Situation Theory Reconsidered Jeremy Seligman Abstract Werecallalargelyforgottenintellectualproject:thatofprovidingaformaltheory of situations that does justice to informal ideas about situations and informa-tion ﬂow with the ‘situation theory’ community of the late 1980s and early 1990s.Instead of defending speciﬁc desiderata, and in the spirit of Barwise’s ‘BranchPoints’, we record some the difﬁculties that deﬁned the project by posing a se-ries of twelve questions. Drawing on the theory of channels and information ﬂow(Barwise and Seligman, late 1990s), with some modiﬁcations and extensions, weprovide a version of situation theory that answers some of these questions. One of the main extensions is to allow probabilistic constraints. We also consider a morerecent proposal by van Benthem to capture many of situation theory’s insights usinga modal logic closely related to dependancy logic and use this as an alternative butcomparable way of answering our questions. Key words: situation theory, channels, constraints, information ﬂow, probability,perspective Zuang Zhou was wandering when he saw a peculiar kind of magpie. ‘What kind of bird isthat!’ he exclaimed. ‘Its wings are enormous but they get it nowhere; its eyes are huge butit can’t even see where it’s going!’ Then he hitched up his robe, strode forward, cocked hiscrossbow and prepared to take aim. As he did so, he spied a cicada that had found a lovelyspot of shade. Behind it, a praying mantis, stretching forth its claws, prepared to snatch thecicada. The peculiar magpie was close behind, ready to make off with the praying mantis.Zhuang Zhou, shuddering at the sight, said, ‘Ah! - things do nothing but make trouble foreach other - one creature calling down disaster on another!’ He threw down his crossbow,turned about and hurried from the park, but the park keeper [taking him for a poacher] racedafter him with shouts of accusation. ‘Mountain Tree’ Zhuangzi 1 Philosophy, The University of Auckland, New Zealand, e-mail: [email protected]
1 The translation from this third century B.C. Chinese text is abridged with modiﬁcations from Thesaurus Linguae Sericae http://tls.uni-hd.de/home_en.lasso .1 2 Jeremy Seligman In the late 1980s and early 1990s, at the time I was a graduate student, a researchproject out of Stanford, speciﬁcally the newly created Centre of Studies in Languageand Information (CSLI), inspired and promoted by Jon Barwise and John Perry,created a minor whirlpool of intellectual excitement that inﬂuenced me greatly andmany of my peers. The project was that of Situation Theory: the attempt to provide aformal theory of information based on the concept of a ‘situation’. The above quota-tion captures for me the essential insight that lay behind this work: when reasoningand acting in the word we do so within a limited context; when we change perspec-tive different information is available and this makes a signiﬁcant difference. Ourconceptual boundaries can always be expanded, or even contracted, and since logic,inference and rational activity in general takes place within a conceptually boundedspace, an appreciation of the fragility and versatility of our concepts is essential foran understanding of the capacity and application of reason.Johan van Benthem has had a persistent interest in the continuation of these ideas,has written on the subject on several occasions [28, 13, 14] and has prompted me,on many occasions, to do more to represent this line of thought to a wider commu-nity. I have not succeeded to meet his expectations, partly because my own interestshave shifted, to some extent, but mostly because it is very hard. ‘Situation Theory’(henceforth: ST) is somewhat of a misnomer. There never was a theory in any veryprecise sense of the word, only a more-or-less shared idea about what such as the-ory should achieve - a vague set of desiderata together with a conviction that thereshould be nothing vague about it. ST should provide a set of conceptual primitiveson the basis of which the older absolute metaphysics and theory of language andlogic, would be replaced by an alternative that took seriously the essential role thatcontext, or ‘situatedness’ plays in our thinking. Jon Barwise, in particular, had avision of ST in which ‘theory’ should be understood in the sense of ‘set theory’. Itwould serve as a foundation for the information sciences in the way that set theoryserves as a foundation for mathematics.Yet there was also a revisionary aspect to the project. At the time the dominant ap-proaches to providing a systematic semantic theory were those of Donald Davidson(mostly within the philosophical community) and Richard Montague (within thelogico-linguistic community). While differing in important philosophical details,these approaches shared a global