* On Abstraction
@ 1998-07-10 0:00 Ralph Silverman
0 siblings, 0 replies; only message in thread
From: Ralph Silverman @ 1998-07-10 0:00 UTC (permalink / raw)
From nntp.seflin.org!z007400b Wed May 6 15:10:13 1998
Path: nntp.seflin.org!z007400b
From: z007400b@bc.seflin.org. (Ralph Silverman)
Newsgroups: comp.ai.philosophy
Subject: On Abstraction
Date: 4 May 1998 19:54:26 GMT
Organization: SEFLIN Free-Net
Lines: 1354
Message-ID: <6il6di$4o6@nntp.seflin.org>
NNTP-Posting-Host: bc.seflin.org
X-Newsreader: TIN [version 1.2 PL2]
--subtlety and artificial intelligence ( ai )
a) early ideas ...
long before ai was realized in practice
... and before modern
electronic binary digital computer
( @ 1945 ) ...
idea of
thinking automaton
was based on model of
precision calculator
and
subtlety of ideation and speech
was ( largely ) ruled out ...
especially in 'science fiction'.
such speculation and supposition was
reasonably based on fundamentals of
operation of automated cybernetic systems
then known ... to be rigid and formalistic
...
b) general intelligence and
general purpose computer ...
advent of
general purpose computer
( electronic binary digital programmable
computer )
was, largely, intended simply to implement
foundations of many 'special purpose'
systems, substitutable on the same hardware
by programming ... and the type of intelligence
manifested by such may be termed
specialized intelligence
...
however, emergently, such capabilities have
given rise to feasible capabilities
of adaptive intelligence more closely reflecting
general human intelligence ...
( as specialized systems become more adaptive ...
feasibility emerges ... )
c) abstraction
levels of abstraction relating similar ideas
are very familiar as e.g. ,
all imaginable men
all men
all men known
joe ( a named man )
joe now ( i.e. at this time )
...
much of the 'great tradition' of
western philosophy
( especially 'metaphysics' ... )
has been devoted to untangling issues
related to such abstraction ...
( at least since the time of
plato
and
aristotle
)
now, in software engineering, idea
of 'abstraction' increasingly enters discussion
( e.g. on internet, as, e.g.
comp.lang.c ) ...
at least in regard to relation of
higher level languages ( hll s )
to
lower level languages ( lll s )
;
where an eerie echo of the issues
of ancient philosophy may be noted ...
d) emergence operations and data types
...
in arithmetic, supposing just non-negative
integer numbers, addition is relatively
non-emergent, since addition of any two
such will outcome same type ...
however ...
subtraction, ( viewable as 'undo' operation,
related to addition ) ,
allows 'emergence' of negative outcome
( even when operands are limited to originating
type ! )
...
and a similar relation between
multiplication
and
division
,
whereby non-integer numbers emerge ...
e) abstraction, generalization and vagueness
abstraction is the fundamental feature of
scientific and technical thought ...
as developed by us ...
through generalization ... specific systems
may be understood in terms ultimately reduced
to powerful, simple rules ...
e.g. when ohm's law is found; dc circuit
characteristics may be measured;
( e.g. voltage, resistance ), with devices
commonly available ...
however, frequently,
abstraction and generalization
lead to puzzling problems related to
vagueness
.
e.g. newtonian generalized abstract idea of
velocity
has proven
simplistic
in application to physical systems,
due to ( inter alia ) evident
unforeseen and unnoticed relation
of velocity and mass ...
and plausibly,
vagueness
( in many forms ) is as endemic to
abstract thinking as
heat dissipation
entropy
and
hysteresis
are to physical technology ...
whereby,
vagueness
plays ( in thinking ) a role
remarkably similar to such ...
f) european grammars ...
a simple, effective ontology
based on grammatical structure
of european languages ...
has served, profoundly, as
the basis of philosophical study
of abstraction, as well as
scientific reality models
( and formalized logic )
( at least ) since time of
aristotle
...
at basis of this model are
individuals
^^^^^^^^^^^
( substance, etc. )
rooted in grammatical form of
noun
^^^^
...
