{"id":73,"date":"2014-01-04T10:33:57","date_gmt":"2014-01-04T00:33:57","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/2014\/01\/04\/identity\/"},"modified":"2014-01-06T11:22:37","modified_gmt":"2014-01-06T01:22:37","slug":"identity","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2014\/01\/04\/identity\/","title":{"rendered":"Identity"},"content":{"rendered":"


\nLet X<\/i> be an ensemble and x<\/i> an individual. This individual may or may not be aware of their membership status wrt X<\/i>, and may or may not correctly understand their status<\/p>\n\n\n\n\n
<\/td>\nBx<\/sub><\/i>[ x<\/i> ∈ X<\/i> ]<\/td>\nBx<\/sub><\/i>[ x<\/i> ∉ X<\/i> ]<\/td>\n<\/tr>\n
x<\/i> ∈ X<\/i><\/td>\nIdentity<\/td>\nFalse Alienity<\/td>\n<\/tr>\n
x<\/i> ∉ X<\/i><\/td>\nFalse Identity<\/td>\nAlienity<\/td>\n<\/tr>\n<\/table>\n

<\/p>\n\n\n\n\n
<\/td>\n~Bx<\/sub><\/i>[ x<\/i> ∈ X<\/i> ]<\/td>\n~Bx<\/sub><\/i>[ x<\/i> ∉ X<\/i> ]<\/td>\n<\/tr>\n
x<\/i> ∈ X<\/td>\nLatent Identity<\/td>\nPre-Identity<\/td>\n<\/tr>\n
x<\/i> ∉ X<\/i><\/td>\nPre-Alienity<\/td>\nLatent Alienity<\/td>\n<\/tr>\n<\/table>\n

Let X<\/i> be an ensemble.
\nWe say x<\/i> is a Conscious Member<\/u> of X<\/i> if x<\/i> ∈ X<\/i> & Bx<\/sub><\/i>[ x<\/i> ∈ X<\/i> ]
\nX<\/i> is a Conscious Ensemble<\/u> if (∀x<\/i> ∈ X<\/i>) Bx<\/sub><\/i>[ x<\/i> ∈ X<\/i> ]<\/p>\n

    \n
  • Note that it is widely accepted that groups are necessarily conscious ensembles; i.e.:
    \nγ(G<\/i>) → (∀x<\/i> ∈ G<\/i>) Bx<\/sub><\/i>[ x<\/i> ∈ G<\/i> ]\n<\/ul>\n

    \nThe conscious memberships of an individual define its Identity<\/u> wrt society<\/i>. Thus for the individual x<\/i> who is a conscious member of ensembles X1<\/sub>, \u2026, Xn<\/sub><\/i>, the identity of x<\/i> is that collection, and we write:
    \nID<\/i>(x<\/i>) = {X1<\/sub>, \u2026, Xn<\/sub><\/i>} iff x<\/i> ∈ X1<\/sub><\/i> ∩ \u2026 ∩ Xn<\/sub><\/i> & Bx<\/sub><\/i>[ x<\/i> ∈ X1<\/sub><\/i> ∩ \u2026 ∩ Xn<\/sub><\/i> ]<\/p>\n

    \nSome sets of ensembles are mutually exclusive wrt membership. A collection of such ensembles δ = {X1, \u2026, Xn}, that minimally covers another ensemble, X<\/i>, is a Division<\/u> of that ensemble and we write δ|X<\/i>. Thus,
    \n{X1<\/sub>, \u2026, Xn<\/sub><\/i>} is a division of X<\/i> iff:<\/p>\n

      \n
    1. X1<\/sub>, \u2026, Xn<\/sub><\/i> are relatively disjoint, and\n
    2. X<\/i> ⊂ ∪i=1,\u2026,n<\/sub><\/i> Xi<\/sub>, and\n
    3. For i = 1, \u2026, n<\/i>, X<\/i> ∩ Xi<\/sub><\/i> ≠ ∅.\n<\/ol>\n

