# Impossible

Background: There are no existing data regarding risk factors for impossible mask ventilation and limited data regarding its incidence. The authors sought to determine the incidence, predictors, and outcomes associated with impossible mask ventilation.

## Impossible

Methods: The authors performed an observational study over a 4-yr period. For each adult patient undergoing a general anesthetic, preoperative patient characteristics, detailed airway physical exam, and airway outcome data were collected. The primary outcome was impossible mask ventilation defined as the inability to exchange air during bag-mask ventilation attempts, despite multiple providers, airway adjuvants, or neuromuscular blockade. Secondary outcomes included the final, definitive airway management technique and direct laryngoscopy view. The incidence of impossible mask ventilation was calculated. Independent (P

Results: Over a 4-yr period from 2004 to 2008, 53,041 attempts at mask ventilation were recorded. A total of 77 cases of impossible mask ventilation (0.15%) were observed. Neck radiation changes, male sex, sleep apnea, Mallampati III or IV, and presence of beard were identified as independent predictors. The receiver-operating-characteristic area under the curve for this model was 0.80 +/- 0.03. Nineteen impossible mask ventilation patients (25%) also demonstrated difficult intubation, with 15 being intubated successfully. Twelve patients required an alternative intubation technique, including two surgical airways and two patients who were awakened and underwent successful fiberoptic intubation.

Conclusions: Impossible mask ventilation is an infrequent airway event that is associated with difficult intubation. Neck radiation changes represent the most significant clinical predictor of impossible mask ventilation in the patient dataset.

Classical Logic Violators: another definition has it thatimpossible worlds are worlds where the laws of classicallogic fail (see e.g. Priest 1997a). A world complying with intuitionistic logic, and where instances of the Law of Excluded Middle fail, will beimpossible in the third sense.

Contradiction-Realizers: a still more specific definition hasit that an impossible world is a world where sentences of the form\(A\) and \(\neg A\) hold, against the Law ofNon-Contradiction (see e.g. Lycan 1994). Impossible worlds of thefourth kind will be impossible in the third sense, but not vice versa.Our intuitionistic world above will have the Law of Non-Contradictionhold unrestrictedly: it will be impossible in the third, but not inthe fourth sense.

Another argument on behalf of impossible worlds, quite pervasive inthe literature, comes from counterpossible reasoning (e.g.Beall & van Fraassen 2003, Chapter 4; Nolan 1997; Restall 1997;Brogaard & Salerno 2013). This is reasoning from suppositions,assumptions, or conditional antecedents which are not only false, butimpossible. We can reason non-trivially from impossible suppositions,by asking what would be the case, were (say) the Law ofExcluded Middle false. To say that we reason non-triviallyfrom an assumption means just that we accept some conclusions butreject others on the basis of that assumption. If we hypotheticallysuppose the Law of Excluded Middle to be false, for example, then wewould likely conclude that intuitionistic logic would be preferable toclassical logic, given that supposition. We are unlikely to concludethat classical logic would be a satisfactory logic, or that scarletwould be a shade of green, given that supposition. The point readilygeneralizes to reasoning about entire theories and to seriousphilosophical and logical debates. We often reason from suppositionsabout the truth of certain logical, mathematical, or metaphysicaltheories which, if in fact false, are necessarily false, because ofthe very nature of their subject matter.

Impossible worlds are useful within this approach because thesewould-be possibilities often turn out to be impossible. Our beliefsare often (covertly) inconsistent with one another. Moreover, ourknowledge and belief is not closed under (classical) logicalconsequence: we do not know or believe all consequences of what weknow or believe. It is hard to accommodate these features using onlypossible worlds. Possible worlds models usually generate the problemof logical omniscience (see epistemic logic), which we will discuss in section 5.3.

One other application of impossible worlds concernsperceptual impossibilities. When we see an Escher drawing ora Penrose triangle, our experience has content. But that content isimpossible: such structures cannot be realised. The content of ourexperience in such cases is naturally captured using impossibleworlds. Splitting that content into smaller internally consistentparts would lose the essential feature of the whole. This issue isexplored in Mortensen 1997.

