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Categorical Logic: Terms and Propositions
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This lecture notes discusses the topic "terms and propositions" in Categorical Logic.
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Categorical Logic: Terms and PropositionsAs we may already know, our main goal in logic is to determine the validity of
arguments.
And in categorical logic, we will employ the Eight (8) Rules of Syllogisms for us to be
able to determine the validity of an argument. But since the 8 rules of syllogisms talk
about the quantity and quality of terms and propositions, then it is but logical enough to
discuss the nature of terms and propositions before we delve into the discussion on the
8 rules of syllogisms. In what follows, I will discuss the nature of terms and propositions.
First of all, logicians define a term as an idea expressed in words either spoken or
written. Of course, an idea is understood as the mental representation of something.
Hence, when one says, for example, “a table”, then we have at term, that is, a “table”.
Classification of Terms
There are four (4) classifications of terms in terms of quantity, namely: singular,
collective, particular, and universal.
A singular term is one that stands for only one definite object.
Examples:
1) Table
2) Peter
3) Tree
A collective term is one that is applicable to each and every member of a class taken as
a whole but not to an individual taken singly.
Examples:
1) Orchestra
2) Platoon
3) Choir
A particular term is one that refers to an indefinite number of individuals or groups.
Some signifiers of a particular term are: some, a number of, several, almost all, a few
, of, practically all, at least one, not all, and the like. Hence, if a term is signified by at
least one of these signifiers, then we conclude that that term is a particular one.
Examples:
1) Some Asians
2) Almost all students
3) Several politicians
A universal term is one that is applicable to each and every member of a class. Some of
the signifiers of a universal term are: no, all, each, every, and the like.
Examples:
1) All Asians
2) Every politician
3) No student
A proposition, on the other hand, is a judgment expressed in words either spoken or
written. When we say a judgment, it refers to the mental act of affirming or denying
something.
Example:
1) President Trump is a good president.
2) President Trump is not a good president.
The first example above is an act of affirmation because the copula (or linking verb) is
does not contain a negation sign “not”. The second example is an act of negation
because the copula (or linking verb) is contains a negation sign “not”.
Kinds of Propositions used in Logic
There are two types of propositions used in logic, namely, categorical and hypothetical
propositions. On the one hand, a categorical proposition is one that expresses an
unconditional judgment. For example, we may say “The Japanese people are hard-
working.” According to logicians, this proposition is a categorical one because it does
not pose any condition. On the other hand, a hypothetical proposition is one that
expresses a conditional judgment. For example, we may say “If it rains today, then the
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