Reduction and Elimination in Philosophy and the Sciences

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Ding-Ontology of Aristotle vs. Sachverhalt–Ontology of Wittgenstein — Serguei L. Katrechko
be substituted, in predicate interpretation of being as
relations, by a verbal modified sentence like ‘It’s stoning’ 3 .
Let’s pass now to a more detailed analysis of the
ontology of the Tractatus which could be conceived in
different ways. So, interpretation of the ontology of the
Tractatus Logico-Philosophical (TLP) proposed by the
author of this article will be presented above. Basically, it
will be proceeded from the point that the TLP ontology
gives a logical description of the world, i.e. is a logic
ontology; it does not postulate that there are some
unchangeable ‘entities’ like Aristotelian ‘things’, i.e. it is of
non-substantial character 4 .
Peculiarity of the TLP ontology is that it strives to
describe the world as a system of combinations
(interacting bodies), choosing isomorphism of the world
and the language as an important heuristic principle. To
solve this problem a definite balance of statics
(synchronism) and dynamics (diachronism) is needed.
Logic analysis allows to fix a snapshot of the present ‘state
of affairs’ (Sachlage) or facts (Tatsache). Further, this
‘picture of the world’ may be specified and enriched by
discovering new facts and observing results
(consequences) of the old ones. The proposed
interpretation of the Tractatus emerged from reflections on
the translation of the term ‘Sarhverhalt’ which was
translated into Russian not with a standard equivalent
‘sobytie’ but with an original term ‘so-bytie’ (where
‘bytie’=esse (Lat.), or =‘Being’; Wittgenstein, 1994;
Кozlova, 1995) thus, marking co–existence (common
existence/being) of objects, i.e. inevitability of existence of
an object ‘excluded from the possibility of combining with
others’ (prop. 2.0121). While classical ontology thinks of an
object as something self-sufficient (closed), the TLP
ontology regards it open, inviting other ‘things’,
demonstrating ‘so–bytie–nost'’ (in the Russian language
that is similar to ‘co–existence–ness’); each thing is
predetermined by its own system of correlations for it ‘is,
as it were, in a space of possible states of affairs’
(prop. 2.013).
‘Simple facts’ (Sachverhalte), ultimately accumulated
into totality, determining the logical world of the TLP
ontology (since complex facts consist of simple ones), are
isomorphic to simple sentences describing a state of affair
(A book is on the table), i.e. has a «А–х–В» structure, with
«–х–» denoting a particular combination (relation) between
А and В (prop. 2.01). Propositions 2.01 — 2.02 grasping
main differences between the TLP ontology and the
ontology of things seem to be essential in conceiving the
specificity of the TLP ontology. While Aristotle believes that
initial elements of the world are unchangeable entities «А»
and «В» predetermining «–х–», Wittgenstein states the
priority of the «–х–» functional relation. However, we
cannot imagine objects in isolation, and their extracting
(‘exclusion’) from the combined system leads to a gross
idealization inadmissible in a common case, which
Wittgenstein tries to fight.
What makes the basis for the ontology turn carried
out in the Tractatus? If we take the book (‘lying’) on the
table as the object of our analysis, we can use
conventional body and visual language, since all objects of
our world belong to the ‘continuous substance’
3 Here, we don’t distinguish the ontology connected with the language of
verbs and the ontology of facts (resp. sentences) that can be identifies. Each
sentence states this or that fact of the action done. Though, this do not exclude
distinguishing the ontology of actions as a separate type of ontology.
4 For the first time, this kind of interpretation was proposed on the forum ‘The
World of Tractatus’, as well as in the works [Katrechko, 1999; 2002].
(Descartes). Substantiality, in this case, means that the
changes taking place with the book might be neglected;
the book will stay a book, with its identity predetermined by
its essence. But if we need to describe a process, say, an
electric current impulse and its magnetic field, the current
(or the magnetic field) stops to be a constant thing with its
own unchangeable essence existing like a book. The
example with the current encourages us to be more critical
to postulating Aristotelian entities, although the essence of
the Wittgenstein’s turn is connected not with the dynamic
nature of the current but, rather, with the fact that it
demonstrates the example of an imperceptible ‘thing’
(contrary to the example with the book) which indicates
lack of means for body and visual description typical for
classical ontology; the world consists not only of spacial
objects but of non-visual ‘state of affairs’ as well, and while
describing the world, should the description has a claim on
adequacy and universality, those points must be observed.
According to Wittgenstein, there is a universal language of
description, and that is logics, in the broad sense,
conceived as the teaching of functions (G. Frege). E.g.,
the ‘state of affairs’ of the current can be described by a
formula (compare with Sachverhalt) showing the
dependence of the strength of the current on the tension
and resistance, acting here as basic constituencies. In a
general case, any state of affairs is given by a logic and
functional space, with strength lines ‘combining’ the
‘things’ within and, by that, predetermining their
characteristics while their ‘intersections’ correspondingly
constitute a particular ‘thing’.
In a sense, correlation of the ontology of things and
the ontology of facts is similar to correlation of atomic
particles and field structure in physics. The ontology of
facts postulating the priority of field structures in respect of
particles is holistic contrary to the elementary ontology of
things. According to up-to-date mathematics, difference
between the ontology of things and the ontology of facts
can be explained in the following way. The present
mathematics based on the theory of sets grounds is well
concorded with classical ontology: the set is seen as a
specific objectification of properties, i.e. is being
interpreted as a meta-object, and the sign giving the set
acts as its intrinsicality. For the ontology of ‘state of affairs’,
the language of the mathematic theory of categories
seems to be more appropriate since today it is considered
as a serious alternative to the theory of sets approach.
Within this theory, the objects are defined not by an
internal but by an external mode, through the system of
arrows, corresponding to combinations (relations) of the
given object.
It’s clear that in the ontology of facts (the predicate
ontology, generally), the status of things become different.
At the initial stage of cognition, no individual things, in their
usual sense, occur but there are indefinite objects – quasithings
– interacting with each other that can be presented
in the mode of fussy sets. While the facts are accumulated
in the process of experience the borders of the sets will be
specified due to class division and ‘intersections’ of the
one-type facts, and, at a stage, they will be detailed so that
quasi-things will turn into ordinary, habitual for us –
individual – things.
Let’s explain the aforesaid on an example with a
hammer. Under prop. 1.1 of the Tractatus, initially we have
no ‘hammer’ thing (resp. notion of a hammer), we have
only a fact of ‘hammering in something with the help of
something’ which can be described by the «А–х–В»
sentence. Here, the hammer is correlated with the active
component of the fact ‘that–with–which–is–hammered–in’,
this function will correspond to, for instance, the following