perspective on language and its relationship tonon-linguistic reality, in which ‘reference’ and ‘truth’ play a central role. Languagerefers to certain aspects of reality in a largely context-independent way, allowing usto describe it truly or falsely, and logic is a matter of monitoring which inferencesare sure to be truth-preserving, notwithstanding a serious interest in context by suchphilosophers as David Kaplan and John Perry, who drew our attention to those as-pects of language, such as demonstratives and indexicals, that depend essentiallyon the context of use. The ST project aimed to push these insights further, insert-ing context into the picture at every point. Reference occurs in and is inﬂuenced bycontextual factors, and what we take to be true descriptions are never true simplicter Situation Theory Reconsidered 3 but true about some speciﬁc part of reality. 2 Or to put it in the jargon of the time,the concepts of reference and truth need to be ‘situated’. So, instead of propositions,which are true or false by deﬁnition, the focus of situation theory should be ‘infons’- units of information - that may or may not be ‘supported’ by small parts of theworld, known as ‘situations’. Likewise, in place of universally valid laws of logicand natural science, ST aimed to make a place for ‘constraints’ that held locallybut not necessarily everywhere. Even the basic division of the world into objects,properties and relations, was taken to be relative to a ‘scheme of individuation’ -something that we impose on the world - allowing for different ways of doing this.There were several fully articulated theories made some progress toward this goal.Perhaps the most well-known is the use of non-well-founded set theory, as devel-oped by Peter Aczel  and others, to model situations as sets of ‘infons’: the basicunits of information. The locality of a situation is thereby understood in a purelyinformational sense: the information supported by a situation is just the informationit contains, and its identity is determined extensionally: distinct situations are dis-tinguished by supporting different infons. The use of a universe of sets as a generalmodelling tool and, in particular, the use of the ∈ relation to represent a ‘part’ or‘component’ is unsurprising; the innovation here was to extend this representationof parts to allow for circularity. This enabled Barwise and Etchemendy, in , togive a very smooth situation-theoretic account of The Liar and other self-referentialpropositions. This was extended by Aczel, Lunnon and others [2, 20, 27] to a the-ory of ‘structure objects’ in which the relation of membership from set theory isgeneralised to that of a structural component, with associate operators for substitu-tion and abstraction. The focus of the structured-object models of situation theory(henceforth: SOST) was on the provision of a highly ‘intensional’ account of situa-tions, infons, propositions and properties, in which syntactic structure is mirrored inthe semantics, allowing for very precise control over identities, such as whether ornot the infon that a = b is the same as the infon that b = a . As such, it was a victimof its own success. There were simply too many choices to be made, and little senseof having reached explanatory bedrock.For me, another weakness of the SOST models was that they ignored what I ﬁndto be be most interesting part of the project: to account for the role of differentrepresentationalperspectivesinourreasoningandhowshiftingfromoneperspectivetoanotheropensupnewvistas.Forthisoneneedssomestoryabouthowinformationin very different systems of representation can be related. A central example forresearchers at the time, which has been pursued in great depth subsequently, is therelationship between diagrammatic and sentential reasoning. When we representinformation diagrammatically, certain inferences are more easily made; others aremore difﬁcult. Likewise, the signiﬁcance of signs (natural and artiﬁcial) dependson their particular context. A pile of stones on the bank of a river indicates where 2 John Barwise later came to associate this essential aboutness of descriptive language with theviews of the English philosopher J. Austin, expressed mostly clearly in  and called the resultingnotion of proposition ‘austinian’. This was an essential ingredient of Barwise and Etchemendy’saccount on the Liar Paradox in . 