Alican,

Fundamental difference:  A vague statement has a broad range of meaning.  A more precise statement has a narrower range of meaning.  Therefore, a vague statement is more likely to be true.  A more precise statement is more likely to false.

Alican:  Doesn't narrowing down the meaning of a symbol typically lead to a more "precise" interpretation? 

Yes.  And therefore, the more precise statement is more likely to be false.

Alican:   Also, from my observation of Alex's work, in my opinion, that's what he is trying to achieve. 

Yes.  And that is why I keep telling him to avoid turning a true but vague statement into a precise but false statement.

Example:  Buying an ice cream cone, and specifying a perfect sphere of vanilla ice cream that is exactly 10 centimeters in diameter in a cone that is precisely  9,7 cm in diameter at the top and 15 cm in length.

That is very precise, very stupid, and likely to get yourself laughed at or thrown out of the store.

I used a trivial example of an ice cream cone.  But the same principle applies to every statement about a continuum of any kind.  The degree of precision should be appropriate to the requirements of the subject matter.  That is true of a continuum of any and every kind for any purpose of any and every kind.

John

John and Alex,

@John

Doesn't narrowing down the meaning of a symbol typically lead to a more "precise" interpretation?

If a set of symbols (or sign vehicle) signifies a more limited set of immediate objects, it results in a more specific reference. This increased specificity can lead to
a more focused interpretation (the effect or interpretation in the mind). Overall, sign creation will be more "precise". 

E.g., Number 1 and word One. The latter symbol can be interpreted with more things, while the former is less. Overall, isn't the sign-making with Number 1 easier or, in your discussion words, more "precise"?
If I understood something wrong, please correct me.

@Alex

 Also, from my observation of Alex's work, in my opinion, that's what he is trying to achieve. Also correct me, Alex, if I understood wrong.

Best,
Alican%40mail.gmail.com.