbally abused by the other Argument against the person “you too”; makes one person appear hypocrital or arguing in bad faith General rule applied to a specific case that it was unintended to cover Arguer distorts opponents argument in order to make it more easy to attack “Ignoratio Elenchi” premises pertain to another conclusion, often vaguely related to the correct conclusion Arguer diverts the attention of the reader to another somewhat related subject; comes from red herring being used to throw hounds off track
**identify the fallacy of relevance Section 3: Fallacies of Weak Induction Fallacy of Weak Induction
Appeal to Unqualified Authority
Appeal to Ignorance
Hasty Generalization
The connection between the premises and conclusion are not strong enough to support the conclusion “Argumentum ad Verecundiam” arguer cites an unqualified authority of a witness that lacks credibility; the person might be an authority in more than one field, or it might be something where no one can be considered an authority “Argumentum ad Ignorantiam” issue usually involving something that is incapable of being proven or something that has not yet been proved There is reasonable likelihood that the sample is not representative of the group; take something that happens to a selection and applies it to the whole group
False Cause
Post Hoc Ergo Propter Hoc Non Causa Pro Causa Oversimplified Cause
Gambler’s Fallacy Slippery Slope Weak Analogy
The link between the premises and conclusion relies on an imagined causal connection post hoc ergo propter hoc non causa pro causa oversimplified cause gambler’s fallacy Temporally based false cause Nontemporally based false cause False cause; many/other factors actually cause something, but the arguer only gives credit to one False cause; the conclusion of an argument depends on the supposition that independent events in a game of chance are causally related Conclusion rests on an allegedly (usually unlikely) chain of events Analogy that is not strong enough to support the conclusion that is drawn
**identify the fallacy of weak induction Section 4: Fallacies of Presumption, Ambiguity, and Grammatical Analogy Fallacy of Presumption
Begging the Question
Complex Question False Dichotomy Suppressed Evidence
The premises presume what they purport to prove Arguer creates the illusion that inadequate premises provide adequate support for the conclusion (1) leave out false premises (2) conclusion restates premises (3) circular reasoning Two or more questions take the guise of one question eg: Are you still…? A disjunctive premise presents 2 unlikely alternatives as if they were the only ones available The arguer ignores a premise that would weaken or disprove their argument
Fallacy of Ambiguity Equivocation
Amphiboly Fallacy of Grammatical Analogy Composition
Division
Arise from some form of ambiguity in either the premises or conclusion The conclusion of an argument depends on the fact that a word or phrase is used, either explicitly or implicitly, in two different senses in the argument The arguer misinterprets an ambiguous statement and then draws a conclusion based on this faulty information These arguments are grammatically analogous to other good arguments The conclusion of an argument depends on the erroneous transference of an attribute from the parts of something onto the whole The conclusion of an argument depends on the erroneous transference of an attribute from the whole of something onto its parts
**identify the fallacies of presumption, ambiguity, and grammatical analogy Section 5: Fallacies in Ordinary Language **detect fallacies from regular daytoday conversation and publications
Chapter 9: Analogy and Legal and Moral Reasoning Section 1: Analogical Reasoning Analogue Primary Analogues Secondary Analogues Principals Involved in Evaluating Arguments from Analogy
items that the thing is being compared to Analogue that has similarity to the thing that is being compared Analogue that it is concluded that the second thing has because of how similar it is to the first one that has this trait (1) relevance of the similarities (2) number of similarities (3) nature and degree of disanalogy
(4) number of primary analogues (5) diversity among primary analogues (6) specificity of the conclusion
Relevance of the Similarities Number of Similarities Nature and Degree of Disanalogy Disanalogy Number of Primary Analogues Diversity Among the Primary Analogues Specificity of the Conclusion
Strongermore relevance (function and function Weakerless relevance (cosmetics and function) Strongermore primary analogues Weakerless primary analogues Strongerless disanalogies Weakermore disanalogies Differences between the 2 things being compared (eg: heavy and little traffic and good gas mileage) Strongermore primary analogues Weaker less primary analogues Strongergreater diversity Weakerless diversity Strongerless specific (“good”) Weakermore specific (“at least as good as”)
**evaluate the argument from analogy using the 6 principles **identify the primary and secondary analogues Section 2: Legal Reasoning **requires a more creative manipulation of previous instances Section 3: Moral Reasoning **identify the counter analogy (abortion argument)
Chapter 13: Hypothetical/Scientific Reasoning Hypothetical Method
