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Correspondingly, there are two kinds of 'negative trust' or better of 'mistrust'; two opposites
of trust: mistrust in Y as for being good/able/reliable/..; suspicion, worry, and diffidence
towards Y :
Negative Trust-1 or Mistrust it is when X believes that Y is not competent or able, or that
his behavior is not predictable and reliable. X isn't afraid of Y being malevolent, indifferent,
irresponsible, or with other defects; she is just convinced that Y cannot/will not realize her
goal g effectively. He doesn't have the needed qualities and virtues ( powers of ).
Negative Trust-2 or Diffidence/Suspicion it is more than this. At the explicit level it is some
sort of 'paradoxical trust': X believes that Y has powers and abilities, and also that he can
intend and realize something; but something bad (for X )! X is not simply predicting a failure
( X cannot rely on Y ), but probable harms from Y , because of Y 's bad powers or dispositions. 3
4.2 Lack of Trust 4
Both the previous forms of negative trust clearly imply 'lack of trust', since the belief that 'Y is
NOT reliable for g; one cannot trust him (as for
)' ( formula (4.1) is true) - which logically
excludes that 'Y is reliable' - is just a sub-case of the mental state: ' X does NOT believe that Y
is reliable/trustworthy' (where 'Not ( Bel X q )' denotes the absence of such Belief in X 's mind):
...
Not ( Bel X ( Trustworthy Y ))
(4.1a)
We actually call this mental state 'lack of trust'.
This belief - per se - is clearly compatible with and can also cover another idea: ' X does
NOT believe that Y is reliable/trustworthy' Not (Bel X (Not (Trustworthy Y))) . This is when X
doesn't know, has no idea: the case of ignorance or pending judgment. When ' X does NOT
believe that Y is trustworthy', either she believes that Y is not trustworthy, is unreliable; or she
doesn't know how to evaluate Y . The 'lack of trust' covers both mistrust and doubt :
Not ( Bel X ( Trustworthy Y ))
Not ( Bel X ( Not ( Trustworthy Y )))
(4.1b)
What we have just said does not imply that there is trust only when it is enough for entrusting
('delegating' and rely on) 5 or that there is 'lack of trust' or even 'mistrust' when the agent
decides not to entrust Y . Logical relations should not be mixed up with quantitative criteria,
which are necessary for the decision. These logical relations of inclusion or incompatibility
define some 'spaces'. Within the space of ' X trusts Y ' (with some degree) then X has no
mistrust or doubts about Y ; however, this does not entail that X trusts Y enough to entrust him.
3 Perhaps Y might even realize X 's goal g; but by exposing X to serious risks and dangers.
4 One might prefer - for this case - the term 'no trust' and to limit the expression 'lack of trust' just for case 4.1,
where trust is not 'sufficient'. However, actually this does not correspond to the current use of the expression (we try
to be as coherent as possible). It is in fact normal to say something like: 'But this is lack of trust!' when for example
X has delegated Y but is full of doubts and worries, and would like to continuously check Y's work.
5 It is a typical, correct, non-contradictory expression to say: 'I trust Y, but not enough' . This is because 'I trust Y '
can mean two different things: (i) 'I have a certain amount of trust (positive evaluations) about Y '; or, (ii) 'I have a
sufficient amount of trust in Y to entrust him, rely on him'. This thanks to the pragmatic implications of the sentence
'I trust Y ' and to the meaning of 'to trust' not just as disposition but as decision and action (that presupposes the
'sufficiency' of the evaluation).
 
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