Wednesday 27 July 2011

The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 2(d), p. 556

Show that the following derivability claim holds:
  1. (x)Mx
  2. (x)(¬ Mx ⊃Mx)
  3. Mx ......... 1 UI x/x
  4. Mx ¬ ¬ Mx ......... 3 Add.
  5. ¬ ¬ Mx ∨ Mx ......... 4 Comm.
  6. ¬ Mx ⊃ Mx ......... 5 MI
  7. (x)(¬ Mx ⊃ Mx) ......... 6 UG

Friday 15 July 2011

The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 6(f), p. 557

The following set of sentences is inconsistent. Prove.
  1. ¬ (∃y)Jy ......... Assumption
  2. ¬ (∃x)¬ Hx ......... Assumption
  3. (z)(Jz ¬ Hz) ......... Assumption
  4. (y) ¬ Jy ......... 1 QC
  5. (x) ¬ ¬ Hx ......... 2 QC
  6. (x)Hx ......... 5 DN
  7. Jz ¬ Hz ......... 3 UI z/z
  8. ¬ Jz ......... 4 UI y/z
  9. Hz ......... 6 UI x/z
  10. ¬ Hz ......... 7,8 DS
  11. Hz ¬ Hz ......... 9,10 Conj.

Thursday 7 July 2011

Varying the narrative

If people want structure because structure conveys deliberate and intelligent design, and is thus more likely to make a success of their enterprise, give them structure! I was asked last week to share a pattern or template for a speech which would arouse curiosity and be persuasive.

It is a bizarre request – the kind of request which stems from a sense of insecurity, and, these days, from the copy-paste mentality. But what the hell, here is a narrative pattern sometimes used in movies which is a variation on the linear, run-of-the-mill narrative. It is cyclical and it is breathtakingly simple: open 5 story lines and close them in reverse order. Example 1:

This washing powder will take out the most stubborn stains.

This washing powder is safe for your skin.

This washing powder gives a very high yield.

This washing powder does not promote scale build-up.

This washing power smells divine.

It is in fact based on a balanced formula of specially selected plant extracts from French Polynesia. Anti-scale agents have been added for maximum protection for your washing machine. And you never run out of it: one scoop per wash and you’re done. Washing by hand? No problem. It contains a moisturizer to make your hands feel like a baby’s bottom. And if you still think that stain has not vanished, give your spectacles a good wipe.

Example 2 is a based on a speech which I made to illustrate the point of a cyclical narrative. The title: “Customer kings on the Saturday supermarket run” just happened to suggest itself after the speech, in fact. There are only 3 loops here. I have marked them like this: (1), (2), (3), (3), (2), (1).

(1) Take a customer, say Mr Rudi Arrogand, who gets into a state at the supermarket check-out early Saturday afternoon because the check-out scanner has given a different price reading than the price displayed on the shelf. He gets into a strop, waves his arms about, says he wants to speak to the manager. Have his rights been violated or his expectations frustrated? If so what rights? The right to be king when you’re spending money?

(2) Let’s take a different scenario. On a Tuesday, Mr Rudi Arrogand is working on an insurance claim at his desk at Ever Prudent, the insurance company. His boss wants all last month’s claims processed before the end of the day. Rudi says to a colleague of his that he hates the job, especially being expected to turn down claims on a technicality and telling this to clients. It’s a soul-destroying job. And working long hours for that kind of money! The corporation takes advantage of him. He scowls at the motivational poster in the office. Rudi will not hesitate to give you his full considered opinion of his company’s forthcoming employee performance evaluation either.

(3) Let’s skip around a bit more. At a get-together with some of his wife’s friends on a Sunday afternoon in an out-of-town restaurant Rudi is generous with his money, buys a drink for Greg Smarter, an up-and-coming bank manager, expounds on the virtues of free market economy, and blames the general decline in standards for all of life’s small inconveniences. Where is he coming from? What makes Rudi tick? What is he after?

(3) Well, Rudi is just another middle class misanthrope with aspirations for a job where he is his own boss, he gets paid the difference in the salary that separates him now from buying that land he has set his sights on, his wife looks up to him as head of family and as Mr Clever, and everybody generally gives him respect.

(2) What’s stopping him from getting what he wants? Well, his mindless job at the insurance company, unfair system where people who he thinks are half as intelligent as him get paid twice as much, and just not knowing the right people. The job sucks the life out of him. At every turn people take advantage of him.

(1) But Rudi calls the tune when he goes shopping. Take that supermarket, for example. He is keeping the supermarket staff in employ by spending his money there. The ritual of his holding out cash in return for the contents of his trolley is a magical moment – that’s when all the privileges man has ever enjoyed are momentarily vested in him. He is king. They are all rip-off artists and cheats at the supermarket. They don’t give him respect. But he is higher up the food chain being on the other side of the till. However grudgingly, the staff and the other customers in the queue must admit it – he thinks.

Wednesday 6 July 2011

The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 5(b), p. 557

Show that the set of sentences: (x)(Rx ¬ Rx) is inconsistent. The proof:
  1. (x)(Rx ¬ Rx) ......... Assumption
  2. Rx ¬ Rx ......... 1 UI x/x
  3. (Rx ¬ Rx) • (¬ Rx ⊃ Rx) ......... 2 BE
  4. Rx ¬ Rx ......... 3 Simp.
  5. ¬ Rx ¬ Rx ......... 4 MI
  6. ¬ Rx ......... 5 Taut.
  7. ¬ Rx ⊃ Rx ......... 3 Simp.
  8. ¬ ¬ Rx Rx ......... 7 MI
  9. Rx ∨ Rx ......... 8 DN
  10. Rx ......... 9 Taut.
  11. Rx ¬ Rx ......... 10,6 Conj.