(1) (2) (3)
occurrence of a problem formulating a hypothesis drawing implications from the hypothesis
(4)
testing the implications
**radium, Neptune, atmospheric pressure, spontaneous generation Empirical Hypothesis Theoretical Hypothesis
Hypothesis Acceptance Depends On: Adequacy Internal Coherence External Consistency Fruitfulness
Concern the production or occurrence of something that can be observed Concerns how something should be conceptualized; never proved, but confirmed on varying degrees (1) adequacy (2) internal coherence (3) external consistency (4) fruitfulness The extent to which a hypothesis fits the facts The extent to which the component ideas of a hypothesis are rationally connected Does the hypothesis agree/disagree with other, wellconfirmed hypotheses The extent to which a hypothesis suggests new ideas for future analysis and confirmation
Chapter 14: Science VS. Superstition A PRIORI Independent of sensory experience Math & Logic Universal hypotheses based on necessity and universality Analytic truths where the subject is contained in predicate
A POSTERIORI From a sensory experience Natural Sciences Empirical hypotheses based on contingent and particular things Some roses are red, so probably all roses are red
the science that evaluates arguments group of statements with one or more premises and one conclusion where the premises purport to prove the conclusion sentence that is either true or false whether a statement is true or false Statements that set forth the reason or evidence The statement that the evidence claims to support or imply therefore, thus, entails that, as a result, etc. Since, as indicated by, owing to, etc. Reasoning process expressed by an argument Meaning or information content of a statement Fundamental elements are terms; evaluated as good or bad depending on how the terms are arranged; Aristotle Involves possibility, necessity, belief, and doubt; Aristotle
**identify the premises and conclusion Section 2: Recognizing Arguments Factual Claim Inferential Claim Simple Noninferential Passage Warning
A claim that presents evidence or reason Claim that the alleged evidence supports or implies something Unproblematic passages that lack a claim that anything is being proven Simple noninferential passage; form of expression that is intended to put someone on guard against a dangerous
Piece of Advice
Statement of Belief / Opinion
Loosely Associated Statements
Report
Expository Passage
Illustration Argument from Example Explanation
Explanandum Explanans Conditional Statement Sufficient Condition Necessary Condition
or detrimental situation Simple noninferential passage; form of expression that makes a recommendation about some future decision or course of conduct Simple noninferential passage; expression about what someone happens to believe or think about something Simple noninferential passage; may be about the same general subject, but they lack a claim that one of them is proved by the others Simple noninferential passage; group of statements that convey information about some topic or event Kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence; the objective is not to prove the topic sentence, but to expand or elaborate on it Expression involving one or more examples that is intended to show what something means or how it is done; the example is not meant to prove anything Basically an illustration where the examples purport to prove something Expression that purports to shed light on an event or phenomenon; the event/phenomenon is usually accepted as a matter of fact statement of an explanation that describes the event/phenomenon being explained; the fact statement of an explanation that actually does the explaining; the explanation “if (antecedent), then (consequent)” A if the occurrence of A is all that is needed for the occurrence of B B if A cannot occur without the
occurrence of B **determine if it is an argument **where is the conclusion **if not an argument, what kind of nonargument **determine whether a condition is necessary or efficient Section 3: Deduction and Induction
Deductive Argument
Inductive Argument
Deciding b/w Deductive and Inductive Argument Based on Math
Argument from Definition
Categorical Syllogism Hypothetical Syllogism Disjunctive Syllogism Prediction
Argument incorporating that claim that it is impossible for the conclusion be false given that the premises are true; involve necessary reasoning; general to particular Argument incorporating that claim that it is improbable that the conclusion be false given that the premises are true; involves probabilistic reasoning; particular to general (1) occurrence of indicator words (2) actual strength of the inferential link between premises and conclusion (3) form or style of argumentation Deductive; the conclusion depends on some purely arithmetic or geometric computation or measurement Deductive; the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion Deductive; consists of 2 premises and 1 conclusion; each statement begins with “all”, “no”, or “some” Deductive; consists of 2 premises and 1 conclusion; “if…, then…” for one or both of its premises Deductive; consists of 1 premises and 1 conclusion; “either…or…” Inductive; proceeds from our knowledge of the past to a claim about the future
