{"id":604,"date":"2026-02-13T16:13:15","date_gmt":"2026-02-13T06:13:15","guid":{"rendered":"https:\/\/stevewatson.info\/blog\/?p=604"},"modified":"2026-02-13T16:44:01","modified_gmt":"2026-02-13T06:44:01","slug":"information","status":"publish","type":"post","link":"https:\/\/stevewatson.info\/blog\/2026\/02\/13\/information\/","title":{"rendered":"Information"},"content":{"rendered":"\n<p class=\"has-black-color has-text-color has-link-color wp-elements-823b703c2175ea8d553333088f8d56ae\">An important aspect of communication relates to the transfer of information, but the treatment of information as a sociological phenomenon cannot be limited to its associations with communication alone: of equal importance are questions of creation, access, accumulation, transformation, function, social effect, etc. To address such issues, we will need to begin with an appropriate understanding of what \u2018information\u2019 means in the sociological context. Unfortunately, \u2018information\u2019 in that context (or in most others for that matter) is a term that is more widely used than analysed; and we do not get much relevant enlightenment from the few fields of study where it has been treated rigorously such as Computer Science and Communication Studies. The definitions and investigations of information and its characteristics appropriate to those fields are those inspired by the work of Shannon and Weaver ((1949) <em>The Mathematical Theory of Communication<\/em>, Urbana, IL: University of Illinois Press) and are concerned with quantitative aspects of \u2018information\u2019 such as the amount of uncertainty in a variable or the ability to reconstruct messages sent over noisy channels rather than anything relevant to the questions mentioned above.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-d4cdab6e6f4f034f69208b1ced88ce1a\">The (non-quantitative) understanding of information that is intuitively appealed to in most other fields is rather that identified by Dretske (1981\/1999, <em>Knowledge and the Flow of Information<\/em>, CSLI:LSJU) as the <em>nuclear<\/em> sense of the term. There (p 44) he argues that \u201cRoughly speaking, information is that commodity capable of yielding knowledge, and what information a signal carries is what we can learn from it\u201d and (p. 45) \u201cA state of affairs contains information about X to just that extent to which a suitably placed observer could learn something about X by consulting it.\u201d As Dretske acknowledges, information is supposed to yield true beliefs, and so we can loosely say that information has to be true: although we may speak colloquially of \u2018false\u2019 information or of \u2018misinformation,\u2019 the nuclear sense rejects that possibility. On this view then, a state of affairs could be said to contain information when a true proposition which is apt for belief could be derived from that state of affairs.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-8b701730458bd45c76b80e1cb28a897d\">This, though better, is still not an appropriate approach to information as a sociological phenomenon. The truth of a claim that is current in society is of no particular interest to the sociologist, and the effect that that claim has on society is only indirectly (and often very weakly) related to its truth or falsity. The sociologically important characteristic of such a claim \u2013 which is apt for belief on the part of some agent(s) \u2013 is the degree to which and the manner in which it affects the actions of those in the society associated with that claim in the relevant way. The relationship between this and the nuclear view of information is that the effect of the claim can be related to the belief on the part of the relevant agents that the claim is a true (or false) one