{"id":130,"date":"2015-09-19T21:16:10","date_gmt":"2015-09-19T11:16:10","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/?p=130"},"modified":"2015-09-19T21:16:10","modified_gmt":"2015-09-19T11:16:10","slug":"institutions","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2015\/09\/19\/institutions\/","title":{"rendered":"Institutions"},"content":{"rendered":"

A class of ensembles can be defined for which the EX includes the acceptance of a norm formation. Amongst the subclasses of this we shall seek to define a class of \u2018institutions\u2019 that is suitable to play the theoretical role assigned to institutions in HLSTs (but without assuming that those theoretical roles in any particular HLST are well-defined or reflective of sociological reality.) In sociological theories institutions are generally reckoned to be significant features of a society, and there seems to be some primitive notion that underlies the use of the term, but as is often the case the precise definitions offered cover a range of related possibilities. The Stanford Encyclopedia of Philosophy<\/em> (Miller, S. 2011, s.v.<\/em> \u2018Social Institutions\u2019, \u00b61) provides a reasonable overview of the issues and begins by referring to a pair of representative definitions. The first by J. Turner (1997,\u00a0The Institutional Order<\/em>, New York: Longman, p. 6): \u201ca complex of positions, roles, norms and values lodged in particular types of social structures and organising relatively stable patterns of human activity with respect to fundamental problems in producing life-sustaining resources, in reproducing individuals, and in sustaining viable societal structures within a given environment.\u201d\u00a0And the second by Rom Harr\u00e9 (1979, Social Being<\/em>, Oxford: Blackwell, p. 98): \u201cAn institution was defined as an interlocking double-structure of persons-as-role-holders or office-bearers and the like, and of social practices involving both expressive and practical aims and outcomes.\u201d From such evidence, the consensus seems to be that an institution is a set of norms, rules of behaviour, etc. that creates a structure of interacting roles into which participants in the institution fit, and which is seen to have the function of achieving some end (whether or not it also has other functions.)<\/span><\/p>\n

The interactions defined by the norm formation have effects on the individual agents in the ensemble but they are defined in terms of subsets of the ensemble. The norm formation that is constitutive of the ensemble describes its functions and the means by which they are to be performed. Moreover, the rationality of any such norm formation will be judged by the consistency of its propositions with the supposed functions to be performed. However, the fact that there is a supposed \u2018function\u2019 for an institution is not<\/em> essential to its sociological characterization. That essential character is rather the system of interactions and roles that are created by the norm formation that characterizes the ensemble. In what follows therefore, institutions will be defined in terms of their sociologically relevant characteristics in the first place, and may then be tested for satisfactoriness in the theories in which institutional entities have a place. So:<\/span><\/p>\n

Let X<\/em> be a set of agents, R<\/em> = {r1<\/sub><\/em>, \u2026, rn<\/sub><\/em>} \u00cc 2X<\/sup><\/em> with (“x<\/em> \u00ce X<\/em>) ($ri<\/sub><\/em> \u00ce R<\/em>) [x <\/em>\u00ce ri<\/sub><\/em>], N<\/em> a norm formation.<\/span><\/p>\n

\u00ce<\/em> = (X<\/em>, R<\/em>, N<\/em>) is an Institution<\/u> if<\/span><\/p>\n

    \n
  1. N<\/em> \u00cc NO<\/sub><\/em>(X<\/em>)<\/span><\/li>\n
  2. (“ri<\/sub><\/em> \u00ce R<\/em>) ($n<\/em> \u00ce N<\/em>) ($rj<\/sub><\/em> \u00ce R<\/em>) (“x<\/em> \u00ce ri<\/sub><\/em>) ($Cx<\/sub><\/em> \u00cc k<\/em>x<\/sub><\/em>) (“cx<\/sub> <\/em>\u00ce Cx<\/sub><\/em>)<\/span><\/li>\n<\/ol>\n

    [g<\/em>(n<\/em>, cx<\/sub><\/em>) & ($y<\/em> \u00ce rj<\/sub><\/em>) ($ax<\/sub><\/em> \u00ce a<\/em>x<\/sub><\/em>) [g<\/em>(n<\/em>, ax<\/sub><\/em>) & e<\/em>(x<\/em>, ax<\/sub><\/em>, c<\/em>(x,y<\/em>}<\/sub>, qy<\/sub><\/em>, y<\/em>))] ]<\/span><\/p>\n

