Previously on THG…

April, 1985 A train from Paddington to Bodmin…

The Mystery of…. Modus Ponens

Lewis Carroll

Achilles and the Tortoise

[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!

m c : m d *, m i

Compound Messages cannot be True (or False)

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

Selection of ‘if’ accords the dependent message the status of an hypothesis

Which means: It is being treated as true… …whether or not it really is.

Logic

IfIf Oswald didn’t shoot Kennedy, somebody else did

Hypothetical ‘if’- message

Logical ‘if’- message

Stand Alone If P, then Q There is an Antecedent And a Consequent

If Oswald didn’t shoot Kennedy, somebody else did whines, we beat him Oswald didn’t shoot Kennedy (YES)

Contraposition If P, then Q If not Q, then not P

If Oswald didn’t shoot Kennedy, somebody else did whines, we beat him If nobody else shot Kennedy, then Oswald did (YES)

Time and Tense Tense: time registered by form Time: time the message is about

If Oswald didn’t shoot Kennedy, somebody else did whines, we beat him Tense: Past Time: Past (Tense = Time)

Logical ‘if’-messages Pass Stand-Alone Contrapose Tense = Time

Logical ‘if’-messages … … are condensed arguments

If P, then Q P. So Q

If Oswald didn’t shoot Kennedy …then somebody else did

Oswald didn’t shoot Kennedy So: Somebody else did

Logical ‘if’-messages Cannot have Truth-values Are condensed Arguments Their standard is Deductive validity

Non-logical hypothetical messages The dog – if it was a dog – ran off If it rained, it didn’t rain hard If the Mayor is married, his wife did not accompany him

Non-logical hypothetical messages If it didn’t run off, it wasn’t a dog If it rained hard, it didn’t rain If his wife did accompany him, the Mayor is not married

Non-logical hypothetical messages The dog – if it was a dog – ran off If it rained, it didn’t rain hard If the Mayor is married, his wife did not accompany him

Non-logical hypothetical messages Affirm the Consequent Are not condensed Arguments Pass Stand-Alone Don’t Contrapose Tense = Time

The Mystery of…. 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.

If, as we now know, Oswald didn’t shoot Kennedy… …then 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!

October 1932

?

What the fuck?

I mean, er.. what the fucking fuck?

We are young men and women of high spirit and noble ideals. We are philosophers, interested in the semantics of English ‘if’. What in God’s name are we doing here?

We’re going to watch a high-stakes Poker-game

Achtung!

Four Threes

Four Nines

Achtung!

Gondorff knows what Lonnegan holds.

Experiment 1

If Gondorff calls …… ……he will win.

If Gondorff calls …… ……he will lose.

Experiment 2

If Gondorff had called.. …he would have won.

If Gondorff had called.. …he would have lost.

Gibbardian Stand-offs Alan Gibbard

Henry Gondorff is …..

Sly Pete

Achtung!

Gondorff knows what Lonnegan holds.

If Gondorff calls, he will lose Gondorff holds a losing hand. So if he calls, he will lose.

If Gondorff calls, he will win. Gondorff wants to win. He knows what Lonnegan holds. He will not call with what he knows to be a losing hand. So if he calls, it will be with a winning hand.

If Gondorff had called, he would have lost. Gondorff held a losing hand. So if he had called, he would have lost.

If Gondorff had called, he would have won. Gondorff wanted to win. He knew what Lonnegan held. He would not have called with what he knew to be a losing hand. So if he had called, it would have been with a winning hand.

Curious Incidents Two people could quite reasonably come to opposite verdicts Does-will and had-would differ only in tense – and so does the reasoning The reasoning is inductive – it involves an exercise of the imagination The reasoning supports the verdict – it isn’t part of the message

Fantasy ‘if’- messages

Stand Alone If P, then Q There is no Antecedent And so no Consequent

If Gondorff calls, he will win whines, we beat him Gondorff calls (NO)

If Gondorff had called, he would have won whines, we beat him Gondorff had called (NO)

Contraposition If P, then Q If not Q, then not P

If Gondorff calls, he will win If Gondorff will not win, he doesn’t call (NO)

If Gondorff had called, he would have won If Gondorff would not have won, he hadn’t called (NO)

Time and Tense Tense: time registered by form Time: time the message is about

If Gondorff calls, he will win whines, we beat him Tense: Present Time: Future (Tense < Time)

If Gondorff had called, he would have won whines, we beat him Tense: Past Past Time: Past (Tense < Time)

Henry Gondorff was played by Paul Newman

Doyle Lonnegan was played by Robert Shaw

Waistcoat by Sally Bayley

Fin