For example, the Pythagorean theorem exists in the sense that it belongs in Euclidean geometry. Surely it did not come into existence before someone in the Pythagorean school invented it. But it has been in conceptual existence, i.e. in geometry, ever since. Not that geometry has an autonomous existence, i.e. that it subsists independently of being thought about. It is just that we make the indispensable pretence that constructs exist provided they belong in some body of ideas—which is a roundabout fashion of saying that constructs exist as long as there are rational beings capable of thinking them up. Surely this mode of existence is neither ideal existence (or existence in the Realm of Ideas) nor real or physical existence. To invert Plato’s cave metaphor we may say that ideas are but the shadows of things—and shadows, as is well known, have no autonomous existence. — Mario Bunge

Start with a relatively simple situation. A behavioral biologist is observing a baboon troop. Over a period of several hours he records the episodes in which one of the animals grooms another, carefully noting the names of the animals (who groomed whom) and the time interval through which grooming occurred. Each entry in the notebook records the perceptual acquisition of a belief. Focus on any one.The observer is initially scanning the troop. He sees the male he calls “Caliban” approach the female he calls “Miranda.” There is a sequence of facial expressions and gestures, at the end of which Caliban crouches behind Miranda and plucks at her fur. Our biologist presses a button on his stopwatch and quietly moves to a position from which he can gain a better angle on the interaction. After a few minutes, Miranda shrugs and moves away. Another button on the stopwatch is pressed, and the biologist writes in the notebook, “Caliban—Miranda, 6:43.” That notation serves as an extension of declarative memory, something from which the biologist can later retrieve the belief that Caliban groomed Miranda for a period of six minutes and forty-three seconds. — Philip Kitcher

I once knew an arrogant sculptor who snapped at some remarks about artistic style that were made in his presence. It was proposed during a con­versation that one might design a computer capable of generating count­less new works in the style of an already known author or musician. The sculptor objected to this notion, not in the manner of a luddite, but that of someone quite confident in a specific philosophical position: "there is no such thing as a style apart from the sum total of works an artist has pro­duced." Whatever the merits of this position, they are opposed by the entire phenomenological tradition, and in my view rightly so. A style is actually not a mere concept abstracted from numerous singular cases, but an actual reality that none of its manifestations can exhaust. One can hear a newly discovered Charlie Parker recording and immediately recognize the style; one can and will say that "that solo is really classic Bird," even though up till now it was not part of the known Parker oeuvre. We sense that a certain person does not really belong in Brooklyn or in the military just by their general style, without being able to pinpoint any disqualifying factors. In this sense, styles are no different from intentional objects as defined by Husserl, which lie beyond any of their current profiles and even any of their possible profiles. We can say of any object that it is not a bun­dle of specific qualities, nor a bare unitary substratum, but rather a style. — Graham Harman