4 Jeremy Seligman it is safe to ford; smoke rising from some point on the horizon means that there isa ﬁre there. The provision of a systematic account of such regularities was also adesideratum of the situation theory project but was overlooked in the SOST models.All of this was motivation for the development of the theory of classiﬁcation andchannels in , in which Barwise and I attempted to provide an account of infor-mation ﬂow that is more or less independent of an account of information content.Van Benthem, in , makes a useful distinction that will help to make this pointclearer. The deﬁning feature of information-as-range is the elimination of possibili-ties. When you pick a card from a pack without showing it to me, I know only that itis one of 54 possible cards. If I then learn that it is red, this number is cut in half. Theinformation that I have gained can be identiﬁed with this reduction of possibilities.Identifying the informational content of a sign with the range of possibilities con-sistent with it was the approach taken by Bar-Hillel and Carnap in their seminal .It is also implicit in the Tarskian approach to semantics and the ubiquitous conceptof a ‘Californian proposition’: a set of possible worlds.Information-as-range is to be distinguished from information-as-correlation , thesecond of van Benthem’s categories, according to which the informational con-tent of an event is given by other events with which it is correlated. The mercuryaligned with ‘70 ◦ ’ on the thermometer indicates that the air temperature is 70 ◦ Fbecause of the correlation between the temperature and the height of the mercury.The correlation, in this case, is due to certain laws of natural science, the particularconstruction of the thermometer with its helpful gradations, the physical proximityof the mercury bulb to the surrounding air, the relative kinetic stability of the air, thesrcin of the instrument (America, where the Fahrenheit scale is commonly used)and many other contingencies. In situation theoretic parlance, the correlation is dueto a ‘constraint’ that holds in the situation being described. Science typically stud-ied correlations from a probabilistic or statistical point of view. This is consideredin Section 2.5, below.From a slightly more abstract perspective, we can see that information-as-range oc-curs wherever there is a classiﬁcation of things into types. By knowing the type ortypes of an unknown thing, or ‘token’, one has some, albeit incomplete, informationby having eliminated those other things that are not of the same type. Information-as-correlation occurs when there is a systematic relationship between things of dif-ferent types. In  this is captured by the concept of a ‘channel’, in which thetypes and tokens of one classiﬁcation are related to those of another. The theory of classiﬁcation and channels from  is therefore very much in alignment with vanBenthem’s distinction.Yet despite these thematic connections and a number of common examples, muchwas left unsaid about the relationship between  and the earlier project of situa-tion theory. This paper will explore some more explicit connections in more detail,including an elaboration of van Benthem’s approach as an alternative interpretationof ST. Situation Theory Reconsidered 5 1 Twelve questions about Situation Theory Situation theory begins with the idea that reality is composed of situations whichdiffer in the information they support . The smallest unit of information is called an infon , which is the situation theoretic analogue of an atomic proposition. From thevery start, it is worth noting that situations, as constituents of reality, most naturallyfall within the scope of metaphysics, whereas the issue of what information theydo or do not support is at least partly epistemological. The development of the the-ory is characterised by conﬂicting intuitions from these two traditional domains of philosophy. We write s | = σ to mean that situation s supports infon σ . For example, suppose σ is the informationthat I am typing. This is supported by the situation s that I am currently part of, orrather one such situation because I participate in many simultaneously, some of which contain others. We write s t to mean that situation s is part of situation t , taking this to be a partial order (reﬂex-ive, transitive and antisymmetric). Situations are subject to certain constraints thatbind together infons more or less strongly. Given infons σ and τ , we write σ ⇒ τ for the constraint that σ involves τ . For example, the constraint I am typing slowly ⇒ I am typing would relate situations supporting the antecedent infon to those supporting the con-sequent infon quite strongly, whereas the constraint I am typing ‘slowly’ ⇒ you are reading ‘slowly’ is a little more tenuous. The relationship between the three relations , | = and ⇒ raises a number of questions, none of which were answered deﬁnitively by the earlypioneers of ST. 1.1 Parts and Persistence Question 1. Do situations support all the information supported by their parts? 3 A positive answer to this question amounts to acceptance of the following principle: 3 Considered by Barwise in  as Choice 6.