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It is important to stress that, in order to talk about a contradiction, we need
to make the reasoning system L A explicit. For instance, the set of preferences
f Pab ; Pba g is not inconsistent with respect to a reasoning system L A that does not
impose irreflexivity. Thus, in order to claim that some attitudes are inconsistent, the
individuals have to agree on the reasoning framework that grounds the inconsistency
claims.
The point is that any contradiction depends on the reasoning system that is
adopted to evaluate the matter at issue. Imagine two agents that have apparently
conflicting preferences but that do not share the common reasoning rules that define
what a contradiction is. For example, the preferences of agent 1 and agent 2 may
be incompatible from the point of view of agent 1 but not from the point of view
of agent 2. Agent 1's most preferred option may be a , whereas agent 2 may have
two equally most preferred options a and b . That is, 1 is reasoning according to the
rules of preferences that we have presented before, namely she/he linearly orders
alternatives, whereas 2 has a partial order on alternatives. In that case, 1 believes that
the policy a has to be implemented, whereas 2 believes that both a and b have to
be implemented. In such a case, the disagreement is on the nature of the alternatives
and that is reflected on the rules that norm reasoning about such matters. Thus, the
conflict is at a more abstract level: it is about the reasoning principle that norms
the matter at issue. It is important to stress that also claiming principles is a form
of propositional attitude, thus the conflict of principle is a type of conflict that fits
the definition that we have presented, provided the agents agree on the reasoning
framework that judges conflicting principles. By iterating this argument, we could
imagine situations of an indeterminate regressus : in order to acknowledge that we
are in conflict on a certain matter, we need to agree on the principles that establish
such conflict, but if we are in conflict on such principles, we need other principles
that establish the conflict about principles and so on. However, it is not clear whether
such a situation can be classified as a conflict, namely it is not clear on what ground
agents in such a scenario can claim to have conflicting attitudes. Although such a
situation is theoretically possible and interesting to investigate, in this paper we want
to focus on types of conflicts that are actually recognizable by the agents involved,
and that require an agreement on what conflicting attitudes are. Hence, we shall not
discuss this type of situations further. In this work we shall assume that the blame of
inconsistency is shared among the individuals, namely that they agree on a common
reasoning system that specifies what is a contradiction between sets of propositional
attitudes, and we leave cases of asymmetric blame for future work.
2.4.3
Social Agentive Groups and Social Contradiction
We have seen that SCT defines how to aggregate the propositional attitudes of a
number of possibly conflicting heterogenous agents into a single set of attitudes.
In particular, SCT and JA provide a way to view the group as a single agent and to
ascribe propositional attitudes to the group itself. We present some elements of an
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