[FOM] VERY (was: PA inconsistencies)

[Arnold Neumaier]

On 2018-08-18 21:11, José Manuel Rodriguez Caballero wrote:
> First, I will focus on the operation VERY, as defined by Jean Benabou,
> because I consider that this is the first step to properly understand
> Voevodsky's discourse. [...]
> 
> Sam Sanders wrote: If VERY has vague properties (like small and large etc),
> then I would point to Nonstandard Analysis, in which vague properties may
> be formalised.
> 
> If we use Nonstandard Analysis for defining VERY, then a bounded number of
> VERY will be operative and an unbounded number of VERY will be inoperative.
> Notice that in the expression
> 
> VERY, VERY good job
> 
> the word VERY is operative, whereas in the expression
> 
> VERY, VERY, VERY, VERY, VERY, VERY, VERY, VERY, VERY, VERY, VERY good job
> 
> the word VERY is not operative. It do not think that 11 VERYs is an
> unbounded number.

The proper way to formalize vague statements such as VERY is not
nonstandard analysis but fuzzy logic. See, e.g., my paper

   Fuzzy modeling in terms of surprise,
   Fuzzy Sets and Systems 135 (2003), 21-38.
   http://www.mat.univie.ac.at/~neum/ms/fuzzy.pdf

where very appears naturally as a modifier, see Table 2 in
Section 6, along with other modifiers in the scale:

   extremely, very, probably, perhaps, hardly, not

Arnold Neumaier