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Transcript of Http://users.ox.ac.uk/~ball0888 /lectures /logic.
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http://users.ox.ac.uk/~ball0888
/lectures
/logic
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Fantasy Logic League
A weekly competition…
…in the art of deduction
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Previously on THG…
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22 November, 1963
Nightmare on Elm Street
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Oswald Sentences
• [A] If Oswald didn’t shoot Kennedy, then somebody else did.
• [B] If Oswald doesn’t shoot Kennedy, then somebody else will.
• [C] If Oswald hadn’t shot Kennedy, then somebody else would have.
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The scientific study of:
English Grammar
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MissAnn
Widdecombe
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Spinster of this parish…
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…and, indeed, of all the other parishes as well
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A woman of many parts…
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….clumsily assembled
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Truly, the face that ate a
thousand chips.
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Miss Anne Widdecombe at the Conservative Party Conference
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A Counterblast
• English has NO infinitive
• English has NO moods – neither indicative nor subjunctive nor any other
• English has but TWO tenses – present and past
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•Madness!
•Ignorance!
•Stupidity!
•Snobbery!
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Ambiguity
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We must have the worst JCR food in Oxford
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That dart might have landed in
baby’s eye
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Sentencevs.
Message
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Truth is not a property of Sentences
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Truth is a property of Messages
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Message determines
Sentence
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If Oswald didn’t shoot Kennedy, then somebody else did
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April, 1985
A train from
Paddington
to Bodmin…
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The Adventure of….
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The curious incident of the dog in the night-time
• “Is there any point to which you would wish to draw my attention?”
• “To the curious incident of the dog in the night-time”
• “The dog did nothing in the night-time.”
• “That was the curious incident,” remarked Sherlock Holmes.
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The Mystery of….
Modus Ponens
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Modus Ponens•P•If P, then Q
•So: Q
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•Oswald didn’t shoot Kennedy…
•And if Oswald didn’t shoot Kennedy…
•…then somebody else did.
•So: Somebody else did.
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April, 1985
Oxford
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The Reverend Charles
Lutwidge Dodgson
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Lewis Carroll
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Lewis Carroll"What the Tortoise Said to Achilles,"
Mind 4, No. 14 (April 1895): 278-280.
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Zeno of Elea
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A Farewell to Arms
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Zeno of Elea
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Achilles and the Tortoise
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Achilles and the Tortoise
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• [A] Someone shot Kennedy
• [B] Oswald didn’t
• So [Z] Somebody else did
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• [A] Someone shot Kennedy
• [B] Oswald didn’t
• [C] If A and B, then Z
• [D] If A and B and C, then Z
• [E] If A and B and C and D, then Z
• [F] If A and ……oh, forget it!
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•Words/Sentences
•Ideas/Messages
•Logic
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Words
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• Although it was very hot, Her Majesty wore a cardigan
• Because it was very hot, Her Majesty stripped off
• Since there are no trees in Orkney, it is a desolate place
• Unless I have made a mistake, the answer is 42
• Whether or not you like them, carrots are good for you
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• Despite the fact that Mike Tyson is a convicted rapist, this government let him in
• Even if Grannie was gunned down this morning, she’s chirpy enough now
• If Oswald didn’t shoot Kennedy, somebody else did
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Compound Sentences
Compounded out of prior sentences
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 66: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/66.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 67: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/67.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 68: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/68.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 69: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/69.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 70: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/70.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
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The Independent Sentence
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 73: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/73.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 74: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/74.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 75: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/75.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 76: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/76.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 77: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/77.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 78: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/78.jpg)
The Subsidiary String
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 80: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/80.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 81: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/81.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 82: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/82.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
![Page 83: Http://users.ox.ac.uk/~ball0888 /lectures /logic.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649c945503460f94951923/html5/thumbnails/83.jpg)
Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
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A Subordinating Conjunctionprefixed to
The Dependent Sentence
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A Subordinating Conjunctionprefixed to
The Dependent Sentence
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• Although it was very hot, Her Majesty wore a cardigan
• Her Majesty wore a cardigan, although it was very hot.
• Her Majesty - although it was very hot -wore a cardigan
• Her Majesty wore - although it was very hot - a cardigan
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• Although Her Majesty wore a cardigan, it was very hot
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Ideas
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
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Compound Messages
Compounded out of prior messages
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• Independent message: mi
• Dependent message: md
• Status modifier: *
• Compound message: mc
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mc : md * , mi
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Ambiguity
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• (In those days) Her Majesty wore a cardigan
(Yesterday) Her Majesty wore a cardigan
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• (In those days) Her Majesty wore a cardigan
(Yesterday) Her Majesty wore a cardigan
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• (In those days) Her Majesty wore a cardigan
(Yesterday) Her Majesty wore a cardigan
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mc : md * , mi
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
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• Despite the fact that Mike Tyson is a convicted rapist, this government let him in
• Even if Grannie was gunned down this morning, she’s chirpy enough now
• If Oswald didn’t shoot Kennedy, somebody else did
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Selection of ‘if’ grants accords the dependent message the
status of an hypothesis
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Which means:
It is being treated as true…
…whether or not it really is.
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?• Structure
• Truth
• Affirmation
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mc : md * , mi
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Compound Messages cannot be True (or False)
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Although it was very hot, Her Majesty wore a cardigan
Because it was very hot, Her Majesty stripped off
Since there are no trees in Orkney, it is a desolate place
Unless I have made a mistake, the answer is 42
Whether or not you like them, carrots are good for you
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• Despite the fact that Mike Tyson is a convicted rapist, this government let him in
• Even if Grannie was gunned down this morning, she’s chirpy enough now
• If Oswald didn’t shoot Kennedy, somebody else did
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mc : md * , mi
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The Independent message is affirmed outright, unless there is rational reason to
think otherwise
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• Although it was very hot, Her Majesty wore a cardigan
• Because it was very hot, Her Majesty stripped off
• Since there are no trees in Orkney, it is a desolate place
• Unless I have made a mistake, the answer is 42
• Whether or not you like them, carrots are good for you
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• Despite the fact that Mike Tyson is a convicted rapist, this government let him in
• Even if Grannie was gunned down this morning, she’s chirpy enough now
• If Oswald didn’t shoot Kennedy, somebody else did
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Logic
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October 1928
The 20th Century Limited
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Waistcoat by Sally Bayley
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THE END