      \n
    • R<\/em>(\u00ce<\/em>) = R<\/em> is the Roleset<\/u> of \u00ce<\/em>. The elements of R<\/em>(\u00ce<\/em>) are the Roles<\/u> of \u00ce<\/em><\/span><\/li>\n
    • |\u00ce<\/em>| = X<\/em> is the membership of \u00ce<\/em><\/span><\/li>\n
    • N<\/em>(\u00ce<\/em>) = N<\/em> is the Ruleset<\/u> of \u00ce<\/em>. The elements of N<\/em>(\u00ce<\/em>) are the Rules<\/u> of \u00ce<\/em><\/span><\/li>\n<\/ul>\n

      Let \u00ce<\/em> = (X<\/em>, R<\/em>, N<\/em>) be an institution, ri<\/sub><\/em>, rj<\/sub><\/em> \u00ce R<\/em>. Write \u00e1ri<\/sub><\/em>, rj<\/sub><\/em>\u00f1N<\/sub><\/em> iff<\/span><\/p>\n

      ($n<\/em> \u00ce N<\/em>) (“x<\/em> \u00ce ri<\/sub><\/em>) ($Cx<\/sub><\/em> \u00cc k<\/em>x<\/sub><\/em>) (“cx<\/sub> <\/em>\u00ce Cx<\/sub><\/em>)<\/span><\/p>\n

      [g<\/em>(n<\/em>, cx<\/sub><\/em>) & ($y<\/em> \u00ce rj<\/sub><\/em>) ($ax<\/sub> <\/em>\u00ce a<\/em>x<\/sub><\/em>) [g<\/em>(n<\/em>, ax<\/sub><\/em>) & e<\/em>(x<\/em>, ax<\/sub><\/em>, c<\/em>{x<\/em>,y<\/em>} <\/sub>, qy<\/sub><\/em>, y<\/em>)]]<\/span><\/p>\n

        \n
      • e. There is a norm in N<\/em> such that in contexts governed by that norm, and for any x<\/em> in ri<\/sub><\/em> there is an action governed by that norm that has an act effect on some y<\/em> in rj<\/sub><\/em>.<\/span><\/li>\n
      • Read this as ri<\/sub><\/u><\/em> Acts On rj<\/sub><\/em> Under N<\/em><\/u> (or ri<\/sub><\/u><\/em> Acts On rj<\/sub><\/em> In <\/u>\u00ce<\/u><\/em>)<\/span><\/li>\n
      • N<\/em>: ri<\/sub><\/em> \u00be\u00ae rj<\/sub><\/em>, or, if the action element is part of a graphical representation of a collection of actions all governed by the same norm formation, then let N<\/em> be a label for that representation.<\/span><\/li>\n
      • Alternatively, \u00ce<\/em>: ri<\/sub><\/em> \u00be\u00ae rj<\/sub><\/em><\/span><\/li>\n
      • Note that this is modelled on the definition given for agent interactions<\/span><\/li>\n
      • I<\/em>RAD<\/em>(\u00ce<\/em>) = {<ri<\/sub><\/em>, rj<\/sub><\/em>>: ri<\/sub><\/em>, rj<\/sub><\/em> \u00ce R<\/em>(\u00ce<\/em>), \u00e1ri<\/sub><\/em>, rj<\/sub><\/em>\u00f1N<\/sub><\/em>}, the Institutional<\/u> Role Action Diagram<\/u>.<\/span><\/li>\n<\/ul>\n

        Let \u00ce1<\/sub><\/em> = (X<\/em>1<\/sub><\/em>, R<\/em>1<\/sub><\/em>, N<\/em>1<\/sub><\/em>) and \u00ce2<\/sub><\/em> = (X<\/em>2<\/sub><\/em>, R<\/em>2<\/sub><\/em>, N<\/em>2<\/sub><\/em>) be institutions.<\/span><\/p>\n

          \n
        1. If ($r<\/em> \u00ce R1<\/sub><\/em>) ($q<\/em> \u00ce R2<\/sub><\/em>) q<\/em> \u00cc r<\/em> then \u00ce2<\/sub><\/em> Supports<\/u> \u00ce1<\/sub><\/em><\/span><\/li>\n
        2. If ($r<\/em> \u00ce R1<\/sub><\/em>) ($q<\/em> \u00ce R2<\/sub><\/em>) q<\/em> = r<\/em> then \u00ce1<\/sub><\/em> and \u00ce2<\/sub><\/em> Intersect<\/u><\/span><\/li>\n<\/ol>\n

