Whether
we’re conscious of it or not, there is logic in language. By logic, I mean the coherent connection of ideas in a proposition. Consider this example, “Encircle
the letter T, if the statement is true and encircle F, if it is false.”[1] At
a cursory glance, the meaning of this statement is clear. But in careful analysis, it turns out that
its meaning is logically incoherent, or there is logical inconsistency of its
meaning.
The
statement above is a complex one consisting of two hypothetical statements
(if-then phrase) but the main proposition is conjunctive –that is, two
hypothetical statements are connected by the word “and”. To paraphrase it, the proposition will go as
follows, “If the statement is true, then encircle the
letter T and if it is false, then encircle F.”
As
mentioned above the meaning of the statement is clear enough. But if you consider the word and connecting the first hypothetical proposition
and the second one, its meaning will become incoherent because the truth-value
of the former (first hypothetical) does not coincide with the latter (the
second hypothetical). To further our
consideration particularly on the word and,
it is construed that the same statement is presumed to be true and false at the same time,
which is against the laws of any person of logical mind. This is the main reason why that statement is
logically incoherent or logically inconsistent.
It is construing that each given item (statement) in that part of exam
can be true and false.
In
an actual exam, a student can encircle T and F in the same given item. For example,
T F 1. The sun rises at 6:00 am.
A
student can encircle T and F at the same time, and he/she is correct by virtue
of the given instruction since it goes, “Encircle T, if the statement is true and
encircle F, it is false.” This is funny!
But it could happen if he/she thinks that the given item is true and
false. But at the outset, the
instruction (of this exam) becomes even funnier because of its logical
inconsistency.
I
think the best way to state it is this way, “Encircle
the letter T, if the statement is true, or
encircle F, if it is false.” This time we have a disjunctive proposition
–a disjunctive proposition offers us an alternation, meaning “If the statement
is true, then choose T, or it is false, then choose F.” The word “or” warrants us that the same
statement is not or cannot be true and false at the same time. In the
actual exam, a student is only to choose T or F, not T and F.
[1]
This line is culled from a test paper as a given instruction for a “true or
false” type of the exam.
