Aristotelian logic
Bust of Aristotle
11. Aristotle has passed into history, among other things, like the first systematizing logic. In fact, his proposals in this field, together with the contributions of the Stoics, have been virtually all logic to the nineteenth century. Kant himself, who takes the Aristotelian classification of trials as basis for the transcendental deduction of the categories of understanding, a fundamental aspect of his work, the minimum advance is strange logic, since Aristotle, in contrast with the rising tide of science since the Renaissance, as both seem to offer a way of certain knowledge.
12. Logical works of Aristotle (Categories, On Interpretation, Prior Analytics, Posterior Analytics and Topics) were grouped in a set called Organon, that philosophers traditionally interpreted as a propaedeutic, a preparation for philosophy. This sought to emphasize that knowledge the laws of reasoning was essentially a prerequisite for any further study and should be in possession of such knowledge who I want to get in the field of philosophy. Unlike modern formal logic, Aristotelian logic assumes that the forms of thought replicate what happens in reality is, there are extra-mental things as they are conceived by the mind, so that the categories of mind are objective categories, categories of reality. Thus the categories of thought and acquire an ontological sense that nature has pointed out preparatory philosophical tradition. 13. Logic Aristotle deals with the study of concepts, with particular attention to the preachers, and the categories (predicaments), complete with analysis of the judgments and forms of reasoning, with particular attention to the categorical or deductive reasoning syllogisms, as forms of demonstration are particularly suited to scientific knowledge. 2.
CONCEPTS
21. The concept is understood as the intellectual representation of an object, differing, therefore, sensed, perceived, imagined or remembered. The properties of the concepts are
understanding and extension
: The first denotes the essential characteristics that contains a concept, and the second number, the number of subjects to which may be applicable, which can preach. The greater the number of features that contains a concept, the lower the number of subjects that may be covered, and vice versa. Based on these features can be built
known
logical trees, as did Porphyry (third century AD), in which concepts are classified establishing between them a relationship of hierarchy and subordination, from highest to lowest extension.
hierarchy and subordination of the concepts as the logical tree Porfirio: BE Accident Formless Substance
:
God, angels - Corporal
- No Living:
genera and species of minerals - Living
-
Insensitive:
genera and species of plants -
- Sensible Sound:
Male, individual Luis, Juan, Pedro -
Irrational: - Gross
individual Rocinante, Platero -
-
22. Of course, there are many kinds of concepts. According to its extension may be universal, particular and singular, according to their understanding: simple and compound, expressed as a single substance, or essence accompanied by a quality they can also be, according to his understanding, concrete and abstract, compatible or incompatible, positive or negative , light or dark. The greatest interest to Aristotle were universal concepts and different types of attribution or predicable. Predicates are universal concepts that can be applied, then, to many individuals. In the Posterior Analytics Aristotle refers to five predicable, or general modes of attribution: genus, species, difference, and the accident itself. Gender representa la parte de la esencia que es común a varias especies; la especie representa la esencia del ser; la diferencia expresa la parte de la esencia que no es común, sino característica de la especie; propio, o propiedad, expresa una cualidad que acompaña necesariamente a la especie, y el accidente expresa una cualidad contingente, que puede estar o no en el ser. - 23. Los géneros supremos en los que se pueden clasificar los seres son las categorías, o predicamentos. En sus obras "Categorías" y "Tópicos" Aristóteles fija en diez su número, estableciendo una distinción fundamental entre la sustancia y los accidentes. La sustancia es la categoría fundamental, lo que existe en sí mismo; los accidentes son categorías que existen en otro ser, en la sustancia. Aristóteles clasifica los accidentes en 9 grupos: cualidad, cantidad, relación, acción, pasión, lugar, tiempo, situación, hábito externo. (En los "Analíticos posteriores" nos habla sólo de ocho categorías accidentales, suprimiendo las dos últimas, que son englobadas como aspectos de las restantes). En la medida en que las categorías remiten a las formas de ser extramentales adquieren un marcado contenido ontológico, dando por supuesto que las cosas son captadas por la mente tal como son en realidad.