then, related to
individuals
are
properties
^^^^^^^^^^
( which may be
primary ( essence, essential )
( related to
existence ( being ) )
or
secondary ( accidental, variable )
)
...
properties
are related to grammatical form of
adjective
^^^^^^^^^
...
relations
( e.g. taller, shorter, longer )
are closely associated with
properties
( e.g. tall, short, long )
whereby what ( modernly ) may be termed
a
relational operator
associates
relational operands
( or )
relata
( generally in an ordered form )
...
such are commonly seen in programming
as, e.g. ...
/* pseudocode */
if( joe_height >= fred_height ) { /* ... */ }
else { /* ... */ }
...
and
arithmetic operators
and
arithmetic operands
,
similarly as comparative relations,
e.g.
( + - * / )
( and others ... )
...
and in common computer programming
( general purpose algorithmic languages )
as, e.g.
fortran_iv
algol_60
pascal
the 'c' programming language
modula_2
etc.
variable
^^^^^^^^
serves role similar to
individual
... rooted in
noun
...
value of variable
^^^^^^^^^^^^^^^^^
is similar to
property
^^^^^^^^
which may be compared in relations
or serve as arithmetic operand,
etc.
type
^^^^
of variable is similar to
essence
^^^^^^^
e.g.
long
double
char
char*
etc.
/* ... from 'c' programming language */
g) translation and emergence
two forms which have 'emerged'
in higher level languages,
>=1960s are;
-- ( if else ) form ...
-- generalized loop form
1) ( if else ) form
as, e.g.
if ( /* ... */ ){ /* ... */ }
else { /* ... */ } /* pseudocode */
2) generalized loop form
as, e.g.
do{ /* ... */ }while( /* ... */ ); /* pseudocode */
while( /* ... */ ){ /* ... */ } /* pseudocode */
such forms
do not have analogues in
traditional assembler,
as, e.g.
a86 ( eric isaacson )
chasm
etc.
but may effectively be reduced to such like,
as commonly is done automatically by
compiler systems
...
problems of abstraction
aa) non-decidability ...
suppose:
a policy to divide assets
by two when challenged ...
in circumstances where assets are
'granular'; such may be effective
if assets are of even number ...
however,
if of odd number ...
policy leaves
non-decided
^^^^^^^^^^^
how to proceed ...
rules based on
generalization and abstraction
frequently will encounter
non-decidables
when applied without restriction ...
bb) subtlety ...
supposing a rigid response model
then ...
either
---lockup
or
---inappropriate response
is likely outcome ...
however,
subtle response to 'unforeseeable'
non-decidables and paradoxes,
well may be possible to engineer
...
if
reasonable objective study of
abstraction and generalization
is made ...
cc) vagueness, paradox and the arbitrary
if vagueness is not banished from
a domain; then, generally,
difficulty ( e.g. paradox ) results
...
however ...
generally,
banishment of vagueness requires
rules and/or distinctions more or less
arbitrary ...
as instanced in ( very ancient )
sorites paradox
...
recently, ( march 31, 1998 ) in
( local newspaper printing of )
dilbert
following comic dialogue was found
...
**************************
dilbert ...
is it my imagination,
or is your necktie
getting shorter every
day?
wally ...
heh heh...
[new frame]
i'm gradually moving
toward casual cloths.
in six months this
necktie will be
gone and no
one will notice.
[new frame]
dilbert ...
everyone noticed
when you went
bald.
wally ...
i'm bald?
**************************
here
subtlety
of thought
is related to sophistication
in method of reasoning about
abstraction, vagueness and the
arbitrary ...
dd) map analogy ...
analogy may be made between
abstraction and mapping ...
while a complete model of world
might be useful where globe or map
is used ... such is not feasible
...
reasonably,
similarly ...
limited capability
of
human nervous system
renders unfeasible model of entire universe
as simple 'look up' means ...
