Phil 105 New Chapter 4 Entailment

Q: What does a deductively valid argument mean?

A: A deductively valid argument means that the premises entail the conclusion, not pretending to look like entailment.

Q: What does entailment refer to in deductive arguments?

A: Entailment refers to a condition in maximum suppositional strength deductive arguments where the premises entail the conclusion.

Q: What does entailment ensure about the premises and conclusion?

A: Entailment ensures that the premises guarantee the truth of the conclusion, meaning the conclusion must be true.

Q: When premises entail the conclusion, what assumption is made about knowledge of the world?

A: When premises entail the conclusion, we assume that we know everything about the world.

Q: What are implicit premises?

A: Implicit premises are additional premises that are obvious truths of the world and are taken for granted in an argument.

Q: Why is it hard to recognize entailment in complex arguments?

A: If an argument is too complex, it is hard to recognize if the premises entail the conclusion.

Q: What is one helpful way to test entailment in complex arguments?

A: For complex arguments, assuming the premises are true can help see if they guarantee the conclusion.

Q: How can complex arguments be analyzed to test entailment?

A: Complex arguments can be broken down into steps to see if each guarantees an interim conclusion, ensuring that the original premises entail the conclusion.

Q: What does flipping the argument mean?

A: Flipping the argument means to start with the conclusion and end with the premises.

Q: What is another meaning of flipping the argument?

A: Flipping the argument also means to consider that if the conclusion is false, then the premises cannot be true at all.

Q: What does it mean if the premises are true but the conclusion is false when flipping an argument?

A: It means that the premises do not entail the conclusion.

Q: What does it mean when two arguments have the same form?

A: Two arguments have the same form when the general recipe for an argument is the same.

Q: What is a sentinel connective?

A: A sentinel connective refers to two individual clauses being connected to form a bigger sentence.

Q: What is logical form?

A: Logical form refers to the general building blocks of an argument.

Q: Why is modus ponens deductively valid?

A: Modus ponens always has a deductively valid argument based on the position of the sentences and the use of conditionals.

Q: Can an argument be deductively valid without having a valid logical form?

A: Yes, some arguments are deductively valid despite lacking a deductively valid form, because logical form is used to identify validity, not prove it.

Q: What is a hypothetical syllogism?

A: Hypothetical syllogism is a deductively valid argument form derived from applying modus ponens twice.

Q: Why can’t logical forms like hypothetical syllogism have degrees of certainty?

A: Because modifying them with degrees of certainty decreases the chances of recognizing a deductively valid argument.

Q: When is the negation of a sentence true or false?

A: The negation of a sentence can be true or false depending on whether the original sentence is true or false.

Q: What does the truth of a disjunction depend on?

A: The disjunction of a sentence depends on whether one statement is true or one statement is false.

Q: Why is disjunctive syllogism deductively valid?

A: Disjunctive syllogism is deductively valid because if one option is false, you can conclude that the other sentence is true.

Q: How can entailment be verified through similar words?

A: Entailment can be verified by seeing if similar words from the same grammatical category form an argument with either true premises and false conclusion or false premises and true conclusion.

Q: Is the form of an argument always deductively valid?

A: No, the form is not always deductively valid because some new arguments do not create true premises and true conclusions.

Q: What are counterexamples in arguments?

A: Counterexamples occur when one feature in a particular category is not true.

Q: Does the inability to find counterexamples prove deductive validity?

A: No, the inability to come up with counterexamples does not mean that an argument is deductively valid.

Q: What is one reason to overlook deductive validity?

A: One reason to overlook deductive validity is focusing only on whether it has a deductively valid logical form.

Q: What is a second reason to overlook deductive validity?

A: A second reason to overlook deductive validity is poor premises.

Q: Can false or partially true premises still guarantee the truth of the conclusion?

A: Yes, even false or partially true premises can guarantee the truth of the conclusion.

Q: What is a third reason to overlook deductive validity?

A: A third reason to overlook deductive validity is that some arguments are too complex or tricky to recognize suppositional strength or logical form.

Q: How do predicate forms help in evaluating arguments?

A: Predicate forms help decouple our evaluation of the conclusion from our evaluation of the support provided by the premises.

Q: What are deductively invalid forms?

A: Deductively invalid forms are fallacies that trick us into believing an argument has a logical form when it does not.

Q: What is affirming the consequent?

A: Affirming the consequent is a deductively invalid logical form that reverses modus ponens, where P is inferred.

Q: What is denying the antecedent?

A: Denying the antecedent is a deductively invalid logical form that reverses modus tollens, where Not Q is inferred.

What is the structure of Modus Ponens?

§  If P, then Q

§  P

§  Therefore Q

What is the structure of Modus Tollens?

·      If P, then Q

·      Not Q

·      Therefore, not P

What is the structure for Hypothetical Syllogism?

·      If P, then Q

·      Q then R

·      Therefore, P then R

What are some characteristics of disjunctions?

o   Doesn’t use conditionals

o   Uses disjunctions (words that basically state two statements)

o   Can be considered a binary connective

o   Considers both options/statements or considers one statement/option only

What is disjunction syllogism? What’s the structure

o   A combination of Disjunctions and Hypothetical Syllogism

§  Structure

·      If not P or Q

·      Then not Q (or P)

·      Therefore, not P (or Q)

What is deductively valid predicate form? How is it used?

o   A type of logical form that depends on the deeper meanings of the sentences

§  Can be organized by creating variables for the phrases and names

·      Then creating a coherent predicate form

o   Adding new words in place of your variables

What is the purpose of counterexamples ?

§  To prove an invalid deductive argument

·      And show that a general universal claim is false

What must a counterexample have?

True premises and false conclusions

What is an important consideration with flipping the argument?

 the premises could be true and the conclusion is false which means that the premises does not entail the conclusion