Question

GEOMETTRY: how do you tell the difference from inductive reasoning and deductive reasoning?

Answer 1

mikeaaro...



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Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. It is used to ascribe properties or relations to types based on tokens (i.e., on one or a small number of observations or experiences); or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is employed, for example, in using specific propositions such as:

This ice is cold.
A billiard ball moves when struck with a cue.
...to infer general propositions such as:

All ice is cold.
All billiard balls struck with a cue move.
Inductive reasoning has been attacked several times. Historically, David Hume denied its logical admissibility. During the 20th century, most notably Karl Popper and David Miller have disputed the existence, necessity and validity of any inductive reasoning, even of probabilistic (bayesian) ones.
Deductive reasoning was developed by Aristotle, Thales, Pythagoras, and other Greek philosophers of the Classical Period (600 to 300 B.C.). Aristotle, for example, relates a story of how Thales used his skills to deduce that the next season's olive crop would be a very large one. He therefore bought all the olive presses and made a fortune when the bumper olive crop did indeed arrive.[5]

Deductive reasoning is dependent on its premises. That is, a false premise can possibly lead to a false result, and inconclusive premises will also yield an inconclusive conclusion. [6]

Alternative to deductive reasoning is inductive reasoning. Many incorrectly teach that deductive reasoning goes from general information to specific information and that inductive reasoning travels in the opposite direction. This is not accurate. Deductive reasoning applies general principles to reach specific conclusions, whereas inductive reasoning examines specific information, perhaps many pieces of specific information, to derive a general principle. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. Once Newton induced that principle, he applied it deductively to make many predictions. Galileo applied it to deduce the existence of a planet disturbing's Uranus's orbit, a planet that would eventually be named Neptune.[7][not in citation given]

Both types of reasoning are routinely employed. One difference between them is that in deductive reasoning, the evidence provided must be a set about which everything is known before the conclusion can be drawn. Since it is difficult to know everything before drawing a conclusion, deductive reasoning has little use in the real world. This is where inductive reasoning steps in. Given a set of evidence, however incomplete the knowledge is, the conclusion is likely to follow, but one gives up the guarantee that the conclusion follows. However it does provide the ability to learn new things that are not obvious from the evidence.

Deductive reasoning is supported by deductive logic (which is not quite the same thing).

For example:

All apples are fruit.
All fruits grow on trees.
Therefore all apples grow on trees.
Or

All apples are fruit.
Some apples are red.
Therefore some fruit is red.
Intuitively, one might deny the major premise or the conclusion; yet anyone accepting the premises accepts the conclusion.

Deductive reasoning should be distinguished from the related concept of natural deduction, an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs.

Answer 2

Inductive reasoning is a form of reasoning that makes generalizations based on individual instances.

Example:
Everybody I know drinks beer.
Therefore, everybody on Earth drinks beer.

(Note: Inductive reasoning allows for the possibility that the conclusion is false, even when the premise (or premises) are true.)

Deductive reasoning attempts to show that a conclusion necessarily follows from a set hypotheses that are assumed true.

Example (Classic):
All men are mortal.
Socrates is a man.
Therefore, Socrates is motal.