If English then logic

Answers please

2012-02-04T14:48:00.000-08:00

If I don’t see the whole picture, I am entitled to the conclusions I draw; and if my conclusions are not true, my inferences can still be valid. It is very difficult to see the bigger picture today, indeed.

The modern propaganda, be it commercially driven or born of the zany enthusiasm of an end user basking in the reflected glory of his smart gadget, is that we are a mobile society. Current mobility, which is without precedence, calls for faster, more powerful and more portable technology.

A report out yesterday by the medical establishment suggests (my information comes from the BBC) that we are becoming more sedentary, less mobile and more vulnerable to medical conditions such as diabetes, hypertension and heart disease. The chief culprit is obesity, itself caused by a lack of exercise and a sedentary lifestyle. The question is: do sedentary people need all this mobile technology?

We are told we have to pay for art the market price which it commands, of which the major component is copyright. I eye with humility recordings of classic composers which are priced outside my budget. The packaging is enticing: rippling flesh and flowing robes on box covers, brilliant colour, copious notes.

I own Bach, Mozart and Beethoven concertos, released by a reputable label Archiv or Deutsche Gramophone, conducted by Trevor Pinnock (recently performing at the Warsaw Philharmonic Hall) which, by all accounts, are budget releases: black and white cover art (the box shows a detail of a baroque façade which is so indistinct it could be anywhere), CD sleeves rather than boxes, definitely not a display item. Question: given that Pinnock / DG are names of unquestionable stature, what would I be paying for buying some of the fancier releases? I could go to a local church, take a picture of a painting featuring rippling flesh and flowing robes, then go to my local Tesco, buy the kit (colour printer at al), and make the cover art at home. Is this why I have to pay double the price of the budget releases?

Poland is in the crosshairs of the EU for failing to implement the biodiversity recommendations. Broadly speaking, biodiversity is meant to ensure that we do not lose the local varieties of fruit and vege at the expense of bland imports. As an apple lover, I pity the loss of local varieties but celebrate as well the many different varieties on offer all year round: starting with Geneva, through Paula Red, Celesta, Orange Pippin, Mackintosh, Lobo, Cortland, Champion, Jonathan, Jonagold, to Gloucester, and many more.

From what I know, shops in Scandinavia, the UK, and parts of continental Europe stock only two varieties: red and green. In Poland, in addition to the wide range of apples in the supermarkets, one can get the local varieties at the specialist greengrocers. What is the fuss about?

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(7)

2012-02-04T12:36:00.000-08:00

Prove valid, as usual:

(∃x)[Px • (y)(Py ⊃ y=x) • Qx]
(∃x) ¬ ( ¬ Px ∨ ¬ Ex]
∴ ( ∃x)(Ex • Qx)
(∃x) (¬ ¬ Px • ¬ ¬ Ex] ......... 2 DeM
(∃x) (Px • Ex] ........ 4 DN
Pa • (y)(Py ⊃ y=a) • Qa ......... 1 EI x/a
Pm • Em ......... 5 EI x/m
(y)(Py ⊃ y=a) ......... 6 Simp.
Pm ⊃ m=a ......... 8 UI y/m
Pm ......... 7 Simp.
m=a ...... 9,10 MP
Em ......... 7 Simp.
Ea ......... 11,12 Id
Qa ......... 6 Simp.
Ea • Qa ......... 13,14 Conj.
(∃x)(Ex • Qx) ......... 15 EG

Of wants and needs, and pirates and robbers

2012-01-26T14:15:00.000-08:00

Glory be to inventors and artists for making our lives easier and more pleasant! Bless the freedom of expression and the market economy and that bring us the benefits of their creation. And long live the free internet!

I don’t see a contradiction between my statements, and I refuse to be shown. Maybe it’s a generational thing – I think of the internet as a means to getting and paying for what I want if I really want it. ‘Paying’ and ‘touching’ are the operative words here. That is how I buy music, movies and books. And I have yards and yards of shelves at home to show that my money is where my mouth and heart are.

I don’t think the same way of things that I need but don’t want. There are certain books I don’t think much of but have to use with students. I think they are rubbish, that they pander to the desire of modern society to see itself in a certain way, and that they have been churned out by their hundreds merely to squeeze every penny from bewildered students and depression-prone teachers. The prime example is the whole English language teaching industry.

