Como instrumento de apoyo para la realización de ejercicios relacionados con las figuras y los modos del silogismo, presentamos un programa realizado en JavaScrip por profesores de la Universidad de Washington que nos puede ayudar, mediante el uso del ordenador, en la realización de tales ejercicios. El programa chequea las 256 formas diferentes de silogismos y nos señala acerca de ellos lo siguiente:
METODO DE TRABAJO EN CLASE
Como primer paso los alumnos deberían haber entendido
correctamente los elementos básicos del silogismo como, por ejemplo, que están
formados por proposiciones categóricas del tipo A,E,I,O. Tambien deberían
conocer todo lo que se refiere a las figuras y los modos del silogísmo
asi como los criterios de distribución y las reglas de los silogismos.
Comprendido bien todo esto, los alumnos deberían realizar en su libreta ejercicios
sobre silogísmos en dónde lleven a cabo la formalización de los mismos,
la descripción de la figura y el modo al que pertenecen, asi como la
explicación del por qué son válidos o inválidos.
Despues de haber llevado a cabo este trabajo previo es cuando nos podemos servir de la ayuda del ordenador con el objeto de cerciorarnos acerca de la corrección o incorrección de nuestro trabajo. En este sentido, vamos a reconocerle al ordenador y al programa, su autoridad en el tema. Para utilizar el ordenador debemos llevar a cabo los pasos siguientes:
Introducir, en las casillas correpondientes, las formas del silogismo en lo que se refiere a la premisa mayor, la menor y la conclusión. Por ejemplo, si en la libreta de clase hubieramos hecho el silogismo siguiente: Todo hombre es mortal. Todo griego es hombre. Todo griego es mortal; entonces deberíamos introducir en la casilla su esquema formal que sería: Todo M es P. Todo S es M. Todo S es P.
A continuación chequear cada una de las premisas con el objeto de averigüar si están bien distribuidas o no. Se supone, claro está, que cada alumno en su libreta, ya tiene realizado lo mismo que, ahora, al ordenador le pedimos que haga.
El ordenador nos señalará tambien el nombre del silogísmo tanto en su aspecto formal (AEA) como, si éste es válido, en su nomenclatura tradicional (Barbara, Celarent....). Por supuesto, cada alumno en su libreta debería tener ya hecho este ejercicio que deberá contrastar, y si quiere tambien discutir, con lo que dice el ordenador.
Finalmente, si el silógismo es inválido, el ordenador nos da tambien una breve explicación del por qué.
La máquina silogística nos permite evaluar las 256
formas diferente de silogismos. Coloca en las casillas correspondientes la premisas
y la conclusión que se correspodan con los ejercicios a realizar en clase y que
se supone tienes finalizados en tu libreta.
Tambien se puede ir directamente a la version-rápida de esta máquina silogística. Alli de un modo sencillo se puede comprabar si los ejercicios realizados son válidos o inválidos..
The concept of distribution used in an explanation of why certain syllogisms are valid, is a contested one. As "The Oxford Companion to Philosophy" has it: "This theory is obscure" i.e. the theory making use of this concept, and "the traditional rules are flawed". Nevertheless, I have chosen to make use of this concept, and the traditional rules in creating the syllogistic machine, for historical reasons, but also as the criticism I have seen of the concept of distribution and the traditional rules, seems to leave much to be desired.
The traditional theory goes somewhat like this: A term is distributed in a sentence, if the same is said of all elements of the term's extension. In the sentence "All S are P", for instance the same is said of all elements of the extension of S, i.e. that they are P, but not so of all the elements of the extension of P. These may all be S, but the sentence in question does not say this. So, in "All S are P", S is distributed, whereas P is undistributed.
In "No S is P" the same is said of all elements in the extension of S, i.e. that they are not P, and the same is said of all elements of the extension of P, i.e. that they are not S, so in this instance, both terms are distributed.
In "Some S is P" we do not say the same of all Ss, and the same goes for the extension of P, so in this instance, neither of the terms is distributed.
Finally, in "Some S is not P" we do not say the same of all Ss, but on the other hand we say of all Ps that they are not a certain S, so in this instance only P is distributed.
