Basic Concepts in Logic
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Questions and Answers

Which of the following forms of argument is invalid?

  • Modus Ponens
  • Disjunctive Syllogism
  • Affirming the Consequent (correct)
  • Denying the Antecedent

    • A valid argument cannot have any false premises.

    False

    What is the structure of a Modus Ponens argument?

    If A, then B. A. So, B.

    If it is raining, then the ground is _____.

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

    Which of the following is a valid conclusion in the statement: 'If Tom lives in Kingston, then Tom lives in Jamaica. Tom lives in Kingston.'

    <p>Tom lives in Jamaica.</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Valid Argument = An argument where if the premises are true, the conclusion must also be true Invalid Argument = An argument that does not guarantee a true conclusion even if the premises are true Affirming the Consequent = An invalid form of argument where the consequent is affirmed to conclude the antecedent Modus Ponens = A valid form of argument involving conditional statements</p> Signup and view all the answers

    The conditional statement 'If A, then B' suggests that B must be true if A is true.

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

    Provide an example of a conditional statement.

    <p>If it is sunny, then I will go for a walk.</p> Signup and view all the answers

    What type of argument guarantees the conclusion based on the premises?

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

    An invalid argument has premises that guarantee the conclusion.

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

    What is included in a valid argument?

    <p>True premises and true conclusion.</p> Signup and view all the answers

    If the premises are true and the conclusion is false, then the argument is _____ .

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

    Match the types of statements with their outcomes:

    <p>True premises + True conclusion = Valid Argument False premises + True conclusion = Invalid Argument True premises + False conclusion = Invalid Argument Unknown truth value = Unknown Argument</p> Signup and view all the answers

    Which of the following can be a part of a logically sound argument?

    <p>True premises and true conclusion</p> Signup and view all the answers

    The Power of Logic is an example of a logic book that contains sensible examples.

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

    What is a scenario where premises do not guarantee the conclusion?

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

    What is Modus Tollens an example of?

    <p>Denying the Consequent</p> Signup and view all the answers

    Denying the Antecedent is a valid argument form.

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

    What is the conclusion when using Modus Tollens if the premises are: 'If A then B' and 'Not B'?

    <p>Not A</p> Signup and view all the answers

    In the statement 'If you are healthy or wealthy, then you are lucky', the negation would lead to the conclusion that you are not _____.

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

    Which argument form is defined as: If A, then B; If B, then C; So, if A, then C?

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

    Modus Tollens leads to the conclusion that if the first implication is false, the second implication must also be false.

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

    Provide an example of a conclusion derived from the Modus Tollens form using the statement: 'If Tom lives in Kingston, then Tom lives in Jamaica.'

    <p>Tom does not live in Kingston.</p> Signup and view all the answers

    Match the fallacies with their descriptions:

    <p>Modus Tollens = Denying the Consequent Denying the Antecedent = Invalid argument form Hypothetical Syllogism = Transitional reasoning Affirming the Consequent = Invalid reasoning</p> Signup and view all the answers

    What is the logical form of the arguments presented in the examples?

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

    In Disjunctive Syllogism, if 'Either A or B' is true and 'Not A' is true, then 'B' must also be true.

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

    Provide an example of a Disjunctive Syllogism.

    <p>Either it is raining or it is sunny. It is not raining, so it is sunny.</p> Signup and view all the answers

    The statement 'A or B' is called the __________ of the simpler statements 'A' and 'B'.

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

    What does the disjunction 'A or B' typically imply in its exclusive sense?

    <p>A or B but not both.</p> Signup and view all the answers

    Match the terms related to Disjunctive Syllogism with their definitions:

    <p>Disjunction = A statement that asserts either one of two options is true Negation = The opposite of a true statement Disjuncts = The simpler statements that make up a disjunction Conclusion = The result that follows from premises</p> Signup and view all the answers

    If it is true that 'Either A or B', but 'Not B' is true, then we conclude __________.

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

    Explain why the argument 'If Tom loves his dog, then Tom will walk his dog every day' is valid.

    <p>Because it follows the structure of hypothetical syllogism where the conclusion logically follows from the premises.</p> Signup and view all the answers

    In disjunctive syllogism, which of the following statements is an example of the form used?

    <p>Either A or B; If A, then C; If B, then D; therefore, either C or D.</p> Signup and view all the answers

    The statement 'Either you keep your promise or you don’t keep your promise' is an example of a constructive dilemma.

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

    What is the conclusion of the argument: 'If Jenny is a neurologist, then she is a doctor. Jenny is NOT a doctor.'?

    <p>So, Jenny is a neurologist.</p> Signup and view all the answers

    A constructive dilemma typically starts with a disjunction stating 'Either A or B' followed by two conditional statements: 'If A, then C' and 'If B, then _____.'

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

    Match each premise with its conclusion in an argument context.

    <p>If A, then C = So, C or D If B, then D = So, either C or D If Jenny is NOT a doctor = So, Jenny is a neurologist If A, then B = So, A</p> Signup and view all the answers

    Study Notes

    Basic Concepts in Logic

    • Logic is the study of methods for evaluating whether premises of an argument adequately support or provide good evidence for its conclusion.
    • Logic is roughly the study of methods for evaluating arguments.
    • Logic is the science of reasoning.
    • An argument is a set of statements where some statements are intended to support another.
    • Arguments can be split into premises and conclusion.
    • Premises are statements offered as evidence, conclusions are the claims being supported.

