LOGIC

Index :

1 - Etymology logic .
2 - Defining logical real .
3 - Types of logic.
- Naturally.
- Scientific .
4 - Definition of arguments.
5 - Types of arguments.
- Categorical syllogisms .
* Structure .
* Figure .
* Mode .
- Topics deductive .
* Definition .
* Structure .
* Examples .
* Say it is valid or invalid .
- Modus ponens .
- Modus tollens .
- Hypothetical argument .
- Argued disjunctive .
1 - Etymology logic .

The science that is based on laws , rules and forms of scientific knowledge is known under the name of logic. It is a formal science that lacks content because it focuses on the study of inference valid alternatives .

That is, proposes to study the methods and principles appropriate to identify the correct reasoning against which it is not.

The etymology lets you know that the term 'logic' comes from the Latin word logic, which in turn derives from the Greek logikos ( logos, "reason" or "study") . The Greek philosopher Aristotle , have experts in historical matters , pioneered by using the notion to name check of the arguments as indicators of truth in science , and in presenting the syllogism as a valid argument .

2 - Defining logical real .

The logic is a formal science that studies the principles of valid demonstration and inference . The word derives from the ancient Greek λογική ( logike ) , which means " endowed with reason , intellectual, dialectical , argumentative " which in turn comes from λόγος (logos ) , "word , thought, idea , argument , reason, or principle" .

Just as the traditional object of study is the field of chemistry , and biology of life, the logic is the inference . The inference is the process by which conclusions are derived from logic investigates premisas.1 principles by which inferences are acceptable, and others not. When an inference is acceptable, what is its logical structure , not the specific content of the argument or the language used . For this reason the logic is considered a formal science , like mathematics , rather than an empirical science .

http://es.wikipedia.org/wiki/L % C3 % B3gica

3 - Types of logic.

Logic has a usual meaning of language must distinguish between the material logic is the ability to reason and scientific logic is an orderly and thoughtful to help us understand the natural logic .

· Natural Logic :

You learn effortlessly and put into practice when we interact with others , it is also the ability to reason correctly .

· Scientific logic :
It is what we study , the logic makes the student acquires the habit of resorting to the reasoning , it is also a theory and technical knowledge which enables the improvement of natural logic .

http://www.buenastareas.com/ensayos/logica-natural/1269988.html

4 - Definition of arguments.

Argument is called the content of a speech , book, film , play, etc., exposed synthetically , in its essential aspects . When someone wants to know what was discussed in one of the cases cited , you may be asked to relate the argument , then receive information on the topics addressed .

Argumentative texts whose function is to convince the recipient by reasons that what is affirmed or denied is the right thing regarding questionable reality and not obvious . No such need to present arguments that a monkey belongs to the animal kingdom , but to argue that man is not carnivorous by nature , or to be decriminalized drug use . Its function is then persuaded by the rationale and logical reasoning .

* Categorical syllogisms :

The syllogism , in its simplest form ( categorical syllogism regular) , consists of three propositions : two premises and data of the syllogism and a conclusion. In the syllogism are three terms :

a) The minor term , which is recognized for playing the role of subject in the conclusion. It is symbolized by the letter " S " .

b ) The term senior , who is recognized for playing the role of predicate in the conclusion. It is symbolized by the letter " P " .

c ) On average, it is recognized that not in the conclusion and serves to establish the relationship between the premises . It is symbolized by the capital letter "M " .

Each term appears in two propositions :

a) The major term appears in a premise so called " major premise " and as a predicate of the conclusion.

b ) The middle term appears in both premises performing any function (subject or predicate ) .

c ) The minor term appears in a premise so called " minor premise " and as a subject in the conclusion.

· FIGURE:

· The "figure" of the syllogism syllogism is the structure of which depends on the position of the middle term in the premises. There are four figures in the categorical syllogism :

· A) First figure, which is when the average ranks of the subject in the major premise and the predicate in the least .

· B ) Second figure, which is when the average plays the predicate in both premises .

· C ) Third figure, which is when the average plays the role of subject in both premises .

· D ) Fourth figure, which is when the average plays the predicate in the major premise and the subject in the least .
· Can be represented schematically as follows:

first

second

third

quarter

MP

PM

MP

PM

SM

SM

MS

MS

SP

SP

SP

SP

Mode syllogism :

Syllogism mode depends on the amount and quality of the premise and conclusion.