           <\/p>\n\n\n\n
           <\/p>\n

          Examples:<\/strong><\/span><\/p>\n

           <\/p>\n

          A typical institution is the Family. Now the family, like many other institutions \u2013 and all the most interesting ones \u2013 has a vast number of constitutive norms, most of them informal or unexpressed, and which differ from instance to instance of the institution. The family in Saudi Arabia or China is a different institution from the family in Australia. It\u2019s certainly also true that different versions of the institution are to be found within what generally count as social boundaries: for example, the family of Black-Americans is different from the family of Ozark Americans. The subdivisions of normative typology can be made presumably down to an arbitrarily low level if we assume that the only reasonable way to operationalise the concept of belief or desire is to infer it from the behaviours that they are supposed to produce in an intentional agent. (The nature of the constitutive norms is a vital topic of sociological study.) To speak of a family in loose terms, however, is to speak necessarily of an idealised or common or otherwise generalised version. We shall consider only a fragment of a standardised version of the institution of the family here.<\/span><\/p>\n

           <\/p>\n

          Let Family be \u00cefamily<\/sub><\/em> = (X<\/em>, R<\/em>family<\/sub><\/em>, N<\/em>family<\/sub><\/em>)<\/span><\/p>\n

          X<\/em> is the general population of the society in question.<\/span><\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Nfamily<\/sub> <\/em>= {n1<\/sub><\/em>, n2<\/sub><\/em>, n3<\/sub><\/em>, n4<\/sub><\/em>, \u2026} where<\/span><\/p>\n

          n1<\/sub><\/em> = \u2018If a man and woman have a child then they should be the father and mother of that child\u2019<\/span><\/p>\n

          n2<\/sub><\/em> = \u2018Parents don\u2019t have sex with their children\u2019<\/span><\/p>\n

          n3<\/sub><\/em> = \u2018Parents protect their children\u2019<\/span><\/p>\n

          n4<\/sub><\/em> = \u2018Parents should be married\u2019<\/span><\/p>\n

          \u2026<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Note that the norm formation proposed for this institution includes explicit definitions for some of the role memberships. That is not necessarily true of all institutions, for which the norm formations may appeal to concepts defined elsewhere.<\/span><\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 R<\/em>family<\/sub><\/em> = { r1<\/sub><\/em>, r2<\/sub><\/em>, r3<\/sub><\/em>, r4<\/sub><\/em>, \u2026} where<\/span><\/p>\n

          r1<\/sub><\/em> = Fathers\u00a0\u00a0\u00a0\u00a0\u00a0 = {x<\/em>: x<\/em> \u00ce X<\/em> & Male<\/em>(x<\/em>) & ($y<\/em> \u00ce X<\/em>)[Offspring_of<\/em>(y<\/em>, x<\/em>)]}<\/span><\/p>\n

          r2<\/sub><\/em> = Mothers\u00a0\u00a0\u00a0\u00a0 = {x<\/em>: x<\/em> \u00ce X<\/em> & Female<\/em>(x<\/em>) & ($y<\/em> \u00ce X<\/em>)[Offspring_of<\/em>(y<\/em>, x<\/em>)]}<\/span><\/p>\n

          r3<\/sub><\/em> = Parents\u00a0\u00a0\u00a0\u00a0\u00a0 = {x<\/em>: x<\/em> \u00ce r1<\/sub><\/em> \u00da x<\/em> \u00ce r2<\/sub><\/em>}<\/span><\/p>\n

          r4<\/sub><\/em> = Children\u00a0\u00a0\u00a0 = {x<\/em>: x<\/em> \u00ce X<\/em> & ($y<\/em> \u00ce X<\/em>)[ Offspring_of<\/em>(x<\/em>, y<\/em>) ])}<\/span><\/p>\n

          r5<\/sub><\/em> = Married Persons<\/span><\/p>\n

          \u2026<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Membership of the role of \u2018Married Person\u2019 is not defined by the norms included in the fragment above.<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The predicate functions used above are undefined, but have the obvious definitions.<\/span><\/p>\n

           <\/p>\n

          It is clear even from the fragment presented that institutions do not exist in isolation. It may turn out that each institution essentially depends for its character upon its position in a system of interlocking institutions \u2013 in the same way that the meanings of words in a language can hardly be said to exist in isolation. To illustrate the systematic nature of institutions we present a fragment of a formal model of the institution of Marriage.<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Let Marriage be \u00cemarriage<\/sub><\/em> = (X<\/em>, R<\/em>marriage<\/sub><\/em>, N<\/em>marriage<\/sub><\/em>)<\/span><\/p>\n

