I was a disappointment to Roger in the matter of Symbolic Logic. He was more academic than I could ever have been. I often felt, during my time in Jacob’s department, that somebody would unmask me for a fraud. Each decent essay mark came as a new surprise to me and a temporary reprieve. It was a feeling not unlike the relief of waking to find that one has only dreamed it. That one has not in truth walked down the High Street in one’s grubby vest on Saturday morning. I had been drawn to Philosophy for no other reason than that it seemed, after the solid pragmatism of the greengrocer’s shop, to be elevated by a marvellous uselessness. It was the subtlest kick in the teeth I could deliver to my mother and aunts who saw me enshrined as the director’s personal secretary. Having embarked upon it, I found it often crazily high falutin’. Jacob, who thankfully had his feet so firmly on the ground, was, of course, my grand exception. Because he taught so well, because he was not above making it perfectly clear that he had a political ideology which directed his approach, because he had roots in German history and intellectual life, these things enlivened a lot of what he said. When he talked to us about Kant, for instance, he made it seem as controversial as if the postillion had just delivered the stuff into our hands from eighteenth-century Koningsberg. He would pick delightful energetic holes in Marxist epistemology for us with the licence of the converted. Since most of us leaned towards the left, we loved him in his critical analyses for never giving comfort to the right. Then came the business of Symbolic Logic.
I had been taught mathematics at school by the games mistress who did it on the side and did it badly. Mathematics, she said, was ‘exercise for the brain’. All I ever saw was sums with the numbers taken away. I never saw that system glowing with the beauty of pure reason which Roger saw. I was confirmed in my arty bias against it in the war of the two cultures. I liked the things of the heart. How could I therefore enter into a relationship with a’s, b’s and x’s? It was manifestly true, also, that the girls from my school who went off to university to do sciences were those who couldn’t compete with men for places in History and English. I was, therefore, a humanities bigot. Scratch me and I still am. Only because Roger’s beauty and high culture took my breath away did I forgive him for his nasty fluids in jars and his collections of fossils chipped from the walls of old quarries. Then all of a sudden, in the middle of my arty education, came propositions expressed in the language of the games mistress.
‘I hate it,’ I said to Roger, of the p’s and q’s, the following weekend. We were lying on the grass on Port Meadow watching sailing boats weaving between the ducks.
‘I’ll explain it to you,’ Roger said. On the back of his William Byrd, which he had in his pocket, he wrote, ‘If p then q. Not q … so not p.’
‘If all bread were sliced bread,’ Roger said, ‘we would have no need of a bread knife, right?’
‘Except if you spread jam with the bread knife,’ I said. A thing he always did. Roger ignored me.
‘We cannot do without the bread knife, so not all bread is sliced. Okay?’
‘Okay,’ I said.
‘You are required to express this as ‘If p then q. Not q therefore not p,’ because symbols are more use to you than the specific examples of the bread and bread knife.’
‘Yes,’ I said, because I loved him, though for me all that mattered was the bread, glowing in a bag labelled Mother’s Pride. As the afternoon wore on, Roger liquidated not only the bread, but also ‘if’, ‘then’ and ‘not’. The sliced bread had become bracket p hook q close bracket stroke q turnstile stroke p. The jam was nowhere. The strokes had to do with falsehood, I remember. They denoted that, within the proposition, was an odious damned lie. We classified propositions in rows of ones and zeroes. An hour later I drifted off in the axiomatic method.
‘If a binary constant is flanked by a propositional variable,’ Roger said, ‘then the scope–’ I noticed, at that point, that a small boy had caught a fish.
‘He’s caught a fish,’ I said. Because Roger was, at that stage, still in love with me, he didn’t get nasty.
‘Katherine,’ he said, ‘what use is your philosophy going to be to you without maths? You’ll be like an architect with no engineering. Trust that father of mine to take you on with no maths, the shallow buffoon.’ I had not considered my usefulness. The only use I had for my self was in pleasing Roger. I had dimly begun to notice that men students were different. That they thought about careers and research grants, while I thought about cultivating a range of accomplishments to gratify a grade A husband.
‘Not all of it is to do with p and q,’ I said, which was perfectly true.
‘What isn’t is an obsolete mish-mash of malignant demons and morality,’ he said. His quarrel was with Jacob not with me, but, because he was slightly paranoid, he saw me often as Jacob’s emissary.
‘Mathematically, you are like a person who pre-dates the invention of the printing press,’ he said. ‘I have to go and sing.’ Roger sang in the cathedral choir. He went off, summoned by bells, like somebody, one might almost say, who pre-dated the theory of evolution. He began to teach me algebra that evening in the waiting room of the railway station – and left me shamed by my incompetence. I got on the train feeling uneasily that Roger would prefer not to make love to a woman who had an emotional block about substituting signs for concepts.