I am taking the word ‘map’ to mean pretty much the same as what philosophers of science refer to as ‘theories’. And ‘territory’ to mean ‘reality’. So by a ‘tower’ of maps, I mean a series of theories, each reducing to a ‘lower-level’ theory. For example, one map might be a theory of infinitely divisible material bodies with state properties like density, temperature, and elasticity. At the next level down in the tower of maps, we might have an atomic theory with 92 elements. Next a theory in which the elementary particles include electrons, neutrons, and protons. Next down, we have the standard model with QCD. Then some super-symmetric Kaluza-Klein GUT. Etc.
Is there a base-level theory (‘map’) that reduces to an underlying ‘reality’, rather than to a lower-level map? I suppose we will never know—can never know—whether such a reality exists and what it ‘looks like’. Certainly, we never know whether our current lowest-level map is the final one.
The thing that strikes me is that a ‘reduction’ is really a relation (a morphism?) between maps—an association between the entities and observables at one level with those at the next level down. In doing a reduction, we are constructing in our minds a relation or morphism between maps which also exist in our minds. I am simply saying that if you postulate a new kind of thing—a ‘reality’ or ‘territory’ that exists outside our minds, you may solve some philosophical puzzles, but you create others. For one thing, we need to have two kinds of reduction in our epistemology—one taking maps to territories, and one taking maps to maps. I say, “Why bother! Let’s follow Occam’s advice and stick to maps rather than adding this new entity—the ‘territory’ - without necessity.”
I’m not sure what you mean by this.
How does one make maps into a tower? What would such a tower of maps look like? How is this different from a “territory” containing a tower of maps?
I am taking the word ‘map’ to mean pretty much the same as what philosophers of science refer to as ‘theories’. And ‘territory’ to mean ‘reality’. So by a ‘tower’ of maps, I mean a series of theories, each reducing to a ‘lower-level’ theory. For example, one map might be a theory of infinitely divisible material bodies with state properties like density, temperature, and elasticity. At the next level down in the tower of maps, we might have an atomic theory with 92 elements. Next a theory in which the elementary particles include electrons, neutrons, and protons. Next down, we have the standard model with QCD. Then some super-symmetric Kaluza-Klein GUT. Etc.
Is there a base-level theory (‘map’) that reduces to an underlying ‘reality’, rather than to a lower-level map? I suppose we will never know—can never know—whether such a reality exists and what it ‘looks like’. Certainly, we never know whether our current lowest-level map is the final one.
The thing that strikes me is that a ‘reduction’ is really a relation (a morphism?) between maps—an association between the entities and observables at one level with those at the next level down. In doing a reduction, we are constructing in our minds a relation or morphism between maps which also exist in our minds. I am simply saying that if you postulate a new kind of thing—a ‘reality’ or ‘territory’ that exists outside our minds, you may solve some philosophical puzzles, but you create others. For one thing, we need to have two kinds of reduction in our epistemology—one taking maps to territories, and one taking maps to maps. I say, “Why bother! Let’s follow Occam’s advice and stick to maps rather than adding this new entity—the ‘territory’ - without necessity.”
I hope that explanation helped.