From: rz@mips.complang.tuwien.ac.at (Richard Zach)
Subject: Re: Assertiveness of Non-divinity
Reply-To: zach@csdec1.tuwien.ac.at
Organization: Technische Universit"at Wien
Date: Wed, 11 Nov 1992 12:00:46 GMT

In article <1992Nov08.235324.21646@bnr.ca>, bcash@crchh410.BNR.CA (Brian Cash) writes:
|> science: 1)systematized knowledge derived from observation, study, etc.
|>          2)a branch of knowledge, esp. one that systemizes facts,
|>            principles, and meathods
|>          3)skill or technique
|> 
|> How are the first two different from logic?  (not all logic/philosophy
|>  is introspective).  
|> 
|> {side note: how is the last definition different from "art"? :-) }
|> 
|> Math quantifies and models reality: it helps us relate to what we observe.
|> 
|> Brian /-|-\

1) is *natural* science (and i would also classify a couple
of the humanities as belonging here: eg, anthropology, linguisics,
sociology). The object of natural science is to build theories
that model the domain of knowledge (eg, "natural laws"),
to test these theories agains OBSERVATION, and to change/update
theories depending on what you observe. A theory is then basically
a logical/mathematical model of the domain, and you use logic/
mathematics to reason in that domain. The conclusions you draw
can be used to test the model: eg, you use quantum mechanics to
predict the existence of a new particle, and the people at
CERN go about looking for it.

2) is other sciences (esp humanities) and, to some extent,
"classical" biology (systematization of fauna and flora)

Logic, at least as understood until the 1800's is the study of (human)
rational thought. In that sense, it is PURELY introspective
(a logical argument does have nothing to do WHATSOEVER
with observation). Logic and mathematics may be MOTIVATED
by the need to obtain (formal) systems of reasoning for the
models/theories discussed in (1), but by themselves, they
are independent of empirical data and observation.
In particular, logic as it is understood since about 1900
(model theory, set theory, proof theory, etc) is not even
motivated by any natural science: it is a FOUNDATION for
mathematics and computer science ("formal sciences")
and an object of study in ITSELF.

In the widest sense, I would agree that every "science"
(and also logic and mathemetics) could be subsumed under (2)
as a systematic area of study, but then so is theology.
In this respect, theology is very similar to logic; only
that the foundations (the "axioms") of logic are less
debatable than those of theology. After all, Kurt G"odel
(considered by some the most important logician since
Aristotle) gave a "logical" proof of the existense of God.
The second difference is that logic can be done almost
purely syntactically (i.e., by manipulating symbols only),
WITHOUT reference to outward concepts. Theology cannot,
because it REFERS to outward concepts (and their purported
"reality").

{
3) that's a whole different concept altogether. And I would
say that it depends on what particular subject you are 
talking about, whether it is "art" or "science". Probably
"art" requires more creativity than "science". Anyuway,
this has nothing to do with logic.
}

-- 
Richard Zach                         Technische Universitaet Wien
[zach@csdec1.tuwien.ac.at]     Abteilung fuer Formale Logik 185.2
Newsgroups: alt.atheism