( also, perhaps,
paradox of 'set inclusion' ...
related to self-reference ... )
...
thus ... abstraction may serve
similarly as 'simplified'
map or model
as basis for generalized thought
...
if effectiveness of e.g. world mapping
in e.g. navigation were to make this
basis of 'reality model' then much could
be learned about basis of geography from
mapping ...
however ...
if physical foundations of map are taken
simply as foundations of geography ...
then paper and ink might similarly
be taken as foundational reality
...
of course, such would be a mistake !
possibly ... grammar based ontology ....
which so well has served ...
may also have limits ... e.g.
in very large application e.g.
cosmology
or in very small applications e.g.
micro-physics
...
ee) paradox types
arguably, 'paradoxes'
which seriously threaten
stability of ai system
may be classified
in two categories ...
1) physical 'paradoxes' ...
representative of
physical 'paradoxes'
is ancient 'paradox' of
zeno
known as
flying arrow paradox
...
arguably,
this 'paradox' has defied
solution until development of
quantum theory
and
relativity theory
in 20th century ...
however ... evidently,
modern thinking in physics
renders
flying arrow paradox
tractable ...
2) philosophical paradoxes ...
evidently, most important
philosophical 'paradoxes',
fall into three major types ...
---liar 'paradox'
---russell 'paradox'
---sorites paradox
...
-- liar 'paradox' ...
liar 'paradox' is ancient.
modernized version is presented ...
***
statement A) statement A is false.
***
to appearances, circumstances that
make statement A true also make
statement A false ... and
circumstances that
make statement A false also make
statement A true ...
and hence;
liar 'paradox' does not settle
on truth value ...
-solution of liar 'paradox' ...
statement A above is in form
of 'truth claim' or assertion
...
any true statement is compatible
with assertion of truth of same
as e.g.
statement B) joe is in the room.
statement C) statement B is true.
truth of statement C is necessary
for truth of statement B ...
hence for any statement
( e.g. statement B )
a 'and' form developing such
should preserve truth value ...
as ...
statement B [modified]) joe is in the room AND statement B is true.
similarly developing statement A
reveals this to be a simple
contradiction ...
statement A [modified]) statement A is false AND statement A is true.
****
...
russell's paradox
evidently is attributable to
cantor
zermelo
and
russell
understanding of
russell paradox
may best be rooted in older
paradox of barber
...
--barber paradox
suppose regulations
intended to assure that
all men shave
...
rules ---
rule A) all men will shave
( exclusive )or
be shaved.
rule B) all and only those men
not shaving themselves
will be shaved by the barber.
rule C) the barber must be a man.
end rules ---
problem here ...
does the barber shave himself ?
if he does shave himself ...
then ( rule B ) is violated ...
if he does not ...
then ( if ( rule A ) is not violated ...
then ( rule B ) is violated ... )
barber 'paradox' may rest on some faith
in infallible applicability of rules ...
because ( if appropriately stated ),
certainly, no such barbers are found
...
--russell paradox ...
russell paradox relates to
set theory
however, from experimental period;
where modern form of such
was not yet determined ...
modern set theory, as taught in schools,
is of very nominalist form ...
set name is simply
notation form
representing unordered collection of
members
^^^^^^^
( individuals )
and is not
reified
;
( set is not an individual or 'thing' ).
thus, in such modern set theory,
a set may not be a member of a set
and a ( set of sets ) is not possible
... and ( instead )
similar seeming forms e.g.
superset
subset
proper subset
are used ... to represent such set
relations as applicable ...
--statement of russell 'paradox'
***
supposing a set ( S )
such that
the members of ( S )
are
all and only
sets which are not members of themselves
...
is ( S ) a member of ( S ) ?
either response is unsustainable ...
and question will not settle ...
***
in
russell 'paradox'
much similarly as with
barber 'paradox'
;
rules determine specification
of 'entity' which can not
be actual ...
so, evidently,
russell 'paradox'
simply manifests deficiency of
such rules ... and not some
profound 'paradoxical' feature
of human language and thought
...
--sorites paradox
statement of sorites paradox ...
