25 June 1999, 917 words
It seems to me that the present controversy over school textbooks has arisen because members of Cabinet don't actually know what 1 is. One - in the pronoun sense - really can't blame them. The difficulty in defining 1 was actually solved only about a hundred years ago, and it is quite obvious that the UNC regime is still living somewhere in the early 19th century. That is why Education Minister Adesh Nanan continually threatens teachers and school principals with legal action, and why his leader Prime Minister Basdeo Panday tells Tent City vendors he has a "rod of correction". However, since Mr. Panday apparently doesn't even know the difference between 1 and many, I suspect his rod isn't all that threatening.
Now you may be wondering how people who have attained the highest offices in the land can be so dumb. (My own suspicion is that it's a necessary qualification.) But this school textbooks issue seems to go beyond mere innumeracy. The great mathematician Giuseppe Peano provides a possible solution. According to Peano, a class consisting of one member is not identical with that one member. For example, "Prime Minister of Trinidad and Tobago" is a class and has only one member - i.e. Mr. Panday. But to identify a class with its only member is to introduce insoluble problems into the logic of collections and therefore of numbers. And this government in one highway contract, one airport contract, the INNCogen deal, the NFM rice deal, the NP consultancy and three (3) budget presentations has yet to get any of the numbers right.
It turns out, though, that this whole single-textbook idea has little to do with improving education and everything to do with a conditionality for accessing a World Bank loan. The money will no doubt come in useful for finagling GNP and unemployment figures in the year 2000. That kind of math the UNC is actually quite good at. Yet they could still have avoided all this brouhaha if they understood the concept of 1.
The problem starts with the Prime Minister believing he is the Prime Number. The Scholastics held that one and being were convertible terms. This made it impossible to define1, but Mr. Panday clearly feels that once he says is 1 is 1. That, as Peano pointed out, is what happens when you think a class and its member are one. The fact is, though, that arithmetic was wrongly conceived by everybody before Gottlob Frege published his axioms. Everyone thought that number resulted from counting, which made it quite difficult to go above twenty, unless you were male and willing to count while not wearing pants.
What got mathematicians in trouble was the fact that things that are counted as 1 can also be counted as many. This problem still gives politicians headaches. For example, one electorate is also many voters; and two ethnic groups are also 500,000 Triniafricans or 500,000 Trinindians. The UNC has thinks the solution lies in soppy lyrics about "making T&T one again", but since they clearly have no idea what 1 is, their attempt is doomed to failure.
What they fail to realize is that what makes anything 1 is not its physical constitution, but the question "Of what is this an instance?" The number you arrive at by counting is the number of some collection. Thus, the number of UNC financiers totals, say, three. The dollars they have contributed is, say, three million. But the collection of financiers has whatever number it does have before you count it - i.e. one. The dollars the financiers have got back in inflated contracts is, say, several hundred millions. Even if you add another financier who gets Government contracts, the collection remains one, though the instances of financiers are now four and the instances of nepotism will therefore multiply by any pertinent factors (eg. how many girlfriends/relatives/friends the financier has).
Now in order to decide what is an instance and what is a collection, you must use a propositional function. Contrary to what you might think, this does not involve a proposition about a function, even if you're Brian Kuei Tung liming at the Parrot. A propositional function is just an expression containing a variable and becoming a proposition, true or false, as soon as a value is assigned to the variable. Thus, "X is the book chosen by the Textbook Evaluation Committee" is a propositional function. If in place of X, we put Integrated Mathematics for Primary Schools, we get a the proposition Integrated Mathematics for Primary Schools is the book chosen by the Textbook Evaluation Committee". This, of course, is a false proposition, since no one book was chosen by the TEC.
One, you see, is a characteristic, not of things, but of certain propositional functions which have the following property - there is an X which makes the function true and which is such that, if Y makes the function true, X=Y. In the case of the textbooks issue, however, there isn't a single letter in the alphabet which can make this particular proposition true. That is because the TEC submitted a list (one collection) of several textbooks from which principals were to be allowed to choose one text for their school (one instance), thus ending up both with1 and a true proposition. But Cabinet Ministers obviously think one instance is the same as one collection, and they even more obviously have no concept of truth at all.
Copyright ©1999 Kevin Baldeosingh