24. Los conceptos son actos mentales que expresamos mediante el lenguaje. A esa expresión lingüística the concept is called "term", and is subject to the same classification given to the concepts. The terms may be also, if we look at the object expressed, unambiguous, and similar mistakes. Are unequivocal terms that refer to a single concept, and always apply the same sense or meaning. Mistakes are the terms that we can express different concepts being applied in each case with a different meaning (León has a cathedral, the lion is the king of the jungle). The term that expresses different concepts but have a common fund called analog (John is healthy, this climate is healthy). The analysis of the different types of analogy interesó mucho a los filósofos medievales y algunos problemas de la relación entre lo divino y lo humano fueron tratados con el desarrollo del análisis de los distintos tipos de analogía.
3. LOS JUICIOS
31. La relación de dos conceptos da lugar a la formulación de un juicio. Si se da entre ambos una relación de conveniencia decimos que el juicio es afirmativo, y en caso contrario, negativo. El sujeto del juicio es el concepto del que se afirma o niega algo; el predicado es el concepto que se afirma o niega del sujeto. Aristóteles distingue en los juicios la materia y la forma. La materia o contenido del juicio son los conceptos que se relacionan; la forma es la relación que se establece including through the verb to be. Aristotle is the subject of the hearing with a sign (S) and the predicate with another (P) to try to separate the matter of the form and the shape of the trial "John is tall" is represented as "S is P" and trial as "John is not high" and "S is not P".
32. The trials are divided into different groups according to the amount (depending on the length of the subject: universal, particular, singular), quality (according to the quality of copulation: affirmative and negative), the relationship (according to the relationship between subject and predicate: categorical, hypothetical and disjunctive) and mode (depending on how expressing the relationship between subject and predicate: apodictic, assertoric and problematic). It follows an orderly classification of all forms of trial, in the case of categorical judgments, for example, give the following classification, combining the quantity (universal and particular) and quality (affirmative and negative:
Judgement yes, is represented with the letter A.
Judgement negative, is represented with the letter E.
Particular Judgement yes, is represented with the letter I.
negative Particular Judgement, was represented by the letter O .
33. The allocation of these letters to represent the forms of the categorical view is back to Aristotle and comes from the Latin words "Af-I-rmo" and "refuse", and is what has traditionally been used among us to refer to the Aristotelian classification of trials. Aristotle also looks at how opposition between trials (ie, diversity among the trials with the same subject and predicate), deducting a set of rules about the truth of those that must be met regardless of the concepts choose to form judgments.
34. On the basis of such rules can be established relations of opposition among the different types of judgments, as are contrary, contradictory subcontrarios or subordinates, determining its truth value depending on the type of object to another trial known. Can be represented by the following: -
-
- As was the case with concepts, which are mental acts that are expressed by linguistic terms, the judgments are mental acts that are expressed by propositions, ie by a set words or grammatical sentence. The same view can express different propositions (for example, using different languages), and sometimes the same proposition can refer to different judgments ("this is my home" spoken by two different people).
-
4. THE REASONING
41. The argument is a sequence of trials in which starting from a known proposition is found one or more unknown. Aristotle in the Posterior Analytics, covers both the inductive and deductive reasoning, but believes that scientific knowledge is achieved by deducting the particular from the general, that is, with knowledge of the causes. Aristotle privileges, therefore, the analysis of deductive reasoning, especially deductive reasoning or categorical syllogism.
42. Just as we distinguish in the trial a subject and a way we do the same with the reasoning, the proximate matter of reasoning are the trials, and the remote matter concepts (which are the subject of trials). The way is legitimate nexus or connection between history and the subsequent trials and is expressed by conjunctions such as "then", "therefore", "therefore", through which performs the inference process, the consequence judgments about others. Aristotle argues that this process is subject to rules for determining its correctness or incorrectness, so that, if the judgments which are partly true, and the inference is made according to the rules defined (if the inference is valid , so) the conclusion is necessarily true. The inference process not therefore depend on the subject of reasoning, but its form.