***
rule 0) suppose a man ( S ) is rich ...
then
loss of one cent ( of man's fortune )
is insufficient to make ( S )
not rich ...
end rule 0)
problem)
but if applied recursively ...
( rule 0 ) may result in ( S )
poverty ... whereby ( S )
has no money ...
thus ( S ) may be rich and also
have no money if ( rule 0 )
is valid and recursively applicable ...
***
( of course, sorites paradox may be applied
in many domains; also sorites paradox is
very ancient ... )
strangely,
at this time, evidently,
sorites paradox ( type )
is the most intractable known
and evident simplicity of
sorites masks a profound basis
...
metalanguage
aaa) intractability of sorites
--arbitrary determination ...
possible
resolution tactic
is arbitrary borders of e.g.
rich
poor
large
bald
etc.
--truth problem ...
however ... if borders are arbitrary ...
then
truth
of judgements, statements ...
which result from such determinations
is jeopardized
( at least in borderline areas )
...
such error might accumulate ...
--reduction response ...
argument might be made that such ideas
are
vague
and reduction to fundamentals is effective
...
however ...
e.g. in case of
rich, not rich, penny
( as earlier described ... )
precise specification
of
fundamental level
also generally is questionable
by similar means and
ontological regress
may be inescapable ...
thus ...
retreat from truth and resolution
of paradox on higher level
'borrows' credibility from faith
that lower level is immune ...
but such should be established
with care ...
bbb) type ... token
a 1960s analytic philosophy
interest
was in
type-token distinction
...
e.g. question
"how many characters
in document ?"
might relate to
types
e.g. 65
(e.g. (a A c C ... @ ... * ... y ... ))
or
tokens
e.g. 5439
...
such distinction is reflected in
computer programming practice ...
where data_types and individuals
of such types are used widely
in practice ...
as e.g.
long id; /* as 'c' pseudocode */
char *name;
etc.
an intermediate form of type
is found widely in common
( and scientific ) language
which is
tokenized
in relation to a more general
type, yet, at least arguably,
not actually an
individual
...
'animal kingdom'
|
|
^^^^^^^^^^^^^^^^^^
| | |
bird mammal ...
| |
... |
|
^^^^^^^^^^^^^^^^^^
| | |
horse dog cat
a small set of
operating system ( os )level
commands
allow creation, traversal, access
of
device directory systems
...
in e.g. unix os,
( ms pc )dos ( >= version 2.* ),
os/2, dr_dos ...
( though command particulars may
somewhat differ among such systems
... )
in such systems
a set of files situates within a
directory
one top level directory for
each device is allowed ...
( though 'physical device'
may optionally be partitioned into
various 'virtual' devices ... )
top level directory is termed
root directory
directories may be 'tokenized'
( subordinated to ) directories
as ...
subdirectories
...
( when fully
formatted
such device commonly has single,
'root' directory created as
default directory ... )
commands as ...
make subdirectory command as e.g.
mkdir
delete subdirectory command as e.g.
rmdir
( commands for directory traversal ... )
as e.g.
( to change 'working directory' ) as e.g.
cd
and such command with 'special argument'
to traverse to 'parent directory' as e.g.
cd ..
and such command with argument
to traverse to 'root directory' as e.g.
cd / ( generally, unix )
cd \ ( generally,
( ms pc dr )dos >= v2.* )
and command for removing file as e.g.
del
rm
...
interestingly, generally, such systems have
been found workable and effective in computer
applications since <= 1980 and are well proven
...
such are not particularly provocative of
operational 'paradox' and have proven
tractable ...
ccc) ken thompson ontology
...
tree structured file-directory
device organization of
unix operating system
reflects capabilities of organization
of information similar to
biological classification
system ...
similarly ...
organization chart
etc ...
such reflects widespread form of
abstraction whereby classifications
( types ) are tokenized relative to
higher level classifications ...
modern set theoretic model is
nominalist, and such relations
are entirely extensional there ...
