Logic Final Review - Chapter Summaries
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Questions and Answers

What are the two types of logical analysis typically used in deductive arguments?

  • Premise analysis and truth value analysis.
  • Truth value analysis and valid vs. Invalid analysis.
  • Logical analysis and truth value analysis. (correct)
  • Which of the following is NOT considered a valid argument form?

  • Hypothetical Syllogism
  • Modus Ponens
  • Modus Tollens
  • Fallacy of affirming the consequent (correct)
  • What are the two types of categorical propositions?

  • Universal and Particular (correct)
  • Universal and Affirmative
  • Affirmative and Negative
  • What is the term called that represents the 'All' or 'Some' part of a categorical proposition that makes the connection between the subject class and the predicate class.

    <p>Quantifier</p> Signup and view all the answers

    What is a 'categorical syllogism'?

    <p>An argument that contains three different terms, each appearing twice; the first term refers to the subject of the argument, the second term refers to the predicate of the argument, and the third term, often referred to as the 'middle term', connects the first and second terms.</p> Signup and view all the answers

    In a categorical syllogism, the main operator is the ______.

    <p>Dot</p> Signup and view all the answers

    Which of the following is considered a 'formal fallacy'?

    <p>Illicit Major</p> Signup and view all the answers

    A 'natural deduction' is a method of proving arguments through the use of rules of inference

    <p>True</p> Signup and view all the answers

    The difference between a tautology and a self-contradiction is that a tautology is always true, while a self-contradiction is always false.

    <p>True</p> Signup and view all the answers

    The term 'propositional logic' typically refers to statements composed of simple propositions that are connected with logical operators, such as 'and', 'or', 'if...then', and 'if and only if'.

    <p>True</p> Signup and view all the answers

    What is a deductive argument that is impossible for the conclusion to be false, assuming the premises are true?

    <p>Valid argument</p> Signup and view all the answers

    What are the two requirements for a deductive argument to be sound?

    <p>The argument is valid AND all the premises are true.</p> Signup and view all the answers

    What are the two conditions that make a deductive argument unsound?

    <p>The argument is invalid OR the argument has at least one false premise.</p> Signup and view all the answers

    What type of argument is it when a conclusion is probably true if the premises are true?

    <p>Strong inductive argument</p> Signup and view all the answers

    What type of argument is it when the conclusion is either probably not true, or a true conclusion does not follow from the premises?

    <p>Weak inductive argument</p> Signup and view all the answers

    What are the two requirements for an inductive argument to be cogent?

    <p>The argument is strong AND all the premises are true.</p> Signup and view all the answers

    What are the two conditions that make an inductive argument uncogent?

    <p>The argument is weak OR the argument has at least one false premise.</p> Signup and view all the answers

    What is a group of statements where one statement (the conclusion) is claimed to follow from the others (the premises)?

    <p>Argument</p> Signup and view all the answers

    A sentence that is either true or false is called a statement.

    <p>True</p> Signup and view all the answers

    What is the information provided as support for a conclusion in an argument?

    <p>Premise(s)</p> Signup and view all the answers

    What is the systematic use of methods and principles to analyze, evaluate and construct arguments?

    <p>Logic</p> Signup and view all the answers

    What are the two possibilities of truth values for every statement?

    <p>True or false</p> Signup and view all the answers

    What is the term used by logicians to refer to the reasoning process expressed by an argument?

    <p>Inference</p> Signup and view all the answers

    What is the information content imparted by a statement?

    <p>Proposition</p> Signup and view all the answers

    What type of argument is it where a conclusion is claimed to follow necessarily from the premises?

    <p>Deductive argument</p> Signup and view all the answers

    What type of argument is it where a conclusion is claimed to be probably true if the premises are true?

    <p>Inductive argument</p> Signup and view all the answers

    A valid deductive argument is impossible for the conclusion to be false.

    <p>True</p> Signup and view all the answers

    An invalid argument is a deductive argument where the conclusion necessarily follows from the premises.

    <p>False</p> Signup and view all the answers

    What type of argument is it when the premises are true, the conclusion is probably true, and the argument is strong?

    <p>Cogent argument</p> Signup and view all the answers

    An uncogent argument is both weak and has at least one false premise?

    <p>True</p> Signup and view all the answers

    What is a compound statement that has two distinct statements, called disjuncts, joined by the word 'or'?