43. Deductive reasoning is a form of reasoning that goes entirely to the parties that is, trying to extract a particular one universal truth. Can be of three kinds: categorical, hypothetical and disjunctive, by type of trial (the relationship) that serves as a starting point. classes of reasoning and examples for: Reasoning
categorical All humans are mortal
The locals are human
After Madrid are fatal
- Hypothetical Reasoning
- If you pass go
rental - Thus
- has approved vacation then go
- disjunctive reasoning
- This path goes north or south
- Thus goes north Then
- not go south
- 44. The syllogism is a categorical deductive reasoning by which, according to two judgments given infer a new one. Thus consists of three propositions (expressing three trials) and three terms (which express three concepts), which are the near and far field of reasoning, respectively. The premise that serves as a starting point called "major premise" and is the general premise that serves as an intermediary is called "minor premise, and is less general than the previous one, the proposition follows from the" major "via the" minor " the conclusion of the argument. 45. With regard to the terms of reasoning, is called "major term" the predicate of the conclusion, which should appear in the major premise, and is represented with the letter P. It's called "lower end" the subject of the conclusion, which also appears in the minor premise, and is represented with the letter S. The "average" is the one in the two premises (major and minor) and not the conclusion, and is represented with the letter M. Therefore, taking the above example of categorical reasoning, we could represent it as follows: Class
reasoning, for example and formal representation. Where the major term is "deadly" - (P)
, the lower end "locals" - (S), and the average
is "human" - (M)
.:
categorical reasoning.
All human are fatal
: M is P The Madrid
- are human
: S is M - Then are Madrid
fatal: S is P - 46. Aristotle distinguishes four valid forms of syllogism, traditionally known as figures of syllogism, and which result from different place of the average, and therefore the rightful role in the premises. The conclusion of all the figures is provided S is P. Valid forms or figures of the syllogism are (although the latter was regarded by Aristotle as a mere variant of the first). valid forms of syllogism, or figures of the syllogism: First figure
- M is P and S is M, then S is P is The average subject in the major premise and preached on lower Second
Figure
P is M and S is M, then S is P - The middle term is predicate in both premises
figure -
Third M is P and M is S , then S is P
The average subject in both premises is -
Figure -
Fourth P is M and M is S, then S is P
The middle term is predicate in the major premise and the minor - Subject
47. These four figures can, in turn, taking into account the quality and quantity of the propositions that compose them, give rise to a total of 64 different modes of syllogism, of which only 19 are still valid reasoning. Its validity is established by Aristotle from determining the legitimacy of laws or rules of the syllogism. Among them, the syllogism must have three terms, which can not be taken at greater length in the conclusion that in the premises, the average has to be universal at least one premise (or both), which two negative premises can not continue any conclusions, etc. -
48. The basis of the syllogism research also raised the curiosity of Aristotle, and that inference based on the validity of the premises, we posed the problem of the infinite resource to justify the reasoning. If each premise must be justified by another, in effect, how to stop the need to justify the beginning of the beginning? This would lead to an infinite process of justification, as Aristotle said there were certain principles that were known intuitively and did not need proof. The most fundamental of all was the principle of contradiction (it is possible that something is and is not at the same time, under the same account) it follows the identity (something is equal to itself) and the equal (both equal to a third are equal to each other), and others that follow from the above.
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this article:
May 2007, webdianoia.com: http://www.webdianoia.com/aristoteles/aristoteles_log.htm
- Bust of Aristotle:
- May 2007, es.wikipedia.org: http://es.wikipedia.org/wiki/Arist% C3% B3teles
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oOo -
12. Logical works of Aristotle (Categories, On Interpretation, Prior Analytics, Posterior Analytics and Topics) were grouped in a set called Organon, that philosophers traditionally interpreted as a propaedeutic, a preparation for philosophy. This sought to emphasize that knowledge the laws of reasoning was essentially a prerequisite for any further study and should be in possession of such knowledge who I want to get in the field of philosophy. Unlike modern formal logic, Aristotelian logic assumes that the forms of thought replicate what happens in reality is, there are extra-mental things as they are conceived by the mind, so that the categories of mind are objective categories, categories of reality. Thus the categories of thought and acquire an ontological sense that nature has pointed out preparatory philosophical tradition. 
43. Deductive reasoning is a form of reasoning that goes entirely to the parties that is, trying to extract a particular one universal truth. Can be of three kinds: categorical, hypothetical and disjunctive, by type of trial (the relationship) that serves as a starting point. 