( reasonably, 'proper subset'
is form reflecting such ... )
...
ddd) nominalism ?
philosophical movement of
first half 20th century ...
logical positivism
and also developments in
set theory
symbolic logic
transfinite mathematics
have profoundly advanced
nominalism ...
such developments respond to
efforts to generalize
set theory
( and the like )
as a general model of
abstract thinking,
( e.g. work of g. frege )
...
such efforts to generalize
set theory
then generated problems
related to 'paradox',
( e.g. russell 'paradox' )
...
why should a generalized model of
abstract thinking attempt the
'paradoxical';
and what, if anything,
is deficient re. nominalism ?
-- 'table and chairs' ontology ...
truth-functional and
( integer ) arithmetic bias
of early 1900s thinking ...
might seem to justify nominalism
in schematization of thinking ...
basis of thinking in
individuals
arguably is supported in
( integer )
number theory
and common thought ...
however ...
-- in ordinary thinking ...
subjects frequently are not
presently in being ...
but are components of
plans
...
and common use of abstraction system
for such purpose is critical to
thinking ...
also ...
use of abstraction system to
test
plan performance and to
evaluate
results of such
...
'nominalist' abstraction model
makes most mysterious
such ( planning ) uses ...
which uses would seem, generally,
as important at least
an application of
abstraction system as is
truth assertion ...
shall radically different
abstraction systems
be inferred for use with
plans
and such;
and ( alternatively ) with
truth assertion
?
-- roots of 'table and chairs' ontology
in aristotle ...
long and widely criticized
feature of aristotle ontology ...
teleology
relates to
realization
of concrete circumstances through
purpose
and, reasonably, such relates to
abstract thinking: whereby generalized,
even, vague, idea is realized ...
'tokenized' or 'realist'
abstraction model
far better serves such purpose ...
-- nominalism is aristotle's 'grammar based'
ontology ... with foundation removed ...
with 'high level' abstraction capabilities
removed and nominalism remaining ...
'common sense' foundation of
aristotle ontology is gone also ...
...
individuation within
phenomenal world has proven
problematic over long period ...
as ...
parmenides
heraclitus
plato
spinoza
hume
and
modern micro-physics
relativity theory
...
( also, arguably individuation is
problematic re.
'real' number system ... ) ...
eee) historic trends in ontology
prior origins of
pre-socratic philosophy
remain mysterious ...
however ...
prior most secretive
pythagorian brotherhood
is known ...
as well as some features ...
metaphysical trends of
pre-socratic philosophy
and philosophy of
plato
aristotle
etc.
suggest 'overarching' trend of thinking
...
--mathematical - geometrical - harmonic
standard ...
evident interest in mathematics topics
as 'unchanging' basis of thought
served as foundation of
pythagorian
world view ...
similarly as ...
frege
whitehead
russell
wittgenstein
in 20th century ...
attempts to apply such standard
to generalized thinking
( including re. world of phenomena
... )
lead to
'interface problem'
whereby fitting of
'precision' language
to world of phenomena lead to
paradox
vagueness
non-determinacy
reference problems
along various routes ...
two major trends in
pre-socratic philosophy
( re. metaphysics ) ...
are ...
parmenides - zeno
heraclitus
each reflecting
( evidently prior ... )
recognition of such misfit ...
--parmenides
school of parmenides ( and related )
views power of ideas as primary
and denies 'common sense' view of
world of phenomena ... especially
in relation to dynamics of such ...
--hearclitus
school of heraclitus ( and related )
views dynamics of reality as primary
...
denies features of 'common sense'
... view of world of phenomena
( e.g. substance, 'thing',
referents of common nouns ... )
thereby initiating opposition
played out repeatedly over
thousands of years ...
( e.g. spinoza
hume
... )
--data discipline ...
related
data_structure
fundamental algorithms
may be termed
data discipline
as, e.g.
stack
binary tree
etc.
...
data discipline
resembles
ontology
through
topology
( much as
set theory
resembles
symbolic logic
) ...
thinking about topology of an
ontology
_as though_ such were a
data discipline
is useful ... particularly
through nature of
topology
of such ...
e.g. re. idea of
set of sets
implicit in
russell 'paradox'
...
especially idea of
self-membership ...
suppose
set ( C ) is a member of set ( B )
set ( B ) is a member of set ( A )
set ( A ) is a member of set ( C )
such topology resembles
cycle
of
network theory
known, generally, to provoke
operational problems ...