Argument from Analogy Generalization Argument from Authority Argument Based on Signs
Causal Inference Particular Statement General Statement
Inductive; depends on the existence of an analogy or similarity between 2 things or states of affairs Inductive; proceeds on the knowledge of a selected sample to some claim about the whole group Inductive; concludes that something is true because a presumed expert or witness has said that it is Inductive; proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes Inductive; proceeds from the knowledge of a cause to a claim about an effect, or conversely, from the knowledge of an effect to a claim about a cause Makes a claim about one or more particular members of a class Makes a claim about all of the members of a class
**determine whether it is deductive or inductive **what type of deductive argument **what type of inductive argument Section 4: Validity, Truth, Soundness, Strength, Cogency
Valid Argument
Invalid Argument
Sound Argument
Deductive arguments; impossibility of a false conclusion given true premises; the conclusion follows with necessity from the premises; **can have a valid argument with false premises Deductive arguments; possibility of a false conclusion given all true premises; conclusion does not follow necessarily from the premises; **can have an invalid argument with true premises and a true conclusion Deductive arguments; valid argument with all true premises
Unsound Argument Strong Argument Weak Argument Cogent Argument
Uncogent Argument
Deductive arguments; invalid argument, has one or more false premises, or both; Inductive argument; conclusion follows probably from the premises Inductive argument; conclusion does not follow probably from the premises Inductive argument; strong with all true premises that meet the total evidence requirement Inductive argument; weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these
**determine whether the deductive argument is (a) valid or invalid and (b) sound or unsound **determine whether the inductive argument is (a) strong or weak and (b) cogent or uncogent
Chapter 6: Propositional Logic Section 1: Symbols and Translation Operators/Connectives Propositional Logic Simple Statement Compound Statement Negation Conjunction Disjunction Implication
Symbols that express the relationships between two letters that represent statements Fundamental elements are whole statements (propositions) Does not contain any other statement as a component Contains at least one simple statement as a component ~ (tilde) not, it is not the case that (dot) and, also, moreover V (wedge) Ore, unless > (horseshoe)
Equivalence Biconditional Statement Main Operator WellFormed Formula
if…then…, only if… use “SUN” Ξ (triple bar) If and only if Expresses the relationship of material equivalence Operator that has as its scope everything else in the statement Syntactically correct arrangement of symbols
**translate into symbolic form Section 2: Truth Functions Truth Function Statement Variables Statement Form
Truth Table
Any compound proposition whose truth value is completely determined by the truth value of its components Lowercase letters that can stand for any statement Arrangement of statement variables and operators where substitution of statements in place of variables results in a statement Arrangement of truth values that shows every possible case of the truth value of the compound proposition
**identify the main operator **determine the truth values of statements Section 3: Truth Tables for Propositions Logically True / Tautologous Logically False / SelfContradictory Contingent
Classification of compound statements with all true values under the main operator Classification of compound statements with all false values under the main operator Classification of compound statements
Logically Equivalent Contradictory Consistent Inconsistent
with at least one true and one false value under the main operator Comparison of compound statements where both have the same truth value on each line Comparison of compound statements where they have opposite truth values on each line Comparison of compound statements where there is at least one line where they both have true truth values Comparison of compound statements where there is no line on which the truth values are both true
**classify the statement **compare the statements Section 4: Truth Tables for Arguments **a line in which all premises are true and there is a false conclusion indicates an invalid argument. **if there is no line where the above exists, then it is valid. Section 5: Indirect Truth Tables **working backwards from the truth value of the main operator, only looking at the lines where the conclusion is false, then among those only looking at lines where the premises are true. Section 6: Argument Forms and Fallacies
Argument Form
Disjunctive Syllogism Hypothetical Syllogism
Arrangement of statement variables and operators such that the uniform replacement of the variables by statements results in an argument P V Q ~P Q P>Q
Modus Ponens Modus Tollens
Affirming the Consequent
Denying the Antecedent
Constructive Dilemma Destructive Dilemma Grasping by the Horns Escaping between the Horns
