{"id":71,"date":"2012-07-06T12:38:55","date_gmt":"2012-07-06T02:38:55","guid":{"rendered":"http:\/\/stevewatson.info\/blog\/2012\/07\/06\/norms\/"},"modified":"2012-07-06T13:01:41","modified_gmt":"2012-07-06T03:01:41","slug":"norms","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2012\/07\/06\/norms\/","title":{"rendered":"Norms"},"content":{"rendered":"<p><font color=\"#000000\">Amongst the beliefs that are important in the subjective determination of interest-maximising behaviour are some that impose restrictions on the kinds of actions that the agent believes are permissible in certain circumstances. Such beliefs are beliefs about norms of action. Actions which fall outside the range permitted by the appropriate norms are not taken <i>even where taking them would lead to greater total satisfactions than any other action.<\/i><\/p>\n<p>A <u>Norm<\/u> is an action-directing rule, n, for which<\/p>\n<blockquote><p>\n\t(&exist;C<sub>x,applies<\/sub> &sub; C<sub>x<\/sub>) (&exist;&alpha;<sub>bad<\/sub>(x) &sub; &alpha;(x)) (&forall;c<sub>x,0<\/sub> &isin; C<sub>x,applies<\/sub>) (&forall;a<sub>x<\/sub> &isin; &alpha;<sub>bad<\/sub>(x)) [n &#038; a<sub>x<\/sub> |\u2013 &perp; ]\n<\/p><\/blockquote>\n<ul>\n<li>An equivalent condition might be written positively as<br \/>\n\t(&exist;C<sub>x,applies<\/sub> &sub; C<sub>x<\/sub>) (&exist;&alpha;<sub>good<\/sub>(x) &sub; &alpha;(x)) (&forall;c<sub>x,0<\/sub> &isin; C<sub>x,applies<\/sub>) (&forall;a<sub>x<\/sub> &notin; &alpha;<sub>good<\/sub>(x)) [n &#038; a<sub>x<\/sub> |\u2013 &perp; ]<\/p>\n<li>C<sub>x,applies<\/sub> and C<sub>x<\/sub> are sets of contexts for x. C<sub>x<\/sub> is the set of all possible contexts for x.<\/li>\n<li>The condition that makes n normatively prescriptive is a logical condition: the forbidden action is logically inconsistent with the norm. Accurate logical reasoning is at least a part of the process by which x goes about determining his action in the circumstances, though we cannot depend upon it being a main part or that it will be very accurate.<\/li>\n<\/ul>\n<table cellpadding=\"5\" cellspacing=\"0\" border=\"1\" width=\"100%\">\n<tr>\n<td>\n<b>Example:<\/b><\/p>\n<p>The reason for the indirect nature of the previous description of norms is that it is likely that the norms occur in a variety of forms. An example of the form of a simple norm might be:<\/p>\n<blockquote><p>\n\t(&forall;c<sub>x<\/sub> &notin; C<sub>x,war<\/sub> &cup; C<sub>x,self-defense<\/sub>) (&forall;a<sub>x<\/sub> &isin; &alpha;<sub>kill<\/sub>(x)) [~a<sub>x<\/sub>]\n<\/p><\/blockquote>\n<p>which would be the form of the general statement that \u2018Except in war or in self-defence, thou shalt not kill.\u2019<\/p>\n<p>Consider the case that might apply if x has been insulted. The reasoning could include<\/p>\n<ol start=\"i\">\n<li>c<sub>x,0<\/sub> &isin; C<sub>x,insult<\/sub><\/li>\n<li>(&exist;a<sub>x<\/sub> &isin; &alpha;<sub>kill<\/sub>(x))(&forall;a<sub>x<\/sub>\u2019 &ne; a<sub>x<\/sub>) [T(C(a<sub>x<\/sub>, c<sub>x,0<\/sub>, x), I(x), x) > T(C(a<sub>x<\/sub>\u2019, c<sub>x,0<\/sub>, x), I(x), x)]<\/li>\n<li>&there4; a<sub>x<\/sub>\t(by i., ii.)<\/li>\n<\/ol>\n<p>which is to say that the decision would be made to kill. But if the reasoning included the norm as sketched above, we would have <\/p>\n<ol start=\"i\">\n<li>c<sub>x,0<\/sub> &isin; C<sub>x,insult<\/sub><\/li>\n<li>(&exist;a<sub>x<\/sub> &isin; &alpha;<sub>kill<\/sub>(x))(&forall;a<sub>x<\/sub>\u2019 &ne; a<sub>x<\/sub>) [T(C(a<sub>x<\/sub>, c<sub>x,0<\/sub>, x), I(x), x) > T(C(a<sub>x<\/sub>\u2019, c<sub>x,0<\/sub>, x), I(x), x)]<\/li>\n<li>&there4; a<sub>x<\/sub>\t(by i., ii.)<\/li>\n<li>(&forall;c<sub>x<\/sub> &notin; C<sub>x,war<\/sub> &cup; C<sub>x,self-defense<\/sub>) (&forall;a<sub>x<\/sub> &isin; &alpha;<sub>kill<\/sub>(x)) [~a<sub>x<\/sub>]<\/li>\n<li>C<sub>x,insult<\/sub> &cap; (C<sub>x,war<\/sub> &cup; C<sub>x,self-defense<\/sub>) = &empty;<\/li>\n<li>c<sub>x,0<\/sub> &notin; C<sub>x,war<\/sub> &cup; C<sub>x,self-defense<\/sub><\/li>\n<li>&there4; ~a<sub>x<\/sub>\t(by iv. &#038; vi.)<\/li>\n<li>&there4; &perp;\t(by iii. &#038; vii.)