Jon A, Gary F, and Jeff BD,

Jon
The most important difference between linguistics and logic
is that linguistics is descriptive while logic is normative.

No.  Grammars and dictionaries have traditionally been considered
normative.  Note l'Académie française.  Modern linguists emphasize
the descriptive aspects in order to claim that they are scientists.

Furthermore, Truth is the normative goal of logic.  Language is
the primary means for communicating and reasoning about truth.
That kind of reasoning is usually called informal.  Formal logics
are a helpful, but secondary innovation.

Gary
Peirce invested the greater part of his attention to semiotics in
what he called speculative grammar, which is not a normative science
but a descriptive one.  The connection between logical “grammar” and
linguistic “grammar” is by no means accidental.

Jeff
What reasons do you have for thinking that speculative grammar--as it
is studied in philosophy--is not a branch of semiotic considered as a
normative science?

Every empirical science must describe and make testable predictions
about some observable phenomena.  The value judgments that state
preferences for some kinds of phenomena make a descriptive science
normative.  Engineering, for example, is normative because it makes
value judgments, such as "Bridges and airplanes should not fall down."

In any case, I agree with Gary that there is a strong connection
between grammars of formal logics and grammars of language.  This
point is independent of whether you consider logic and linguistics
purely descriptive or both descriptive and normative.

Jon
Peirce advises a non-psychological approach to logic, which he defines
as formal semiotic, using "formal" to mean "quasi-necessary", which
is the moral equivalent of "normative" to us.

I agree with the text up to the word 'using'.  But the word 'formal'
is a synonym for "according to form", not 'quasi-necessary'.  In the
Century Dictionary, Peirce's definitions of 'form', 'formal', and
'formalism' emphasize the surface patterns (AKA syntax).  See the
attached formalSign.jpg.  To see his definitions of the other terms,
see http://www.global-language.com/century/

The connections among formal, quasi-necessary, moral, normative,
and truth are indirect.  Peirce explicitly said that diagrammatic
reasoning draws quasi-necessary conclusions by observing patterns
by perception, in Greek 'aisthesis'.  Those perceptual patterns are
the basis for aesthetics, the first of the three normative sciences.

The word 'moral' implies ethics, the second of the normative sciences.
Ethics in action and behavior is determined by the beauty of the action
and its consequences in the social setting.  Wanton destruction of the
social fabric is unethical because it is ugly.

Third, truth is determined by aesthetics and ethics in reasoning and
communication.  Truth is good and beautiful.  Falsehood is bad and ugly.

In short, Peirce would never claim that the term 'formal' is a synonym
for 'quasi-necessary', which he would never claim is equivalent to
'normative' by any version of ethics or morality.

John
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