Deductive Reasoning

When the problem has been defined and in the analysis. We may be able to provide certain categories of these problems, this may provide knowledge about general solutions that can be used. In short, when asked for solutions to the equation

, we know that this is an equation order of two (often called a quadratic equation). We can change it in the form of standard.



and using abc formula to solve

EXAMPLE 1

Solve equations

given equation is a quadratic equation with one variable. We know that all quadratic equations with one variable () can be solved using abc formula.



can be solved using the formula square:











In Example 1 we apply the general rule in specific cases. We reasoned general rule quadratic equation is valid when used on a particular or any quadratic equation. Such a type of logic called Deductive Logic, which means applying a general statement in a more specific statement.

Deductive logic and formal structure of logic has been studied for many years, thousands of years. One of the scientists of ancient logic, and the most famous, was Aristotle (384-322 BC). He was a pupil of the famous philosopher Plato and a teacher of Alexander the Great, explorers from the mainland Greece to India. Aristotle's philosophy is very influential, its influence reaches the Catholic Church brought by St. Thomas Aquinas, even affecting modern philosophy. Over the centuries - old, Aristotle developed logic becomes part of lawyers and political studies and is used to distinguish a valid argument and what does not.

For Aristotle, logic is a necessary tool in any investigation / research, and the syllogism is the result of all the fruit of thought. Syllogism is an argument which is formed by two statements, called premises (major premise and minor premise), followed by a conclusion or conclusions. For all the premises are given, if the conclusion of the argument guaranteed (in the sense not find a disclaimer in any manner whatsoever), the argument is valid. If the conclusion is not guaranteed (in the sense at least there is a rebuttal that does not justify the conclusion), the argument is invalid.

One popular Aristotle's syllogism is as follows:

1. All men die
2. Socrates is a man
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So, Socrates died

Major premise is applied to the minor premise led to an indisputable conclusion, then the argument is valid. Note that the deductive logic that is used in example 1 has a structure similar to Aristotle's syllogism about Socrates.

1. All second order equation in one variable can be solved by the formula abc.
2. is the second order equation in one variable.
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can be solved using the formula abc.

All syllogism in general can be written in:

1. If A, then B
2. X is A
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Then, X is B

Deductive logic is the perfect application to use Venn diagrams. Valid and invalid often misinterpreted by right and not right. Consider the following example.

1. All doctor is male
2. My mother was a doctor
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So, my mother male

The argument above is a valid argument. However, a valid argument does not show the right conclusions. A mother is not likely to be men! Validity and truth do not have the same understanding. Valid argument to say when the resulting conclusions based on the indisputable premise that given. Here is not said about the truth of a given premise. Therefore, in determining the validity of the argument, we do not currently determine whether the verdict was correct or not. Valid argument to say if the premise is given, obtained logical conclusion. It is true, if the premise that given a valid argument is true, the conclusion is obtained also true.

Consider the following examples.

1. All artists are political activists
2. Tantowi Yahya is a political activist
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So, Tantowi Yahya is an artist


Glance these conclusions appear valid. This is because we all know that Tantowi Yahya is an artist. However, if we perform the analysis, the conclusion is not logically derived. The first premise suggests that there are some political activists are an artist, which means there are some others who are not artists. The second premise is a specific statement that Tantowi John was a political activist. Tantowi could have been an artist, but could not (apart from general knowledge) based on the premise. So the logical conclusion is not obtained, because of possible artists Tantowi not cause this argument is invalid. However, the argument is said to be invalid does not mean to say that the verdict was wrong, as proof, We all know that Tantowi Yahya is an artist. So the conclusion in the argument above statement is true, however, based on the premise, the argument is not a valid argument.