The algorithm that evaluates the different syllogisms in the syllogistic machine, makes use of this property of premises and conclusion. Given the status of distribution of the terms in the conclusion, it makes certain demands on the status of distribution of the premises. If a term is distributed in the conclusion, it should also be distributed in the premise in which it occurs. Also the middle term should be distributed at least once. Violation of these rules are called "illicit premise" (major or minor) and "undistributed middle" respectively.
There is only one further rule, and that is that exactly one premise should be negative (E or O), if the conclusion is negative. If the conclusion is affirmative (A or I), however, both premises should be affirmative.
Traditionally three main quantities of sentences were distinguished: Universal, particular and singular. "All logicians are philosophers" exemplifies the first, "Some logician is a philosopher" exemplifies the second, whereas "Socrates is a philosopher" exemplifies the third.
The syllogistic machine includes only universal and particular sentences. This is according to the traditional manner of exposition. For, singular sentences where treated as universal ones. The subject terms of singular sentences were seen as terms with an extension of only one element, e.g. "Socrates is a philosopher" was seen as equivalent to "All socrateses are philosophers", with the proviso that there is only one of the "socrateses".
There are two qualities of sentences. A sentence can be either affirmative or negative. "All S are P" is consequently a universal affirmative sentence. "No S is P" is universal and negative. "Some S is P" is particular and affirmative and, finally, "Some S is not P" is particular and negative.
These sentence forms were given short names, in a manner typical of the mnemonic strategies of the Middle Ages. The universal affirmative was called "A" (from the first vowel in the Latin "Affirmo"). The universal negative was called "E" (from the first vowel in the Latin "Nego"), whereas the particular affirmative and particular negative were called "I" and "O" respectively (from the second vowel in "Affirmo" and "Nego" respectively).
A categorical syllogism is an argument with two premises and one conclusion, where each of these three sentences are of one of the forms "A", "E", "I" or "O".
Traditionally, syllogisms were put in a standard form before described or evaluated. The conclusion was put at the bottom with the two premises on top of it. The premise containing the predicate term of the conclusion "P" was put at the top, and was called the major premise, whereas the premise containing the subject term of the conclusion, was called the minor premise, and was put in between.
In addition to the subject and predicate terms of the conclusion, premises contain one additional term, the so called "middle term". This term is not found in the conclusion but it ensures that the premises together say enough of the relation between subject term and predicate term in order for the conclusion to follow (i.e. in case the syllogism is a valid one)
In describing the form of a certain premise, it is not enough to say e.g. that it is of form "A" and a major premise. This merely gives the information that the premise in question is universal and affirmative, and that it contains the predicate term of the conclusion, in addition to the middle term. One also has to know whether the middle term is subject term or predicate term of the premise, in question.
This also goes for entire syllogism; It is not enough e.g. to say that the major is of form "A", the minor of form "E" and the conclusion is of form "I", one also has to know the order of terms in the premises, and this is what is called the figure of the syllogism.
There are four figures: If the middle term is at the left in the major and at the right in the minor, the syllogism is of figure 1, if both middle terms are at the right it is of figure 2, if both middle terms are at the left it is of figure 3, and the remaining constellation is reserved for figure 4.
Traditionally syllogisms were named using the sequence of one-letter names of the respective sentence forms, first the major, followed by the minor and the conclusion and finally the number of the figure. "AAA-1" for instance, is the name of a syllogism of figure one where all the sentences are affirmative and universal.
Also so called mnemonic names of valid syllogisms were construed, names that were intended to be learned by heart. These names contain three vowels each; the vowels that make up the name of the corresponding syllogism: Barbara accordingly is the mnemonic name of the valid syllogism AAA-1.
Ed Stephan of Western Washington University has provided this medieaeval poem, with the mnemonic names of all syllogisms of the four figures that were regarded as valid. He found it in Roger Holmes (1939:80) "The Rhyme of Reason"
Barbara, Celarent, Darii, Ferioque, prioris:
Cesare, Camestres, Festino, Baroco, secundae:
Tertia, Darapti, Ditamis, Datisi, Felapton, Bocardo, Ferison, habet:
Quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison.
Este es un versión más sencilla de la máquina silogística. Eliga cualquiera de las 256 formas de silogismos y compruebe su válidez o invalidez.