I received an offline note about how nominalism and realism relate
to the issues of reductionism and the methods for grouping things
into sets. (01)
Following is my response. (02)
John Sowa
__________________________________________________________________ (03)
Those are totally independent ideas, which can be mixed and matched
in any way you want: (04)
- Nominalism vs. realism is the issue of whether the laws of nature
refer to something real or whether they are arbitrary patterns
that somebody has merely given a name to. (05)
- Grouping things in sets is used in every approach. Nominalists
would say that all groupings are more or less arbitrary, and
realists would insist on looking for the principles for grouping. (06)
- Reductionism is the idea that there is an ultimate foundation
that everything else can be reduced to -- e.g., biology can
be reduced to chemistry, and chemistry can be reduced to
physics. In effect, belief in foundations is more realist
than nominalist. However, you can have debates between
realists and nominalists at each level about the reality
of the principles discovered at that level. (07)
My personal preference is for realism about the laws of nature. (08)
I prefer to use the word 'set' for a grouping that is neutral
with respect to the existence or nonexistence of some principle
for grouping. (09)
I prefer to use the word 'type' for groups that are determined
by some principle -- either a law of nature or a human choice. (010)
Although I agree that the principles of biology are based on
chemistry and the principles of chemistry are based on physics,
I also believe that there are laws at each level that would
be extremely difficult, and probably humanly impossible, to
translate directly to the lowest possible level. (011)
In computer system design, we develop many different levels:
high-level languages such as Java, a lower-level interface
for the Java Virtual Machine (JVM), a still lower level for
some machine architecture, such as the X86 or Power, and
multiple levels of functional units for supporting a machine
interface, which is mapped to some kind of computer circuitry,
which is itself mapped to silicon chips. (012)
Multiple levels of compilers can "reduce" complex algorithms
to chips, but it's humanly impossible to understand more than
one level of reduction at a time. To correct any bugs, it's
necessary to go back to the top level and recompile. (013)
In other words, God might be able to implement and understand
reductionism, but humans can't. (014)
John Sowa (015)
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