Logic chapter 1 basics Flashcards
Define an argument in the context of logic.
An argument is a sequence of propositions where the initial propositions are premises or hypotheses, and the final proposition is the conclusion.
Describe the difference between deductive and inductive arguments.
A deductive argument is one where the conclusion necessarily follows from the premises, while an inductive argument provides reasonable grounds to accept the conclusion but does not guarantee it.
How does the truth of premises affect the acceptance of a conclusion in an argument?
If the premises are true and the argument is strong, one should accept the conclusion.
What is the primary focus of logic regarding arguments?
Logic is mostly interested in deductive arguments.
Describe an example of an inductive argument.
Premise 1: Billy has caught the bus on time every day so far. Premise 2: Billy is taking the bus tomorrow. Conclusion: Billy will likely catch the bus on time tomorrow.
Give an example of deductive argument.
A deductive argument is a form of reasoning where the conclusion necessarily follows from the premises. For example: Premise 1: All humans are mortal.
Premise 2: Socrates is a human. Conclusion: Socrates is mortal.
How does an inductive argument differ from a deductive argument?
An inductive argument draws a general conclusion based on specific observations, while a deductive argument provides a conclusion that is logically guaranteed if the premises are true.
Provide an example of a deductive argument involving integers.
Premise 1: x < y. Premise 2: y < z. Conclusion: x < z.
What is the significance of the premises in a deductive argument?
The premises in a deductive argument are crucial because they provide the foundation from which the conclusion is drawn, ensuring that if the premises are true, the conclusion must also be true.
Define truth-functional logic.
Truth-functional logic (TFL) is a mathematical system aimed at formalizing how to correctly reason about and construct good arguments involving propositions or declarative sentences.
Describe a proposition or declarative sentence.
A proposition or declarative sentence is a statement that can be evaluated as either true or false, making an assertion about reality or the properties of some system.
Identify types of sentences that are not considered propositions.
Questions, exclamations, and imperatives are not examples of propositions.
Explain the significance of propositions in logic.
Propositions are significant in logic because they serve as the basic units of meaning that can be evaluated for truth or falsity.
What is the role of assertions in propositions?
Assertions in propositions are statements that claim something about reality or the properties of a system, allowing them to be classified as true or false.
Describe the conditions for an argument to be considered invalid.
An argument is considered invalid if there exists a case where all premises A1, A2, …, An are true and the conclusion B is false.
