Answer Key
1. Taking the notions of quantity, quality and distribution of terms, discuss the nature of four categorical
propositions with examples.
(10)
Every standard-form categorical proposition either affirms or denies some class relation. If the
proposition affirms some class inclusion complete or partial, its quality is affirmative. If the
proposition denies class inclusion, complete or partial, its quality is negative. Propositions A and I
come from the Latin word AffIrmo (I affirm) while E and O from the word nEgO (I deny). If the
proposition refers to all the members of the class designated by the subject term its quantity is
universal. A and E propositions are universal in quantity. If the proposition refers to some members
of the class designated by the subject term its quantity is particular. I and O propositions are particular.
Every categorical proposition has a quantifier, subject term, the copula and predicate term.
If the proposition refers to all the members of its class – designated by the subject or predicate terms,
a term in that proposition is said to be distributed. A proposition distributes its subject but not the
predicate. E proposition in asserting that the whole class of S is excluded from the class of P
distributes both its terms. I proposition makes no such assertion about each and every member of the
classes designated by the subject and predicate terms. O proposition does not distribute its subject
term but the predicate term. When something is excluded the whole class is being referred to.
2. Discuss the characteristic features of traditional and modern symbolic logic and how is modern
symbolic logic an advancement over the traditional logic.
(10)
Traditional Aristotelian logic is built upon the system of syllogisms, the building blocks of which are
the terms referring to the classes and their relations which gives us four standard-form categorical
propositions. The assertions made by the propositions about the classes is unconditional. The analysis
of class relations and validity or invalidity of categorical syllogisms the main concern of deductive
reasoning. Various rules related to quality, distribution of terms give us the syllogistic rules to
determine validity as well as invalidity. With Boolean interpretations, Venn technique is also
employed to find out validity-invalidity. Modern logic does not analyze categorical propositions. It
identifies fundamental logical connectives on which deductive arguments depend. These truthfunctional connectives are: conjunction, negation, disjunction, implication and bi-conditional.
The analysis of deduction requires an artificial symbolic language in which logical relations can be
formulated with precision. Classical logic did understand the value of symbols and Aristotle used
symbols as variables in his own analyses, modern symbolic logic has devised and used symbols
much more effectively. And in this sense the difference is that of degree than that of kind.
The relations of classes are not central for modern logicians. Instead, they analyze the internal
structure of propositions and arguments. Modern symbolic logic therefore is not encumbered as there
is no need to transform deductive arguments into syllogistic forms. There are forms of deductive
arguments that syllogistics cannot adequately address. With versatile symbolic language and tools
modern symbolic logic can be said to be an advancement over the traditional logic.