Understanding Logic: Deductive vs. Inductive Reasoning

The question asks about the type of logic that uses known results, definitions, and rules of inference to prove something. Let's look at the two types mentioned: Deductive logic and Inductive logic.

What is Deductive Logic?

Deductive logic is a type of reasoning where a conclusion is reached based on known facts, definitions, axioms, and rules of logic. If the premises (the known facts or statements) are true, then the conclusion derived through valid deductive steps must also be true. It moves from general principles to specific conclusions. Think of it as following a set of rules or a recipe precisely to get a guaranteed outcome.

Key characteristics of Deductive logic:

• Uses known information (premises) that are assumed to be true.
• Applies established definitions and rules of inference.
• Aims to prove a conclusion that necessarily follows from the premises.
• If the premises are true and the reasoning is valid, the conclusion is guaranteed to be true.

An example of deductive logic:

• All men are mortal. (Premise 1 - Known fact)
• Socrates is a man. (Premise 2 - Known fact)
• Therefore, Socrates is mortal. (Conclusion - Necessarily follows)

What is Inductive Logic?

Inductive logic is a type of reasoning where a general conclusion is drawn from specific observations or instances. It moves from specific observations to a general hypothesis or theory. The conclusion reached through inductive reasoning is probable, but not necessarily guaranteed, even if the specific observations are true.

Key characteristics of Inductive logic:

• Based on specific observations or data.
• Infers a general pattern, rule, or theory.
• The conclusion is a generalization and is probable, not certain.
• Used extensively in science to form hypotheses based on experimental data.

An example of inductive logic:

• Every swan I have ever seen is white. (Specific observations)
• Therefore, all swans are white. (General conclusion - This could be proven false by seeing a black swan)

Comparing Deductive and Inductive Logic

Let's compare the two types of logic based on how they reach conclusions:

Answering the Question

The question describes a logic that "uses known results, definitions and rules of inference to prove something". Looking at our definitions and comparison:

• Deductive logic starts with known results, definitions, and uses rules of inference (like logical rules) to reach a conclusion that is proven (necessarily true if the premises are true).
• Inductive logic starts with specific observations and infers a probable general conclusion. It doesn't "prove" something in the same way that deductive logic does; it suggests a likely truth.

Therefore, the description perfectly matches Deductive logic.

Based on this analysis:

• Statement I: Deductive logic - This matches the description.
• Statement II: Inductive logic - This does not match the description.

The logic described is only Deductive logic (I).