    <p>Disjunction</p> Signup and view all the answers

    A strong inductive argument is one with strong premises and a conclusion that is highly likely to be true.

    <p>True</p> Signup and view all the answers

    A weak inductive argument is one with weak premises and a conclusion that is highly likely to be true.

    <p>False</p> Signup and view all the answers

    What is an argument with missing premises, missing conclusions, or both?

    <p>Enthymemes</p> Signup and view all the answers

    What is a conditional statement that is used to imply an argument?

    <p>Rhetorical conditional</p> Signup and view all the answers

    What is the first step in diagramming an argument?

    <p>Number the statements as they appear in the argument.</p> Signup and view all the answers

    What is a diagram that shows the relationship between a single premise and a single conclusion?

    <p>Simple diagram</p> Signup and view all the answers

    What is a diagram that reveals the occurrence of independent premises?

    <p>Convergent diagram</p> Signup and view all the answers

    What type of argument is it when an attack is made on the alleged character flaws of the person making the argument, rather than the argument itself?

    <p>Ad hominem abusive</p> Signup and view all the answers

    What is a fallacious argument that relies on a mistaken use of the principle behind making a generalization?

    <p>Generalization Fallacy</p> Signup and view all the answers

    What type of fallacious argument is it when a rule or generalization is inappropriately applied to a situation?

    <p>Rigid application of a generalization</p> Signup and view all the answers

    What type of fallacious argument is it when a generalization is argued from a small sample that is unlikely to represent the population?

    <p>Hasty Generalization</p> Signup and view all the answers

    What type of fallacious argument is it when an attribute of the individual parts of something is mistakenly transferred to the whole?

    <p>Composition</p> Signup and view all the answers

    What type of fallacious argument is it when an attribute of the whole is mistakenly transferred to the individual parts of something?

    <p>Division</p> Signup and view all the answers

    What type of fallacious argument is it when a causal connection is assumed to exist between two events, when there is no actual causal connection between them, or they assumed causal connection is unlikely to exist?

    <p>False Cause</p> Signup and view all the answers

    What type of fallacious argument is it when the first event is assumed to have caused the second, just because it happened before?

    <p>Post Hoc</p> Signup and view all the answers

    What fallacious argument is it when a series of occurrences is connected, such that a first event is claimed to directly lead to a second, and so on, until a final unwanted situation is reached?

    <p>Slippery slope</p> Signup and view all the answers

    Fallacies of unwarranted assumptions are arguments that assume the truth of some unproved or questionable claim.

    <p>True</p> Signup and view all the answers

    What type of fallacious argument is it when a premise is simply reworded in the conclusion?

    <p>Begging the question</p> Signup and view all the answers

    What is a fallacious argument that relies solely on the arousal of a strong emotional state or psychological reaction to gain acceptance of a conclusion?

    <p>Fallacies based on emotional appeals</p> Signup and view all the answers

    What kind of fallacious argument is it when an argument manipulates a psychological need or desire, such as the desire to belong to a popular group, to gain acceptance for the conclusion?

    <p>Appeal to the people</p> Signup and view all the answers

    The appeal to pity fallacy is a type of fallacious argument that relies on the threat of harmful consequences to gain acceptance?

    <p>False</p> Signup and view all the answers

    What type of fallacious argument is it when an argument relies on a threat of harmful consequences to gain acceptance for a conclusion?

    <p>Appeal to fear or force</p> Signup and view all the answers

    What type of fallacious argument is it when an argument relies on the opinions of people who either have no expertise, training, or knowledge relevant to the issue at hand, or whose testimony is not trustworthy?

    <p>Appeal to an unqualified authority</p> Signup and view all the answers

    What is a false dichotomy, a type of fallacious argument?

    <p>It is when an argument is made as if only two options are possible, where in fact there are more options.</p> Signup and view all the answers

    What is a mistake in reasoning that occurs in ordinary language and concerns the content of the argument rather than its form?

    <p>Informal fallacy</p> Signup and view all the answers

    What is an immediate argument created by changing the quality of a given proposition, and replacing the predicate term with its complement?

    <p>Obversion</p> Signup and view all the answers

    What is an immediate argument formed by interchanging subject and predicate terms of a proposition?

    <p>Conversion</p> Signup and view all the answers

    What is an immediate argument formed by switching subject and predicate terms in a proposition and replacing both with their complements?

