Deductive thinking

What is deductive thinking ? Elementary my dear Watson!

Deduction happens when we decide that, no matter what, it is impossible that the conclusion we are considering is false, given that all the premises of our argument are true.

For example, if we know for a fact that San Diego is west of Denver, and we know that Denver is west of Detroit and New York, then we can infer with deductive certainty that San Diego is west of New York.

Mathematics uses deduction. Algebra and geometry are exercises in deduction. Playing a game can also be an exercise in deduction, and so can filling out an income tax return. Both games and tax returns are things that require us to apply strict rules and laws. One of the ways that we know that little children can reason deductively is to observe that they can play games that require following rules, even playground rules.

An example of a deductive argument might be as follows : All men are mortal. George Bush is a man. Therefore, George Bush is mortal.

We should be able to answer the following questions:

   1. What are the premises?
   2. What is the conclusion?
   3. Are the premises true or false?
   4. Do the premises provide sufficient support for the conclusion?

With deductive thinking:
* if the premise is true
* the conclusion must also be true.
We can say that deductive thinking refers to the use of scientific processes by people (in everyday life as well as scientific investigation). General rules can arise from deduction but there are potential pitfalls in relation to the validity of premises upon which these rules are based.
 
  In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.

Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories.

  Deductive reasoning, sometimes called deductive logic, is reasoning which constructs or evaluates deductive arguments. In logic, an argument is said to be deductive when the truth of the conclusion is purported to follow necessarily or be a logical consequence of the premises and (consequently) its corresponding conditional is a necessary truth. Deductive arguments are said to be valid or invalid, never true or false. A deductive argument is valid if and only if the truth of the conclusion actually does follow necessarily (or is indeed a logical consequence of) the premises and (consequently) its corresponding conditional is a necessary truth. If a deductive argument is not valid then it is invalid. A valid deductive argument with true premises is said to be sound; a deductive argument which is invalid or has one or more false premises or both is said to be not sound (unsound).

 Deductive logic

An argument is valid when it is impossible for its premises to be true and its conclusion to be false, or, to put it another way, if the premises were true the conclusion would have to be true, or again, the conclusion follows necessarily from the premises. An argument can be valid even though the premises are false. Note, for example, that the conclusion of the following argument would have to be true if the premises were true, (even though they are, in fact, false):

    All fire-breathing rabbits live on Mars
    All humans are fire-breathing rabbits
    (Therefore,) all humans live on Mars

The argument, however, is not sound. In order for a deductive argument to be sound, the premises must be true.

A theory of deductive reasoning known as categorical or term logic was developed by Aristotle but was superseded by propositional (sentential) logic and predicate logic.

Deductive reasoning is sometimes contrasted with inductive reasoning. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. In the 19th century, Adams and LeVerrier applied Newton's theory (general principle) to deduce the existence, mass, position, and orbit of Neptune (specific conclusions) from perturbations in the observed orbit of Uranus (specific data).

  Deductive reasoning is how theorems are proven in mathematics and how Sherlock Holmes was able to see through the shroud of mystery that always surrounded his cases. Deductive reasoning can be taught, but it is its regular practice that yields the benefits to students. The brain is a muscle and exercising it through logic, analysis, and critical thinking is what gives it the strength to question, to learn, and to discover.

 When learning becomes a simple, repetitive pattern of memorization and multiple-choice test-taking, students' brains do not get many chances to grow and evolve. Students become like filing cabinets for facts and figures, rather than engaged participants in their own educations. Teaching deductive reasoning and exercising it regularly helps students see the patterns and underlying assumptions that govern all human knowledge.

 Refer the website http://www.prufrock.com/productdetails.cfm?PC=441 for interesting puzzles for kids.

SOURCES:
http://ww2.nscc.edu/qep/basics/critical_thinking.htm

http://www.jcu.edu.au/office/tld/learningskills/thinking/deductive.html

http://www.socialresearchmethods.net/kb/dedind.php

http://en.wikipedia.org/wiki/Deductive_reasoning

http://www.criticalthinking.com/company/articles/deductive-reasoning-ski...