{"id":5171,"date":"2015-01-27T19:02:36","date_gmt":"2015-01-28T00:02:36","guid":{"rendered":"http:\/\/www.noahgreenstein.com\/wordpress\/?p=5171"},"modified":"2015-10-08T00:14:02","modified_gmt":"2015-10-08T04:14:02","slug":"punny-logic","status":"publish","type":"post","link":"https:\/\/www.noahgreenstein.com\/wordpress\/2015\/01\/27\/punny-logic\/","title":{"rendered":"Punny Logic"},"content":{"rendered":"

Update 12 Feb: This post had been expanded upon and, after submission, accepted for publication in Analysis<\/a> published by Oxford University Press. View the final version here<\/a>.<\/strong><\/p>\n

[draft]<\/p>\n

It is hard to explain puns to kleptomaniacs because they take things literally.<\/p><\/blockquote>\n

On the surface, this statement is a statement of logic, with a premise and conclusion.<\/p>\n

Given the premise:<\/p>\n

Kleptomaniacs take things literally.<\/p><\/blockquote>\n

We may deduce the conclusion:<\/p>\n

It is hard to explain puns to kleptomaniacs.<\/p><\/blockquote>\n

Now, whether the conclusion strictly follows from the premise is beside the point: it is a pun, and meant to be funny. However, as a pun, it still has to make some logical sense.<\/em> If it didn\u2019t make any sense, it wouldn\u2019t, and couldn\u2019t, be funny either. While nonsense can be amusing, it isn\u2019t punny.<\/p>\n

What is the sense in which the conclusion logically follows from the premise then, and how does this relate to the pun?<\/p>\n

Puns play off ambiguity in the meaning of a word or phrase. In this case the ambiguity has to do with the meaning of to take things literally<\/strong>. It can mean to steal<\/code>, or it can mean to only use the simplest, most common definitions of terms<\/code>.<\/p>\n

In the first meaning, by definition, kleptomaniacs steal, i.e. they literally take things.<\/p>\n

So then \u201ctake things literally\u201d<\/strong> is true.<\/p>\n

In the second meaning, by deduction, since puns play off multiple meanings of things, it is hard to explain a pun to someone who only uses the single, most common definition of a term. That is, if they take things literally, they won\u2019t recognize the multiple meanings required to understand a pun.<\/p>\n

So if someone \u201ctakes things literally\u201d<\/strong> it is true that it is hard to explain puns to them.<\/p>\n

Therefore, between the two meanings, we can informally derive the statement: it is hard to explain puns to kleptomaniacs because they take things literally.<\/p>\n

However, if we wanted to write this out in a formal logical language, then we would need a formal way to represent the two meanings of the single phrase.<\/p>\n

Classically, there is no way to give a proposition multiple meanings. Whatever a proposition is defined as, it stays that way. A<\/code> can\u2019t be defined as B<\/code> and then not defined as B<\/code>: (A=B & A\u2260B)<\/code> is a contradiction and to be avoided classically. But let\u2019s start with a classical formulation:<\/p>\n

Let:<\/p>\n

TTL1<\/sup><\/code> mean to Take Things Literally, in the 1st<\/sup> sense: to steal<\/p>\n

TTL2<\/sup><\/code> mean to Take Things Literally, in the 2nd<\/sup> sense: to use the most common definitions of terms.<\/p>\n

Then<\/p>\n

    \n
  1. \u2200x [ Kx \u2192 TTL1<\/sup>x ]
    \nFor anyone who is a Kleptomaniac, Then they take things literally (steal)<\/li>\n
  2. \u2200y[ TTL2<\/sup>y \u2192 Py ]
    \nFor anyone who takes things literally (definitionally), Then it is hard to explain puns to them<\/li>\n<\/ol>\n

    What we want, however, is closer to:<\/p>\n

      \n
    1. \u2200z [[ Kz \u2192 TTLz] \u2192 Pz ]
      \nFor anyone who is a Kleptomaniac, Then they take things literally, Then it is hard to explain puns to them<\/li>\n<\/ol>\n

      with only one sense of TTL, but two meanings.<\/p>\n

      Since TTL1<\/sup> \u2260 TTL2<\/sup>, we can\u2019t derive (3) from (1) and (2), as is. And if TTL1<\/sup> = TTL2<\/sup>, then we would have (1) A\u2192B, and (2) B\u2192C, while trying to prove (3) A\u2192B\u2192C, which logically follows. However, there would no longer be a pun if there was only one meaning of TTL.<\/p>\n