          X<\/em> is the general population of the society in question.<\/span><\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Nmarriage<\/sub> <\/em>= {n1<\/sub><\/em>, n2<\/sub><\/em>, n3<\/sub><\/em>, n4<\/sub><\/em>, \u2026} where<\/span><\/p>\n

          n1<\/sub><\/em> = \u2018parents should be married\u2019<\/span><\/p>\n

          n2<\/sub><\/em> = \u2018A man and a woman who are married have sex only with each other\u2019<\/span><\/p>\n

          n3<\/sub><\/em> = \u2018A married couple cooperate\u2019<\/span><\/p>\n

          n4<\/sub><\/em> = \u2018A marriage is performed by a celebrant\u2019<\/span><\/p>\n

          \u2026<\/span><\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 R<\/em>marriage<\/sub><\/em> = { r1<\/sub><\/em>, r2<\/sub><\/em>, r3<\/sub><\/em>, r4<\/sub><\/em>, \u2026} where<\/span><\/p>\n

          r1<\/sub><\/em> = Males<\/span><\/p>\n

          r2<\/sub><\/em> = Females<\/span><\/p>\n

          r3<\/sub><\/em> = Celebrants = {x<\/em>: x<\/em> \u00ce X<\/em> & ($y,z<\/em> \u00ce X<\/em>)[ Marries<\/em>(x<\/em>, y, z<\/em>) ])}<\/span><\/p>\n

          r4<\/sub><\/em> = Married Persons\u00a0\u00a0\u00a0 = {x<\/em>: ($y,z<\/em> \u00ce X<\/em>)[ Marries<\/em>(y<\/em>, x, z<\/em>) ]}<\/span><\/p>\n

          r5<\/sub><\/em> = Parents<\/span><\/p>\n

          \u2026<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Here membership of the role of \u2018Married Person\u2019, which was not defined in the institutional norms of marriage above, is defined by the institutional norms of marriage.<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 r5<\/sub><\/em> \u00ce Rfamily<\/sub><\/em> = r4<\/sub><\/em> \u00ce Rmarriage<\/sub><\/em> (amongst others) so \u00cefamily<\/sub><\/em> intersects with \u00cemarriage<\/sub><\/em> and these two institutions support one another.<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Note that the role of married persons might very well be defined by the appropriate norm formations as {x<\/em>: ($y,z<\/em> \u00ce X<\/em>)[ (Male<\/em>(x<\/em>) \u00db Female<\/em>(z<\/em>)) & Marries<\/em>(y<\/em>, x, z<\/em>) ]} which indicates how the recent controversy over \u2018same-sex marriage\u2019 may be interpreted as a controversy not just over moral rights but over the very constitution of the institution of marriage.<\/span><\/p>\n

          \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Note that in the two examples given, the participants in the institutions are assumed to be the general population. That is simply a convenience and is probably not accurate.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          Institutional Functions<\/em><\/strong><\/span><\/p>\n

          Questions must arise as to the degree to which any set of norms can be unambiguously identified as forming a natural basis for an institution. Two observations may be made with respect to this: first, that the identification of such norm formations is an appropriate study of sociologists and will be sensitive to the type of theory being proposed (as it is unlikely that institutions form natural kinds;) and second, that the most profitable direction of enquiry into the \u2018essence\u2019 of any institution must be toward the function of the institution.<\/span><\/p>\n

          Ideal Functions<\/u><\/em><\/span><\/p>\n

          Let X<\/em> be a set of agents in the general population of the society in question.<\/span><\/p>\n

          Let \u00ce<\/em> = (X<\/em>, R<\/em>, N<\/em>) be an institution as defined.<\/span><\/p>\n

          We define an Ideal Institutional Context Consequence Function<\/u> as:<\/span><\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 CI<\/sub><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = cX,1<\/sub><\/em> iff<\/span><\/p>\n

          (“x<\/em> \u00ce X<\/em>)[ g<\/em>(N<\/em>, cx,0<\/sub><\/em>) \u00de [(ax,0<\/sub> <\/em>= Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>)) \u00de (\u00a3N<\/sub><\/em>(ax,0<\/sub><\/em>)\u00da\u00afN<\/sub><\/em>(ax,0<\/sub><\/em>)]] \u00de C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) = cX,1<\/sub><\/em><\/span><\/p>\n

            \n
          • In the above we make the obvious extension to the context consequence function:<\/span><\/li>\n<\/ul>\n

            C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) = \u00c8x<\/sub><\/em>\u00ce<\/sub>X<\/sub><\/em> C<\/em>(ax,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>).<\/span><\/p>\n

