SAT R&W 5: Inferences

Inference

Inference is the process of reaching a conclusion from evidence, premises, and reasoning. In science, it connects observations or data to claims about phenomena that may not be directly observed.

How do premises, inferences, and conclusions relate in an argument?

Premises are propositions accepted or assumed as starting points. An inference uses those premises to support a conclusion, which is the resulting proposition.

What is logical reasoning?

Logical reasoning is the process of using premises and evidence to reach a conclusion in a rigorous way. An argument consists of propositions serving as premises and a conclusion supported by them.

Deductive reasoning

Deductive reasoning applies general rules or premises to reach a logically necessary conclusion about a specific case. If the argument is valid and its premises are true, the conclusion must be true.

Inductive reasoning

Inductive reasoning uses particular observations or evidence to support a broader, general conclusion. Its conclusion is probable rather than logically certain and can be revised by new evidence.

Abductive reasoning

Abductive reasoning infers the explanation that best accounts for the available evidence. Unlike deduction, it does not guarantee certainty; unlike induction, it is focused on explaining observations.

How do deduction, induction, and abduction differ in the certainty and purpose of their conclusions?

Deduction seeks logically certain consequences from premises. Induction generalizes from observations, while abduction proposes the most plausible explanation for observations; both are uncertain and evidence-dependent.

Validity

An argument is valid when its conclusion follows logically from its premises because of the argument's form. Validity does not depend on whether the premises or conclusion are actually true.

Soundness

A deductive argument is sound if it is valid and all of its premises are true. A sound argument necessarily has a true conclusion.

Can a deductive argument be valid even when its conclusion is false?

Yes. If at least one premise is false, a valid argument can produce a false conclusion; validity concerns only whether the conclusion follows from the premises.

Why is the argument form 'All A are B; all C are B; therefore all C are A' invalid?

Sharing a category B does not establish that C is contained within A. For example, apples and bananas can both be fruits without bananas being apples.

Syllogism

A syllogism is a structured deductive argument commonly containing two premises and a conclusion. Its validity depends on the logical relationship among the statements, not on the subject matter.

Logical consequence

A statement is a logical consequence of premises when it must be true whenever those premises are true. Deductive inference aims to identify such necessary consequences.

Fallacy

A fallacy is an error in reasoning that makes an inference unreliable or invalid. Fallacies may arise from an incorrect logical form or from misleading assumptions and reasoning habits.

Why can additional evidence change an inductive or abductive conclusion?

Inductive and abductive conclusions are supported by evidence rather than guaranteed by logic. New observations can increase, decrease, or overturn the plausibility of a generalization or proposed explanation.

What is an analogical inference?

An analogical inference uses similarities between two cases to suggest that they may share another characteristic. The inference is only as strong as the relevance and extent of the similarities.

How can a reader distinguish a reasonable inference from unsupported speculation?

A reasonable inference is directly supported by details in the text and requires only a modest logical step. Unsupported speculation introduces information, motives, or outcomes that the text neither states nor sufficiently implies.

How should a reader draw a conclusion from implicit information?

Combine relevant details from the passage, account for their context, and choose the conclusion that those details most strongly support. Do not treat an unstated possibility as established merely because it is conceivable.

How should a reader make a prediction based on a passage?

Project the pattern, claim, or situation established by the passage into the most immediate likely development. The prediction should follow from the text's evidence rather than from outside assumptions.

What makes a non-deductive inference strong?

A non-deductive inference is strong when its premises make the conclusion highly likely, even though they do not guarantee it. The strength depends on the relevance, amount, and reliability of the evidence.

How should an inference question in a reading passage be evaluated?

Identify the relevant textual evidence, determine what conclusion it supports, and reject choices that go beyond the evidence, contradict the passage, or rely mainly on outside knowledge.

What is the difference between a text's evidence and an inference drawn from it?

Evidence consists of the explicit facts, descriptions, or claims presented in the text. An inference is the conclusion a reader reasonably derives by connecting that evidence.