Social Meaning and Technical Meaning

Social Meaning and Technical Meaning
The distinction and contrast between social
meaning and technical meaning is engagingly
given by certain expressions that can be taken
either way, such as:
1. How could he?
2. Where does the grizzly bear sleep?
3. How do you clean a firearm?
4. Check your mirrors.
In a given context, one meaning is much more
presumed than the other, and so a joke can
be based on switching the meaning, as in:
Question: Where does the grizzly bear sleep?
Answer: Wherever it wants to.
Question: How do you clean a firearm?
Answer: Very carefully.
An instance of sincerely misinterpreting
a social meaning as technical meaning
occurs in Willa Cather’s ‘My Antonia’.
An instance of jokingly misinterpreting
a social meaning as a technical meaning
occurs in the film ‘Full Metal Jacket’.

Linguistic note in mathematics

Linguistic note in mathematics:
One specifies angles as ‘congruent’ only
at the very beginning of a school-course
in geometry, or on a tournament test in
mathematics. Everywhere else the angles
are simply said to be equal, even if, for
diagramatic purposes, the notation of
congruence must be employed. For example,
two triangles are similar if, and only if, their
corresponding angle are EQUAL (not ‘congruent’),
and the base angles of an isosceles triangle are
EQUAL (not ‘congruent’), and when two parallel
lines are cut by a transversal, corresponding
angles are EQUAL (not ‘congruent’) and so on. There
are two notions of an angle: the geometric one (‘two
rays emanating from a common vertex’) and the
numerical one (the measure of the geometric
angle), and one transitions fairly quickly, and
permanently, from the geometric notion to the
numerical notion. A enlightening juxtaposition
of the two notions occurs in the inscribed-angle
theorem. The ‘inscribed angle’ is the geometric
angle and the corresponding ‘subtended angle’,
which is its measure, is the numerical angle.