Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
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170<br />
D<strong>in</strong>g-Ontology of Aristotle vs. Sachverhalt–Ontology of Wittgenste<strong>in</strong> — Serguei L. Katrechko<br />
be substituted, <strong>in</strong> predicate <strong>in</strong>terpretation of be<strong>in</strong>g as<br />
relations, by a verbal modified sentence like ‘It’s ston<strong>in</strong>g’ 3 .<br />
Let’s pass now to a more detailed analysis of <strong>the</strong><br />
ontology of <strong>the</strong> Tractatus which could be conceived <strong>in</strong><br />
different ways. So, <strong>in</strong>terpretation of <strong>the</strong> ontology of <strong>the</strong><br />
Tractatus Logico-Philosophical (TLP) proposed by <strong>the</strong><br />
author of this article will be presented above. Basically, it<br />
will be proceeded from <strong>the</strong> po<strong>in</strong>t that <strong>the</strong> TLP ontology<br />
gives a logical description of <strong>the</strong> world, i.e. is a logic<br />
ontology; it does not postulate that <strong>the</strong>re are some<br />
unchangeable ‘entities’ like Aristotelian ‘th<strong>in</strong>gs’, i.e. it is of<br />
non-substantial character 4 .<br />
Peculiarity of <strong>the</strong> TLP ontology is that it strives to<br />
describe <strong>the</strong> world as a system of comb<strong>in</strong>ations<br />
(<strong>in</strong>teract<strong>in</strong>g bodies), choos<strong>in</strong>g isomorphism of <strong>the</strong> world<br />
<strong>and</strong> <strong>the</strong> language as an important heuristic pr<strong>in</strong>ciple. To<br />
solve this problem a def<strong>in</strong>ite balance of statics<br />
(synchronism) <strong>and</strong> dynamics (diachronism) is needed.<br />
Logic analysis allows to fix a snapshot of <strong>the</strong> present ‘state<br />
of affairs’ (Sachlage) or facts (Tatsache). Fur<strong>the</strong>r, this<br />
‘picture of <strong>the</strong> world’ may be specified <strong>and</strong> enriched by<br />
discover<strong>in</strong>g new facts <strong>and</strong> observ<strong>in</strong>g results<br />
(consequences) of <strong>the</strong> old ones. The proposed<br />
<strong>in</strong>terpretation of <strong>the</strong> Tractatus emerged from reflections on<br />
<strong>the</strong> translation of <strong>the</strong> term ‘Sarhverhalt’ which was<br />
translated <strong>in</strong>to Russian not with a st<strong>and</strong>ard equivalent<br />
‘sobytie’ but with an orig<strong>in</strong>al term ‘so-bytie’ (where<br />
‘bytie’=esse (Lat.), or =‘Be<strong>in</strong>g’; Wittgenste<strong>in</strong>, 1994;<br />
Кozlova, 1995) thus, mark<strong>in</strong>g co–existence (common<br />
existence/be<strong>in</strong>g) of objects, i.e. <strong>in</strong>evitability of existence of<br />
an object ‘excluded from <strong>the</strong> possibility of comb<strong>in</strong><strong>in</strong>g with<br />
o<strong>the</strong>rs’ (prop. 2.0121). While classical ontology th<strong>in</strong>ks of an<br />
object as someth<strong>in</strong>g self-sufficient (closed), <strong>the</strong> TLP<br />
ontology regards it open, <strong>in</strong>vit<strong>in</strong>g o<strong>the</strong>r ‘th<strong>in</strong>gs’,<br />
demonstrat<strong>in</strong>g ‘so–bytie–nost'’ (<strong>in</strong> <strong>the</strong> Russian language<br />
that is similar to ‘co–existence–ness’); each th<strong>in</strong>g is<br />
predeterm<strong>in</strong>ed by its own system of correlations for it ‘is,<br />
as it were, <strong>in</strong> a space of possible states of affairs’<br />
(prop. 2.013).<br />
‘Simple facts’ (Sachverhalte), ultimately accumulated<br />
<strong>in</strong>to totality, determ<strong>in</strong><strong>in</strong>g <strong>the</strong> logical world of <strong>the</strong> TLP<br />
ontology (s<strong>in</strong>ce complex facts consist of simple ones), are<br />
isomorphic to simple sentences describ<strong>in</strong>g a state of affair<br />
(A book is on <strong>the</strong> table), i.e. has a «А–х–В» structure, with<br />
«–х–» denot<strong>in</strong>g a particular comb<strong>in</strong>ation (relation) between<br />
А <strong>and</strong> В (prop. 2.01). Propositions 2.01 — 2.02 grasp<strong>in</strong>g<br />
ma<strong>in</strong> differences between <strong>the</strong> TLP ontology <strong>and</strong> <strong>the</strong><br />
ontology of th<strong>in</strong>gs seem to be essential <strong>in</strong> conceiv<strong>in</strong>g <strong>the</strong><br />