    <p>Contraposition</p> Signup and view all the answers

    What is an argument that has exactly two premises and a conclusion?

    <p>Syllogism</p> Signup and view all the answers

    What is a syllogism constructed entirely of categorical propositions?

    <p>Categorical syllogism</p> Signup and view all the answers

    What is the subject of the conclusion in a categorical syllogism?

    <p>Minor term</p> Signup and view all the answers

    What is the predicate of the conclusion in a categorical syllogism?

    <p>Major term</p> Signup and view all the answers

    What is the term that occurs only in the premises of a categorical syllogism?

    <p>Middle term</p> Signup and view all the answers

    What is the first premise of a categorical syllogism?

    <p>Major premise</p> Signup and view all the answers

    What is the second premise of a categorical syllogism?

    <p>Minor premise</p> Signup and view all the answers

    What fallacy occurs in a categorical syllogism when the middle term in a categorical syllogism is distributed in both premises, but not the conclusion?

    <p>Undistributed middle</p> Signup and view all the answers

    What fallacy occurs when a categorical syllogism has a negative premise and an affirmative conclusion?

    <p>Affirmative conclusion/negative premise</p> Signup and view all the answers

    What special type of enthymemes involves missing parts, which are intermediate conclusions, each of which becomes a premise in the next link in the chain?

    <p>Sorites</p> Signup and view all the answers

    What type of arguments have logical equivalences between their statement forms?

    <p>Replacement rules</p> Signup and view all the answers

    What type of arguments are rules of inference that apply only to an entire line?

    <p>Implication rules</p> Signup and view all the answers

    What are the statements that follow from the application of a rule of inference in a logical proof?

    <p>Justifications</p> Signup and view all the answers

    What is the application of a set of small-scale logical maneuvers or devices in a proof?

    <p>Tactic</p> Signup and view all the answers

    What is the overarching strategy in a logical proof that defines the overall goal and direction of the proof?

    <p>Strategy</p> Signup and view all the answers

    What is the rule of inference that allows replacing logically equivalent expressions within a proof?

    <p>Principle of replacement</p> Signup and view all the answers

    De Morgan's rule is a replacement rule.

    <p>True</p> Signup and view all the answers

    The transposition rule is a replacement rule.

    <p>True</p> Signup and view all the answers

    The exportation rule is an implication rule.

    <p>False</p> Signup and view all the answers

    What is a special kind of proof where the conclusion is inferred from the premises by following rules of inference?

    <p>Natural deduction</p> Signup and view all the answers

    What is the logical operation where the combination of two statements is true only if both statements are true?

    <p>Conjunction</p> Signup and view all the answers

    What is the logical operation where the combination of two statements is true if at least one of the statements is true?

    <p>Disjunction</p> Signup and view all the answers

    A statement that is necessarily false is called a tautology.

    <p>False</p> Signup and view all the answers

    Logic is the systematic use of methods and principles for the evaluation of arguments.

    <p>True</p> Signup and view all the answers

    What is a compound statement made up of two conditionals, one indicated by the word 'if' and the other by the phrase 'only if'?

    <p>Biconditional</p> Signup and view all the answers

    What is a statement that has the entire well-formed formula in its scope?

    <p>Main operator</p> Signup and view all the answers

    What are two types of fallacy that occur in deductive arguments?

    <p>Formal and informal fallacies</p> Signup and view all the answers

    What is a statement that has exactly one premise?

    <p>Immediate argument</p> Signup and view all the answers

    What is an argument that has more than one premise?

    <p>Mediate argument</p> Signup and view all the answers

    What is a set of statements that have identical truth tables under the main operator?

    <p>Logically equivalent statements</p> Signup and view all the answers

    What is an argument that is sometimes true and sometimes false?

    <p>Contingent statement</p> Signup and view all the answers

    A formal fallacy is restricted to deductive arguments?

    <p>True</p> Signup and view all the answers

    Modus ponens is an invalid argument form?

    <p>False</p> Signup and view all the answers

    Modus tollens is a valid argument form?

    <p>True</p> Signup and view all the answers

    An invalid argument form that is a formal fallacy is called modus tollens?

    <p>False</p> Signup and view all the answers

    The fallacy of denying the antecedent is a formal fallacy?

    <p>True</p> Signup and view all the answers

    The truth value of a truth-functional proposition is uniquely determined by the truth values of its components.

