OK, so I’ve been watching football.\u00c2\u00a0 And there are occasions to think about logic.\u00c2\u00a0 During the beer commercials.\u00c2\u00a0 First, though, a quick tutorial on deductive semantic fallacies.\u00c2\u00a0 An argument is fallacious on deductive semantic grounds when the truth of the argument’s premise\u00c2\u00a0does not guarantee the truth of the argument’s conclusion (provided the proper analysis of the terms of the logic). A classic fallacious move to make inferences between two forms of statements in categorical A-Form.<\/p>\n
All S are P, so All P are S<\/p><\/blockquote>\n
The pattern is conversion – you switch the subject and predicate term in the proposition form.\u00c2\u00a0 It’s valid for E- and I-Forms, so it’s fine for these:<\/p>\n
No S are P, so No P are S<\/p>\n
No cats are lizards, so No lizards are cats<\/p>\n
Some S are P, so Some P are S<\/p>\n
Some Texans are Republicans, so Some Republicans are Texans<\/p><\/blockquote>\n
The trouble is that with A-form propositions, conversion is fallacious.\u00c2\u00a0 So we can intuitively see the fallacy with the following conversion forms:<\/p>\n
All triangles are polygons, so All polygons are triangles<\/p>\n
All cats are mammals, so All mammals are cats<\/p><\/blockquote>\n
That’s fallacious, and since it’s a bad way to convert, we call it illicit conversion.<\/em>\u00c2\u00a0 Now, to the commercials.\u00c2\u00a0 See the following Corona commercial, effectively playing during every timeout for every NFL game this weekend.\u00c2\u00a0 HERE<\/a>.\u00c2\u00a0 Here’s the free association that stands in for reasoning:<\/p>\n
Some beaches have sand; Some beaches are backyards; Some beaches inspire ideas; Some beaches have beats; Some beaches are better after sunset; Every beach is different, but All beaches have Corona<\/p><\/blockquote>\n
The commercial has scenes of beaches, bars, mixing rooms, back yards, concerts, campgrounds and so on. Each is some poignant scene, but not all have beers in them.\u00c2\u00a0 The inductive evidence presented is that, given their special definition of beach (effectively meaning ‘special place’), it’s not the presence of Corona that makes them that.\u00c2\u00a0 Rather, it, at best, is that the presence of Corona can contribute to a place being a beach.\u00c2\u00a0 Consequently, it isn’t that All beaches have Corona<\/em> that they’ve shown.\u00c2\u00a0 It only takes the first scene (the sandy beach with no beers) to be a counter-example.\u00c2\u00a0 Instead, the best that the evidence could show is that All places where there are Coronas are beaches in the relevant sense<\/em>.\u00c2\u00a0 Trouble is, they conclude with All beaches have Corona.\u00c2\u00a0 <\/em>Illicit conversion off weak evidence for enumerative induction.<\/p>\n","protected":false},"excerpt":{"rendered":"
OK, so I’ve been watching football.\u00c2\u00a0 And there are occasions to think about logic.\u00c2\u00a0 During the beer commercials.\u00c2\u00a0 First, though, a quick tutorial on deductive semantic fallacies.\u00c2\u00a0 An argument is fallacious on deductive semantic grounds when the truth of the argument’s premise\u00c2\u00a0does not guarantee the truth of the argument’s conclusion (provided the proper analysis of … Continue reading Some beaches are illicit conversions<\/span>