Did you read the next part of my comment where I said "that the distance of one mountain is given the label '8,849 m' is a consequence of our measurement"? — Michael
Yes I read that, and it is why I accused you of being ambiguous with "distance". In the first sentence you said there is a distance "even if we never measure it". In the following statement you gave the distance a number. The number you designate as the "label" of the "distance", but this is only produced as a consequence of measurement, as you agree. The ambiguity is that in the first sentence "distance" as referring to something which exists independent of measurement, refers to something extremely vague and general. In the second use, the "label" refers to a specific value, which requires measurement. The thing labeled as the "distance" is a specific value, whereas the "distance" in the first instance is a general unspecified separation. This ambiguity invites equivocation, such that one might think that "distance" is used in the same way both times, so that "distance" as the specific value which is dependent on measurement is the same as "distance" in the sense of the vague and general separation between the two things which is supposed to be independent from measurement.
It's certainly not "obvious". Space is often thought of as being mind-independent, notably by scientific realists, and I suspect also most laymen. Idealists, scientific instrumentalists, and Kantians may think differently, but such positions are not self-evident. — Michael
I have to disagree with this. I believe the idea that "space" as independent came about from the union of space and time, in the concept of space-time. So the mind-independent substance believed in by scientific realists is not "space" per se, but "space-time".
This is an important distinction to make, because classically "space" was a static medium designated by the coordinate system employed by geometers. Since it was logically necessarily to think of space as static, to prevent the principles of geometry from changing randomly, it was known by geometers to be separate, distinct from the real world within which things are continually changing. It was an eternal ideal. So it was clear and obvious to the scientifically minded, that space was a mind-dependent ideal.
However, extending way back to ancient times there was significant difficulty in understanding the reality of motion. Ancient Greeks, I believe the atomists, demonstrated logically that unless there was some sort of empty space, "void", motion would be impossible. Every piece of matter would be contiguous with other matter and nothing could move anywhere. This produced the need to assume an independent "space". But since this "space" is independent of the mental constructs which describe the "space" that makes up the volume of an object, describing instead the space between objects, an incompatibility between the two senses of "space" was created. The "space" of an object which accounted for the static unchangingness of the object, and the "space" between an object which accounted for the activities of things.
The conclusion we can draw, is that what is referred to as "space-time", as the supposedly real and independent substance, (the concept which supports the real motion of objects), is fundamentally incompatible with our conceptions of "space", which is an ideal constructed and used in coordinate systems. This is why fundamental axioms of "space", like Euclid's parallel postulate are found to be inconsistent with the concept of "space-time", and those realists you refer to turn to non-Euclidian space. "Space-time" is what is supposed to be real, not "space".
I should note that I use "materialism" and "physicalism" interchangeably, and that physicalism "encompasses matter, but also energy, physical laws, space, time, structure, physical processes, information, state, and forces, among other things." — Michael
Notice, that by including "energy" "time", "physical processes", you are no longer talking about "space". You are talking about "space-time" which is fundamentally different, and as explained above, incompatible with "space". So when you make an argument concerning "space", and you allow that "space" refers to what is known as space-time, you produce significant ambiguity, most likely resulting in an equivocal conclusion.