    <p>True</p> Signup and view all the answers

    Statement forms can stand for any arrangement of logical operators and statement variables?

    <p>True</p> Signup and view all the answers

    Argument forms are arrangements of logical operators and statement variables that result in a logical argument?

    <p>True</p> Signup and view all the answers

    A truth table is a method for determining the truth values for a truth-functional compound proposition.

    <p>True</p> Signup and view all the answers

    What are the logical operators that are used to translate ordinary language statements into propositional logic?

    <p>Logical Operators</p> Signup and view all the answers

    A compound statement can have both simple statements and logical operators?

    <p>True</p> Signup and view all the answers

    In propositional logic, the word 'not' is used to denote negation?

    <p>True</p> Signup and view all the answers

    A simple statement can contain logical operators.

    <p>False</p> Signup and view all the answers

    The 'horseshoe' symbol is used to denote conditional statements?

    <p>True</p> Signup and view all the answers

    What is a statement that is a statement letter or an arrangement of operators and statement letters, such that the result is a grammatically correct symbolic expression?

    <p>Well-formed formula</p> Signup and view all the answers

    The scope of an operator refers to the statements that it governs.

    <p>True</p> Signup and view all the answers

    What is a statement that is always true?

    <p>Tautology</p> Signup and view all the answers

    An exclusive disjunction is true when both disjuncts are true.

    <p>False</p> Signup and view all the answers

    An inclusive disjunction is true only when one, but not both, of the disjuncts is true.

    <p>False</p> Signup and view all the answers

    The word 'if' typically precedes the antecedent of a conditional statement?

    <p>True</p> Signup and view all the answers

    An event is a sufficient condition for another event to be realized when the first event ensures that the second event is realized?

    <p>True</p> Signup and view all the answers

    An event is a necessary condition for another event to be realized when the first event is essential for the second event to be realized?

    <p>True</p> Signup and view all the answers

    A biconditional is a compound statement made up of two conditionals, one indicated by the word 'if' and the other by the phrase 'only if'.

    <p>True</p> Signup and view all the answers

    A well-formed formula is a compound statement, where an arrangement of operators and statement letters results in a grammatically correct symbolic expression.

    <p>True</p> Signup and view all the answers

    Each operator in a logical expression governs a unique scope of statements.

    <p>True</p> Signup and view all the answers

    The main operator is the operator that governs the entire well-formed formula.

    <p>True</p> Signup and view all the answers

    A truth-functional proposition is one where its truth-value is uniquely determined by the truth values of its components.

    <p>True</p> Signup and view all the answers

    Study Notes

    Logic Final Review - Chapter Summaries

    • Chapter 1: What Logic Studies
      • Deductive Arguments: A valid deductive argument is one where, assuming the premises are true, the conclusion cannot be false. An invalid argument is possible for a false conclusion, even if premises are true. A sound argument is a valid argument with all true premises. An unsound argument is either invalid or has at least one false premise.
      • Inductive Arguments: Strong inductive arguments are where the conclusion is probable if the premises are true, otherwise it is weak. Cogent arguments are strong with all true premises, and uncogent arguments are weak or have at least one false premise.
      • Argument: A group of statements where one is a conclusion and others are the premises intended to support it.
      • Statement: A sentence either true or false.
      • Logic: The systematic use of methods and principles for evaluating/constructing arguments.
      • Truth Values: Every statement either true or false. Each statement has a truth value.
      • Proposition: The meaning or information content of a statement.
      • Inference: The process of reasoning in an argument.
      • Premise Indicators: Words/phrases like "because," "since," etc.
      • Conclusion Indicators: Words/phrases like "therefore," "thus," etc.
      • Explanation: Provides reasons for an event's occurrence, not an argument.

    Logic Final Review - Chapter 2 & 3 Summaries

    • Chapter 2:

      • Inferential Claims: Passages making a reasoning process explicit or implicit are inferential claims. If expressed, it's explicitly, if implied, it is implicitly.
      • Explanation: Shows reasons for how or why something occurred, not an argument, so it's non-inferential.
      • Truth Value Analysis: Determines the strength with which premises support the conclusion.
      • Logical Analysis: Determines the strength with which the premises support the conclusion.
    • Chapter 3:

      • Diagramming Arguments: Depicts relationship between premises and conclusion in an argument.
      • Simple Diagram: Displays connection between one premise and one conclusion.
      • Convergent Diagram: Shows independent premises supporting a conclusion.
      • Dependent Premises (Linked Diagram): Premises working together to support the conclusion, where falsity of one weakens the others' support.
      • Divergent Diagram: Displays a single premise supporting multiple conclusions.
      • Serial Diagram: One argument's conclusion becomes a premise in another.

