In the following, I will use the predicate calculus symbols, ¬ and ∧, for ``not'' and ``and'', in the context of the description of affective interpretations of a situation. Thus, for example, ¬V ∧ N means ``the situation is perceived as NOT a Violation, AND as Normal''. As mentioned above, the degrees of violation of the subjective moral order form three categories, which may be labelled ``no violation''(Level 1), ``funny violation''(Level 2), and ``offensive violation''(Level 3). No violation occurs when there is no perceived violation (¬V). A funny violation occurs when a perceived violation is juxtaposed with a simultaneous view of the situation as normal (that is, as having no violation)(V ∧ N). Offensive violation occurs when there is a perceived violation but there is no competing view of the situation as normal, or where the competing view is driven out by the strength of affective commitment to the principle being violated (V ∧ ¬ N).
N and V form a very interesting kind of logic, which is worth some discussion. If taken as logically independent, four combinations are possible, as in Table 2:
It may be assumed that N and V are each the negation of the other: normality is the absence of violation, and violation is the absence of normality. If we make this assumption, then there is but a single predicate, rather than two (where ¬V = N and ¬N = V ), and only two combinations would seem to be logically consistent: N ∧ ¬V , and ¬N ∧ V. These may be reduced by identity and the meaning of ∧ thus:
Furthermore, the other two possibilities can be demonstrated to be just one, by substituting equivalents ¬V and ¬N for N and V, respectively:
This much follows from elementary logic. It also follows that if N and V are elementary propositions, then the combination N ∧ V is logically inconsistent. The facts of a situation must be logically consistent if it is a real (and thus logically possible) situation. This is an apparent paradox, which we must unravel if the present theory of humor is to be considered logically consistent. There are two considerations which avoid inconsistency here. First, note that N and V are not elementary or atomic propositions; they have limited scope over specific aspects of complex situations, and thus they implicitly have some kind of argument structure, which might be made explicit with notation like N(p_{1}) and V(p_{2}). If p_{1} and p_{2} are distinct (though perhaps overlapping) sets of propositions in the representation of a complex situation, then the combination N(p_{1}) ∧ V(p_{2}) is logically consistent. That is, these ``different views of the same situation'' may highlight different elements of it and thus may derive the N and V affective interpretations separately, from non-identical bases. Second, the emotional inferences made by an observer from the apparent facts of a situation may be made by rules of likelihood or probable association rather than of logical necessity. Such inferences are sometimes incorrect, or rather, uncertainly correct; and the mind could represent them as such. While the mind cannot logically consider two inconsistent inferences to be both definitely true at the same time, the mind could still merely consider them, without attaching a definite truth value to both, and this mental state would be logically consistent. The first of these approaches makes stronger empirical claims, and requires fewer assumptions about human reasoning, so let us use it until it is proven that it is not applicable in some case of humor interpretation. Therefore let us not consider N and V to be logically inferred elementary propositions with definite and mutually inconsistent truth values, but rather let us consider them to be predicates which apply to non-identical sets of propositions representing different aspects of a situation. That is, an N or V affective interpretation is a predicate which represents an emotional attitude: this part of the situation or this perspective on it is pleasant; that other part of the situation or that other perspective on it is frightening, and so forth. pleasant(p_{1}) and frightening(p_{2}) are affectively meaningful predicates applied to propositions or aspects of the situation labelled as p_{1} and p_{2}. Thus if a complex situation includes two sets of factual propositions, p_{1} and p_{2}, then the interpretations N(p_{1}) and V(p_{2}) are not logically inconsistent, both because their truth value is not well-defined, and because, as predicates applying to different propositions, they do not contradict one another. The inconsistency appears at the level of the entire situation seeming to be both normal and not-normal, but it is the different aspects of the situation which lead to the contrary emotional interpretations, whether through ambiguity, temporal sequencing, or mere complexity in the situation. Thus affective ``absurdity'' is both logically possible and to be expected.
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