              \n
            • In most reasonable interpretations of the modal operators modal disjunction above could be replaced with a simple \u00af<\/span><\/li>\n
            • Although the IICCF uses the same function letter as the standard context consequence function, the functions are easily distinguished by the arguments.<\/span><\/li>\n
            • The function is an ideal<\/em> function since the definition describes the context consequence of every relevant agent doing as the institutional norms require. This is never likely to be the actual situation even if every agent was an acceptant of those norms \u2013 unless the norms simply describe the actions of every agent, in which case it will apply by fiat; but we discounted that interpretation of norms in the relevant chapter.<\/span><\/li>\n<\/ul>\n

              What we mean by the function of an institution may not, however, be best captured by defining it as the immediate consequence of the relevant agents acting consistently with its norms. It may be that given certain sorts of contexts as starting points, the immediate consequence of the operation of the institution does not achieve the intuitively felt \u2018function\u2019 of that institution. Thus we may seek a definition that captures the notion of \u2018in the long run\u2019.<\/span><\/p>\n

              We describe the Ideal Institutional Context Consequence Sequence<\/u> as:<\/span><\/p>\n

              C<\/u><\/em>I<\/sub><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = <cX,i<\/sub><\/em>: 0 < i<\/em>, cX,i<\/sub><\/em>+1<\/em><\/sub> = CI<\/sub><\/em>(\u00ce, <\/em>cX,i<\/sub><\/em>, X<\/em>)><\/span><\/p>\n

              One possible notion of function might be:<\/span><\/p>\n

              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 c<\/em> is an ideal function of \u00ce<\/em> iff ($i<\/em>)[c<\/em> \u00ce C<\/u>I<\/sub><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em>]<\/span><\/p>\n

              This would, however, have the consequence of making trivialities or human universals be the functions of any institution. For example, the fact that humans walk on two legs would on this definition be a consequence of the institution of Marriage, since it occurs in every context of the ideal institutional sequence. This is unlikely to be a satisfactory notion.<\/span><\/p>\n

              Define instead an Ideal Strict Institutional Context Consequence Function<\/u> as:<\/span><\/p>\n

              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 CI<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = cX,1<\/sub><\/em> iff cX,1<\/sub><\/em> = { p<\/em> \u00ce CI<\/sub><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>):<\/span><\/p>\n

                \n
              1. (“x<\/em> \u00ce X<\/em>)[ g<\/em>(N<\/em>, cx,0<\/sub><\/em>) \u00de [(ax,0<\/sub> <\/em>= Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>)) \u00de (\u00a3N<\/sub><\/em>(ax,0<\/sub><\/em>)\u00da\u00afN<\/sub><\/em>(ax,0<\/sub><\/em>)]] \u00de<\/span><\/li>\n<\/ol>\n

                p<\/em> \u00ce C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) &<\/span><\/p>\n

                  \n
                1. ($X\u2019<\/em> \u00cc X<\/em>)(“x<\/em> \u00ce X\u2019<\/em>)[ g<\/em>(N<\/em>, cx,0<\/sub><\/em>) & (ax,0<\/sub> <\/em>= Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>)) & ~(\u00a3N<\/sub><\/em>(ax,0<\/sub><\/em>)\u00da\u00afN<\/sub><\/em>(ax,0<\/sub><\/em>)] \u00de<\/span><\/li>\n<\/ol>\n

                  p<\/em> \u00cf C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) \u00a0\u00a0\u00a0\u00a0\u00a0 }<\/span><\/p>\n

                    \n
                  • p<\/em> is a propositional description of some fact concerning the context of x<\/em> or X<\/em> as appropriate. Each context cx<\/sub><\/em> or cX<\/sub><\/em> is a set of such propositions. This was simply assumed to be clear earlier, but now needs to be made explicit.<\/span><\/li>\n<\/ul>\n

                    And the Ideal Strict Institutional Context Consequence Sequence<\/u> as:<\/span><\/p>\n

                    C<\/u><\/em>I<\/sub><\/em>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = <cX,i<\/sub><\/em>: 0 < i<\/em>, cX,i<\/sub><\/em>+1<\/em><\/sub> = CI<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,i<\/sub><\/em>, X<\/em>)><\/span><\/p>\n

                    In fact according to the normal usage of the term \u2018function,\u2019 we have already defined an ideal institutional function in the definition of the ideal strict institutional context consequence function; however, the use of the term in the discussion of institutional functions generally is best understood as a predicate or predicates, which we may define thus:<\/span><\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 p<\/em> or c<\/em> is an Ideal Institutional Function<\/u> of \u00ce<\/em> given cX,0<\/sub><\/em> iff \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ($i<\/em>)[c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em>] or<\/span><\/p>\n

                    ($i<\/em>)[c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em> & p<\/em> \u00ce c<\/em>]<\/span><\/p>\n

