ONT Intension & Extension; abstract & concrete - the struggle with dichotomies
The struggle with dichotomies results more so from a failure to consider the
underlying neurocognitive processes that we as a species use to 'map'
reality. In particular to realise that we use self-reference and so
recursion to extract details, and so make our 'parts lists' but at the
species level we are using the same set of categories, qualitative
categories, to describe the differences where we tie the species set to a
context and so 'make a difference'.
Thus the dichotomy of intent/extent and that of abstract/concrete all
reflect a general mapping to the dichotomy of particular/general which is
reflected in the neurocognitive focus on WHAT/WHERE.
The species methodology splits between the concept of idealism (the 'one',
differentiation/intergration within a single box) and materialism (the
'many', intergration across boxes) or from Kant's perspective the
identification of analytical truths vs synthetical truths where the
analytical reflects the encapsulation of <something> and zooming-in for
details through self-reference. This is very precise, allowing for
differentiation and intergration WITHIN the box, but also 'sterile',
reflecting the 'parts list' perspective. The synthetical perspective
reflects integration BETWEEN boxes and as such is more implicit in
identifying meaning when compared to the explicit nature of the analytical
but also reflects a link to local 'reality'.
The analytical perspective introduces us to nesting in logics where each
level of differentation introduces a 'new' logic:
[1] A / NOT-A : reflects propositional calculus where we deal with 'wholes'
[2] A+A, A+NOT-A / NOT-A + A, NOT-A+NOT-A : reflects predicate calculus and
the extention of [1] through the introduction of the notion of SOME. gets
into wholes & parts
[3] There are eight categories here reflecting the refinement of [2] as well
as the inclusion of symbol processing in the form of relational emphasis -
gets into the introduction of modal, fuzzy, indicative calculi and so
wholes, parts, static relationships (representations in space - symbols),
dynamic relationships (representations in time - habits, contracts etc)
included in [3] is the necessary categorisation of oscillations where
complex patterns cannot be reduced to a level other than as an oscillation
across categories. This can reflect failure to derive enough categories to
cover 'reality' or, of regardless of how many categories we define we still
get oscillations, we are dealing with a 'complex' pattern outside the
sensory limits of the species or its technology. (
http://pages.prodigy.net/lofting/paradox.html )
At level [3] (which BTW is not a level but the same space as [1] and [2] but
differentiated more) we find a good set of qualitative categories, linked
directly to feelings within the species and so applied universally.
The recruitment and abstraction of those basics allows for development that
reflects tetration rather than just exponentiation such that 8 leads to 64
to 4096 to 16 million + and what prevents any further development is loss in
identifying differences.
In the context of meaning, with the dichotomies, they do NOT represent
oppositions, they represent complementarities where in the below list the
left is a particular that has emerged from, been extracted and encapsulated
from, the right:
abstract <- concrete
intension <- extension
here are some more so you can 'get the picture'
'dot' precision <- 'field' precision
explicit <- implicit
control (static, hierarchic) - flux (flat, dynamics)
particular - general
expend energy - conserve energy
Analytical - Synthetical
Analytical - Dialectical
Absolute (no change) - Relative (change)
Archetypal - Typal
Pure - Mixed
Differentiate - Intergrate
'the one' - 'the many'
Spirit(spiritual) - Matter(material)
Transcend - Transform
Discrete - Continuous
Plato - Democratus
(difference) - (sameness)
[sameness] - [difference]
Idealism - Materialism
metaphysical - physical
as interpreted - as received
Belief - Law
Ontological - Epistemological
Subject - Object
Objective - Subjective
Within - Between
Algebraic - Geometric
theological (particular) - philosophical (general)
exploit - protect
positive - negative
delusion - illusion
'refined' - 'raw'
[raw] - [refined]
vector - waypoint
universal context - local context(s)
what IS (interpreted) - what is NOT
what WAS (interpreted) - what could have been
What WILL BE (interpreted) - what could be
Manic - Phobic
The process of evolution allows for the development of the left column to
become dominant due to its precision BUT the roots are still in the right
column. Development of concepts by the left and the feeding back of those
'into' the right allow for a 'drift' of both sides to the middle.
Furthermore, the dynamics involved, functioning in a hierarchic context,
allows for 'abstract' to be considered as 'concrete' - IOW the general
categories will remain but context 'shift' emphasis.
Best,
Chris.
------------------
Chris Lofting
websites:
http://pages.prodigy.net/lofting
http://www.ozemail.com.au/~ddiamond
http://www.eisa.net.au/~lofting
Lists:
http://www.yahoogroups.com/group/semiosis
http://www.yahoogroups.com/group/ichingplus
> -----Original Message-----
> From: owner-standard-upper-ontology@majordomo.ieee.org
> [mailto:owner-standard-upper-ontology@majordomo.ieee.org]On Behalf Of
> Seth Russell
> Sent: Tuesday, 22 January 2002 9:39
> To: John F. Sowa; Robert E. Kent
> Cc: Jon Awbrey; SUO; Ontology
> Subject: Re: SUO: Re: ONT Intension & Extension
>
>
>
> From: "John F. Sowa" <sowa@bestweb.net>
>
> > If the intent of c1 includes the intent of c2, then the
> > extent of c1 is a subset of the extent of c2.
>
> I'm stuggeling with this. Is there such a thing as an IntensionalClassA
> defined by a rule such as 'if the object has no feathers and has two feet'
> and a correspoinding ExtensionalClassA defined by asserting its instances?
>
> Are we saying that there *are* two separate abstract things here, and not
> just one?
>
> Is proving
> (equal IntensionalClassA ExtensionalClassA)
> the same as proving
> (forall (?X) (instance (KappaFn ?X ?FORMULA) ?X)))
> where
> (KappaFn ?X ?FORMULA) defines an ExtensionalClass
> and
> (instance ExtensionalClassA ?X) defines an ExtensionalClass.
>
> ??
>
> http://robustai.net/mentography/intensionExtension.gif
> http://robustai.net/mentography/intensionExtension3.gif
>
> Seth Russell
>
>