From: Lee Daniel Crocker (lcrocker@calweb.com)
Date: Thu Feb 13 1997 - 17:17:16 MST
Some people seem to be using "Truth" as a name for "The nature of
objective reality, in complete detail". But this isn't useful or
meaningful, because used in this sense, there can be no falsehood:
reality just is, and if one refers to it completely, there can be
nothing that isn't part of that.
The question, then, is out of that existence, where does the
meaningful notion of true/false come from? My answer is that
"True" and "False" are properties of /assertions/, so to understand
truth we must first understand the nature of assertion. I will
simplify by leaving out the communicative sense of the word, and
concentrate solely on assertions made to oneself, so differing
mental models do not complicate the picture. I will further
simplify by leaving out the notion of time/causality so that we
can imagine a complete universe frozen in time except for the
single mind here making assertions about it.
What, then, is an assertion? It is clearly some state, property,
or pattern existing in the mind that /represents/ some part of
reality. Since our mind is a finite subset of reality, we can't
simply represent the whole thing--that would be just making a copy
of the universe. We must perform /data compression/. This, then,
is what I see as the fundamental nature of all thought: we cannot
be omniscient, so we store as much data as we can as compactly as
we can, along with /rules/, i.e., algorithms for reproducing some
representation of reality in greater detail than we have stored.
The representation of the universe in our mind consists of data,
including sense experience, and algorithms, some perhaps innate and
others created after birth. Those we create after birth are formed
in much the way a computer performs data compression: by searching
for patterns in the inputs and generating rules the reproduce them
from smaller representations.
An assertion, then, (to oneself, remember) is a representation of
some of your de-compression rules. The assertion "I saw a dog this
morning" contains many rules and references to stored data--some
that represent patterns you have found in dogs, mammals, mornings,
your own vision; some rules you have created to represent the
relationship between the stored sense-memories and reality, your
representations of yourself, and hundreds of other rules and data
chunks that serve to produce representations in short-term memory
("recall") for comparison with other recollections and more pattern
finding and rule making. Patterns can be found in the rules, and
rules can be shared on different datasets, and meta-rules used to
compress sets of rules, etc.
What is "truth" in the static-universe sense? It must be stronger
than merely lossless compression--that's just "consistency", in that
no input data are lost. "Truth" must express a strong relationship
to reality itself--for a rule to be "true" it must not only retain
all data that are put into it, but all /possible/ data. In other
words, it must losslessly compress /all/ data that represent any
property of whatever parts of reality it is meant to describe. If
there does not exist any property of reality that the rule would
eliminate, then it is "true".
Let's get a bit more concrete: Since we do not wish to catalog in
our mind the charge of every particle we meet, we can compress those
data with rules like "those things fitting the description of an
electron in all aspects except charge will have a single fixed value
for charge, either positive or negative." We can compress data for
other particles with the rule "electrical charges always come
discretely quatized in packets the size of the electron-charge."
If there exists any particle anywhere in the universe that doesn't
fit this pattern, then our rule would produce false data for it, and
it is therefore false.
How can we determine truth? I think it's clear that we can't. We
cannot know that our internal representation of reality covers all
properties of it, or that there does not exist a single counterexample
for any rule, or that we will be able to find all the properties of
reality and a complete set of rules. We can, however, judge the
consistency of our rules with themselves and the data we apply them
to, and inconsistency is a sufficient condition for falsehood (since
true rules are a superset of consistent rules).
The quest for truth, then, is a quest for data, and rules sufficient
to compress all the data we need into representations we can use, and
that are never inconsistent. But since multiple rule sets can be
consistent with all data collected so far, how can we choose among
competing theories? Heuristics. How much data does the rule compress
(i.e. expressive power)? How compactly can we store the rule itself
(i.e. Ockham's razor)? How many opportunities does the rule afford for
finding counterexamples (i.e. testability)?
-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lcrocker.html>
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