PL202: Introduction to Logic - The Scope and Foundations of Logic

Comprehensive practice flashcards covering logic definitions, standard form, deductive validity, inductive strength, counterexamples, soundness, and argument evaluation from Professor Brown's PL202 course.

How is logic formally defined in the lecture?

Logic is defined as the science of reasoning, with the primary aim of distinguishing good reasoning from bad reasoning.

How does logic differ from descriptive sciences such as physics and psychology?

Unlike physics (which describes how the physical world is) or psychology (which describes how people actually reason), logic is normative and prescriptive—it specifies how we should reason.

What is the logical definition of an argument?

An argument is a collection of sentences, one of which is called the conclusion and the rest of which are called premises.

In logic, what is a sentence, and how does it differ from questions or commands?

A sentence is a declarative statement capable of being true or false (possessing a truth value), whereas imperative commands, questions, and exclamations cannot be true or false.

What four structural features are required for an argument to be in standard form?

1. Premises are presented one per line; 2. A horizontal line is drawn under the final premise; 3. The conclusion is placed below the horizontal line; 4. Every line is numbered.

What are common examples of premise indicators and conclusion indicators?

Premise indicators include words like "since," "after all," and "as." Conclusion indicators include words like "therefore," "thus," "so," "hence," "consequently," "accordingly," and "it follows that."

In the Monty Python Argument Sketch, how does the man in glasses define an argument in contrast to contradiction?

He defines an argument as "an intellectual process" consisting of "a connected series of statements intended to establish a proposition," contrasting it with contradiction, which is merely "the automatic gainsaying of any statement the other person makes."

What is the formal definition of a deductively valid argument?

An argument is deductively valid (or valid) if and only if there is no possible scenario (or case) in which all the premises are true and the conclusion is false.

What does it mean to say that deductively valid arguments are "truth preserving"?

It means that the truth of the premises guarantees the truth of the conclusion; whenever all the premises are true, the conclusion must also be true.

Which combination of truth values between premises and conclusion is impossible in a valid deductive argument?

A valid argument can never have all true premises and a false conclusion.

Can a deductively valid argument have an actually false conclusion?

Yes. For example: "1. Either Professor Brown is a philosopher or she is a lawyer. 2. She's not a philosopher. 3. So she's a lawyer." The argument is valid because if the premises were true, the conclusion would have to be true, even though in reality the conclusion is false.

Why is an argument with contradictory premises (e.g., "1. It is raining. 2. It is not raining. 3. Therefore, dinosaurs are not extinct.") considered logically valid?

Because the premises contradict each other, there is no possible scenario where all the premises are true at the same time; therefore, there is no possible scenario where all premises are true and the conclusion is false.

What is a counterexample in deductive logic?

A counterexample is a possible scenario or case in which all of an argument's premises are true while its conclusion is false, proving that the argument is invalid.

What is the standard of goodness for an inductive argument, and how is it defined?

An inductive argument is good if it is strong, meaning it is plausible, reasonable, or probable to accept the conclusion if the premises are accepted, though the premises do not guarantee the conclusion with absolute certainty.

How does enumerative induction differ from explanatory reasoning (inference to the best explanation)?

Enumerative induction moves from observed specific instances to a broader generalization or future instance (e.g., snowing every recorded January in Michigan implies it will snow next January), while explanatory reasoning infers a hypothesis that best explains observed evidence (e.g., seeing food mess on the counter and inferring a daughter made a late-night snack).

What is the formal definition of soundness?

An argument is sound if and only if it is deductively valid and all of its premises are actually true.

Why do logicians focus primarily on validity rather than soundness?

Determining soundness requires empirical investigation to check whether premises are factually true in the actual world, which is the domain of specific sciences and not the job of a logician.

What are the three steps required to construct an "adequate explanation" (informal proof) of whether an argument is valid?

Step 1: State clearly whether the claim is correct or incorrect; Step 2: Explicitly state the definition of the key logical term(s) (such as validity); Step 3: Spell out every inferential step showing how the definition connects to the conclusion.

In Alexander Hamilton's argument in Federalist Papers, No. 80, what indicator phrase introduces the conclusion?

The phrase "it will follow that" serves as the conclusion indicator.

In logic, what type of formal derivation method is represented in this figure?

A formal proof using a natural deduction system.

What argument is implied in this Garfield comic strip, and why is its written transcription not in standard form?

The comic implies the argument: 1. It is never a party until Jon arrives; 2. Jon has arrived; C. Therefore, it is a party. The transcribed version fails standard form because the lines are unnumbered and there is no horizontal line separating the final premise from the conclusion.