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Algebra (all content)

Course: Algebra (all content)>Unit 18

Lesson 9: Deductive and inductive reasoning

Inductive & deductive reasoning

Sal discusses the difference between inductive and deductive reasoning by considering a word problem. Created by Sal Khan and Monterey Institute for Technology and Education.

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• What is inductive
• Inductive reasoning is when you start with true statements about specific things and then make a more general conclusion. For example: "All lifeforms that we know of depend on water to exist. Therefore, any new lifeform we discover will probably also depend on water." A conclusion drawn from inductive reasoning always has the possibility of being false. If the possibility that the conclusion is wrong is remote, then we call it a strong inductive argument. If there's a reasonably good chance the conclusion is wrong, then we call it a weak inductive argument.
• Is most science based on inductive or deductive reasoning?
• I believe inductive as most facts are unknown
• R.I.P. that 2020 population
• Is it fair to say that deduction is a theorem and induction is a postulate?
• No. Both theorems and postulates are elements of deductive reasoning. Inductive reasoning is noticing a pattern and making an educated guess based on that pattern.

Here's the test. Do we know for certain that the population of the town will be higher in 2020 than it was in 2010? No -- the fact that the population has risen every ten years in the past is interesting, but if the factory in town shuts down or there is a natural disaster, then the population might well drop. Of course, you wouldn't be very observant if you failed to notice that the population has been steadily rising and that it is reasonable to assume that it won't stop now. But since there is no airtight logical proof that the population will go up, our reasoning is inductive and not deductive.
• Doesn't the example in this video involve Inductive AND Deductive reasoning? Because inductive reasoning is used to make a generalization about the rate of population change. But then Deductive reasoning is used to draw specific information from the generalization just made. What am I missing?
• I do see your point there. Thing is, you've got to remember what deductive reasoning is; I guess the easiest way of putting it would be that it's the reverse of inductive. Inductive reasoning starts from the bottom to the top (in this case, 1950 to 2020), and deductive reasoning goes from the top back to the bottom.
We can only make a generalization about the future, but to make a prediction about history would use deductive reasoning since we know there was a decrease every year. However, I do like your thinking!
• How do you use both types of reasoning
• so deductive reasoning is using the given facts to make new more understandable facts?
• You got it. When we study deductive reasoning, we learn that we have to be careful to avoid guessing or new ambiguity, we must stick to fact.
(1 vote)
• So basically inductive reasoning has to be proved with facts and deductive reasoning is already proved but adds info?