    Logic Final Review - Chapter 4 Summaries

    • Chapter 4: Informal Fallacies
      • Personal Attacks: Argument rejected due to attack on the person, not the argument's merit.
        • Ad hominem abusive: Attacking someone's character instead of their argument.
        • Ad hominem circumstantial: Argument rejected due to person's circumstances.
        • Poisoning the well: Attacking someone before they can present their case.
        • Tu quoque: Avoiding issue by claiming the other person is a hypocrite.
      • Emotional Appeals: Relying solely on emotional arousal to manipulate.
        • Appeal to the people: Exploiting the desire to belong to a group for support.
        • Appeal to pity: Using pity or mercy to support a conclusion.
        • Appeal to fear or force: Using threats to force acceptance of action.
      • Weak Inductive Argument Fallacies: Incorrect use of generalization principle.
        • Rigid Application: Using a generalization inappropriately.
        • Hasty Generalization: Generalizing based on insufficient evidence
        • Composition: Mistakenly transferring attributes of parts to the whole or members of a class to the class itself.
        • Division: Mistakenly transferring attributes of the whole to the parts or attributes of a class to its members.

    Logic Final Review - Chapter 5 Summaries

    • Chapter 5: Categorical Propositions
      • Class: A group of objects.
      • Categorical Proposition: Relates two classes.
      • Subject Term: The term which comes first in a categorical proposition.
      • Predicate Term: Term that comes second.
      • Quantifiers: Words describing quantity (all, no, some).
      • Quality: Affirmative or negative (e.g., all S are P; some S are not P).
      • A-proposition: All S are P.
      • E-proposition: No S are P.
      • I-proposition: Some S are P.
      • O-proposition: Some S are not P.

    Logic Final Review - Chapter 6 Summaries

    • Chapter 6: Categorical Syllogisms
      • Syllogism: A deductive argument with two premises and a conclusion.
      • Categorical Syllogism: A syllogism composed entirely of categorical propositions.
      • Minor Term: Subject term of the conclusion.
      • Major Term: Predicate term of the conclusion.
      • Middle Term: Appears only in the premises.
      • Major Premise: Contains the major term.
      • Minor Premise: Contains the minor term.
      • Rules of Categorical Syllogisms: Several rules to ensure validity.
      • Methods of Conversion, Obversion, Contraposition: Techniques to change categorical propositions.
      • Formal Fallacies:
      • Undistributed Middle: Middle term undistributed in both premises
      • Illicit Major: Major term undistributed in conclusion, but distributed in a premise.
      • Exclusive Premises: Both premises are negative.
      • Affirmative Conclusion/Negative Premise: Negative premise but affirmative conclusion.
      • Negative Conclusion/Affirmative Premises: Affirmative premises but negative conclusion.
      • Existential fallacy: Particular conclusion from two universal premises

    Logic Final Review - Chapter 7 Summaries

    • Chapter 7: Propositional Logic
      • Logical Operators: Symbols representing logical connections between statements (not, and, or, if-then, if and only if).
      • Simple Statements: Statements with no other statements or operators.
      • Compound Statements: Statements with logical operators linking simpler statements.
      • Conjunction (dot): Connecting with "and."
      • Disjunction (wedge): Connecting with "or."
      • Conditional (horseshoe): Connecting with "if-then."
      • Biconditional (triple bar): Connecting with "if and only if."

    Logic Final Review - Chapter 8 Summaries

    • Chapter 8: Natural Deduction
      • **Rules of Inference: ** Methods to derive conclusions from premises, including Modus Ponens (MP),Modus Tollens (MT), Hypothetical Syllogism (HS), and Disjunctive Syllogism (DS).
      • Replacement Rules: Logically equivalent statements, including De Morgan's rules, Commutation, Association, Distribution, Double Negation.
      • Proofs: Sequences of steps using inference rules to validly derive a conclusion.
      • Strategies: Methods for finding proofs (e.g. Simplification, Conjunction, Addition).

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