Reasoning between theories. A general framework for doing epistemology with logic.

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3 ABSTRACTION Admittedly, and contrary to the above claim that epistemic logic needs to be augmented with adequate bridgeprinciples, the theorems of these logical systems are often defended by interpreting them as models of the knowledge or belief only idealised agents have, or as capturing norms for what it means for agents to be rational (for a critical assessment, see Stalnaker (1991)). Yet, this is not sufficient to avoid the slippery slope of revisionary arguments. Even if read as a normative constraints or as a descriptive account of idealised agents, this form of 'idealised rationality manoeuvres' still fails to explain away all the oddities of these logics (most importantly the problem of irrelevant knowledge or belief). The key insight that explains the source of the pessimistic view and the failure of idealised rationality manoeuvres, is that we have to connect theories which operate at different levels of abstraction. To see how the above insight can be put to work, reconsider once more Hendricks' suggestion that formal epistemology may provide the structure that is required to regiment the mainstream epistemologist's strategies (mainly, the construction of counter-examples). Still, if we are after sufficiently flexible bridge principles, the latter description is easily misunderstood. Whereas the received view implies that we should use formal structures to spell out and complete the informal structures mainstream epistemologists revert to, the present proposal is that formal structures should be used to reason about less explicitly formalised structures. Crucially, this strategy does not presuppose that the structures we intend to link are equally fine-grained; that is, it does not presuppose that formal and mainstream theories should operate at the same level of abstraction. This last proviso, is one that is directly inherited from the method of abstraction, one of the main methodological leads in the philosophy of information (Floridi & Sanders, 2004). In this context, the contribution of this method is double: it structures the search for adequate bridge principles, and gives an independent explanation of why standardly conceived bridge principles (e.g. bridge axioms formulated in the object language) are bound to fail. On the formal level, the idea that we can use one structure to reason about another structure finds its roots in Barwise and Seligman's work on information flow (Barwise & Seligman, 1997). The crux of their theory is that since a proximal structure may carry information about a distal structure, the former may be used to reason about the latter. A direct consequence of this approach is that such reasoning is at least incomplete, and most often also non-monotonic. Since many puzzles in epistemic logic (think, for instance, of the problem of coping with the trade-off between syntactic detail and semantic generality for the individuation of meanings or the content of beliefs) suggest that our intuitive structures are, at least in some respects, more fine-grained than their formal counterparts, the present picture seems more accurate than Hendricks' proposal. The provisional conclusion we may draw from this, is that bridge-principles should reflect this idea of reasoning about one structure or theory by means of another structure or theory. The added benefit of making these insights formally precise resides in the explanation it yields of why acceptable bridge-principles are not only comparatively weak, but also non-monotonic. This connection to nonmonotonic reasoning is already present in Barwise and Seligman's work, its application to bridge principles, to the contrary, is original to this proposal. The proposed formal strategy is surely not the only option, but it can successfully be contrasted to its main contenders. The structure of revisionist arguments and the ensuing slide towards the empty logic as the one true standard of deduction has for a long time been one of the arguments for moving to nonmonotonic logical systems, and adaptive logics in particular (Batens, 1997, 2007). Relatedly, the general diagnosis that bare consequence relations (classic-like, monotonic entailments) have a deductive yield which is either too small or too large (or even both) has also been a core motivation for their development. When compared to the above proposal, systems of adaptive logic can be considered as logical systems which incorporate the bridge-principles that are adequate for a certain domain of practical reasoning. Despite being the more common approach, a nonmonotonic revision (or extension) of the canons of logic does not deny an interpretation which refers to reasoning between theories that operate at different levels of abstraction either. In very general terms, one could say that the conception of bridge principles as links between levels of abstraction explains why the move to nonmonotonicity is unavoidable. The adaptive approach, on its side, allows us to focus on the fine structure of such reasoning between levels of abstraction. In that respect, both approaches do belong to complementary, rather than rivalling enterprises. Since this complementarity also surfaces at the more detailed formal level (note that, just like the envisaged bridge principles, the functioning of adaptive logics cannot be exhaustively characterised by a set of axioms that can be formulated at the level of the objectlanguage), it surely must be kept in mind. 4 EXPECTED RESULTS AND BENEFITS The basic idea and the main challenges being outlined, it remains to be detailed what can be obtained from applying the proposed strategy for devising bridge principles between formal and mainstream theories. As mentioned, it is the plan to go beyond the traditional epistemological focus on epistemic and doxastic states, and also beyond the equally traditional logical focus on (deductive) reasoning. This is achieved by looking at the communicative notions of assertion and testimony, and the formal insights drawn from dynamic epistemic logic. As a result, on both sides of the formal/mainstream divide, the bridges we intend to build should relate both static and dynamic aspects, as well as single-agent and social or interactive aspects of epistemic concepts. Even more important than the scope of this inquiry, is the fact that the proposed strategy allows us to represent features of the relation between formal and mainstream epistemology that cannot be brought out by its contenders. To begin with, when compared to recent but still fairly traditional proposals like Streumer 's "For all propositions p1, ..., pn and q, if the conjunction of p1, ..., and pn entails q, then there is a reason against a person s both believing that p1, ..., and that pn and believing the negation of q" (Streumer, 2007), the proposed strategy should definitely yield principles which account for more than the minimal logical constraints suggested by Streumer. Next, when compared to straightforward nonmonotonic approaches which couch the bridge-principles into the logical system itself, the proposed strategy should be able to bring out a number of distinctions that are obscured by the latter approach. Two such distinctions are the difference between what could be called logical and epistemic or doxastic entailments, and the difference between abstraction and idealisation. One, admittedly partial, way to bring out the former, proceeds by recognising that non-monotonic inferences are epistemic or doxastic entailments that can be formalised as conditional belief or knowledge operators. As for the latter, the difference between idealisation and abstraction bears on whether we interpret the epistemic properties predicted by our formal models as properties of agents, or as properties of the modelling framework. Crucially, when understood as properties of agents, oddities of the system come up as idealisations of the agent's cognitive capabilities, whereas as properties of the modelling framework one can call them abstractions (for our bridge principles should then precise that the model does not carry information about those features which, at first sight, appear to be idealised). Evidently, such differences are to some extent obscured when bridge principles are couched into the formal model itself. Finally, two very general virtues of the present proposal are that it aims to show why and how logical modelling deserves its place in formal epistemology, and that it turns the often crude traditional revisionary arguments into reasons for refining a formal model. This is a project that goes beyond the more evident question of how logical epistemology could incorporate mainstream epistemologist's insights (van Benthem, 2006), and also a more accurate and fruitful way to look at the practice of formal modelling.
AcronymFWOTM465
StatusFinished
Effective start/end date1/10/0830/09/14

Flemish discipline codes

  • Philosophy, ethics and religious studies