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Transcript of Http://users.ox.ac.uk/~ball0888 /lectures /logic.
http://users.ox.ac.uk/~ball0888
/lectures
/logic
Fantasy Logic League
A weekly competition…
…in the art of deduction
Previously on THG…
22 November, 1963
Nightmare on Elm Street
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.
The scientific study of:
English Grammar
MissAnn
Widdecombe
Spinster of this parish…
…and, indeed, of all the other parishes as well
A woman of many parts…
….clumsily assembled
Truly, the face that ate a
thousand chips.
Miss Anne Widdecombe at the Conservative Party Conference
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
•Madness!
•Ignorance!
•Stupidity!
•Snobbery!
Ambiguity
We must have the worst JCR food in Oxford
That dart might have landed in
baby’s eye
Sentencevs.
Message
Truth is not a property of Sentences
Truth is a property of Messages
Message determines
Sentence
If Oswald didn’t shoot Kennedy, then somebody else did
April, 1985
A train from
Paddington
to Bodmin…
The Adventure of….
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.
The Mystery of….
Modus Ponens
Modus Ponens•P•If P, then Q
•So: Q
•Oswald didn’t shoot Kennedy…
•And if Oswald didn’t shoot Kennedy…
•…then somebody else did.
•So: Somebody else did.
April, 1985
Oxford
The Reverend Charles
Lutwidge Dodgson
Lewis Carroll
Lewis Carroll"What the Tortoise Said to Achilles,"
Mind 4, No. 14 (April 1895): 278-280.
Zeno of Elea
A Farewell to Arms
Zeno of Elea
Achilles and the Tortoise
Achilles and the Tortoise
• [A] Someone shot Kennedy
• [B] Oswald didn’t
• So [Z] Somebody else did
• [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!
•Words/Sentences
•Ideas/Messages
•Logic
Words
• 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
• 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
Compound Sentences
Compounded out of prior sentences
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
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
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
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
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
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
The Independent Sentence
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
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
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
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
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
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
The Subsidiary String
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
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
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
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
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
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
A Subordinating Conjunctionprefixed to
The Dependent Sentence
A Subordinating Conjunctionprefixed to
The Dependent Sentence
• 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
• Although Her Majesty wore a cardigan, it was very hot
Ideas
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
Compound Messages
Compounded out of prior messages
• Independent message: mi
• Dependent message: md
• Status modifier: *
• Compound message: mc
mc : md * , mi
Ambiguity
• (In those days) Her Majesty wore a cardigan
(Yesterday) Her Majesty wore a cardigan
• (In those days) Her Majesty wore a cardigan
(Yesterday) Her Majesty wore a cardigan
• (In those days) Her Majesty wore a cardigan
(Yesterday) Her Majesty wore a cardigan
mc : md * , mi
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
• 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
Selection of ‘if’ grants accords the dependent message the
status of an hypothesis
Which means:
It is being treated as true…
…whether or not it really is.
?• Structure
• Truth
• Affirmation
mc : md * , mi
Compound Messages cannot be True (or False)
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
• 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
mc : md * , mi
The Independent message is affirmed outright, unless there is rational reason to
think otherwise
• 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
• 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
Logic
October 1928
The 20th Century Limited
Waistcoat by Sally Bayley
THE END