and therefore a good (or bad) guide to actions, where good and bad can be understood as meaning likely to lead to good or bad results for the relevant agents. That something like this is involved in the non-specialist use of the term \u2018information\u2019 is suggested by, for example, the use of the term \u2018information society\u2019 when the subject of discussion ranges over all forms of production, consumption, and exchange of claims regardless of their relationship to truth. (Further considerations on the characteristics that should be considered in the formulation of a definition of \u2018information\u2019 for sociological purposes may be found in H. Garfinkel (ed. A. Rawls) (2008) <em>Toward a Sociological Theory of Information<\/em>, Boulder CO: Paradigm, pp.110 ff.)<\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-9a73c5edf899e5bee45e1a5b84b1e790\"><strong><em>Adduction and Information<\/em><\/strong><\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-bf272619dea30ffcd92d3eb26fabd923\">The nature of the processes by which information in this relevant general sense is derived from a state of affairs is both uncertain and to a certain degree beyond the scope of our interest. The discussion will therefore be conducted at a level of abstraction that does not prejudge that nature. It will be assumed that the only relevant criteria here are that the processes are systematic and that they are dependent upon the contents of the state of affairs in question<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-333291108c99cfe6ff8a70d8302d9aaa\"><em><u>Propositional Function: Adduction<\/u><\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-3e39f65823ac0625890c97b8a44c7806\">A possible way that the world is may be represented as a set of propositions describing the world,<\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-ba4ed5fbb85244a3b7c4212041a82843\">Define \u03c3, a <u>State of Affairs<\/u>, as:<\/p>\n\n\n<p style=\"padding-left: 40px;\"><em>\u03c3<\/em> = {<em>\u03c3<sub>i<\/sub><\/em>: <em>i<\/em> \u2208 \u2115, <em>s<sub>i<\/sub><\/em> \u2208 <em>\u2119<\/em>, <em>\u03c3<sub>i<\/sub><\/em> is a partial description of the way the world is} where<\/p>\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-ac2010ab6b265cb767089869b6755e9f\"><em>\u03c3<\/em> is a consistent set<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-6d7b99ec36fce27a8ce2224bd952c08f\">A state of affairs is a subset of a complete description of the world.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-16c784fb6cf0a22e047228125000aeba\"><em>\u03a3<\/em> = \u222a{<em>\u03c3<\/em>: <em>\u03c3<\/em>&nbsp;is a state of affairs} is the <u>Possible States of Affairs<\/u><\/li>\n<\/ul>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-e8c5345c58a108ac97845b323e7f47fb\">Let <em>h<\/em> be a function such that<\/p>\n\n\n<p style=\"padding-left: 40px;\"><em>h<\/em>:\u03a3 \u2192 \u2119<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-0fa870ba0362227b3618698bdd6527d0\"><em>h<\/em> is an <u>Adduction<\/u> from a state of affairs <em>\u03c3<\/em>&nbsp;iff<\/p>\n\n\n<p style=\"padding-left: 40px;\">(\u2200<em>p<\/em> \u2208 <em>\u2119<\/em>) [<em>h<\/em>(<em>\u03c3<\/em>) = <em>p<\/em> \u21d2 (\u2203<em>S\u2282\u03c3<\/em>) [<em>h<\/em>(<em>\u03c3<\/em>\\<em>S<\/em>) \u2260 <em>p<\/em>]]<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-b3f78a9fde0b4865add2cd33756de3c6\">\u00bb <em>An adduction is the production of a proposition apt for belief from a description of a state of affairs<\/em><em> s<\/em><em>. It is sensitive to the contents of <\/em><em>s<\/em><em>. This is a non-triviality condition.