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Categorical Syllogism Analyzer CSA version 3.17 May 21, 1987 Copyright (c) 1987 by Chris Lord Abstract This program is meant as a first step in the 'understanding' of categorical syllogisms. A syllogism is analyzed for structure and validity. If the syllogism is not valid, the reason for its invalidity is given. Note, this program cannot determine the truth of syllogisms, only the logical validity of them. Garbage in, garbage out. Introduction First in the understanding of categorical syllogisms is an understanding of categorical propositions. A categorical proposition makes one definite assertion affirming or denying that one class, the subject, is included in a second class, the predicate, either in whole or in part. For example in the notation of LISP, (ALL MEN ARE MORTALS). Each proposition is composed of the following parts: Quantifier : _A_l_l men are mortal The only quantifiers allowed in categorical propositions are NO, ALL and SOME. Subject (S) : All _m_e_n are mortal The subject of a proposition is generally a class description. Verb copula : All men _a_r_e mortal The copula is a form of the verb 'to be.' Generally page 1 Categorical Syllogism Analyzer IS or ARE. Predicate (P): All men are _m_o_r_t_a_l The predicate of a proposition is also a class description. Categorical propositions have what is known as quantity. This is determined by the quantifier. For the quantifiers ALL and NO, the quantity is universal; for the quantifier SOME, the quantity is particular. Quality of a proposition is determined by the combination of quantifier and verb copula. The copula 'ARE NOT' signifies a negative quality as does the quantifier 'NO.' In other words, it denies the predicate of the subject. Affirmative propositions affirm the predicate of the subject. Categorical propositions, having a limited number of combinations of quality and quantity, are referred to by four type identifiers based on their Latin names. 'A' propositions (based on Affirmo) are universal and affirmative. For example: All men are mortal. 'E' propositions (based on nEgo) are universal and negative. For example: No men are mortal. 'I' propositions (based on affIrmo) are particular and affirmative. For example: Some men are mortal. 'O' propositions (based on negO) are particular and negative. For example: Some men are not mortal. Categorical propositions have a distribution which refers to how the subject is distributed among the predicate and how the predicate is distributed over the subject. The following are inherent characteristics of each form of proposition: A) S is D; P is U I) S is U; P is U E) S is D; P is D O) S is U; P is D page 2 Categorical Syllogism Analyzer Categorical Syllogisms Categorical syllogisms are created using three categorical propositions. They are a form of deductive argument in which a conclusion is inferred, or claimed to follow necessarily, from two premisses. For example: (ALL MEN ARE MORTALS) ! the first premiss (major) (ALL FROGS ARE MEN) ! the second premiss (minor) (ALL FROGS ARE MORTALS) ! the conclusion In a syllogism, there are three and only three terms. The subject of the conclusion is known as the minor term, the predicate being the major term. This leaves one other term which is the middle term. The middle term occurs in both premisses, but not in the conclusion; it is used as the connecting term between premisses. The minor premiss contains the minor term and the major premiss contains the major term. The form of a syllogism is given by the three types of the propositions, in the example above this would be (A A A), and a number between 1 and 4 indicating the position of the middle term in the premisses. The exact detail of form is not necessary here. There are several ways to assess syllogisms. One is through the use of Venn diagrams which allows a visual analysis. An alternate method is using a collection of rules that determine valid syllogisms. The second method provides a lexical analysis and is easier to code. Formal Rules There are seven basic rules for determining the validity of categorical syllogisms, eight under boolean (or existential) interpretation. They are given below along with the fallacy when the rule is violated. Rule 1: A categorical syllogism must contain three and only page 3 Categorical Syllogism Analyzer three terms or it commits the fallacy of four terms. Rule 2: The middle term must be distributed at least once or it commits the fallacy of undistributed middle. Rule 3: No term may be distributed in the conclusion which is undistributed in the premisses or it commits the fallacy of illicit major or minor. Rule 4: No categorical syllogism can have two negative premisses or it commits the fallacy of exclusive premisses. Rule 5: If either premiss is negative, the conclusion must be negative or it commits the fallacy of drawing an affirmative conclusion from a negative premiss. Rule 6: A categorical proposition must have at least on universal premiss or it commits the fallacy of two particulars. Rule 7: If one premiss is particular, the conclusion must be particular or it commits the fallacy of drawing a universal conclusion from a particular premiss. Rule 8: (existential interpretation only) A particular conclusion cannot have two universal premisses or it commits the existential fallacy. The Program The actual program is composed of several layers and uses a combination of action-centered and request-centered control mechanisms. The top layer is the user interface which gets the syllogism, calls the necessary functions and reports the results in what is hoped a less cryptic form than represented internally. The syllogism is entered, when prompted, as three separate lists. The conclusion must be last, but the premisses may be in either order. Once entered, each proposition is passed to a formatter which parses each proposition into a form which can be easily dealt with. It is during this page 4 Categorical Syllogism Analyzer process that all non-standard quantifiers (such as MOST and EVERY) are replaced with their categorical equivalents. A future enhancement will also replace synonyms and antonyms with common terms and eliminate plural terms at this stage. Once the propositions are formatted, they are passed to a proposition analyzer which determines the type of each proposition. The next step involves determining the proper order of the propositions. It is standard to have the major premiss first, followed by the minor premiss and finally the conclusion. The properly formatter syllogism is returned for further analysis of the form, in other words where the middle term is located. The last step is to pass the form of the syllogism, and only the form, to the rule base which determines the validity of syllogism. The program includes extensive error trapping at every stage and utilizes a common error handler. This allows for the easy expansion of the number and type of errors trapped. The Future This program is in the early stages of a 'toy.' It is what could best be referred to as a third generation prototype, having its roots in a project last year to analyze categorical propositions. Possible uses would hinge on the expansion of the program to handle poly-syllogisms, syllogisms with multiple premisses such as: No interesting poems are unpopular among people of real taste. No modern poetry is free from affectation. All your poems are on the subject of soap bubbles. No affected poetry is popular among people of real taste. page 5 Categorical Syllogism Analyzer Only a modern poem would be on the subject of soap bubbles. Therefore all your poems are uninteresting. The above syllogism is valid, for those having difficulty interpreting it. Which brings about the major strength of programs such as this, accuracy. An expanded version of this program could easily and quickly determine the validity of the above syllogism. It would not, however, be able to discern whether the actual propositions are true, and hence whether the conclusion is true. Such clear cut language and form is evident in a number of disciplines besides logic. Law and mathematics come immediately to mind. Further possibilities are left to you. Usage Notes CSA is implemented completely in XLISP 1.7 using the subset of common LISP provided and avoiding all XLISP particular functions. To load the program, type: XLISP CSA After loading the initialization file, XLISP will load CSA and print the header lines. To enter a syllogism, type: (CSA) You will be prompted for the two premisses and then the conclusion. Enter the propositions as lists for example: (all men are mortals) (some frogs are men) (some frogs are mortals) Presently, the program will display who the syllogism was parsed along with what it thinks the major, minor and middle term should be. If for some reason it is incorrect in its determining these terms, examine the three parsed propositions and see of the predicates and subjects have been determined correctly, often errors will be in the parsing. page 6 Categorical Syllogism Analyzer Next, the program prints out whether the syllogism is valid or invalid. If the syllogism is determined to be invalid, the first rule that is violated and the fallacy committed is displayed. When completed, the program returns to the prompt; to leave XLISP, enter (EXIT) at the ">" prompt. page 7