Chalk and cheese; chalk first. Gary Hume's Door Paintings are based on the kind of double swing doors you find in the corridors of hospitals and colleges. These simple and recognisable arrangements of circles and rectangles provide the motifs for a series of "abstract" paintings – approximately door-sized and painted in household gloss – that Hume has made from the late 1980s until now. About 20 of them are showing in Modern Art Oxford.
Now in his mid-forties, Hume was a founder member of the Young British Artists. He took part in Damien Hirst's seminal Freeze exhibition, 20 years ago. He was bought by Charles Saatchi early on. These Door Paintings were his opening gambit. And though his later work has wandered all over the place, I don't think he's had a better idea. The doors are so blankly ungiving. Their first move is to thwart all your overtures.
You thought you were meeting a pure geometrical abstraction? No; these forms are all too literally meaningful, a direct quotation from the world, and such a grim, oppressive bit of it. You felt they might have some composing, shape-making? No; the rounds and oblongs are a mere template, methodically and evenly filled in. Or you hoped the paint might be up to something? No; household gloss is wholly unresponsive to the painter's hand, and highly reflective of the viewer, bouncing you back at yourself.
The Door Paintings resist our impulse to find expression or depths or meanings. The flat surfaces shut in your face, a closure that's emphasised by a grim and witty visual pun; the double portholes and hand-plates look like the eye-sockets and nose-holes of a schematic skull.
But that impression of dead-faced cool isn't all the story. The Door Paintings aren't just clever non-paintings, blending the detachment of Pop Art with the rigour of Minimalism, and saying: "Ha ha, you thought you were going to get something out of me, what with me being a painting hanging on the wall, but you will get nothing, nothing, ha ha."
No, their point-blank refusal of normal painterly satisfactions is not their conclusion. It's their premise. The effect is: blank, yes – but oddly, more than blank. They have powerful presence. There's the sheer reality-effect of their resemblance to doors. It's almost a kind of trompe l'oeil. Their rounds and oblongs, their door-sizedness, presses some simple cognitive button so that you can't help feeling you are looking at, not paintings, but institutional doors themselves.
And yet they have more formal activity than you might expect. The colour schemes look bad, almost random, but turn out to be rather subtle and moody. The template shapes are always slightly wonkily drawn. In later ones, other motifs intervene, as a flowing stripe cuts across.
When you get to a picture such as Black Door with Sash, the basic door motif is so decisively crossed with other forms that all sense of cool is dispelled. You're just looking at a painting there seems no reason not to call an abstract. And I suppose there's a nice, solid, DIY craftsmanly quality to it.
Cy Twombly, 80, is a bigger cheese, often ranked as a living Old Master. You may say that his penchant for grand, classical titles nudges the viewer towards that judgement: the latest works in his Tate Modern retrospective are called Bacchus. You couldn't find a body of painting much further from Hume's.
Twombly's art is all about letting go. It's a spontaneous improvisation, a seismograph sensitive to every spasm. It grew out of an engagement with "automatic writing", as practised by the Surrealists. You free up the hand from conscious control, let it run, to say what it wants. In the 1950s, Twombly experimented with drawing in darkness, and left-handed. The first results were fields of abrupt, juddery marks, where pseudo-handwriting vied with vestigial image-making, and scribble and doodle, and gestures tangled up and overlaid.
Everything looked truly out of control, excitingly chaotic – yet surely there was some subliminal, intuitive choreography going on, making it nice. Paint came into it, smeared and blotted on with fingers, in flesh and blood colours. Nutty little diagrams emerged, and obscene body parts. Twombly had invented a highly flexible energy-language that could carry all sorts of feelings: explosive lust, violence, ecstasy, grief, elegy, even comedy.
It was always sustained by an engaging sense that the artist wasn't in control of his feelings. He was all-feeling, a direct and innocent channel for these passions. With that comes the inevitable suspicion that he might really be a faux-naive, putting on the trance-state stuff; and what's more, prettying it up a bit. And then there were the cultural resonances – gods and goddesses, poets, lines of poetry. It's not totally bonkers; you can make a brisk link from wild scribble to the classics via the word "Dionysiac".
Some critics think these verbals are gratuitously pretentious. Others lap them up, and throw in references of their own. Tate Modern's catalogue takes cultural name-dropping to carpet-bombing levels – and it's easier than talking about the pictures.
Personally, I can take them or leave them, all the Apollos and Virgils, the Latin and Italian inscribings. They don't affect the real problem with Twombly. The visual language of automatism, though it can be lively, is too damn tasteful. Chaos means not making any definite statements. Handing it over to the unconscious is a way of staying cool.
So I like some of the more recent work, where Twombly sticks his neck out, takes full responsibility. Quattro Stagione, made in the early 1990s – it exists in two versions, both in the show – is a suite of four tall paintings, supposedly depicting the seasons, whose names are written on them: Primavera, Estate, Autunno, Inverno, of course. And compared with earlier automatic Twombly, it may seem a bit crass.
Each picture puts its meaning into almost a single gesture, played out on a plain ground. Autumn is like tomatoes and other fruit thrown at a board, impacting, sticking, juices streaming. Spring is a row of a complex red gash and scratch-marks. Summer is three yellow wounds. Winter is a blurring collision of white-greys and evergreens.
Apart from the red Spring, the colour symbolism is literal. Still, these four very distinct identities suggest some archetypal agenda. And what's good about them is their open articulacy – the way they create these identities, these emotional hieroglyphs made of paint-gesture and semi-image. I can't think of who else has done it like this.
Gary Hume: Door Paintings, Modern Art Oxford (01865 722 733), to 31 August; Cy Twombly: Cycles and Seasons, Tate Modern, London SE1 (020-7887 8888), to 14 September