My occasional smash-and-grab raids in cyberspace are ways of venting my criticism and contempt for the authors, publishers, market men and promoters. I don’t respect them, so I take them.

Not so with things I value. We ought to pay for things we like, full stop. Paying is a way of showing respect to someone who has made a material impact on our lives. I have taken this view even though I detest the way we – end users and supporters – are manipulated by the people who stand between us and the artists.

I am not sure which has the shakier ground to stand on: online piracy or daylight robbery (perpetrated by, for example, the music industry). To pick and choose which track I want to listen to and then to get it from someone who wants to share it (if I ever wanted to listen to downloaded music on a noisy underground train, which I don’t) is no more of a crime to me than the shabby game of slicing an artist’s output one hundred and fifty different ways, sublicensing it to dodgy labels who buy in bulk and issue: The Best of …, The Greatest Hits of …, The Definitive … Collection, The Ultimate …, and so on, each of which contains only a fraction of the truly best tracks, topped up with a makeweight of ‘never-heard-ofs’, and live recordings.

So ends the week during which I have spoken to a dozen lawyers about the Anti-counterfeiting Trade Agreement (ACTA) who have been issued instructions to support it on behalf of their employers and in relations with their clients, but who have all criticized it roundly in private.

Dread of forms

2012-01-20T14:01:00.000-08:00

A portion of my time every month is filled by form filling. I am sure there are statistics somewhere shedding light on how much time an average human spends filling in forms, just as there are statistics on how much time in our lives we spend sitting on a toilet, tying up shoelaces or clipping nails.

My particular bugbear is forms – the rock at which my sensitive disposition meets the hammer of authority. I have visions of running away from men and women in rubber gloves who have found out about my cul de sac from something I had been manipulated to put down in a form.

Lifestyle choices involving the breaking off of all social relations hold the greater appeal the more years I clock up: if I have nothing to give and nothing to take from society, I should be able to extricate myself from the binds of forms. Forms is other people.

As I am having to fill in rather a lot of forms this month, I have decided to articulate my dread of forms – that old trick of convincing yourself that it is easier to fight the enemy you know. Here is the list:

1. The sheer chore and imposition on my time

2. Being hemmed in by the time limit all form submission inevitably involves

3. Fear of misunderstanding what is wanted from me

4. Prospect of having to redo the form if I spot a mistake

5. Prospect of having the forms sent back / rejected if I let a mistake go undetected

6. I do not think in block capitals, yet block capitals is what I have to use

7. Watch that I don’t get the rows mixed up

8. Rounding – I can’t ever be sure I have rounded off my figures correctly

9. The ratio of information that is not applicable to that which is always makes me think I am liable to err in at least a hundred and fifty different ways

10. Procrustean adjustment – I have to fit the form, not the form me. Forms stretch or reduce me in size.

11. Forms are a peculiar form of interacting – I am never complimented on filling one in correctly, but always punished for screwing up

12. Forms lay a trail that can be followed

The language of forms reinforces the sense of having to surrender my freedom: cells, boxes, lines, grids, bars. What all forms need is a place in the centre of each page called an ‘exercise yard’ where I could rest my pen between changing cells. I dread forms.

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(6)

2012-01-11T13:49:00.000-08:00

Prove the validity:

(∃x)(y){[ ¬ Fxy ⊃ x=y ] • Gx}
∴ (x){ ¬ Gx ⊃(∃y)[ y ≠ x • Fyx]}
* ¬ Gx ......... ACP
* (y){[ ¬ Fay ⊃ a=y ] • Ga} ......... 1 EI x/a
* ¬ Fax ⊃ a=x • Ga ......... 4 UI y/x
* Ga ......... 5 Simp.
* a ≠ x ......... 3,6 Id
* ¬ Fax ⊃ a=x ......... 5 Simp.
* Fax ......... 7,8 MT
* a ≠ x • Fax ......... 7,9 Conj.
* (∃y)( y ≠ x • Fyx) ......... 10 EG
¬ Gx ⊃(∃y)[ y ≠ x • Fyx] ......... 3-11 CP
(x){ ¬ Gx ⊃(∃y)[ y ≠ x • Fyx]} ......... 12 UG

Fox and geese

2012-01-06T13:33:00.000-08:00

This board game first captured my imagination about ten years ago when I was up to my neck in medieval studies. One should study the middle ages for the same reason one gets vaccinated – to build up immunity. Middle ages aside, the game had an instant appeal to me and I scoured shops in the UK in the hope of finding it. Unsuccessfully.