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-a7b5b3c2be9020f8e17290c9d7f0e658\">Write <em>H<\/em>(<em>h<\/em>,<em> \u03c3<\/em>)<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-7bb0174d56c48b8872ee3186a89ab91d\">In this case <em>p<\/em> is an <u>Adduct<\/u> of <em>\u03c3<\/em>&nbsp;by <em>h<\/em>, and we say <em>p<\/em> is <u>Adduced<\/u> from <em>\u03c3<\/em>&nbsp;by <em>h<\/em>.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-936cec0d4a616513d9ac0ccd89d8e516\">Not every adduction will be well-defined for every state of affairs.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-4b1f852a31c6cf8d84d94d6001f02ed3\">An adduction is not guaranteed to yield a true proposition, nor is it even guaranteed to yield a result that is consistent with <em>\u03c3<\/em>.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-d431521e9b7a2844b18896fdddfdb667\">The set of possible adductions is barely constrained by the condition given, and we can be sure that the set of adductions that the agents of a population are actually capable of performing is a much more limited set. The discovery of which possible adductions are actually applied by agents is a matter for empirical (psychological) enquiry and will form part of the agent theory.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-4123b68791c0c8c971b009178b1a9164\">The work of Sperber and Wilson (e.g. (1986) <em>Relevance<\/em>) would suggest that the actually applied adductions will turn out to be more context sensitive or otherwise complex than a mere propositional function. Nevertheless, for the simplicity of this initial development we shall maintain that assumption.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-2fa592e7d60d906f2ac8c02a14687ec6\">Above, <em>h<\/em> is defined as a function on the propositions of<em> \u03c3<\/em>. However, it need not be supposed implausibly that only the complete set of propositions in <em>\u03c3<\/em>&nbsp;should be necessary and sufficient for any particular <em>h<\/em>. We suppose instead that there will be a subset \u03c3<em><sub>h<\/sub><\/em> (proper or otherwise) for which:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-1d2b15f1c42e9e6956f10ca62ef144d5\"><em>h<\/em>(<em>\u03c3<sub>h<\/sub><\/em>) = <em>h<\/em>(<em>\u03c3<\/em>)<\/li>\n<\/ol>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-549e16df945fb16b626a6f8281029375\">\u00bb <em>The propositions of \u03c3<\/em><em><sub>h<\/sub><\/em><em> are collectively sufficient for the adduction to yield the same result<\/em>.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-515c69366365cbe73f325949bc7eaae5\">(\u2200<em>s<\/em><em>\u2208\u03c3<\/em><em><sub>h<\/sub><\/em>) [<em>h<\/em>(<em>\u03c3<\/em><em><sub>h<\/sub><\/em>\\<em>s<\/em>) \u2260 <em>h<\/em>(<em>\u03c3<\/em>)], or<\/li>\n<\/ol>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-7f2d7ea605236e30e49fab523ff22fff\">\u00bb <em>The propositions of \u03c3<\/em><em><sub>h<\/sub><\/em><em> are collectively necessary for the adduction to yield the same result<\/em>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-ab9842fbd41a66e15f2639fca676dcf2\">Call <em>\u03c3<\/em><em><sub>h<\/sub><\/em> so characterized, the <u>Adduction-Relevant State of Affairs<\/u> for <em>h<\/em> on <em>\u03c3<\/em>.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-cbd98ab612a49ec3102960353e556b57\">We need not assume that <em>\u03c3<\/em><em><sub>h<\/sub><\/em> is a unique such subset of <em>\u03c3<\/em><\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-6d80c04cd205ec78bbc8800106a9a330\">Write <em>ARSA<\/em>(<em>\u03c3<\/em><em><sub>h<\/sub><\/em>, <em>\u03c3<\/em>, <em>h<\/em>)<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-1bb0d352234e34df561ecf144a55e2fc\">We will assume in what follows that where appropriate the state of affairs in question is an adduction-relevant one. Including the restriction in each definition, though strictly required, would add clutter to definitions which are already cluttered enough.