                      \n
                    • p<\/em> a proposition, c<\/em> a context as used above<\/span><\/li>\n
                    • where cX,0<\/sub> <\/em>is understood we may disregard it<\/span><\/li>\n
                    • write F<\/em>I<\/sub><\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) or F<\/em>I<\/sub><\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(c<\/em>)<\/span><\/li>\n
                    • an ideal institutional function p<\/em> is Transient<\/u> if <\/span>
                      \n (“i<\/em>)[(c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)I<\/sub><\/em> & p<\/em> \u00ce c<\/em>) \u00de ($j<\/em>>i<\/em>)(“c<\/em>)[c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)j<\/sub><\/em> \u00de p<\/em> \u00cf c<\/em>] ]<\/span><\/li>\n<\/ul>\n

                      and similarly for the ideal institutional function c<\/em>.<\/span><\/p>\n

                        \n
                      • an ideal institutional function p<\/em> is Recurrent<\/u> if <\/span>
                        \n (“i<\/em>)[(c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)I<\/sub><\/em> & p<\/em> \u00ce c<\/em>) \u00de ($j<\/em>>i<\/em>)(“c<\/em>)[c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)j<\/sub><\/em> \u00de p<\/em> \u00cf c<\/em>] ] &<\/span><\/li>\n<\/ul>\n

                        (“i<\/em>)(“c<\/em>)[(c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em> \u00de p<\/em> \u00cf c<\/em>) \u00de ($j<\/em>>i<\/em>) [c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)j<\/sub><\/em> & p<\/em> \u00ce c<\/em>]]<\/span><\/p>\n

                        and similarly for the ideal institutional function c<\/em>.<\/span><\/p>\n

                        Note that every recurrent institutional function is transient.<\/span><\/p>\n

                          \n
                        • an ideal institutional function p<\/em> is Enduring<\/u> if <\/span>
                          \n ($j<\/em>)(“i<\/em>>j<\/em>)($c<\/em>)[c<\/em> \u00ce C<\/u>I<\/sub>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em> & p<\/em> \u00ce c<\/em>]<\/span><\/li>\n<\/ul>\n

                          and similarly for the ideal institutional function c<\/em>.<\/span><\/p>\n

                          Real Functions<\/u><\/em><\/span><\/p>\n

                          Most of the hard definitional work has now been done and we can proceed more quickly through definitions of more immediately useful institutional characteristics. The ideal function of an institution is of interest for someone who wishes to design an institution or who wishes to understand the intention of one who plans an institution, but it is unlikely to accurately describe the function of the institution as it actually operates. That function depends upon being an acceptant \u2013 or behaving as an acceptant \u2013 of the norms that constitute the institution, but we accepted that for various reasons these norms might not always be followed even by an \u2018acceptant.\u2019 It was proposed, for example, that we could adequately capture the belief that x <\/em>will not contravene n<\/em> unless he estimates that the total satisfaction to be gained from doing so is sufficiently greater than the satisfaction to be gained from abiding by n<\/em> in the condition:<\/span><\/p>\n

                          Bx<\/sub><\/em>[ n<\/em> ] \u00de ($Cx,applies<\/sub><\/em> \u00cc k<\/em>x<\/sub><\/em>) ($a<\/em>x,bad<\/sub><\/em> \u00cc a<\/em>x<\/sub><\/em>) (“cx,applies<\/sub> <\/em>\u00ce Cx,applies<\/sub><\/em>) (“ax<\/sub> <\/em>\u00ce a<\/em>x,bad<\/sub><\/em>) (“cx,0<\/sub> <\/em>\u00ce k<\/em>x<\/sub><\/em>)<\/span><\/p>\n

                          [((cx,0<\/sub><\/em> = cx,applies<\/sub><\/em> \u00de n<\/em> & ax<\/sub><\/em> |\u2013 ^) &<\/span><\/p>\n

                          ~Bx<\/sub>\u00ad<\/em>[ (“ax,alt<\/sub><\/em> \u00b9 ax<\/sub><\/em>)[T<\/em>(C<\/em>(ax,alt<\/sub><\/em>, cx,0<\/sub><\/em>, x<\/em>), Ix<\/sub><\/em>, x<\/em>) << T<\/em>(C<\/em>(ax<\/sub><\/em>, cx,0<\/sub><\/em>, x<\/em>), Ix<\/sub><\/em>, x<\/em>)] ])<\/span><\/p>\n

                          \u00de Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>) \u00b9 ax<\/sub><\/em>]<\/span><\/p>\n

                          Should this be the case, or should some other interference in the \u2018ideal\u2019 action of the acceptant of the institutional N<\/em> occur, the ideal function may fail. We need therefore to speak of the actual<\/em> institutional functions.<\/span><\/p>\n

