| | Sam,
All statements would lie in a plane but the level of current knowledge would be at one particular level of magnification and a more basic level would be at a coarser magnification. It is a matter of precision of stipulating the coordinates that correlates with the sophistication of the knowledge. This reminds me of the persistence of concepts during the growth of a given body of knowledge. An extremely-young child, at the most basic and rudimentary level, might refer to any round thing as a ball, and this is correct insofar as the child is concerned. For instance, a picture of a dinner plate (or just a circle drawn on paper), when viewed by the child, might lead to the verbal outburst: "Ball!" (even though in real life a plate is not a ball; and nor is a circle, drawn on paper).
What matters at that "level of conceptual magnification" is whether something is round or not. Only after experience with at least one plate will this child learn that he cannot treat a plate as if it were a ball. At that time (and not before), it will be appropriate to further differentiate things.
There is a historically-chained limit of the human use of things. At different times in history, things got used in new ways. When we used them in new ways, it became "primitive" to continue to view them in the old ways (like referring to a circle drawn on paper as a ball).
Ed
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