The mode of a syllogism is symbolized by the sequence of three vowels case for your combination of premises and conclusion . In each figure there are 64 ways , making a total of 256 , of which only 19 are valid .

figures :

In those words , different for each figure , the vowel letters symbolize the propositions that compose the syllogism in the following order : major premise , minor premise and conclusion. The words in question are:

In the first figure:
BARBARA

Celarent

DARIIFERIO

In second figure :

CESARE

Camestres

festino

baroque

In third figure :

DARAPI

FELAPTON

Disamis

Datisi

bocardo

FERISON

In fourth figure :

BAMALIP

CALEMES

Dimatis

FESAPO

FRESISON

examples:
1 - All dogs are animals and some animals are herbivores
therefore some dogs are herbivores.

2 - All dogs are animals,
and no cat is a dog ;
therefore, no cat is an animal.

3 - all musicians are sensitive .
All poets are sensitive .
All musicians are poets .

· Deductive syllogisms
A deductive argument is one whose conclusion follows from the premises so required . This characteristic is called validity and is what distinguishes it from other types of arguments , such as the inductive and analogical .

A necessary relationship established between premises and conclusion validity is called . Thus , we say that an argument is valid if assuming that the premises are true the conclusion follows necessarily , ie validly other conclusion could not be followed .

The validity of a deductive argument does not depend on the truth of propositions, but simply guess what they are and then I wonder : if the premises are true the conclusion follows necessarily or inevitably so ?

· Structure
Next Subject : are the premises and the conclusion. Premises or previous proposals are those which follow the third. The conclusion, therefore , is the third proposition that follows from the premises. Major premise is called that which is placed first because it contains the predicate of the conclusion , minor premise which placed second, and that the subject of the conclusion.

Remote Subject : are the terms that make up the premises and the conclusion. It's called middle ( M ) , or simply means that it is found only in the premises ; major term (T ) or larger end , the end that the conclusion is the predicate and that is in the major premise , minor term ( t) or lower end , the end that is the subject at the conclusion that ordinarily found on the minor premise .

Form: is the arrangement of the terms and the premises are fit for completion. ( To achieve this condition must be addressed in terms of its position as subjects or predicates and utterances to the quantity and quality) .


· Examples
· Modus ponens
· If A then B
· B
Therefore · A
·
·
· If families have children then increase the birth rate .
Families have children.
Thus the birth rate increases .
·
· If the child does not sleep eight hours then wake up tired .
· The child sleeps eight hours.
· So wake up tired .

MODUS TOLLENS
If P then Q
No Q
Therefore no P


If Falcao is doped then have a penalty.
You will not have a penalty.
Therefore not doped .

If the water runs out then humans disappear.
No humans disappear .
Therefore there is no water .

· Modus ponens

In logic, ponendo modus ponens (Latin: mode that affirms saying ), also called modus ponens and usually abbreviated MPP or MP , is an inference rule has the following form :

If A, then B
A
Thus, B
For example, a reasoning which follows the shape of the modus ponens might be:

If it is sunny , then it is day .
It's sunny.
Therefore, it is daytime .
Another more formal way to present the modus ponens is:

Description :
\ begin {array } { r }
A \ to B \ \
A \ \
\ hline
B
\ end {array }
Yet another way is through notation consequential calculation :

Description : (A \ to B ), A \ vdash B

· Modus tollens

In logic, tollendo modus tollens (Latin , so denying denies ), also called modus tollens and usually abbreviated MTT or MT , is an inference rule has the following form :

If A then B
No B
Therefore, no A
No formal way of presenting the modus tollens using logical connectives is:

Description :
\ begin {array } { r }
A \ ? B \ \
\ neg B \ \
\ hline
\ neg A
\ end {array }
Another way is through calculation consequential notation :

Description : (A \ rightarrow B ) , \ neg B \ vdash \ neg A
In propositional logic representation is as follows: Description : [ ( p \ rightarrow q ) \ wedge \ neg q ] \ rightarrow \ neg p

· Argument hypothetical

If p then q .
. If then r q .

Therefore , if p then r .

That is the formula of the hypothetical syllogism .
A hypothetical syllogism is valid as long as the premises has the form :
" If p then q " . And the premise q on p becomes as follows .
And so on .
•
. If you study logic , know ways to deduce arguments.
. If you know ways to derive valid arguments , then you can learn to raise arguments.

- So, if you study logic, then you can learn to raise arguments.

· Argument disjunctive

· The disjunctive syllogism is similar to the hypothetical mixed , as its major premise is disjunctive while the lowest and conclusion are categorical .
· It also supports two modes : ponendo modus tollens ( yes negative) and modus ponens tollendo ( yes negative ) .
· The formal structure of modus tollens ponendo is:
· A is B or C
Now it is B
Then , there is C
· The formal structure of tollendo modus ponens is:
· A is B or C
Now, not B
Then , B or C is .