<\/li>\n<\/ol>\n<p>Meaning that the decision to kill is impermissible\n<\/td>\n<\/tr>\n<\/table>\n<p>An agent x is an <u>Acceptant<\/u> of the norm n iff x accepts the rule n. We will write<\/p>\n<blockquote><p>\n\tK(n) = {x: B(x)[ n ]}\n<\/p><\/blockquote>\n<ul>\n<li>In this case, there is a condition for accepting that B(x)[ n ] based on the notion that we can discover whether x really accepts a norm by observation of his behaviour. Thus <br \/>\n   \t        B(x)[ n ] &rarr; (&exist;C<sub>x,applies<\/sub> &sub; C<sub>x<\/sub>) (&exist;&alpha;<sub>bad<\/sub>(x) &sub; &alpha;(x)) (&forall;c<\/sub>x,applies<\/sub> &isin; C<sub>x,applies<\/sub>) (&forall;a<sub>x,bad<\/sub> &isin; &alpha;<sub>bad<\/sub>(x))<br \/>\n\t                [n &#038; a<sub>x<\/sub> |\u2013 &perp; &rarr; A(x, c<sub>x,0<\/sub>) &ne; a<sub>x<\/sub>]<br \/>\n\twhich is to say that, if x produces an action in a circumstance in which the norm determines that that action is impermissible, then x cannot be said to accept that norm. <\/li>\n<li>The <i>reasons<\/i> why x might fail this test are many. It might just be that x is not very clever and fails to reason logically accurately; perhaps the norm is too complex for any human; perhaps information is lacking; etc. We do not need to assume that x is actually dishonest. <\/li>\n<li>It would seem, on the face of it anyway, that it\u2019s quite possible that ~B(x)[ n ] &#038; B(x)[ B(x)[ n ]]; and other curiosities of epistemic logic may also apply. It will be necessary eventually to decide which axiomatization of epistemic logic is most appropriate for the operator B. We can ignore the question for now.<\/li>\n<li>The condition given for x being an acceptant of n may not adequately reflect the fuzziness of our belief states, or the degrees to which we believe something. Assuming that we wish to do so, and that this cannot be done by massaging the context variable of the action function as it applies to the conditions under which we will apply the norm, we may propose the following refinement:\n<p>\tB(x)[ n ] &rarr; (&exist;C<sub>x,applies<\/sub> &sub; C<sub>x<\/sub>) (&exist;&alpha;<sub>bad<\/sub>(x) &sub; &alpha;(x)) (&forall;c<\/sub>x,applies<\/sub> &isin; C<sub>x,applies<\/sub>) (&forall;a<sub>x,bad<\/sub> &isin; &alpha;<sub>bad<\/sub>(x))<br \/>\n   \t        [((n &#038; a<sub>x<\/sub> |\u2013 &perp;) &#038; <br \/>\n\t        (&#038;forall>a<sub>x,alt<\/sub> &ne; ax)~B(x)[ (T(C(a<sub>x,alt<\/sub>, c<sub>x,0<\/sub>, x), I(x), x) ] >> T(C(a<sub>x<\/sub>, c<sub>x,0<\/sub>, x), I(x), x)) ])) <br \/>\n\t                &rarr; A(x, c<sub>x,0<\/sub>) &ne; a<sub>x<\/sub>]<\/p>\n<p>\tWhich is simply stating that x will not contravene n unless he estimates that the total satisfaction to be gained by doing so is sufficiently greater than the satisfaction to gained by abiding by n.<\/li>\n<li>The degree of excess expressed by \u2018>>\u2019 is left deliberately vague \u2013 as in other uses of it. (To be set, perhaps, by empirical research.)<\/li>\n<\/ul>\n<p>A <u>Norm Formation<\/u> is a set of norms, N = {n<sub>1<\/sub>, \u2026, n<sub>n<\/sub>}.<\/p>\n<ul>\n<li>an agent x is an acceptant of the norm formation N iff x accepts the rules in n. <br \/>\n\t        K(N) = {x: B(x)[ N ]}<\/li>\n<li>Standard classes of norm formations are conventions, traditions, etc. (which may be analysed later.)<\/li>\n<\/ul>\n<p><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Amongst the beliefs that are important in the subjective determination of interest-maximising behaviour are some that impose restrictions on the kinds of actions that the agent believes are permissible in certain circumstances. Such beliefs are beliefs about norms of action. Actions which fall outside the range permitted by the appropriate norms are not taken even [&hellip;]<\/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-71","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/71","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=71"}],"version-history":[{"count":0,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/71\/revisions"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=71"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=71"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=71"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}