A Freemason is charged - among other things - to study such of the Liberal Arts and Sciences as may lie within the compass of his attainment. These are seven in number and are named as Grammar, Rhetoric, Logic, Arithmetic, Geometry, Music and Astronomy.
    Scholars in the Middle Ages divided these arts and sciences into two groups, three in one and four in the other. Grammar, Rhetoric and Logic became known as the Trivium of ‘Way of Three’, while the other four formed the Quadrivium or ‘Way of Four’.
    Because the Trivium had to be learnt first it was considered by some to be a sort of preparatory study and therefore inferior to the Quadrivium, and those who had progressed to the mathematical sciences tended to look down on those first three as if they were unimportant; so much so that the word ‘trivial’ came to be applied to any matters of little importance and we still use the word in that same sense today without realising that we are slandering three of the Liberal Arts!
    First, then, it is necessary to learn Grammar. One dictionary defines Grammar as ‘the science of language from the points of view of pronunciation, inflexion, syntax and historic development: the art of the right use of language by grammatical rules.’ In other words it is important to know how to read, write and understand good English; and Freemasons are fortunate that the ritual of the Craft became standardised at a time when the English language was at its clearest and most intelligible. Some of the words may seem oldfashioned to modern ears but the meaning still comes through without difficulty.
    Now it is one thing to learn the theory of language and the rules of grammar, but it is quite another thing to be able to speak that language fluently, accurately and with meaning. That is why we must learn Rhetoric, defined in that same dictionary as ‘the theory and practice of eloquence; the whole art of using language so as to persuade others.’ Unfortunately eloquence is a somewhat neglected subject nowadays, and it is no exaggeration to say that the majority of people speak less than well. The word Rhetoric is derived from the Greek Rhetor who was public speaker or ‘town crier’ of old. Clarity of diction therefore, with good use of grammar, is the object of the art of Rhetoric.
    So, we learn to read, write and speak our language; then we must learn to reason. The word ‘Logic’ comes from the Greek logos meaning ‘reason’ or ‘true word’ and appears in the Old Charges of masonry as ‘the art that teacheth to discern truth from falsehood.’ The dictionary calls it ‘the science and art of reasoning correctly.’ Logic is a tremendous subject with proper rules which must be followed to be sure of coming to correct conclusions. Far from being ‘trivial’ in the modern sense, Logic is the basis of all sound argument, and without it the other sciences could never be properly understood.
    We now turn to the Quadrivium and having learnt how to deal with words we proceed to dealing with numbers. The Greek for ‘number’ is arithmos and the Greek for ‘art’ is techne, so our word Arithmetic sums up the art and sciences of numbers. In its simplest form this is no more than straightforward counting and the four regular exercises of addition, subtraction, multiplication and division; but we must remember that it also includes more complicated disciplines such as Algebra, Logarithms and Calculus. It is therefore possible to make a daily advancement in Arithmetic and yet still have more to learn!
    In Geometry we move from numbers to shapes. The word itself means ‘earth measure’ and it deals with the properties of points, lines and angles, surfaces and solids. I must admit that when I was at school, Geometry was one of my favourite subjects - because it made sense to me. Logarithms and calculus I never did understand, but the reasoned arguments of a geometric proposition gave me great satisfaction. If Arithmetic might be considered as the ‘grammar’ of mathematics, then Geometry is certainly its ‘logic’. An operative mason uses the science of Geometry more than any of the others, while the speculative mason finds it a reasonable way of applying mathematical principles to his morals.
    ‘Music?’ one candidate was heard to ask, ‘what has Music got to do with Arithmetic and Geometry?’ Much more than appears at first sight. Music as a science was probably perfected by J.S. Bach whose fugues and counterpoint were mathematically worked out in such a way that he knew they would sound harmonious even without listening to them before he wrote down the sounds. One writer describes Music as ‘the concord of sweet sounds’ and goes on to say that as Music elevates the generous sentiments of the soul, so should the concord of good feeling reign among the Brethren.’ We all appreciate the value of a good organ and the ‘harmony of the Lodge’ is considerably increased by having a good organist - though he now, alas, seems to be one of an endangered species! We must encourage young musicians before it is too late.
    Finally we come to Astronomy, the science which embraces not only all the earth but also all the heavens, from here to infinity. So, how many of these seven arts and sciences will lie within the compass of our attainment? Perhaps it is just as well that we are charged to ‘study’ them and not expected to understand them all - but that is what a ‘daily advancement’ is all about.