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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
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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
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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
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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
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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.
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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.
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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.
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