It is almost 60 years since I studied logic at university.

I would like to be able to say that I signed up for the course in a quest for self-improvement, but the truth is rather more mundane: one of my friends tipped me off that the logic tutor was known to be a very generous marker.

Apparently this was not common knowledge because when I turned up for the first tutorial there was only one other student on parade.

After wrestling with Aristotelian syllogisms and Boolean algebra we both passed the end of year exam with marks in the high seventies.

Whether this was the result of lax marking, or our intellectual brilliance, is not for me to judge, though I would say that I never encountered another tutor who rated my efforts so highly.

The first term was taken up with syllogisms; first formalised by Aristotle more than 2000 years earlier.

The simple example given in all the text books is:

All men are mortal (major premise)

Socrates is a man (minor premise)

Therefore, Socrates is mortal. (conclusion)

At this distance in time, I have little recollection of the course, but I do remember being very surprised to be told at that first tutorial that logical validity and truth are not the same thing.

Logic concerns itself with the form of the argument, not its substance.

So, despite being complete tosh, the following syllogism is perfectly valid because the conclusion follows inexorably from the two premises.

All whales are four-legged, land-dwelling mammals.

Moby Dick was a whale.

Therefore Moby Dick was a four-legged, land-dwelling mammal.

It follows, therefore, that if you can bring your own facts to an argument you can prove almost anything you like.

This is why totalitarian regimes seek to control the media.

If you can assert, without fear of contradiction, that Soviet tractor production far exceeds that of the USA it is not difficult to go on to “prove” that a collectivised economy is superior to one run on free market principles.

Something along these lines was afoot during the recent debate on PCC’s signing of a Memorandum of Understanding (MoU) with Pembrokeshire College over sixth form provision.

The central driver for this agreement is that, as sixth forms are funded on a per pupil basis, small classes don’t generate sufficient income to cover costs so the budget for Key Stages 3 and 4 are being raided to make up the shortfall.

The case was summed up by Chairman John Davies at the Schools and Learning scrutiny committee.

The debate can be seen here, at 25 mins.

Briefly, it is claimed that seven of the county’s eight secondary schools are each currently subsidising ‘A’ level classes to the tune of over £200,000.

Across the piece this amounts to a transfer of some £1.5 million from Key Stages 3 and 4 to Key Stage 5 (‘A’ level).

Of course, if that were true, there would be a compelling case for the changes outlined in the MoU.

Over the years, Old Grumpy has learned to be sceptical about PCC’s facts, so on Monday I wandered up to county hall to examine the evidence for myself.

The first table I was shown, which aims to prove that the full cost of ‘A’ level classes consists of teachers’ salaries + 76%, is reproduced below:

What is immediately noticeable is that the two biggest contributors in percentage terms are Ysgol Dewi Sant and Ysgol Bro Gwaun.

However, as ‘A’ level provision in both these schools is set to be transferred to Pembrokeshire College within the next twelve months, it is difficult to see why they should be included in a calculation that concerns future ‘A’ level provision.

Indeed, I understand these elevated percentages are the result of the sub-optimal allocation of teacher time during the changeover.

If they are excluded the add-on is reduced from 76% to 66% and it is difficult to escape the conclusion that they have been included to lend support to the desired conclusion.

This 76% figure is then used to calculate the overall cost of an ‘A’ level teacher.

There are two versions of this document.

Version 1 reaches the conclusion that the overall cost of a teacher is £86,520 per annum including overheads of £37,361 (76% of teacher costs):

For some reason that wasn’t considered satisfactory so a second version was produced which calculated that the cost of the teacher + overheads to be £102,142:

You will notice that this £16,000 uplift is mainly down to the introduction of something known as TLR (£7,590) + 76% TLR.

I’m not sure what TLR means except that it refers to some sort of payment for extra responsibilities.

Interestingly TLR is one of the items included under management costs in the calculation of overheads (see below), so on the face of it this item is being counted twice.

And questions have been asked about the £58,000 cost of a teacher’s salary.

Is this typical, or is it for one of the more experienced, higher paid members of staff?

This is important because this salary level is taken as the baseline for all ‘A’ level teachers.

And you have to wonder why Greenhill with 157 sixth formers has teacher costs of £601,000 while STP with 165 gets by on £442,600.

One explanation is that they are either measuring different things, or measuring the same things differently.

It is also difficult to reconcile the 76% overheads with the fact that teachers’ salaries account for 70% of the typical school budget.

Seventy percent + 76% of 70% comes to 123% which would mean that ‘A’ level classes were picking up more than their fair share of the total cost of overheads.

And, in any case, there is an argument for saying that only those overheads that would be eliminated by reducing ‘A’ levels should be included in the calculation.

To be fair, when the scrutiny committee met on 3 August it didn’t have most of these calculations before it.

I would suggest the committee should reconvene and try to iron out some of the anomalies I have highlighted.