Abduction and induction, as conceptualized by Charles Sanders Peirce, are two different modes of reasoning. Here's a summary of their differences:

Abduction:

• Definition: Abduction is the process of forming an explanatory hypothesis. It is the reasoning of coming up with a theory that explains observed phenomena.
• Purpose: Used to generate hypotheses and provide possible explanations. It’s the starting point for further investigation.
• Example: If you notice that the lawn is wet, you might abductively hypothesize that it has rained.
• Nature: Preliminary and speculative. The hypothesis needs to be tested further by other methods of reasoning like deduction or induction.

Induction:

• Definition: Induction is the process of reasoning from specific cases to general principles. It involves inferring a general law or proposition from observed instances.
• Purpose: Used to establish the plausibility of hypotheses based on empirical evidence.
• Example: After observing that rain has been associated with a wet lawn several times, you might induce that rain generally leads to a wet lawn.
• Nature: Empirical and probabilistic. Inductive conclusions are considered more reliable than abductive hypotheses, but they are not as certain as deductive conclusions.

Summary:

• Abduction focuses on generating hypotheses, while induction focuses on verifying hypotheses through empirical observations.
• Abduction is often the creative leap to form a new idea, whereas induction evaluates the strength of a hypothesis based on accumulated data.

For more depth into Peirce's philosophy of reasoning, you can refer to resources like the Stanford Encyclopedia of Philosophy: Charles Sanders Peirce's Reasoning.