Rob, (01)
RA> Even if it's inherently imprecise, shouldn't we be as precise
> as we can?
>
> After all, isn't precision a matter of degree? (02)
Yes, precision is a matter of degree. But precision isn't an end
in itself. It is a means to an end. And the end or purpose always
determines what level of precision is appropriate for a given problem. (03)
For example, you need higher precision in ball bearings than in
meat balls. If somebody serves you meat balls that are too perfect,
that's not a good sign. It's probably some mass-produced glop. (04)
If your soil is too acid, you might spread some crushed limestone on
the lawn. Reagent-grade calcium carbonate would be far too expensive. (05)
For more discussion of these issues, see (06)
http://www.jfsowa.com/talks/cmapping.pdf
Concept Mapping (07)
http://www.jfsowa.com/talks/bolzano.pdf
Logic and Ontology as Abstractions from Language (08)
http://www.jfsowa.com/pubs/lgsema.pdf
Language Games, a Foundation for Logic and Ontology (09)
At the end of this note is an excerpt from that last paper. (010)
John (011)
___________________________________________________________________________ (012)
Excerpt from "Language Games, a Foundation for Logic and Ontology" (013)
In his later work, Wittgenstein faced the full complexity of language
as it is used in science and everyday life. Instead of the fixed
boundaries defined by necessary and sufficient conditions, he used
the term 'family resemblances' for the “complicated network of
overlapping and criss-crossing similarities” (1953, §66) in which
vagueness is not a defect: (014)
One might say that the concept ‘game’ is a concept with blurred
edges. — “But is a blurred concept a concept at all?” — Is an
indistinct photograph a picture of a person at all? Is it
even always an advantage to replace an indistinct picture with
a sharp one? Isn’t the indistinct one often exactly what we need? (015)
Frege compares a concept to an area and says that an area with vague
boundaries cannot be called an area at all. This presumably means
that we cannot do anything with it. — But is it senseless to say:
“Stand roughly (ungefähr) there”? (§71). (016)
Frege’s view is incompatible with natural languages and with every
branch of empirical science and engineering. With their background
in engineering, Peirce and Wittgenstein recognized that all measurements
have a margin of error or granularity, which must be taken into account
at every step from design to implementation. The option of vagueness
enables language to accommodate the inevitable vagueness in observations
and the plans that are based on them. (017)
After a detailed analysis of the Tractatus, Simons (1992) admitted
that Wittgenstein’s later criticisms are valid: “We might say that
not everything we say can be said clearly” (p. 357). But Simons was
not ready to adopt language games as the solution: Wittgenstein
“became a confirmed — some, including myself, would say too confirmed
— believer in the messiness of things.” (018)
Yet things really are messy. As Eugene Wigner (1960) observed,
“the unreasonable effectiveness” of mathematics for representing
the fundamental principles of physics is truly surprising. The
basic equations, such as F=ma, are deceptively simple; even their
relativistic or quantum mechanical extensions can be written on
one line. (019)
The messiness results from the application of the simple equations
to the enormous number of atoms and molecules in just a tiny speck
of matter. When applied to the simplest living things, such as a
bacterium, even the fastest supercomputers are incapable of solving
the equations. In any practical calculation, such as predicting the
weather, designing a bridge, or determining the effects of a drug,
drastic approximations are necessary. Those approximations are always
tailored to domain-dependent special cases, each of which resembles
a mathematical variant of what Wittgenstein called a language game.
In fact, he said “We can get a rough picture of [the language games]
from the changes in mathematics” (§23). (020)
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