Deductive vs Inductive Reasoning
All apples grow on trees.
Fruit grows on trees.
Therefore, apples are fruit.
This is deductive reasoning.
True or false?

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- Lime

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- anonymous

False. Indudctive means:generalization: reasoning from detailed facts to general principles. More than just fruits grow on trees so this is a generalization.

- anonymous

This is a syllogism with an incorrect minor premise, giving a conclusion which is not necessarily correct. The conclusion just happens to be correct, but it is not following logically.

- Lime

What would be a good example of deductive reasoning?

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- anonymous

@xKingx Notwithstanding what @tcarroll010 said, the above statement reasons from (what are assumed to be true) given premises to reach a conclusion. It would be deductive reasoning.

- Lime

I am easily confused between the two, although I know inductive reasoning is the process of making a conclusion based on a series of observations and deductive reasoning is the process of making a conclusion based on given facts or statements.

- anonymous

I'm no expert on trees and fruit, so bear with my lack of knowledge of horticulture. You could say something like: All fruit grows on plants (trees, bushes, whatever). Apples are fruit. Therefore, apples grow on plants. When you go from the general to the specific, you use deductive reasoning. The incorrect syllogism above is deductive, though faulty, so @geoffb is right about that. It's just that the question syllogism is poor, deducing wildly. Inductive is when you go from specifics to form general principles. Harder to do.

- anonymous

A good example of inductive reasoning is mathematical induction where you are trying to prove a formula for all "N". You show that something is true for N = 1, you assume it is correct for N = k, and then try to prove it is correct for N = k + 1.

- anonymous

@Lime , I just read your understanding of inductive and deductive, and while not wrong, I can see where it will leave you a little fuzzy. You use "conclusion" in both. If you go more well-defined and use "specific" and "general", you will be in better shape.

- Lime

All N's = 24.
K is half of N.
Therefore, K must equal 12.
Is this more specific than generalized? I'm sorry if I'm still not understanding it just yet..

- anonymous

Yes, that's specific and an example of deductive because you took general principles and drew a conclusion about something specific. Inductive, with an example outside math, would be the general conclusion you might draw about people, based on the culmination of your personal experience. The general conclusion might be in just one area, like your perception of what people do under one and only one circumstance (which might SOUND specific , but it's not). But it concerns just what is specific and what is general. If you say ALL people will panic if someone yells "Fire" in a crowded movie theater. That is still induction. It's because of ALL people, even though you are talking about a very restricted specific situation. You don't have to be right about your induction. It's yours, and all we're doing is describing the formation of it.

- Lime

That definitely clears up deduction for me. So, an induction, is basically an assumption. You can assume that all of the people will panic, and it may or may not be true.

- anonymous

Well, don't hurt yourself by thinking it's an assumption. In this particular example, it would be. On the other hand, if you were (hypothetically) able to observe EVERY human being and saw this behavior, it wouldn't be an assumption. It would be true in itself. My example of mathematical induction is not based on assumption ULTIMATELY. You assume the case for N = k. You then PROVE for N = k + 1, which ultimately wipes out the assumption on N=k because you essentially PROVE for N=k. Mathematical induction is a little tricky, but an excellent example of induction and drawing true, proven general conclusions that are solid and not assumptions.

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