specificity of <strong>the</strong> TLP ontology. While Aristotle believes that<br />
<strong>in</strong>itial elements of <strong>the</strong> world are unchangeable entities «А»<br />
<strong>and</strong> «В» predeterm<strong>in</strong><strong>in</strong>g «–х–», Wittgenste<strong>in</strong> states <strong>the</strong><br />
priority of <strong>the</strong> «–х–» functional relation. However, we<br />
cannot imag<strong>in</strong>e objects <strong>in</strong> isolation, <strong>and</strong> <strong>the</strong>ir extract<strong>in</strong>g<br />
(‘exclusion’) from <strong>the</strong> comb<strong>in</strong>ed system leads to a gross<br />
idealization <strong>in</strong>admissible <strong>in</strong> a common case, which<br />
Wittgenste<strong>in</strong> tries to fight.<br />
What makes <strong>the</strong> basis for <strong>the</strong> ontology turn carried<br />
out <strong>in</strong> <strong>the</strong> Tractatus? If we take <strong>the</strong> book (‘ly<strong>in</strong>g’) on <strong>the</strong><br />
table as <strong>the</strong> object of our analysis, we can use<br />
conventional body <strong>and</strong> visual language, s<strong>in</strong>ce all objects of<br />
our world belong to <strong>the</strong> ‘cont<strong>in</strong>uous substance’<br />
3 Here, we don’t dist<strong>in</strong>guish <strong>the</strong> ontology connected with <strong>the</strong> language of<br />
verbs <strong>and</strong> <strong>the</strong> ontology of facts (resp. sentences) that can be identifies. Each<br />
sentence states this or that fact of <strong>the</strong> action done. Though, this do not exclude<br />
dist<strong>in</strong>guish<strong>in</strong>g <strong>the</strong> ontology of actions as a separate type of ontology.<br />
4 For <strong>the</strong> first time, this k<strong>in</strong>d of <strong>in</strong>terpretation was proposed on <strong>the</strong> forum ‘The<br />
World of Tractatus’, as well as <strong>in</strong> <strong>the</strong> works [Katrechko, 1999; 2002].<br />
(Descartes). Substantiality, <strong>in</strong> this case, means that <strong>the</strong><br />
changes tak<strong>in</strong>g place with <strong>the</strong> book might be neglected;<br />
<strong>the</strong> book will stay a book, with its identity predeterm<strong>in</strong>ed by<br />
its essence. But if we need to describe a process, say, an<br />
electric current impulse <strong>and</strong> its magnetic field, <strong>the</strong> current<br />
(or <strong>the</strong> magnetic field) stops to be a constant th<strong>in</strong>g with its<br />
own unchangeable essence exist<strong>in</strong>g like a book. The<br />
example with <strong>the</strong> current encourages us to be more critical<br />
to postulat<strong>in</strong>g Aristotelian entities, although <strong>the</strong> essence of<br />
<strong>the</strong> Wittgenste<strong>in</strong>’s turn is connected not with <strong>the</strong> dynamic<br />
nature of <strong>the</strong> current but, ra<strong>the</strong>r, with <strong>the</strong> fact that it<br />
demonstrates <strong>the</strong> example of an imperceptible ‘th<strong>in</strong>g’<br />
(contrary to <strong>the</strong> example with <strong>the</strong> book) which <strong>in</strong>dicates<br />
lack of means for body <strong>and</strong> visual description typical for<br />
classical ontology; <strong>the</strong> world consists not only of spacial<br />
objects but of non-visual ‘state of affairs’ as well, <strong>and</strong> while<br />
describ<strong>in</strong>g <strong>the</strong> world, should <strong>the</strong> description has a claim on<br />
adequacy <strong>and</strong> universality, those po<strong>in</strong>ts must be observed.<br />
Accord<strong>in</strong>g to Wittgenste<strong>in</strong>, <strong>the</strong>re is a universal language of<br />
description, <strong>and</strong> that is logics, <strong>in</strong> <strong>the</strong> broad sense,<br />
conceived as <strong>the</strong> teach<strong>in</strong>g of functions (G. Frege). E.g.,<br />
<strong>the</strong> ‘state of affairs’ of <strong>the</strong> current can be described by a<br />
formula (compare with Sachverhalt) show<strong>in</strong>g <strong>the</strong><br />
dependence of <strong>the</strong> strength of <strong>the</strong> current on <strong>the</strong> tension<br />
<strong>and</strong> resistance, act<strong>in</strong>g here as basic constituencies. In a<br />
general case, any state of affairs is given by a logic <strong>and</strong><br />
