the referenced
Stendahl quote :
"Mathematics allows for no hypocrisy and no vagueness." is of course without merit.
you may as well say "Words allow for no hypocrisy and no vagueness."
if it is anything mathematics is an extension and expressive
tool of logic to which all the laws of logic apply.
one of the basic concepts of logic
is that a line of reasoning must be
1 - internally consistent
2 - externally consistent.
both internal and external consistency have to do with the definition of terms.
for example "if A = B and B = C, then A = C."
IF mathematics is defined, as Stendahl does, as an inherently
romantic notion,
THEN Stendahl's deduction is true.
however, since mathematics is only a human tool with no agency for action within itself,
then it is wholly possible for mathematics-the-tool to be applied to a given set of
phenomena according to the precepts of a set of untrue definitions.
romanticism is a scourge. sloppy thinking has always accompanied it.
consider an apothegm attributed to Benjamin Disraeli by Mark Twain :
"There are three kinds of lies: lies, damned lies and statistics."
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interesting PDF on "sloppy thinking" as a characteristic
of the "firefighting mentality" in organizations. the Kepner-Trego PDF
analyzes "firefighting mentality" as a passive coping technique rooted
in a reactionary unwillingness to accept responsibilities associated with
creative adaptation. sounds like romanticism to me ...