Expert I Inductive And Deductive Reasoning (11) In Math 20-2 Flashcards
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Explain the difference between inductive and deductive reasoning
Inductive reasoning is a ‘bottom-up’ approach, where specific observations lead to generalized conclusions, while deductive reasoning is a ‘top-down’ approach, starting from a general statement and narrowing down to specific scenarios.
Deductive reasoning, or deduction, is making an inference based on widely accepted facts or premises
Deductive begins from principles, which can then be applied to specific instances. Inductive begins from specific instances, which can then be generalized into principles.
Deductive: A men are mortals (principle). Socrates is a man. Therefore, Socrates is mortal (instance).
Inductive: Socrates died. Plato died. Pretty much every human has died before reaching 110 or so (instances). So we can conclude that all humans are mortal (principle).
One result of this is that, as you said, inductive reasoning almost always deals with probable statements. And deductive reasoning deals with conclusions that are guaranteed to be true if their premises are true.
deductive = from Latin deductivus “derivative,” from deduct-, past-participle stem of deducere “to lead down, derive” (in Medieval Latin, “infer logically”), from de “down” (see de-) + ducere “to lead” (from PIE root *deuk- “to lead”).
de + duct + ive
down + lead + adjective marker
Inductive
early 15c., “bringing on, inducing,” from Old French inductif or directly from Late Latin inductivus “serving to induce or infer,” from induct-, past participle stem of Latin inducere (see induce). As a term in logic, “based on induction” (q.v.), from 1764.
from Latin inducere “lead into, bring in, introduce, conduct; persuade; suppose, imagine,” from in- “into, in, on, upon” (from PIE root *en “in”) + ducere “to lead” (from PIE root *deuk- “to lead”). Meaning “to bring about” in any way (in reference to a trance, a fever, etc.) is from early 15c.; sense of “to infer by reasoning” is from 1560s.
