What does logic have to say about induction vs deduction?

Answer 1

Induction moves from individual event to principles. For example, suppose you Goose #1 go fly south for the winter, then goose #2 goes, then #3 goes, etc. The more you observe the event, the more you might be entitled to state the general principle, "Geese fly south for the winter." However, all you need is one disconfirming case, that one goose who stayed behind, for the principle to be wrong.

Logicians tried for quite a long time to create a form of induction that would lead to true conclusions, but only met with varying degrees of failure. However, induction is the process by which we all form concepts; i.e., we witness several events, extract a common theme, and hold it as generally true of similar events.

Deduction moves the other way around, from specific statements to an answer. Deduction strives for validity, which is defined as, "A set of statements such that, if the premises are true, the conclusion can not be false." For example:

Premise 1 - All "A"s are "B"s.
Premise 2 - All "B"s are "C"s.
Conclusion - All "A"s are "C"s.

It doesn't matter what A, B, and C are. The argument is valid.

A "Sound" argument in deductive logic is a valid argument with true premises.

Valid argument that is not sound:
1 - All trains are insects.
2 - All insects are forms of transportation.
C - All trains are forms of transportation.

Notice that, though the conclusion is true, the premises are not. This argument would have to be discared, even though it's valid.

Here's a commonly-cited sound argument (valid with true premises):
1 - All men are mortal.
2 - Socrates is a man.
C - Socrates is mortal.

Because deductive arguments use such a powerful form, they're very popular.

Answer 2

Induction mean thinking on your own, figuring things out for yourself. Logic is the basis for inductive reasoning. Deductive reasoning on the other hand is just accepting what is being told or communicated to you and believing it without questioning. If logic is used, all reasoning is inductive.
An example of each: Religon is deductive because one is expected to believe, just because it is in the bible or stated by a clergy, without questioning. Science is inductive because no assumptions are allowed in true scientific study. The facts must be determined by use of logic.

Answer 3

Most people who are unwilling to do their homework will not do well in school. Therefore you will not do well in school. That's induction.

All people who are unwilling to do their homework will not do well in school. You are unwilling to do your homework. Therefore you will not do well in school. That's deduction.

Answer 4

they are tools used to move time in the growth of a mind.