      Where δ is a division of X<\/i> and x<\/i> ∈ X<\/i>, ID<\/i>(x<\/i>|δ) is the element of δ of which x<\/i> is a conscious member. Read it as the Identity of x<\/i> wrt δ<\/U>. Thus: For δ = {X1<\/sub>, \u2026, Xn<\/sub><\/i>}, δ|X<\/i>, ID<\/i>(x<\/i>|δ) = Xj<\/sub><\/i> iff x<\/i> ∈ Xj<\/sub><\/i> & Bx<\/sub><\/i>[ x<\/i> ∈ Xj<\/sub><\/i> ]<\/p>\n

        \n
      • Where δ1<\/i><\/sub>, \u2026, δn<\/i><\/sub> are divisions of X<\/i>, we can call A<\/i> = {δ1<\/i><\/sub>, \u2026, δn<\/i><\/sub>} an Identity Analysis<\/u> of X<\/i>.\n
      • Let A<\/i> = {δ1<\/i><\/sub>, \u2026, δn<\/i><\/sub>} be an analysis of X<\/i>. Then the identity of x<\/i> wrt that analysis is:
        \nID<\/i>(x<\/i>|A<\/i>) = {ID<\/i>(x<\/i>|δ1<\/i><\/sub>), \u2026, ID<\/i>(x<\/i>|δn<\/i><\/sub>)}\n<\/ul>\n

        <\/p>\n\n\n
        \nExample:<\/b><\/p>\n

        A person may be a male, Christian, labourer, for which we write: let ξ1<\/sub> = {\u2018Male\u2019}, ξ2<\/sub> = {\u2018Christian\u2019}, ξ3<\/sub> = {\u2018Labourer\u2019}, x<\/i> ∈ X1<\/sub><\/i>, X2<\/sub><\/i>, X3<\/sub><\/i> such that ξ1<\/sub>(X1<\/sub><\/i>), ξ2<\/sub>(X2<\/sub><\/i>), ξ1<\/sub>(X3<\/sub><\/i>).
        \nIf these are all conscious ensemble memberships their identity wrt society is male, Christian, labourer. <\/p>\n

        A set of ensembles defined by religious affiliation is typically mutually exclusive \u2013 especially if they are conscious ensembles \u2013 since if one is a Christian one can\u2019t be a Buddhist or a Hindu, and if one is a Hindu then one is not Buddhist or Christian, and, of course, if one is Buddhist then one is not Christian or Hindu. Similarly for socio-economically defined ensembles, or educational, or residential ensembles, etc. <\/p>\n

        An example of a division might be the confessional allegiances in a nation. If the citizens are one only of Buddhist or Hindu \u2013 as in Sri Lanka \u2013 then {Buddhists, Hindus} is a division of Sri Lanka. Since there are no Christians (we\u2019ll pretend), {Buddhists, Hindus, Christians} is not a division of Sri Lanka, though it contains one.<\/p>\n

        Suppose we have X<\/i> = Sri Lanka, δ = {Buddhists, Hindus}, then it might be that ID<\/i>(Bob|δ) = Buddhist (if Bob is a Buddhist.)<\/p>\n

        An identity analysis of Sri Lanka might include divisions according to religious and racial and linguistic criteria. Thus we might have X<\/i> = Sri Lanka, δ1<\/sub> = {Buddhists, Hindus}, δ2<\/sub> = {monolingual Tamil, monolingual Singhala, bilingual}, δ3<\/sub> = {Tamil, Singhala}. Then A = {δ1<\/sub>, δ2<\/sub>, δ3<\/sub>} would be an analysis of Sri Lanka. <\/p>\n

        So far as this analysis goes ID<\/i>(Bob|A) = {Hindu, monolingual Tamil, Tamil}\n<\/td>\n<\/tr>\n<\/table>\n

        <\/font><\/p>\n","protected":false},"excerpt":{"rendered":"

        Let X be an ensemble and x an individual. This individual may or may not be aware of their membership status wrt X, and may or may not correctly understand their status Bx[ x ∈ X ] Bx[ x ∉ X ] x ∈ X Identity False Alienity x ∉ X False Identity Alienity ~Bx[ […]<\/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-73","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/73","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=73"}],"version-history":[{"count":0,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/73\/revisions"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=73"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=73"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=73"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}