Http://users.ox.ac.uk/~ball0888 /lectures /logic

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/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


























The Independent Sentence































The Subsidiary String































A Subordinating Conjunctionprefixed to

The Dependent Sentence

A Subordinating Conjunctionprefixed to

The Dependent Sentence


• 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






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





mc : md * , mi









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)









mc : md * , mi

The Independent message is affirmed outright, unless there is rational reason to

think otherwise


• 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




Logic

October 1928

The 20th Century Limited

Waistcoat by Sally Bayley

THE END

Documents

Http://users.ox.ac.uk/~ball0888 /lectures /logic