I don't get 'abstract before physical'. That runs counter to the meaning abstraction. If you read a long scientific paper for instance it will have an abstract, which is a short form summary, condensed from the detail. Likewise abstract conceptual principles are derived by observation of the natural world. We see things that have a circular shape for instance and so we have found it useful to abstract the conceptual relationship between the radius and the area. Spatial relationships don't exist in nature because of our ability to conceptualise them, it is the other way round, we can conceptualise them because they exist in nature.
Hi again torridon,
Thank you for your post. 'Abstract' (as an adjective) means existing in thought without having physical existence.
Contary to your post, "
spatial relationships" do in fact exist in nature. All such relationships are physical not abstract - physical properties of material objects - shapes, sizes, locations, movements etc of individual stones or groups of stones. All such relationships are observable by the senses (sight and touch) and do not exist apart from the stones themselves. They are also imprecise and can be varied with the blow of a hammer.
Mathematical concepts are different. Circles, right angles, 2+2=4 etc do not exist in nature. They exist apart from and do not depend upon any physical object. They are not obseverable by sight or touch, but can only be understood by the intellect. They are also precise and cannot be varied with the blow of a hammer.
Of course, usefulness in economic activities spurred development of mathe, but it took thousands of years because mathematical concepts are not obvious until after they have been discovered. A lengthy maths papyrus from ancient Eygpt (Rhind papyrus) indicates that your "
conceptual relationship between radius and area" of circles was unknown at that time (c. 1650 BC), although calculations of fractions, areas and volumes are abundant in the manuscript.
On the other hand, many of maths significant developments arose from intellectual curiosity alone, long before they had any practical use, e.g. Complex numbers (AD 1545) and non-euclidean geometry (AD 1760). The amazing thing about these very abstract concepts is that they enabled Einstein, Dirac, Higgs etc to forecast the existence of physical things long before such things could be observed empirically. Abstract before physical.
How could these abstract concepts do that unless they were correct independently of the human mind (and from the beginning of time).
I hope you find this interesting
God bless