( similar problem infects system suggested
in russell 'paradox' ... )
recognizing such ... reasonably,
russell 'paradox' system
would seem not to reflect common model
of abstraction, and trouble with such
is intuitive probability ...
topology of such systems is studied much
in
software engineering
...
thus ...
"ken thompson" ontology
( derived from operational data discipline )
might provide topological form of
more acceptably intuitive ( and workable )
ontology ...
fff) sense and reference
( --heading after g. frege ) ...
abstraction system of language
used for thought and speech,
generally, is useful primarily
when effective in representing
reality ...
in ordinary ( speech ) assertion
truth
of assertion is taken as
standard of effectiveness ...
( and, certainly,
is standard in philosophy,
historically ) ...
truth is thought as a relation
between
language entity
( statement
utterance
sentence
and/or etc.
)
and
reality
...
which ( relation )
is a kind of
fitting
correspondence
parallelism
and/or etc.
...
phrases and words used to
identify individuals,
e.g.
this sign
this
the cat
the third person from the left
joe ( a name )
...
are used to
refer
( make reference )
to
individuals
...
commonly,
such is the basis of the relation
between language ( abstraction system )
and reality ...
( in
the 'c' programming language
as traditionally described,
certain forms are
identifiers
( as e.g.
int counter; /* pseudocode */
( here 'counter' is an identifier ... )
)
and such forms similarly
serve a 'noun-like' role ... )
--objectivity ...
evident ancient program leading to
thinking of
parmenides
zeno
heraclitus
plato
aristotle
...
is rooted in high valuation of
objectivity
...
prototypic 'scientific method'
was hoped to 'close'
abstraction system
and lead to 'true', 'objective'
world perspective ...
rooted in number theory
( and the like ... )
while such research well may
have originated, largely,
secretly ... evident
early publications
( parmenides, zeno, heraclitus )
plainly outline problem ...
evident failure of early efforts
result in multi-faceted approaches
... ongoing into present ...
science, mathematics, philosophy,
electronic and computer engineering ...
as we know these today ...
are outcomes of such ...
similar fundamental problems
abound still in this area ...
and solution today
evidently is as remote
as in time of
zeno
...
--roots of objectivity
from time of flourishing of
newton
physics ... until down-fall
of same ...
in 20th century ...
three related
fundamental ideas
have predominated ...
objectivity
causation
determinism
today ...
none of these three
stands untouched
in scientific world view ...
foundation
of program to solve
problems of
abstraction system
through
natural science
is gone ...
though ( in some degree )
such ideas
remain viable partially,
or probabilistically,
usefulness of such ideas
as firm foundation of
abstraction
evidently now is untenable
...
ggg) language games ...
great progress in
approximative and
adaptive software ...
for optimization of
response in circumstances
such that potential
alternative situations and
responses are
unfeasible to list ...
e.g.
financial
program trading
game playing
( e.g. chess )
diagnostic system
logic analysis
scientific, engineering
modeling
typography
space utilization
in two and three dimensions
time optimization
route optimization
generalized resource allocation
adaptive communication network
language translation
tactical system
etc.
such capabilities now
are well established ...
reasonably,
study, modeling and operation
of
abstraction system
might be approached by such methods
...
much as a game ...
also, ( in various ways )
suggestive of
automated representation of
abstraction system
in works of philosophy ...
from ancient to recent ...
as e.g.
plato
philebus
aristotle
organon
metaphysica
...
philosophical investigations
( l. wittgenstein )
.
--
Ralph Silverman
z007400b@bcfreenet.seflin.lib.fl.us
--
Ralph Silverman
z007400b@bcfreenet.seflin.lib.fl.us
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~1998-07-10 0:00 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
1998-07-10 0:00 On Abstraction Ralph Silverman
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox