S.L. Katrechko
Imagination
as fundamental faculty of consciousness
These
are the base hypotheses of our paper (research project):
1. Faculty of imagination is basic
mechanism of conscious activity, which determines other human faculties. Its
main appointment is to form images, or totalities.
2. Philosophical activity is an
interesting manifestation of this faculty. Philosophy itself can be represented
as a kind of «work» with special metaphysical objects; and its
history — as a consecutive change of
«paradigmal» totalities.
3. The development of algorithmic
imagination mechanisms (so-called fantasy mechanism and transition
on meta-level) brings up to appearance of qualitative new type of
«artificial intelligence» systems — intellectual systems.
There are 3 comparatively independent objectives (problems)
within the project:
·
(a) A development
of hypothesis 1 based on Kant’s conception of knowledge;
·
(b) A development
of the line hyp. 1 — hyp. 2;
·
(c) A development
of the line hyp. 1 — hyp. 3.
Kant’s conception of
cognitive process will be modified to solve the problem a [1, 2, 3]. The main idea is that the base of knowledge
is a synthesis of images — totalities carried on out by the faculty of
imagination. It’s this fact predetermines specific character of human
knowledge. The synthetic activity of imagination reveals itself on both levels:
sensibility and understanding (mind). Note, that our interpretation of «image»
as «totality» expands the term comprehension, because totality includes
sensible perception («pictures») — traditional image conception — as well as
intelligible (supersensible) concept. Firstly, Kant’s a priory sensible
and intelligible forms are the «pure» images received with the help of
transcendental faculty of imagination. Secondly, images as products of the
empirical faculty of imagination make up a basement for not only the
sense-perception, but for the intelligible (rational, theoretical) ones. These are the schemes (Kant’s «schematism of the
pure concepts of understanding») of certain kinds of practical activity
(M. Vartofsky).
We offer the following
conception of knowledge activity. Sensibility delivers us only a primary (raw)
empirical material. Faculty of imagination («intellectual intuition» of Leibniz,
«intuition apprehension» of Kant, «eidetic intuition» of Husserl) transforms it
into image
(totality).
For example, a human eye perceives a picture not only as a set of colored
stains and strokes (although such perception is also a result of imagination
apprehension (synthesis) at a lower level), but as a landscape or/and
depictions, such as «a knight», «horse» etc. The same occur, when perceiving
with an ear a combination of music tones, we hear melody in the whole (totality
of melody). After that faculty of understanding (mind) begins its work. The primary
— synthetic — intelligible activity includes, firstly, a generation of concept
based on images, and, secondary, further uniting of the concept into sentences,
witch normal structure is «A – B» (Aristotle). It’s a sentence that plays role
of the elementary language cell (L. Wittgenstein). And the secondary —
logic-analytical — mind activity takes place in the language itself and comprises:
(1) construction reasoning and (2) development and enrichment of language.
The original conception of
philosophical activity as metaphysics will be developed so that to find the
solution of the chief problem b
[4, 5, 6]. The essence of the approach is that the philosophy is a
particular kind of «work» with special «metaphysical objects», or «totalities».
Philosophy differs both from science, which research and deals with «exterior»
objects («physical» objects par
excellence), and from art, which investigates «objects» of the «interior
world» of a person. Philosophy is in some way a rationally discursive activity
(the sphere of rationally-discursive knowledge), which differs both from science
and from art (for example, literature).
What are the «totalities»?
Let's clarify it by considering one of them as an example. One of such objects
is the «world» («universe»), and, in this sense, we often say that philosophy
is the «weltanschauung» (world-outlook). Certainly, the world as some set of
things can be studied by «physics» (sciences in a broad sense), but in this
case a researcher can miss the point that the world is a totality, not just a
simple set of things. Philosophy, being distinct from scientific study, takes
its objects as «totalities», which the subject of knowledge cannot study as
ordinary objects, because the subject-embracing nature of these «totalities»
excludes any standard scientific approach to knowledge in principle. The human
being, as the subject of research, is always «inside» these «objects» and never
can «jump out» of them. Other examples of objects mentioned above («metaphysical
objects», or «totalities» have been obtained with of imagination faculty) are
other Kant’s «idea of reason» («Ego» and «God»), Plato’s «idea», Descartes’ «innate
ideas» and Deleuze’s «concept». Objects of this type (with some reservations)
are many human being-related phenomena, such as «love», «virtue», «conscience»,
«courage», «bravery», «understanding» and so on. «Metaphysical objects» cannot
be given in the frameworks of «physical» experience: they are our mental
constructs. «World», in contrast to any final collection of things, is not
given to us, like a mental construct of a set
(or constellation — N. Goodman’s
example), which a mathematician (human being) creates with available elements,
is not given to him. Specifying the status of these objects, we can say that
the contents of philosophical activity are
metaphysical-transcendental objects, i.e. objects with the boundary status
of their existence. They are, for example, neither subjective nor objective,
neither conscious nor material. In some sense, they are analogues of Husserl`s
phenomenon.
