Logic 1000- critical thinking

Define proposition. Give two examples and two non-examples.

A proposition is something that can be true or false.

Examples: “The moon is made of rock.” (proposition), “She will come home at 5pm.” (proposition).

Non-examples: “Where are you going?” (question), “Please close the door.” (command). Propositions are declarative sentences that assert a statement that can be evaluated for truth value.

 Identify premise(s) and conclusion in this: “Although the forecast was bad, they went ahead with the picnic because they believed the sun would come out.”

Premise(s): “The forecast was bad”, “they believed the sun would come out”.

Conclusion: “They went ahead with the picnic.”In this argument, the premises provide reasons for the conclusion, supporting the decision to proceed with the picnic despite the poor forecast.

 Rewrite and put into standard form: “Given that the battery is dead, the car won’t start, so we need to take it to the mechanic.”

1. Premise: The battery is dead.
   
   

Premise: If the battery is dead, then the car won’t start.

Conclusion: We need to take it to the mechanic 

What question helps you decide whether a passage is an argument or explanation?

“Is the author trying to convince me of something new, or asking me to believe something? (Argument) — or is the author trying to show why something already believed is the case? (Explanation)”.An effective question to determine this is: "Does the passage present reasoning aimed at persuading me to accept a conclusion?" If yes, it indicates an argument; if no, it likely serves as an explanation.

For each example, classify as inductive or deductive and say whether the conclusion necessarily follows (if premises true) or is just probable.

1. “All whales are mammals. All mammals have lungs. Therefore, all whales have lungs.”
   
   

“In the last 50 years, this lake has frozen over every winter. Therefore, it will freeze over next winter.”

1. Deductive — conclusion necessarily follows (valid).
   
   

2. Inductive — conclusion probable, but not guaranteed.

True or False — In inductive arguments, true premises always guarantee a true conclusion. Explain.

False. Inductive arguments never guarantee the conclusion; they make it likely. Even with all true premises, conclusion can still be false.Inductive arguments involve premises that support a conclusion with varying degrees of probability, but they do not ensure certainty. Therefore, true premises can lead to a false conclusion.

What is validity? How is it different from truth?

Validity refers to the logical structure of an argument, where if the premises are true, the conclusion must also be true. Truth, on the other hand, pertains to the actual accuracy of the premises; a valid argument can have false premises but still maintain a correct logical form.

what are some premise indicator words

Words or phrases used to signal the presence of a premise in an argument, such as "because," "since," and "for". Premise indicator words include phrases like "due to," "given that," and "assuming that."

conclusion indicator words

Words or phrases that signal the presence of a conclusion in an argument, such as "therefore," "thus," and "hence." Conclusion indicator words also include phrases like "so," "as a result," and "consequently."

define “proposition” and “argument,” and explain how they differ.

A proposition is a declarative statement that can be either true or false. An argument, on the other hand, consists of a set of propositions, where one or more propositions (premises) support another proposition (the conclusion). The key difference is that a proposition is a single statement, whereas an argument involves a relationship between multiple statements.

give one example of a simple proposition and one of a compound proposition

A simple proposition is "The sky is blue," while a compound proposition is "The sky is blue and it is raining."

the compound proposition joins two simple statementsusing logical connectors like "and" or "or."

distinguish between inductive and deductive reasoning with examples

Inductive reasoning involves drawing general conclusions from specific observations, such as noticing that the sun rises every day and concluding it will rise tomorrow. Deductive reasoning starts with a general principle and applies it to a specific case, like stating that all humans are mortal and concluding that Socrates, a human, is mortal.

A deductive argument guarantees its conclusion:

“All mammals have lungs. Dolphins are mammals. ∴ Dolphins have lungs.”

An inductive argument only makes the conclusion probable:

“Every dolphin I’ve seen has been gray. ∴ All dolphins are gray.”

what makes a deductive argument sound

A deductive argument is sound if it is both valid (the conclusion follows necessarily from the premises) and all premises are true.

Explain the difference between an argument and an explanation.

An argument seeks to prove that something is true, while an explanation assumes it is true and shows why it is true.

Example:

Argument: “The streets are wet, so it must have rained.”

Explanation: “The streets are wet because it rained.”

What does it mean for an argument to be valid according to the 15th edition of Introduction to Logic?

A deductive argument is valid if and only if it is impossible for all the premises to be true and the conclusion false at the same time.

Identify the fallacy: “You can’t trust her opinion on taxes — she doesn’t even have a job.”

This statement commits the ad hominem fallacy, as it attacks the person's character or circumstances rather than addressing the argument itself.

Identify the fallacy: “That idea came from the government, so it must be corrupt.”

Genetic Fallacy – dismissing a claim because of its origin rather than its content.

 What does the Two Wrongs Fallacy involve?

It attempts to justify a wrongful action because someone else committed a similar wrong.

Example: “I stole their notes because they borrowed mine without asking.”

Explain the relationship between truth and validity.

Truth applies to individual propositions, while validity applies to the logical relation between them.

A valid argument can have false premises; validity is about the structure, not content.

Only sound arguments guarantee a true conclusion.