If we want to seek new knowledge of facts about the world, we must rely on…

Concept: An inference is called ampliative when its conclusion asserts more than its premises already contain, and non-ampliative when the conclusion only unpacks information the premises already carry. Only an ampliative inference can add fresh factual content about the world; a non-ampliative one preserves truth perfectly but tells us nothing we did not already have.

Application: The stem asks which kind of reasoning we must rely on to obtain new knowledge of facts about the world. Reasoning that starts from observed particular instances and generalises past them is ampliative: from "every sample of this metal observed so far expanded on heating" it reaches "this metal expands on heating", a claim whose content goes beyond the observations recorded. That surplus content is exactly the new factual knowledge the stem is after, which is why the empirical sciences rest on it. The price paid is that the conclusion is probable rather than certain. The reasoning with this character is Inductive.

How the options differ:

• Inductive — argues from observed particulars to a broader claim; the conclusion carries more content than the premises and is probable rather than guaranteed.

• Deductive — argues from premises to a conclusion already implicit in them; it is truth-preserving and certain, but factually it states nothing that the premises did not.

• Demonstrative — the classical name for conclusive proof from premises already accepted, as in a geometrical demonstration; being a form of deduction, it is non-ampliative in the same way.

• Physiological — a term describing the functions and processes of living organisms, such as respiration and circulation; it names a subject matter within biology.

Cross-check: Ask whether the conclusion could turn out false while the premises stay true. For "All men are mortal; Socrates is a man; therefore Socrates is mortal" that is impossible — and correspondingly nothing new about the world has been learnt. For "every sample tested expanded on heating; therefore this metal expands on heating" it remains possible, precisely because the conclusion reaches past the evidence. The reasoning that risks error is the reasoning that gains new factual knowledge, so the answer is Inductive.