Q>R P>R P>Q P . Q P>Q ~Q ~P Invalid P>Q Q . P Invalid P>Q ~P ~Q (N>I) (C>A) N V C I V A (P > Q) (R > S) ~Q V ~S ~P V ~R Prove the conjunctive premise false by proving either conjunct false Prove the disjunctive premise false
**identify the argument forms **difference between constructive and destructive dilemma **difference between grasping/escaping horns
Chapter 7: Natural Deduction in Propositional Logic Section 1: Rules of Implication I Rules of Implication I
Consist of basic arguments from whose premises imply their conclusion (1) modus ponens (2) modus tollens (3) hypothetical syllogism
(4)
disjunctive syllogism
**use the rules of inference to derive the conclusion Section 2: Rules of Implication II
Rules of Implication II
Conjunction Simplification Addition
constructive dilemma conjunction simplification addition Any two lines can be combined on one line with a conjunction as the main operator A conjunction can be separated into 2 lines if it is the main operator Another variable can be added to a line separated by a wedge as the main operator (1) (2) (3) (4)
**use the rules of implication to derive the conclusion Section 3: Rules of Replacement I Rules of Replacement DeMorgan’s Rule Commutativity Associativity Distribution Double Negation **use the rules to derive the conclusion
Pairs of logically equivalent statements can be substituted for eachother regardless of the main operator ~(P Q) = (~P v ~Q) ~(P v Q) = (~P ~Q) (P v Q) = (Q v P) (P Q) = (Q P) [ P (Q R) ] = [ (P Q) R ] [ P v (Q v R) ] = [ (P v Q) v R ] [P (Q v R)] = [(P Q) v (P R)] [P v (Q R)] = [(P v Q) (P v R)] P = ~~P
Section 4: Rules of Replacement II Transposition Implication Equivalence Exportation Tautology
(P > Q) = (~Q > ~P) (P > Q) = (~P v Q) (P Ξ Q) = [( P > Q) (Q > P)] (P Ξ Q) = [(P Q) v (~P ~Q) [(P Q) > R] = [P > (Q > R)] P = (P v P) P = (P P)
**use the rules to derive the conclusion
Chapter 3:Informal Fallacies
Section 1: Fallacies in General Fallacy Formal Fallacy Informal Fallacy
Defect in an argument that consists of something other than false premises alone One that can be identified merely by examining the form or structure of an argument One that can be identified only by examining the content of the argument
**distinguish between formal and informal fallacies, or if none exists at all Section 2: Fallacies of Relevance Fallacy of Relevance Appeal to Force
Premises are logically irrelevant to the conclusion; ay appear psychologically relevant “Argumentum ad Bacculum” appeal to the stick arguer poses a conclusion to the audience and tells them either explicitly or implicitly that some harm will come
Appeal to Pity Argument from Compassion Appeal to the People
Direct Approach
Indirect Approach
Bandwagon Appeal to Vanity Appeal to Snobbery
Argument Against the Person
Ad Hominem Circumstantial Ad Hominem Abusive
to him/her if they do not accept the conclusion “Argumentum ad Misericordiam” arguer attempts to support a conclusion merely by evoking pity from the audience argument from compassion The pity actually applies to a victim “Argumentum ad Populum” uses the desires of the reader or listener to accept a conclusion Direct and Indirect Approach Appeal to the people; arguer addresses a large crowd and uses emotions and enthusiasm to get them to support him/her Appeal to the people; arguer aims his appeal at individuals in a crowd bandwagon appeal to vanity appeal to snobbery Appeal to the peopleindirect you will be left behind if you do not use the product Appeal to the people indirect associated with admiration Appeal to the peopleindirect you will be elite or exclusive if you use the product “Argumentum as Hominem” occurs between 2 people one arguer attacks the person himself and not the actual argument ad hominem circumstantial ad hominem abusive tu quoque Argument against the person The opponent is affected by the outcome of the situation Argument against the person
Tu Quoque Accident Straw Man Missing the Point
Red Herring
One arguer is verbally abused by the other Argument against the person “you too”; makes one person appear hypocrital or arguing in bad faith General rule applied to a specific case that it was unintended to cover Arguer distorts opponents argument in order to make it more easy to attack “Ignoratio Elenchi” premises pertain to another conclusion, often vaguely related to the correct conclusion Arguer diverts the attention of the reader to another somewhat related subject; comes from red herring being used to throw hounds off track
**identify the fallacy of relevance Section 3: Fallacies of Weak Induction Fallacy of Weak Induction
Appeal to Unqualified Authority
Appeal to Ignorance
Hasty Generalization
The connection between the premises and conclusion are not strong enough to support the conclusion “Argumentum ad Verecundiam” arguer cites an unqualified authority of a witness that lacks credibility; the person might be an authority in more than one field, or it might be something where no one can be considered an authority “Argumentum ad Ignorantiam” issue usually involving something that is incapable of being proven or something that has not yet been proved There is reasonable likelihood that the sample is not representative of the group; take something that happens to a selection and applies it to the whole group