The postulation of special
«metaphysical objects» of philosophical work predetermines specificity of the
language and reasoning («logic») of philosophical discourse, methods of philosophizing.
Let's formulate main hypothesizes we offer for solution of the raised task.
Firstly, the language of a philosophical investigation is the special symbolic
language («symbols» are names (signs) of «metaphysical objects»). The language
of philosophy is the language of «symbols»; «symbols» are the «house» of
philosophy. Thus, as distinct from usual languages, it has not three-level
semantics of the usual language: a level of syntactic words, a level of senses
and a level of meanings (references) (G. Frege), but two-level
(non-referential) semantics: a level of syntactic words and a level of senses.
Symbolical language, on the one hand, limits possibilities of philosophical
discourse (as an appeal to a referent, experience is impossible), but, on the
other hand, expands possibilities of the latter, because philosophy speaks not
only about the real «earthly» world, but also about any «possible world»
(Leibniz). Secondly, the «metaphysical» («symbolical») nature of the
categorical philosophical apparatus predetermines also the specificity of philosophical
reasoning. The structure of reasoning about «pure being» (or «conscience») as
«mental construct» differs in essence from the reasoning about, say, a tree or
other objects of the «earthly» («physical») world. The characteristic of
«metaphysical objects» as «mental constructs» allows raising the question:
which logic describes adequately the introduced «metaphysical objects» and how
much the application of common «down-to-earth» Frege—Russell logic with the
principles of non-contradiction and excluded third is correct ? And more
than that, it is possible that another logic, distinct from usual, «earthly»
logic, operates in the sphere of speculative objects. In particular, according
to the opinion of Russian philosopher and logic N. Vasiljev, validity of
the logic principle of excluded third has a purely «earthly» origin and is
connected with primacy, after Aristotle, of individual existing things. If we,
following Plato, consider classes of subjects as primary (for instance, subject
is a class of tables), the principle of excluded third will be incorrect, since
the table as one of the set of subjects of the class of tables can be
simultaneously both white and non-white, for instance, green or red (of course,
here it is necessary to realize, that the opposite properties are attributed to
the different individuals of the primary Plato’s «subject» — different things
of the same class). The transfer of the concentration from single objects to
classes of objects has allowed Vasiljev to formulate «imagined (paraconsistent)
logic» with the principle of «excluded fourth. By its logical firmness this
logic concedes no point to our habitual logic with the principle of excluded
third, but expands possibilities of our thinking. In this connection it should
be noted that the criticism of the principle of the excluded third by Vasiljev
differs in it motivation from intuitionism. Outlined
at the beginning of the 20th century, Vasiljev’s approach has predetermined the
development of paraconsistent (A. I. Arruda
— N. Da Costa) and truth (Von Wrigth) logic.
Besides, the conception of
the philosophy as the work with «metaphysical objects» allows to implement the
following original interpretation (logical reconstruction) of the accumulated
historico‑philosophical material. Its essence is following. Any
philosophical system can be represented as a certain structure (system) of
basic «totalities» or «symbols», which forms its conceptual framework.
Accordingly, the history of West European philosophy is a consecutive change of
such «symbolic» systems. Three replacing each other «episthemes» (Foucault) or
«paradigms» (Kuhn) of philosophizing can be distinguished in these systems
development: ancient, classical (the New Times) and modern. The distinction of
these three large meta-systems of philosophizing is caused by the change of the
«objects» of the philosophical research during the transition from one
«paradigm» to another. The attention of the ancient thinkers was focused on
such «totality» as COSMOS (WORLD in our discourse) and the basic problem of
philosophical research could be formulated like this: how COSMOS (in contrast
to CHAOS) was possible, i.e. what «entropyless» (meta‑physical)
mechanisms (means) of conversation CHAOS into COSMOS operated there. Various
ancient philosophical systems answered the question differently. For example,
according to Pythagorean school a basis of regulation and harmonicity of COSMOS
was a Number. Parmenid postulated «Uniform», or «Being», as an «entropyless»
principle (source) of COSMOS. The transition from the ancient «paradigm» to New
Times (classical) one is connected with the «splitting» of the one object of
philosophical research of COSMOS into three «ideas of reason» (Kant): «Ego»
(«soul») — «World» — «God». A new interesting object of investigation appears
in a field of vision — «subject» (in contrast to the «object»; «subject versus
object»), for instance, Descartes' «cogito» (the New Times) or «God» (according
to the medieval theology). Correspondingly each philosophical system of this
period, as construction of «metaphysical» object «Ego» — «World» — «God»,
implicitly solves the problem of correlation among these «totalities», which of
them is «primary» and determines the other components of the system. The
transition to the modern type of the philosophical discourse is predetermined
by two «events». The first of them is «Death of God» (Nietzsche); the second is
«Death of the subject» (structuralism, postmodernism). So, on the one hand, it
makes three «ideas of reason» as if «clap» into one — WORLD, and, on the other
hand, instead of the ancient united COSMOS a number of pluralistic «worlds» of
different philosophical systems are appearing. Schopenhauer considers «world»
to be «Will» and «Idea»; for Marx — «world» is, first of all, a system of «social
relations». Husserl, instead of the New Times contraposition «subject vs.