I see now that the internet offers some choice, and I may yet procure a set online if my efforts to make one come to naught. I owe the present revival of my interest in the game to a friend who had asked me for a Christmas gift idea before the holiday. The condition was that it be a ‘brainy’ gift.

I suggested fox and geese. The reason: I had never played it against anyone nor owned a set, but I had played it in my head, against myself, plenty of times, and enjoyed it immensely. To be a gift from the heart rather than the equivalent of a bouquet from a petrol station, it is best if the gift is actually hand-made by the giver. I said as much to my friend, and immediately thought of making one for myself.

I am only just embarking on the project and, to rise to the occasion, I have bought a fox and a goose (eventually I will need anything from 13 to 22 geese) from a German company Schleich that makes rather cute and very realistic miniature animals for children. I will use these to fit a board to.

I am thinking of making the board by scoring the required cross-shaped pattern on a pastry or chopping board. It has to be solid wood to match the workmanship of the Schleich animals and to add a sense of timelessness and quality.

Why does the game appeal to me so much? It is a game of inequality, with, depending on the version, anything from 13 to 22 geese and one fox. The fox has the freedom of movement in every direction along the marked lines; the geese can only move forwards, diagonally forwards or sideways. The goal is for the fox to capture the geese by hopping over a goose to an empty space directly beyond and for the geese to hem the fox in so it can’t move.

What the fox has in the freedom of movement it lacks in numbers. I like the idea of one against many, where the individual must exercise ‘skill, cunning and strategy’ (standard description of the game) to outfox a group (or team). I always side with the lonely predator in nature movies (cheetah, leopard, etc), and in all other areas of life like the balance tipped slightly in favour of freedom rather than security.

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(5)

2012-01-06T05:16:00.000-08:00

The usual: show that the argument is valid. The easiest way: assume a negation of the conclusion (indirect proof).

(∃x)[Px • (y)(Py ⊃ y = x) • Qx]
¬ Qa
∴¬ Pa
* ¬ ¬ Pa ......... AIP
* Pa ......... 4 DN
* Pm • (y)(Py ⊃ y = m) • Qm ......... 1 EI x/m
* (y)(Py ⊃ y = m) ......... 6 Simp.
* Pa ⊃ a = m ......... 7 UI y/a
* a = m ......... 5,8 MP
* ¬ Qm ......... 2, 9 Id
* Qm ......... 6 Simp.
* ¬ Qm • Qm ......... 10,11 Conj.
¬ ¬ ¬ Pa ......... 4-12 IP
¬ Pa ......... 13 DN

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(3)

2011-12-22T11:58:00.000-08:00

Prove that this argument is valid:

Hc ⊃ Kc
Md ⊃ Nd
Hc • Md
c = d
∴ Kd • Nc
Hc ......... 3 Simp.
Kc ......... 6,1 MP
Kd ......... 4,7 Id
Md ......... 3 Simp.
Nd ......... 9,2 MP
Nc ......... 10,4 Id
Kd • Nc ......... 8,11 Conj.

Hyper, hypo, and English

2011-12-16T14:15:00.000-08:00

What is so difficult about a sentence like: ‘There were few people at the market,’ that students of English find it so hard to learn? I have long known people have trouble using and understanding certain types of structures – negations, for example, are processed more slowly than affirmative sentences by the brain – but a fault line, it seems, runs not only between ‘yes’ and ‘no’ but also between ‘less’ and ‘more’, ‘bad’ and ‘good’, ‘small’ and ‘big’, and so on.

In fact the majority of students I have tested default to ‘There were not many people at the market’ when asked to negate ‘There were many people at the market’. For once, they are using pure logic in saying so, even though they do so out of insecurity (about the use of ‘few’, ‘little’, ‘less’ etc) rather than through strict adherence to the instructions.