False Cause
Post Hoc Ergo Propter Hoc Non Causa Pro Causa Oversimplified Cause
Gambler’s Fallacy Slippery Slope Weak Analogy
The link between the premises and conclusion relies on an imagined causal connection post hoc ergo propter hoc non causa pro causa oversimplified cause gambler’s fallacy Temporally based false cause Nontemporally based false cause False cause; many/other factors actually cause something, but the arguer only gives credit to one False cause; the conclusion of an argument depends on the supposition that independent events in a game of chance are causally related Conclusion rests on an allegedly (usually unlikely) chain of events Analogy that is not strong enough to support the conclusion that is drawn
**identify the fallacy of weak induction Section 4: Fallacies of Presumption, Ambiguity, and Grammatical Analogy Fallacy of Presumption
Begging the Question
Complex Question False Dichotomy Suppressed Evidence
The premises presume what they purport to prove Arguer creates the illusion that inadequate premises provide adequate support for the conclusion (1) leave out false premises (2) conclusion restates premises (3) circular reasoning Two or more questions take the guise of one question eg: Are you still…? A disjunctive premise presents 2 unlikely alternatives as if they were the only ones available The arguer ignores a premise that would weaken or disprove their argument
Fallacy of Ambiguity Equivocation
Amphiboly Fallacy of Grammatical Analogy Composition
Division
Arise from some form of ambiguity in either the premises or conclusion The conclusion of an argument depends on the fact that a word or phrase is used, either explicitly or implicitly, in two different senses in the argument The arguer misinterprets an ambiguous statement and then draws a conclusion based on this faulty information These arguments are grammatically analogous to other good arguments The conclusion of an argument depends on the erroneous transference of an attribute from the parts of something onto the whole The conclusion of an argument depends on the erroneous transference of an attribute from the whole of something onto its parts
**identify the fallacies of presumption, ambiguity, and grammatical analogy Section 5: Fallacies in Ordinary Language **detect fallacies from regular daytoday conversation and publications
Chapter 9: Analogy and Legal and Moral Reasoning Section 1: Analogical Reasoning Analogue Primary Analogues Secondary Analogues Principals Involved in Evaluating Arguments from Analogy
items that the thing is being compared to Analogue that has similarity to the thing that is being compared Analogue that it is concluded that the second thing has because of how similar it is to the first one that has this trait (1) relevance of the similarities (2) number of similarities (3) nature and degree of disanalogy
(4) number of primary analogues (5) diversity among primary analogues (6) specificity of the conclusion
Relevance of the Similarities Number of Similarities Nature and Degree of Disanalogy Disanalogy Number of Primary Analogues Diversity Among the Primary Analogues Specificity of the Conclusion
Strongermore relevance (function and function Weakerless relevance (cosmetics and function) Strongermore primary analogues Weakerless primary analogues Strongerless disanalogies Weakermore disanalogies Differences between the 2 things being compared (eg: heavy and little traffic and good gas mileage) Strongermore primary analogues Weaker less primary analogues Strongergreater diversity Weakerless diversity Strongerless specific (“good”) Weakermore specific (“at least as good as”)
**evaluate the argument from analogy using the 6 principles **identify the primary and secondary analogues Section 2: Legal Reasoning **requires a more creative manipulation of previous instances Section 3: Moral Reasoning **identify the counter analogy (abortion argument)
Chapter 13: Hypothetical/Scientific Reasoning Hypothetical Method
(1) (2) (3)
occurrence of a problem formulating a hypothesis drawing implications from the hypothesis
(4)
testing the implications
**radium, Neptune, atmospheric pressure, spontaneous generation Empirical Hypothesis Theoretical Hypothesis
Hypothesis Acceptance Depends On: Adequacy Internal Coherence External Consistency Fruitfulness
Concern the production or occurrence of something that can be observed Concerns how something should be conceptualized; never proved, but confirmed on varying degrees (1) adequacy (2) internal coherence (3) external consistency (4) fruitfulness The extent to which a hypothesis fits the facts The extent to which the component ideas of a hypothesis are rationally connected Does the hypothesis agree/disagree with other, wellconfirmed hypotheses The extent to which a hypothesis suggests new ideas for future analysis and confirmation
Chapter 14: Science VS. Superstition A PRIORI Independent of sensory experience Math & Logic Universal hypotheses based on necessity and universality Analytic truths where the subject is contained in predicate
A POSTERIORI From a sensory experience Natural Sciences Empirical hypotheses based on contingent and particular things Some roses are red, so probably all roses are red