<\/li>\n<\/ul>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-8cb7fed768099f42af251b29ff4f3aa6\"><em><u>Action: Adducement<\/u><\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-3b7dd98f27cd3254909d55383cf71afe\">An agent is able to access the results of an adduction on a state of affairs, <em>\u03c3<\/em>, when it is able to perform an action by which it applies some adduction <em>h<\/em> to that state of affairs and the result of that adduction is added to <strong>B<\/strong><em><sub>x<\/sub><\/em>. Such an action we shall call an <u>Adducement<\/u> for <em>h <\/em>from <em>\u03c3<\/em>. Thus, when an agent <em>x<\/em> performs the adducement, <em>\u03b7<sub>x<\/sub><\/em>\u2208<em>\u03b1<sub>x<\/sub><\/em>, for the adduction <em>h<\/em> from <em>\u03c3<\/em>:<\/p>\n\n\n<p style=\"padding-left: 40px;\"><em>Q<\/em>(<em>\u03b7<sub>x,i<\/sub><\/em>, <em>q<sub>x,i<\/sub><\/em>) \u2283 <em>B<sub>x,i+1<\/sub><\/em>[ <em>h<\/em>(<em>\u03c3<\/em>) ]<\/p>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-3543a4cdbcdf89a19dab409284e07289\">All the normal indices are applicable in the obvious way.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-f9805dbea9c155bac43f72763e5a5427\">Write <em>Add<\/em>(<em>\u03b7<\/em>, <em>h<\/em>, \u03c3) \u2013 though it may not be necessary to include <em>s<\/em> in the arguments.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-441bbd7bfb4c3c4ddb59eb8afd321b74\">We may write <em>\u03b7<\/em><em><sub>h<\/sub><\/em> to acknowledge that the adducement applies the adduction <em>h<\/em><\/li>\n<\/ul>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-2421448366ca79c647c923ec8023982a\"><em><u>Motivation: Interrogation<\/u><\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-2899ddb6259f96667bbe5ce25c3ede10\">Agent <em>x <\/em>performs an adducement (<em>qu<\/em><em>\u00e2<\/em> adducement) when he has a question that he needs answered (or is in a situation that is effectively identical to this) and which he knows or suspects can be answered by an application of an adduction on the facts presented in the current state of affairs.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-17dcf59a3c742a3293a76dce1d620619\">We will adapt an approach to the semantics of questions by Groenendijk &amp; Stokhof (1984, <em>Studies in the Semantics of Questions and the Pragmatics of Answers<\/em>, PhD Thesis, U. Amsterdam,) by which a question may be treated as a partition of the set of all propositions (van Rooy, R. (2003) \u2018Quality and Quantity of Information Exchange\u2019 in <em>Journal of Logic, Language, and Information<\/em>, 12.4 pp. 423-451) where the members of that partition are the correct answers to that question in declarative form.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-27dbf6e27bbf7273fd479dcf603661a3\">Let \u03c9&nbsp;= {<em> \u03c9<\/em><em><sub>i<\/sub><\/em> } \u2208 2<em><sup>\u2119<\/sup><\/em> be a question,<\/p>\n\n\n<p><\/p>\n<p class=\"has-black-color has-text-color has-link-color wp-elements-145d67bd9dba1eef68c508113b9d0b4c\" style=\"padding-left: 40px;\">((\u2200<em>p<\/em>)[~<em>B<sub>x<\/sub><\/em>[ <em>p<\/em>\u2208<em>\u03c9<\/em>\u00a0]] &amp; <br \/><em>B<sub>x<\/sub><\/em>[ (\u2200<em>p<\/em>\u2208<em>\u03c9<\/em>)[ <em>q<sub>x<\/sub><\/em>\u2019 = <em>q<sub>x<\/sub><\/em> \u222a <em>B<sub>x<\/sub><\/em>[ <em>p<\/em>\u2208<em>\u03c9<\/em> ] \u21d2 ( <em>T<\/em>(<em>C<\/em>(<em>A<sub>x<\/sub><\/em>(<em>q<sub>x<\/sub>\u2019<\/em>, <em>c<sub>x<\/sub><\/em>), <em>c<sub>x<\/sub><\/em>), <em>I<sub>x<\/sub><\/em>) &gt; <em>T<\/em>(<em>C<\/em>(<em>A<sub>x<\/sub><\/em>(<em>q<sub>x<\/sub><\/em>, <em>c<sub>x<\/sub><\/em>), <em>c<sub>x<\/sub><\/em>), <em>I<sub>x<\/sub><\/em>)))<br \/><em>\u21d2 D<sub>x<\/sub><\/em>[ (\u2203<em>p<\/em>\u2208<em>\u03c9<\/em>)<em>B<sub>x<\/sub><\/em>[ <em>p<\/em>\u2208<em>\u03c9<\/em>\u00a0] ]<\/p>\n<p><\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-ef87acc2d5dee24823407051b277842c\">\u00bb <em>If x believes that knowing an answer to the question \u03c9<\/em><em>&nbsp;will enable an improvement in that agent\u2019s total satisfaction then x will desire to know that answer<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-ad7e9888cd7b6863a5c02710be88c251\">Under some fairly plausible assumptions for the logic of the <em>B<sub>x<\/sub><\/em> operator<\/li>\n<\/ul>\n\n\n<p style=\"padding-left: 80px;\"><em>B<sub>x<\/sub><\/em>[ <em>p<\/em>\u2208<em>\u03c9<\/em> ] <em>\u21d2<\/em> <em>B<sub>x<\/sub><\/em>[ <em>p<\/em> ]<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-72cb9458711a0bf99499a5ae5cad6d45\">But, given opacity in the <em>D<sub>x<\/sub><\/em> operator, it does not necessarily follow that<\/p>\n\n\n<p style=\"padding-left: 80px;\"><em>D<sub>x<\/sub><\/em>[ (\u2203<em>p<\/em>\u2208<em>\u03c9<\/em>)<em>B<sub>x<\/sub><\/em>[ <em>p<\/em>\u2208<em>\u03c9<\/em> ] <em>\u21d2<\/em> <em>D<sub>x<\/sub><\/em>[ (\u2203<em>p<\/em>\u2208<em>\u03c9<\/em>)<em>B<sub>x<\/sub><\/em>[ <em>p<\/em> ] ]<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-77cb73de2ef27fff074c376e1214fe61\">Let <em>\u03c9<\/em>&nbsp;= {<em> \u03c9<\/em><em><sub>i<\/sub><\/em> } \u2208 2<em><sup>\u2119<\/sup><\/em> be a question, \u03c3&nbsp;a state of affairs, <em>h<\/em> an adduction on<em> \u03c3<\/em>; <em>\u03b7\u2208\u03b1<\/em><em><sub>x<\/sub><\/em> then<\/p>\n\n\n<p style=\"padding-left: 40px;\">( <em>D<sub>x<\/sub><\/em>[ (\u2203<em>p<\/em>\u2208<em>\u03c9<\/em>)<em>B<sub>x<\/sub><\/em>[ <em>p<\/em>\u2208<em>\u03c9<\/em> ] ] \u2208 <em>q<sub>x,i<\/sub><\/em><\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-9987f4d59b5f799161926a57f6175050\">\u00bb <em>If x wants to know an answer to the question \u03c9<\/em><\/p>\n\n\n<p style=\"padding-left: 40px;\">&amp; <em>B<sub>x<\/sub><\/em>[ (\u2203<em>p<\/em>)[<em>p<\/em>\u2208<em>\u03c9<\/em>] \u21d2 (\u2200<em>p<\/em>)[<em>h<\/em>(<em>\u03c3<\/em>)=<em>p<\/em> \u21d2 <em>p<\/em>\u2208<em>\u03c9<\/em>] ] \u2208 <em>q<sub>x,i<\/sub><\/em><\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-957ddb3a7d28cc0d1ccc458718e19183\">\u00bb <em>and believes that if there is an answer to \u03c9<\/em><em> that it would be found by the adduction h on \u03c3<\/em><\/p>\n\n\n<p style=\"padding-left: 40px;\">&amp; <em>B<sub>x<\/sub><\/em>[ <em>Add<\/em>(<em>\u03b7<\/em>, <em>h<\/em>, <em>\u03c3<\/em>) ] <em>\u2208<\/em> <em>q<sub>x,I<\/sub><\/em> )<\/p>\n\n<p>\u00bb <em>and believes that the action \u03b7<\/em><em>\u00a0<\/em><em>which x can perform is an adducement for h from \u03c3<\/em><\/p>\n\n<p style=\"padding-left: 40px;\"><em>\u21d2 A<sub>x<\/sub><\/em>(<em>q<sub>x,i<\/sub><\/em>, <em>c<sub>x,i<\/sub><\/em>) = <em>\u03b7<\/em><\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-d5ed018322e41593d5542f938341e3dd\">\u00bb <em>then x does \u03b7<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-e18e96344aa1eafbd14da11189905ce2\">A more complete description of this condition would include reference to expected outcomes, weighted interests, alternative actions, and so on, but they can be ignored here for the sake of simplicity.