                          Let X<\/em> be a set of agents in the general population of the society in question.<\/span><\/p>\n

                          Let \u00ce<\/em> = (X<\/em>, R<\/em>, N<\/em>) be an institution as defined.<\/span><\/p>\n

                          We define an Institutional Context Consequence Function<\/u> as:<\/span><\/p>\n

                          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 C<\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = cX,1<\/sub><\/em> iff (“x<\/em> \u00ce X<\/em>)[ x<\/em> \u00ce K<\/em>(N<\/em>) & ax,0<\/sub> <\/em>= Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>)] \u00de C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) = cX,1<\/sub><\/em><\/span><\/p>\n

                            \n
                          • The institutional context consequence function describes (obviously) the real consequence of the institution.<\/span><\/li>\n
                          • In the above we must take into full account the brief considerations made when introducing norm-directed behaviour that the action function will need to account for \u2018degrees of belief\u2019 in the norms, possible irrationality, possible epistemological limitations, etc.<\/span><\/li>\n<\/ul>\n

                            We describe the Institutional Context Consequence Sequence<\/u> as:<\/span><\/p>\n

                            C<\/u><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = <cX,i<\/sub><\/em>: 0 < i<\/em>, cX,i<\/sub><\/em>+1<\/em><\/sub> = C<\/em>(\u00ce, <\/em>cX,i<\/sub><\/em>, X<\/em>)><\/span><\/p>\n

                            Define a Strict Institutional Context Consequence Function<\/u> as:<\/span><\/p>\n

                            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 CS<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = cX,1<\/sub><\/em> iff cX,1<\/sub><\/em> = { p<\/em> \u00ce C<\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>):<\/span><\/p>\n

                              \n
                            1. (“x<\/em> \u00ce X<\/em>) [ x<\/em> \u00ce K<\/em>(N<\/em>) & ax,0<\/sub> <\/em>= Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>)] \u00de p<\/em> \u00ce C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) &<\/span><\/li>\n
                            2. ($X\u2019<\/em> \u00cc X<\/em>)(“x<\/em> \u00ce X\u2019<\/em>) [ x<\/em> \u00cf K<\/em>(N<\/em>) & ax,0<\/sub> <\/em>= Ax<\/sub><\/em>(qx,0<\/sub><\/em>, cx,0<\/sub><\/em>)] \u00de p<\/em> \u00cf C<\/em>(aX,0<\/sub><\/em>, cX,0<\/sub><\/em>, X<\/em>) }<\/span><\/li>\n<\/ol>\n

                              And the Strict Institutional Context Consequence Sequence<\/u> as:<\/span><\/p>\n

                              C<\/u><\/em>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>) = <cX,i<\/sub><\/em>: 0 < i<\/em>, cX,i<\/sub><\/em>+1<\/em><\/sub> = CS<\/sup><\/em>(\u00ce, <\/em>cX,i<\/sub><\/em>, X<\/em>)><\/span><\/p>\n

                              Which leads us to the definitions of appropriate predicates as:<\/span><\/p>\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 p<\/em> or c<\/em> is an Institutional Function<\/u> of \u00ce<\/em> given cX,0<\/sub><\/em> iff \u00a0\u00a0\u00a0 ($i<\/em>)[c<\/em> \u00ce C<\/u>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em>] or<\/span><\/p>\n

                              ($i<\/em>)[c<\/em> \u00ce C<\/u>S<\/sup><\/em>(\u00ce, <\/em>cX,0<\/sub><\/em>, X<\/em>)i<\/sub><\/em> & p<\/em> \u00ce c<\/em>]<\/span><\/p>\n

                                \n
                              • write F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) or F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(c<\/em>)<\/span><\/li>\n
                              • The obvious modifications give us also transient, recurrent, and enduring institutional functions.<\/span><\/li>\n<\/ul>\n

                                Intentional Functions<\/u><\/em><\/span><\/p>\n

                                When (“x<\/em> \u00ce X<\/em>)[Dx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) ]] we may speak of p <\/em>being the Desired Institutional Function<\/u>, F<\/em>D<\/sub><\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>)<\/span><\/p>\n

                                If (“x<\/em> \u00ce X<\/em>)[Bx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) ]] the p<\/em> is the Believed Institutional Function<\/u>, F<\/em>B<\/sub><\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>)<\/span><\/p>\n