While the standard conditional logics based on this idea have beenquite successful in the treatment of counterfactuals, the approachentails that any counterfactual whose antecedent is impossible isvacuously true. For if there are no possible worlds at which\(A\) is true, then trivially, all closest \(A\)-worlds(worlds where \(A\) is true) are \(B\)-worlds. This isunsatisfying in many respects, for we often need to reasonnontrivially about theories that (perhaps unbeknownst to us) cannotpossibly be correct; and we often need to reason from antecedents thatmay turn out to be not only false, but necessarily so. (Compare theexample conditionals (1.1) and (1.2) in section 1 for an example.)

Field takes this as an argument to the effect that mathematicalnecessity is not coextensive with logical necessity. But we can turnthe tables around: mathematical necessity is unrestricted and falsemathematical theories are just impossible theories.

The ensuing anarchy can be mitigated to some extent, e.g., by assumingwhat Nolan 1997 calls the Strangeness of ImpossibilityCondition (SIC): any possible world, however weird, should becloser to any possible world \(w\) than any impossible world isto \(w\). Reality will be turned upside down before logical lawsor mathematical truths abandon us. Then it is plausible that theLewis-Stalnaker principles will still hold whenever the relevantantecedent is possible. For then we will consider only theclosest antecedent-worlds when we evaluate the conditional, all ofwhich will be possible worlds: the impossible ones will be too faraway (Berto et al. 2018).

Supporters of impossible worlds disagree over their metaphysicalnature, just as supporters of possible worlds do. If one acceptsontological commitment to worlds of any kind, then one faces thefollow-up question: just what are they, metaphysically speaking?

In his 2010 book, Yagisawa is more distant from Lewisian modalrealism. He still admits impossible worlds and impossibilia,and he rejects ersatz accounts of them. However, he now takes worldsto be points in modal space. Worlds are modal indices for truth, justlike times are temporal indices for it; and modal matters are treatedin a way similar to how four-dimensionalist philosophers, who believein temporal parts, treat temporal matters. According to four-dimensionalists, materialobjects are like temporal worms extended across time: an object has aproperty at time \(t\) by having a temporal stage at time\(t\) which has that property. Analogously, for Yagisawa anobject has a modal property, a property at world \(w\), by havinga modal stage at world \(w\) which has that property.

Should we require impossible worlds to comply with anylogical rules? And if we allow different classes of impossible worlds,each exhibiting different degrees of logical structure, can theseclasses be ordered in a meaningful way? This section focuses on thesetwo issues.

Are there any logical principles which impossible worlds must obey?More precisely, is there any logical inference such that, for any(impossible) world \(w\), if the premises are all true accordingto \(w\), then so is the conclusion? There is at least one suchinference: the trivial inference from \(A\) to \(A\). (Forif \(A\) is true at world \(w\), then \(A\) is true atworld \(w\)!) Are there any others? This is the granularityissue.

To illustrate the extra power (4.2) gives us (over (4.1) and (NP)),consider Simplification, the inference from \(A \wedge B\) to\(A\), or Disjunction Introduction, from \(A\) to \(A \veeB\). (4.2) directly entails that there are worlds where these rulesfail. So, if we find (4.2) plausible, we can infer that impossibleworlds are not, in general, governed by standard paraconsistent logics. A paraconsistent logic is any one in which cont radictorypremises \(A\), \(\neg A\) do not entail arbitraryconclusions. But standardly, paraconsistent logics maintain theprinciple that conjunctions are true just in case both conjuncts are;disjunctions are true just in case at least one disjunct is; anddouble negations \(\neg \neg A\) are true just in case \(A\)is. If we accept (4.2), then these relationships will break down insome impossible worlds.

One very general option is the following. Even though we subscribe tosome unrestricted comprehension principle for impossible worlds, wemay admit that worlds where only the intensional operators, e.g., thebox and diamond of necessity and possibility, behave in a non-standardfashion are less deviant than worlds where also the extensionaloperators, like classical conjunction and disjunction, do. Let us callworlds of the former kind intensionally impossible and worldsof the latter kindextensionally impossible. This picture (inspired by Priest2005, Chapter 1) has some intuitive force to recommend it. Kripkeannon-normal worlds, where only the behaviour of the modal operators isnon-standard (see section 5.1), are intuitively less deviant than open worlds, where all formulas maybehave arbitrarily. Generalizing, the view would entail arranging therespective spheres in such a way that any intensionally impossibleworld is closer to @ than any extensionally impossible one. 041b061a72