<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-45f4dddb5a412c56d4d2eb9dc0a8b274\">Let the antecedent of that conditional be abbreviated as <em>Mot<\/em>(<em>\u03c9<\/em>, <em>x<\/em>, <em>h<\/em>, <em>\u03c3<\/em>, <em>\u03b7<\/em>) and read it as <em>\u03c9<\/em>&nbsp;motivates <em>x<\/em> to apply <em>h<\/em> on <em>\u03c3<\/em>&nbsp;using <em>\u03b7<\/em>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-ada19c64f4e28c64bc393b23424f81e7\"><em>Mot<\/em>(<em>\u03c9<\/em>, <em>x<\/em>, <em>h<\/em>, <em>\u03c3<\/em>, <em>\u03b7<\/em>) <em>\u21d2<\/em> <em>A<sub>x<\/sub><\/em>(<em>q<sub>x,i<\/sub><\/em>, <em>c<sub>x,i<\/sub><\/em>) = <em>\u03b7<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-1b88f95b352636473da431427e71b67f\">Again, note that this assumes success in adductions<\/li>\n<\/ul>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-c60bc5723375f166a888cc964c81f354\"><em><u>Information<\/u><\/em><\/li>\n<\/ol>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-4874489ec1f4832fbf0a64d98779e0a1\">Define the <u>(Total) Information<\/u> contained in <em>\u03c3<\/em>, as<\/p>\n\n\n<p style=\"padding-left: 40px;\"><strong>It<\/strong><em><sub>\u03c3<\/sub><\/em> = {<em>p<\/em> \u2208 <em>\u2119<\/em>: (\u2203<em>x<\/em>)(\u2203<em>\u03c9<\/em>)(\u2203<em>h<\/em>)[<em>H<\/em>(<em>h<\/em>,<em>\u03c3<\/em>) &amp;<em>h<\/em>(<em>\u03c3<\/em>)=<em>p<\/em> &amp; <em>B<sub>x<\/sub><\/em> [(\u2200<em>p<\/em>)[<em>h<\/em>(<em>\u03c3<\/em>)=<em>p<\/em> \u21d2 <em>p<\/em>\u2208<em>\u03c9<\/em>]]]}<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-8229ffcbabc7168c08f76061c9be1fea\">\u00bb <em>The (total) information in a state of affairs is all the statements that are adducible from it by some adduction which some agent believes would thereby answer some question.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-b10174c0f41132c617f704964f45f723\">Note that if no agent believes the adduced statement answers a relevant question, then that statement will not thereby count as information (even if it <em>does<\/em> answer the question.)<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-931a582b33ea915e6446f3fe2dd6d0c9\">We also say of any <em>p<\/em> \u2208<strong>It<\/strong><em><sub>\u03c3<\/sub><\/em> that it is information in <em>\u03c3<\/em>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-0728d39af792706a0ddcf60ad3a33161\">Define the <u>Information Relative<\/u> to <em>x<\/em> contained in <em>\u03c3<\/em>, as<\/p>\n\n\n<p style=\"padding-left: 40px;\"><strong>Ir<\/strong><em><sub>x,\u03c3<\/sub><\/em> = {<em>p<\/em> \u2208 <em>\u2119<\/em>: (\u2203<em>\u03c9<\/em>)(\u2203<em>h<\/em>)(\u2203<em>\u03b7<\/em>\u2208<em>\u03b1<sub>x<\/sub><\/em>) [<em>H<\/em>(<em>h<\/em>,<em>\u03c3<\/em>) &amp;<em>h<\/em>(<em>\u03c3<\/em>)=<em>p<\/em> &amp; <em>Add<\/em>(<em>\u03b7<\/em>, <em>h<\/em>, <em>\u03c3<\/em>) &amp; <br \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>B<sub>x<\/sub><\/em>[(\u2200<em>p<\/em>)[<em>h<\/em>(<em>\u03c3<\/em>)=<em>p<\/em> \u21d2 <em>p<\/em>\u2208<em>\u03c9<\/em>]]]}<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-f58ab39f034192ae6de15428f691c529\">\u00bb <em>The information relative to an agent in a state of affairs is all the statements that may be adduced from it by the agent which he believes may answer some question.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-070a27804018888476b984f19c37bce6\"><strong>Ir<\/strong><em><sub>x,\u03c3<\/sub><\/em>&nbsp;may be an inconsistent set<\/li>\n\n\n\n<li class=\"has-black-color has-text-color has-link-color wp-elements-a1f854924f850f870fb7b38d4fa590e6\">The information relative to a population <em>X<\/em> in <em>\u03c3<\/em>&nbsp;is given in the obvious way<\/li>\n<\/ul>\n\n\n<p style=\"padding-left: 40px;\"><strong>Ir<\/strong><em><sub>X,\u03c3<\/sub><\/em> = \u222a<em><sub>x<\/sub><\/em><sub>\u2208<\/sub><em><sub>X<\/sub><\/em><strong>Ir<\/strong><em><sub>x,\u03c3<\/sub><\/em><\/p>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-48e7077b3383f91859d3d2b53476d148\">Define the <u>Population Informationally Related<\/u> to <strong>i<\/strong> \u2282 <strong>It<\/strong><em><sub>\u03c3<\/sub><\/em>&nbsp;as<\/li>\n<\/ul>\n\n\n<p style=\"padding-left: 