      What is needed is to be able to recompose our understanding of \u2018to take things literally\u2019 in a situation aware way.<\/em><\/strong> We need to be able to have the right meaning of TTL apply at the right time, specifically Meaning 1 in the first part, and the Meaning 2 in the latter.<\/p>\n

      Intuitively, we want something like this, with the scope corresponding to the situation:<\/p>\n

        \n
      1. \u2200z [<\/strong> Kz \u2192 {<\/strong> TTLz ]1<\/sup><\/strong> \u2192 Pz }2<\/sup><\/strong><\/li>\n<\/ol>\n

        In this formula, let the square brackets []<\/strong> have the first meaning of TTL apply, while the curly braces {}<\/strong> use the second meaning. Only the middle \u2014 TTL \u2014 does double duty with both meanings.<\/p>\n

        Achieving this customized scope can be done by using Independence Friendly logic<\/a>. IF logic allows for fine-grained scope allocation.<\/p>\n

        So let:<\/p>\n

        S<\/code> mean to steal.<\/p>\n

        D<\/code> mean to take things definitionally.<\/p>\n

        Then:<\/p>\n

          \n
        1. \u2200x \u2200y \u2203u\/\u2200x \u2203v\/\u2200y [ Kx \u2192 ( x=u & y=v & Su & Dv \u2192 TTLvu ) \u2192 Py ]
          \nIf anyone is a kleptomaniac then there is someone who is identical to them who steals\u2026 and if there is someone who takes things definitionally then there is someone identical to them for whom it is hard to explain puns to\u2026 and the person who steals and the person who takes things definitionally then both Take Things Literally.<\/li>\n<\/ol>\n

          The scope gymnastics are being performed by the slash operators at the start and the equality symbols in the middle part of the equation. What they are doing is specifying the correct meanings \u2014 the correct dependencies \u2014 to go with the correct senses: S<\/code>tealing pairs with K<\/code>leptomania and taking things D<\/code>efinitionally pairs with being bad at P<\/code>uns, while both pairs<\/strong> also meaning Taking Things Literally<\/code>. With both pairs meaning TTL<\/code>, and each pair being composed independently, Equation (5) therefore provides a formalization of the original pun.<\/p>\n

          <\/a>Discussion<\/h4>\n

          Finding new applications for existing logical systems provides a foundation for further research. As we expand the range of topics subject to logical analysis, cross-pollination between these subjects becomes possible.<\/p>\n

          For instance, using custom dependencies to associate multiple meanings to a single term is not only useful in describing puns. Scientific entities are often the subjects of competing hypotheses. The different hypotheses give different meanings \u2014 different properties, relations and dependencies \u2014 to the scientific objects under study. Logically parsing how the different hypotheses explain the world using the same terms can help us analyze the contradictions and incommeasureabilities between theories.<\/p>\n

          On the other hand, while this article may have forever ruined the above pun for you (and me), it does potentially give insight into what humans find funny. Classically, risibility, having the ability to laugh, has been associated with humans and rationality<\/a>. Analyzing this philosophical tradition with the new logical techniques will hopefully provide existential insight into the human condition.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Update 12 Feb: This post had been expanded upon and, after submission, accepted for publication in Analysis published by Oxford University Press. View the final version here. [draft] It is hard to explain puns to kleptomaniacs because they take things literally. On the surface, this statement is a statement of logic, with a premise and conclusion. Given the premise: Kleptomaniacs take things literally. We may deduce the conclusion: It is hard to explain puns to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,16],"tags":[248,251,256,268],"class_list":["post-5171","post","type-post","status-publish","format-standard","hentry","category-independence-friendly-logic","category-logic","tag-fun","tag-independence-friendly-logic","tag-logic","tag-philosophy"],"_links":{"self":[{"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/posts\/5171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/comments?post=5171"}],"version-history":[{"count":24,"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/posts\/5171\/revisions"}],"predecessor-version":[{"id":5518,"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/posts\/5171\/revisions\/5518"}],"wp:attachment":[{"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/media?parent=5171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/categories?post=5171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.noahgreenstein.com\/wordpress\/wp-json\/wp\/v2\/tags?post=5171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}