functional space, with strength l<strong>in</strong>es ‘comb<strong>in</strong><strong>in</strong>g’ <strong>the</strong><br />
‘th<strong>in</strong>gs’ with<strong>in</strong> <strong>and</strong>, by that, predeterm<strong>in</strong><strong>in</strong>g <strong>the</strong>ir<br />
characteristics while <strong>the</strong>ir ‘<strong>in</strong>tersections’ correspond<strong>in</strong>gly<br />
constitute a particular ‘th<strong>in</strong>g’.<br />
In a sense, correlation of <strong>the</strong> ontology of th<strong>in</strong>gs <strong>and</strong><br />
<strong>the</strong> ontology of facts is similar to correlation of atomic<br />
particles <strong>and</strong> field structure <strong>in</strong> physics. The ontology of<br />
facts postulat<strong>in</strong>g <strong>the</strong> priority of field structures <strong>in</strong> respect of<br />
particles is holistic contrary to <strong>the</strong> elementary ontology of<br />
th<strong>in</strong>gs. Accord<strong>in</strong>g to up-to-date ma<strong>the</strong>matics, difference<br />
between <strong>the</strong> ontology of th<strong>in</strong>gs <strong>and</strong> <strong>the</strong> ontology of facts<br />
can be expla<strong>in</strong>ed <strong>in</strong> <strong>the</strong> follow<strong>in</strong>g way. The present<br />
ma<strong>the</strong>matics based on <strong>the</strong> <strong>the</strong>ory of sets grounds is well<br />
concorded with classical ontology: <strong>the</strong> set is seen as a<br />
specific objectification of properties, i.e. is be<strong>in</strong>g<br />
<strong>in</strong>terpreted as a meta-object, <strong>and</strong> <strong>the</strong> sign giv<strong>in</strong>g <strong>the</strong> set<br />
acts as its <strong>in</strong>tr<strong>in</strong>sicality. For <strong>the</strong> ontology of ‘state of affairs’,<br />
<strong>the</strong> language of <strong>the</strong> ma<strong>the</strong>matic <strong>the</strong>ory of categories<br />
seems to be more appropriate s<strong>in</strong>ce today it is considered<br />
as a serious alternative to <strong>the</strong> <strong>the</strong>ory of sets approach.<br />
With<strong>in</strong> this <strong>the</strong>ory, <strong>the</strong> objects are def<strong>in</strong>ed not by an<br />
<strong>in</strong>ternal but by an external mode, through <strong>the</strong> system of<br />
arrows, correspond<strong>in</strong>g to comb<strong>in</strong>ations (relations) of <strong>the</strong><br />
given object.<br />
It’s clear that <strong>in</strong> <strong>the</strong> ontology of facts (<strong>the</strong> predicate<br />
ontology, generally), <strong>the</strong> status of th<strong>in</strong>gs become different.<br />
At <strong>the</strong> <strong>in</strong>itial stage of cognition, no <strong>in</strong>dividual th<strong>in</strong>gs, <strong>in</strong> <strong>the</strong>ir<br />
usual sense, occur but <strong>the</strong>re are <strong>in</strong>def<strong>in</strong>ite objects – quasith<strong>in</strong>gs<br />
– <strong>in</strong>teract<strong>in</strong>g with each o<strong>the</strong>r that can be presented<br />
<strong>in</strong> <strong>the</strong> mode of fussy sets. While <strong>the</strong> facts are accumulated<br />
<strong>in</strong> <strong>the</strong> process of experience <strong>the</strong> borders of <strong>the</strong> sets will be<br />
specified due to class division <strong>and</strong> ‘<strong>in</strong>tersections’ of <strong>the</strong><br />
one-type facts, <strong>and</strong>, at a stage, <strong>the</strong>y will be detailed so that<br />
quasi-th<strong>in</strong>gs will turn <strong>in</strong>to ord<strong>in</strong>ary, habitual for us –<br />
<strong>in</strong>dividual – th<strong>in</strong>gs.<br />
Let’s expla<strong>in</strong> <strong>the</strong> aforesaid on an example with a<br />
hammer. Under prop. 1.1 of <strong>the</strong> Tractatus, <strong>in</strong>itially we have<br />
no ‘hammer’ th<strong>in</strong>g (resp. notion of a hammer), we have<br />
only a fact of ‘hammer<strong>in</strong>g <strong>in</strong> someth<strong>in</strong>g with <strong>the</strong> help of<br />
someth<strong>in</strong>g’ which can be described by <strong>the</strong> «А–х–В»<br />
sentence. Here, <strong>the</strong> hammer is correlated with <strong>the</strong> active<br />
component of <strong>the</strong> fact ‘that–with–which–is–hammered–<strong>in</strong>’,<br />
this function will correspond to, for <strong>in</strong>stance, <strong>the</strong> follow<strong>in</strong>g