    Dissecting Definition of Logic

    • A statement is a declarative sentence that is either true or false.
    • Examples of statements include: Some people are smart, No one is smart, Some people weigh up to 400 pounds.
    • Statements are not suggestions, commands, or questions.

    Deductive and Inductive Arguments

    • Deductive arguments aim to guarantee the conclusion.
    • Inductive arguments aim to make the conclusion probable.
    • Examples of deductive arguments:
      • All philosophers like logic. Ned is a philosopher. So, Ned likes logic.
    • Examples of inductive arguments:
      • Most philosophers like logic. Ned is a philosopher. So, Ned likes logic.
      • Some Americans work in business. Donald Trump is an American. So, Donald Trump works in business.

    Valid and Invalid Arguments

    • A valid argument is a deductive argument where if the premises are true, the conclusion must also be true.
    • Valid arguments guarantee the conclusion from the truth of the premises; but validity doesn’t imply truth.
    • Valid, but not sound arguments, are those whose premises are true but the conclusion isn't guaranteed.
    • Invalid arguments are those where the premises may be true or false, but the conclusion is not guaranteed.
    • A sound argument is one that is valid and all premises are true.
    • Unsound arguments are invalid arguments or arguments in which at least one premise is false.

    Valid and Invalid Arguments & Truth

    • An argument is valid if the truth of the premises guarantees the truth of the conclusion.
    • True premises and true conclusion = Valid
    • False premises and false conclusion = Valid

    Sound & Unsound Arguments

    • A sound argument is a valid argument in which all the premises are true.
    • An unsound argument is an argument that is either invalid or valid but at least one premise is false.

    Evaluation of Inductive Arguments

    • Strong arguments have true premises but don't guarantee their conclusion.
    • Weak arguments are those with false premises leading to an unguaranteed conclusion.

    Arguments Summary

    • Valid arguments with all true premises are sound.
    • Invalid arguments are always unsound.

    Categories of Unsound Arguments

    • Category 1: A valid argument with at least one false premise.
    • Category 2: An invalid argument with all true premises.
    • Category 3: An invalid argument with at least one false premise.

    Conclusion

    • Arguments are not true nor false, they can be valid, invalid, sound, or unsound.
    • Statements are either true or false.
    • Premises and conclusions can be either true or false.

    Forms and Validity

    • Logic is the art of making a good argument and there are two main ways: deductive and inductive reasoning.
    • Deductive arguments are assessed using the famous valid forms method.

    Deductive Arguments

    • The famous valid forms method is used to identify good deductive arguments.

    Understanding Conditional Statements

    • A conditional statement is an “if-then” statement.
    • The if-clause is the antecedent.
    • The then-clause is the consequent.
    • Examples: If Tom goes to school, then Tom gets an education

    Argument Form

    • An argument form is a pattern of reasoning.
    • Argument forms consist of statements that can be valid or invalid.

    Summary of Valid Forms

    • Modus Ponens: If A, then B. A. So, B.
    • Modus Tollens: If A, then B. Not B. So, Not A.
    • Hypothetical Syllogism: If A, then B. If B, then C. So, if A, then C.
    • Disjunctive Syllogism: Either A or B. Not A. So, B or (Either A or B. Not B. So, A)
    • Constructive Dilemma: Either A or B. If A, then C. If B, then D. So, either C or D.

    Valid Argument Form

    • A valid argument form has no invalid substitution instances.
    • All substitution instances are valid arguments and if the premises are true, the conclusion is also true.
    • An argument form with at least one invalid substitution instance is invalid.

    The Famous Forms Method

    • Step 1: Identify component statements and label each with a capital letter.
    • Step 2: Rewrite the argument using capital letters, eliminating stylistic variants.
    • Step 3: Check if the pattern of reasoning is in our list of famous forms.

    Modus Ponens

    • Affirming the antecedent; If A, then B; A; So, B.

    Modus Tollens

    • Denying the consequent; If A, then B; Not B; So, Not A.

    Hypothetical Syllogism

    • This is a three-step argument with two premises and one conclusion: If A, then B; If B, then C; So, if A, then C.

    Disjunctive Syllogism

    • Either A or B; not A; so B. Or (Either A or B; not B; so A)

    Constructive Dilemma

    • Combines conditional and disjunctive statements; Either A or B; If A, then C; If B, then D; So, either C or D.

    Counterexample & Invalidity

    • An invalid argument form has some invalid substitution instances.
    • A counterexample to an argument form is a substitution instance where premises are true but conclusion is false.

    The Counterexample Method

    • Step 1: Identify the argument’s form.
    • Step 2: Find a substitution instance where the premises are true but the conclusion is false.
    • Step 3: Substitute the English statements for the capital letters.

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    Unit 1 - Basic Concepts in Logic PDF

    Description

    This quiz explores the fundamental principles of logic, including the evaluation of arguments, the structure of statements, and the distinctions between deductive and inductive reasoning. Test your understanding of how premises support conclusions and sharpen your critical thinking skills.

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