object», investigates so-called «phenomena», having elaborated the conception
of the phenomenal («vital») world; structuralists suggest that we should
consider «world» to be an aggregate of «language structures». In this variety
of the pluralistic approaches similarity concludes in attempts of thinkers
within the framework of modern «paradigm» of philosophizing to explain the
«world» as a certain primary «entity», i.e. to explain it out of itself
avoiding too «strong» assumptions (hypotheses).
As it was said above the
development of the c in the project
is aimed at the perspective. In contrast to a and b solutions it’s
supposed to define more precisely the offered hypotheses about the main
mechanism of imagination faculty. For this purpose the available investigations
in theory and methodology and practical systems in the «artificial
intelligence» field were analyzed by author. On the other hand, it must be
noted that the author of the project has already turned to the theme «From
logic calculus to intellectual systems». It was studied in a certain way in the
works [7, 8, 9] and the connection a — c imparts some new
seeing to this task. The development of a
gives basic methodological means for construction the new type of intellectual
systems. The well-known metaphor «right mind» versus «left mind» is a general
background of the problem c. But in
this case it’s considerably reinterpreted and specified: activity of «right
mind» stands for the imagination faculty. It allows to propose an original
methodological approach to creation of so-called intellectual systems. The
statement of a problem connected with algorithmic modeling of a faculty of
imagination in «artificial intelligence» is absolutely new by itself.
There are two supplementary
base mechanisms form a faculty of imagination: a fantasy mechanism and transition
on metalevel. A fantasy mechanism makes it possible to «complete» a
partial «picture» to the whole one (image, totality). It can be
clearly demonstrated by the perception 3—dimensional objects, which (it is
obviously) are given as a whole in no sense perception. The essence of
this mechanism is extrapolation given in perception. A mechanism of the transition
on metalevel — the scale-measuring variation — allows to design totalities
by changing (moving away) an observation point. This, for instance, was shown
in the phenomenon mention above (see a):
the perception of a picture (music melody) by a person isn’t only the grasping
of colored spots (separate tunes), but the apprehension of a picture (melody)
in the whole. More exactly, a human being in this case (perceiving a picture)
can occupy 3 positions (points of view): 1 — apprehension of only colored spots
and strokes (position of a «nearest» observer); 2 — apprehension of «images» of
a picture (position of a «middle» observer); 3 — apprehension picture itself as
a picture (position of a «long sight» observer).
In
accordance to it two ideas of modeling faculty of imagination within the framework
of the proof‑search theory, based on transition from logical calculi to
metacalculi — calculi of proof‑search [7, 8], can be postulated.
The first one can be called method of dummy variables
(metavariables). The expansion of expressive opportunities of calculus in it is
attained by the metalevel means: metavariables, metaconcepts etc. Its function
consists in fixing (complete or incomplete at the certain stage of a
derivation) information about a possible structure of the derivable formula,
and in consequent, in obtaining an additional necessary (complete) information,
replacement metavariables on variables or formulas of initial calculus. The
efficiency of such approach is demonstrated by means of so-called FOL—systems
(R. Weyhrauch, [10]). The second idea can be named method of «global processing of information». In this case there is
a possibility to take into account structural information of logical formulas
useful for proof‑search. From this point of view, the approach to a
construction of algorithms for automated reasoning, so called inverse
method proposed by Sergey Maslov, is interesting [11]. Inverse method’s
calculi are metacalculi, in which it
is possible to express structural
information about «gearing» of the variables of the formula. Using of this
information allows to hope for a construction of effective non-exponential
(e.g. propositional) algorithms. It is possible to introduce a modification of
Maslov’s inverse method, which I termed calculus of numbers with index [12].
I regard this calculus as universal proof-search calculus, in which it is
possible to simulate mechanism of faculty imagination. Above all the mechanism
of «creative mistake» in so-called iterative system of automated deduction of
the theorem [13] is a development of great interest, because it is closely
connected with a fantasy mechanism described above.
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