                                The concepts of\u00a0manifest and latent function\u00a0were introduced into sociology by Robert K. Merton (1957, Social Theory and Social Structure<\/em>, New York: Free Press of Glencoe, p. 51). He states there that manifest functions are \u201cthose objective consequences contributing to the adjustment or adaptation of the system which are intended and recognised by participants in the system,\u201d while latent functions are simply \u201cthose which are neither anticipated nor recognised.\u201d They can be defined using the tools developed above. Thus:<\/span><\/p>\n

                                If F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) & (“x<\/em> \u00ce X<\/em>)[Dx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) & Bx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>)]] then p<\/em> is a Manifest Institutional Function<\/u>, F<\/em>M<\/sub><\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>)<\/span><\/p>\n

                                If F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) & (“x<\/em> \u00ce X<\/em>)[ ~Dx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) & ~Bx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) ]] then p<\/em> is a Latent Institutional Function<\/u>, F<\/em>L<\/sub><\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>)<\/span><\/p>\n

                                  \n
                                • Whether this is exactly what Merton had in mind however is open to dispute (Helm, P. 1971, \u2018Manifest and Latent Functions\u2019 The Philosophical Quarterly<\/em>, v. 21, no. 82, pp 51-60) since X<\/em> (the relevant set of agents) is not defined, it isn\u2019t known whether the universal quantifier is intended here, it\u2019s not clear what is intended by \u2018unintended,\u2019 etc.<\/span><\/li>\n
                                • Nor are there distinctions made between transient, recurrent, or enduring functions.<\/span><\/li>\n
                                • Merton also desired to distinguish between functions and \u2018dysfunctions\u2019, which do not assist the system to adapt and adjust to the environment \u2013 but there is no such distinction made above.<\/span><\/li>\n
                                • In short, it isn\u2019t obvious that this is a necessary or useful pair of institutional functions<\/span><\/li>\n<\/ul>\n

                                  If F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) & (“x<\/em> \u00ce X<\/em>)[~Dx<\/sub><\/em>[F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>)] then p<\/em> is what Merton would call an \u2018unintended consequence,\u2019 and in the current terminology we might label it the Undesired Real Institutional Function<\/u>.<\/span><\/p>\n

                                  Institutional Norms<\/em><\/strong><\/span><\/p>\n

                                  From the above it seems that it is possible to use the notion of action governed by norms to define a \u2018function\u2019 of an institution. It is also possible to use the notion of the function of an institution to determine the \u2018essential\u2019 norms of an institution. The point of this is to attempt to establish the boundaries of an institution. For example, referring to the examples above, does the institution of Marriage as understood by the relevant agents exclude, normatively, homosexual pairings? Does the institution of Family allow polyamorous unions or divorces?<\/span><\/p>\n

                                  Let p<\/em> be such that F<\/em>(\u00ce<\/em>)(cX,0<\/sub><\/em>)(p<\/em>) for \u00ce<\/em> = (X<\/em>, R<\/em>, N<\/em>).<\/span><\/p>\n

                                  Suppose that<\/span><\/p>\n

                                    \n
                                  1. ($N1<\/sub><\/em> \u00cc N<\/em>) F<\/em>(\u00ce<\/em>1<\/sub><\/em>)(cX,0<\/sub><\/em>)(p<\/em>) for \u00ce<\/em>1<\/sub><\/em> = (X<\/em>, R1<\/sub><\/em>, N1<\/sub><\/em>) and<\/span><\/li>\n
                                  2. (“N2<\/sub><\/em> \u00cc N1<\/sub><\/em>)~F<\/em>(\u00ce<\/em>2<\/sub><\/em>)(cX,0<\/sub><\/em>)(p<\/em>) for \u00ce<\/em>2<\/sub><\/em> = (X<\/em>, R2<\/sub><\/em>, N2<\/sub><\/em>)<\/span><\/li>\n<\/ol>\n

                                    We may say that N1<\/sub><\/em> is a Minimal Norm Formation<\/u> for the function p<\/em> of the institution \u00ce<\/em><\/span><\/p>\n

                                      \n
                                    • There is no reason to think that any minimal norm formation is unique.<\/span><\/li>\n
                                    • Note that the functions of an institution are not assumed to be unique, and the set of minimal norm formations for p<\/em> in \u00ce<\/em> will also vary with that variable.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                                      A class of ensembles can be defined for which the EX includes the acceptance of a norm formation. Amongst the subclasses of this we shall seek to define a class of \u2018institutions\u2019 that is suitable to play the theoretical role assigned to institutions in HLSTs (but without assuming that those theoretical roles in any particular […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[],"class_list":["post-130","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/130","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/comments?post=130"}],"version-history":[{"count":1,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/130\/revisions"}],"predecessor-version":[{"id":131,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/130\/revisions\/131"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}