40px;\"><strong>Xr<sub>i<\/sub><\/strong><em><sub>,\u03c3<\/sub><\/em>\u00a0= {<em>x <\/em>\u2208<em>\u00a0X<\/em>:<strong>i<\/strong> \u2282 <strong>Ir<\/strong><em><sub>x,\u03c3<\/sub><\/em>\u00a0}<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-a52ac27e15916b13b4186de117707121\">Define the <u>Information Available<\/u> to <em>x<\/em> contained in <em>\u03c3<\/em>, as<\/p>\n\n\n<p style=\"padding-left: 40px;\"><strong>Iv<\/strong><em><sub>x,\u03c3<\/sub><\/em>\u00a0= {<em>p<\/em> \u2208 <em>\u2119<\/em>: (\u2203<em>\u03c9<\/em>)(\u2203<em>h<\/em>)(\u2203<em>\u03b7<\/em>\u2208<em>\u03b1<sub>x<\/sub><\/em>)\u00a0[<em>H<\/em>(<em>h<\/em>,<em>\u03c3<\/em>) &amp;<em>h<\/em>(<em>\u03c3<\/em>) = <em>p<\/em> &amp; <em>Add<\/em>(<em>\u03b7<\/em>, <em>h<\/em>, <em>\u03c3<\/em>) &amp; <br \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <em>B<sub>x<\/sub><\/em> [(\u2200<em>p<\/em>)[<em>h<\/em>(<em>\u03c3<\/em>)=<em>p<\/em> \u21d2 <em>p<\/em>\u2208<em>\u03c9<\/em>] &amp; <em>Add<\/em>(<em>\u03b7<\/em>, <em>h<\/em>, <em>\u03c3<\/em>) &amp; <em>\u03b7<\/em>\u2208<em>\u03b1<\/em><em><sub>x<\/sub><\/em>]]}<\/p>\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-424c7b74b1a7f807b33e04ce85206d4d\">\u00bb <em>The information available to an agent in a state of affairs is all the statements that may be adduced from it by the agent which he believes may answer some question using adductions that he can perform.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list has-black-color has-text-color has-link-color wp-elements-3738a9a5cdc50ab109703404a4b42d90\">\n<li><strong>Iv<\/strong><em><sub>x,\u03c3<\/sub><\/em>&nbsp;may be an inconsistent set<\/li>\n\n\n\n<li>The information available to a population <em>X<\/em> in <em>\u03c3<\/em>&nbsp;is given in the obvious way<\/li>\n<\/ul>\n\n\n<p style=\"padding-left: 40px;\"><strong>Iv<\/strong><em><sub>X,\u03c3<\/sub><\/em> = \u222a<em><sub>x<\/sub><\/em><sub>\u2208<\/sub><em><sub>X<\/sub><\/em><strong>Iv<\/strong><em><sub>x,\u03c3<\/sub><\/em><\/p>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-black-color has-text-color has-link-color wp-elements-9fd5d730a49a91f796e93c3e9ebe0290\">Define the <u>Population Informationally Availed<\/u> of <strong>i<\/strong> \u2282 <strong>It<\/strong><em><sub>\u03c3<\/sub><\/em>&nbsp;as<\/li>\n<\/ul>\n\n\n<p style=\"padding-left: 40px;\"><strong>Xv<sub>i<\/sub><\/strong><em><sub>,\u03c3<\/sub><\/em> = {<em>x <\/em>\u2208<em>\u00a0X<\/em>:<strong>i<\/strong> \u2282 <strong>Iv<\/strong><em><sub>x,\u03c3<\/sub><\/em>\u00a0}<\/p>\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>An important aspect of communication relates to the transfer of information, but the treatment of information as a sociological phenomenon cannot be limited to its associations with communication alone: of equal importance are questions of creation, access, accumulation, transformation, function, social effect, etc. To address such issues, we will need to begin with an appropriate [&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-604","post","type-post","status-publish","format-standard","hentry","category-sociology"],"_links":{"self":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/604","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=604"}],"version-history":[{"count":4,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/604\/revisions"}],"predecessor-version":[{"id":609,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/posts\/604\/revisions\/609"}],"wp:attachment":[{"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/media?parent=604"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/categories?post=604"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stevewatson.info\/blog\/wp-json\/wp\/v2\/tags?post=604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}