Some answers to this question can be found in such apparently unlikely sources as Giordano Bruno, whom unfortunately I know only through reference literature. More answers can no doubt be found in modern neurolinguistic research. Bruno, at any rate, studied the geometry of language, and found that we are suckers for hyperbole, ellipsis, circumlocution, and so on.

In language, we hang on for dear life to a kind of subdued permanent euphoria, which we prefer to call optimism. I don’t think we act by choice so much as under social pressure. It is not cool to focus on the negative. ‘Hyperbola’, ‘hyperbole’, ‘hype’, ‘hyper’ have the same origin – an excess, more than necessary. I would hazard a guess that if modern communication, which is hype-driven, continues on its current course, we will hear people saying ‘not so fantastic’, ‘not so absolutely great’, ‘not the best’ when they simply mean ‘mediocre’.

The ESL publications market is swamped by books which peddle attitudes of amazement, hyperbole and awe. There is no appetite for failure stories or for thinking small. A sentence ‘There were few people at the market’ would suggest some kind of irregularity in the system, deviation from what was expected. Where negatives are used after all, they are often sanitized, as in ‘unsatisfactory’ or ‘insufficient’.

Perhaps it is a cue for pedagogues and publishers: write a book on recession English. The ‘hypo’ language is just as rich and varied, and certainly more representative of the general human condition, as the ‘hyper’ one. I want to see expressions such as ‘run out of’, ‘come short of’, ‘disappointing’, ‘lamentable’, ‘regrettable’, ‘nearby’ (as opp. to ‘far away’), ‘at a trickle’ (as opp. ‘at full blast’), ‘a fraction of the way’ (as opp. to ‘all the way’) and so on.

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(2)

2011-12-14T11:52:00.000-08:00

Prove valid:

(x)(Px ⊃ Qx)
(x)(Qx ⊃ Rx)
Pa • ¬ Rb
∴ a ≠ b
Pa ⊃ Qa ......... 1 UI x/a
Pa ......... 3 Simp.
Qa ......... 5,6 MP
Qa ⊃ Ra ......... 2 UI x/a
Ra ......... 7,8 MP
¬ Rb ......... 3 Simp.
a ≠ b ......... 9,10 Id

City and village time

2011-12-08T13:14:00.000-08:00

I say that in my head I have already moved to a small house in the country and that the five days I spend in the city is just waiting for the train to take me away. I used to say something similar when I worked for a big accountancy firm hunting for language errors in legal and tax opinions and saw my time disappearing down a black hole called ‘time report’. I used to say that I had left my brain in a jam jar at home and that at work I merely surfed the wave of time and motion, counting down to a reunion at home in the evening.

In my village though, my walking speed sends a message that I don’t belong, not yet anyway. To everyone else’s one step, I take two, and my strides are what fitness instructors call a split.

I have now stumbled on some interesting research by psychologists Bornstein and Bornstein and on what promises to be a good read after Christmas, A Geography of Time by Robert Levine – when I hope to make more time for reading.

According to the former, the pace of life is, unsurprisingly, reflected in the walking speed, and that is positively correlated with the population of the town we live in. In the following formula, R is the walking speed in feet per second, and P is the size of the town in thousands (1 = 1000):

R(P) = 0.37lnP + 0.05

If we take the population of Warsaw to be around 2 million, then the walking speed is 2.86 ft/sec. By all accounts, my personal walking speed is faster than that, but I take it to be the average, including that of the elderly, pregnant women and children. The walking speed in Kraśnik, a town of 35 thousand near Lublin, where the abundance of time is rivaled only by natural beauty, is only 1.36 ft/sec.

My problem is I move around like an Exocet missile regardless of where I am, and any roadblock, be it ditherers in the street or people not keeping their appointments, drives me positively insane. An extract from the Geography of Time I have read on the internet quotes an anonymous British traveler as saying: ‘The further East I travel, the sloppier the perception of time becomes. It irritates me in Poland and drives me gibbering in the USSR.’

‘Sloppy’ is the right word to describe time management in Poland. But aside from that, I don’t mind living a two-speed life, if I can only learn how to downshift when I am not in the fast lane.