Prehistory
and background:
Philosophical phenomenology starting from
Brentano and Husserl introduced (or restored from scholastic philosophy) the
conception about intentionality of consciousness. Especially Husserl being a
mathematician in education and early carrier linked that fundamental and
definitive property of consciousness to the essence of mathematical cognition
by means of the concept of “epoché”: Indeed, mathematical cognition remains
open the problem whether the described and investigated objects exist or not.
In other words, mathematical cognition is invariant to and thus independent of
the existence (“reality”) or non-existence of its objects.
Thus attention turns out to be dual to the
phenomenological “intention” in a sense: It postulates its objects as real
independently of whether they exist or not. So, the attention and intention
constitutes a dual pair in dependence whether the objects at issue are declared
as real or not (here “not” does not mean for them to be declared as unreal or
nonexisting, but that they might be real or unreal).
Then one can speak of “attention” as the
reverse operation to “epoché”: The latter takes or removes reality, and the
former gives or adds reality. Thus attention being inherently linked to the
problem of reality turns out to be a fundamental philosophical concept rather
than only a psychological one. For example, if the operation of that
philosophical “attention” is applied to any intention, one would obtain the
corresponding “idea” or “eidos” (i.e. appearance as a whole) in a Platonic
sense, i.e. as “reell”.
Furthermore, “intention” has another
counterpart, “intension” in logic, mathematics, epistemology, and cognitive
science. Intension is what is able to constitutes unambiguously a separated
unit such as a notion, set, image, or any unit of cognition by a finite
definition, i.e. by a finite set of bound variables interpretable as the
logical constant of that unit. An extension as the collection of objects, each
of which satisfies the definition at issue, corresponds to any intension
possibly as an empty one if the definition is contradictory. The collection may
include as existing as nonexisting individuals.
Thesis:
One can introduce the concept of “attension” as
to any unit enumerated above, e.g. as to a notion. It means both all
individuals of the extension as existing and their wholeness as existing, too.
Thus “attension” is relative to “intension” and “extension”, on the one hand,
and to the Platonic “idea” and “eidos”, on the other hand. Furthermore,
“attension” can be defined as the application of the “philosophical attention”
to any explicit or implicit (e.g. contextual) intension.
Attension complements intension to the pair of
both biggest and least element of the mathematical structure of lattice
extended from the intention of consciousness to the idea therefore giving both
logical and ontological structure of the notion or whatever else unit. That structure
orders
the extension in question in a potential taxonomy (i.e. classification of
genera and species), the biggest element of which, i.e. the idea of the thing
defined by the extension or even that thing itself or by itself, is generated
just by the philosophical attention as the corresponding attension.
On the contrary, if the notion or unit is
supplied as usual by any logical or ontological structure, thus its attension
is implicitly certain, too.
A few main arguments:
1 Philosophical phenomenology establishes an
inherent link between: (a) logic and mathematics; (b) philosophy; (c) psychology:
The link relates the three by means a kind of transcendental idealism in the
German philosophical tradition, which Husserl called “solipsistic” in some his
works. Thus a bridge for transfer and reinterpretation between notions of
psychology, logic and mathematics is created under the necessary condition for
those concepts to be considered as philosophical as referred to that kind of
transcendental subject.
2 The initial research of
Husserl about The psychological Foundation of Arithmetic (1890) leaded
him to opposite conclusion in the later Logical
Investigations (1900-1901), namely that psychology (and further philosophy)
should be underlain rather by logic and mathematics. In fact, the initial base
of that synthesis can be found even in Ancient Greece in Pythagoreanism, in the
origin itself of philosophy, and a little later, in Plato’s doctrine and
Euclid’s geometry. The German idealism including the subject and mind as a
fundamental philosophical category had been what allowed of Husserl to add
psychology in that huge synthesis.
3 The link in question is
grounded in the way of cognition in logic and mathematics, philosophy, and the seen
in thus psychology rather than in any reference to reality, to experienced or
experimental data for the reality itself should be inferred in particular by
the new approach of phenomenology: This suggests for reality not to be
presupposed, but to be “bracketed” initially.
4 Indeed, logic and mathematics
do not connect the concept of truth, in their framework, to any confirmation by
external reality. Therefore, they do not presuppose any reality, and their
cognition is independent of reality as a hypothesis or premise. As to
philosophy, it ought not to presuppose reality for the reality itself is its
main problem (Heidegger underlay the problem of being as a deeper one). At
last, psychology should not be referred to reality as far as its object of
research is just that being which seems to be opposed to and thus separated
from reality, namely mind and psychics (Heidegger refuted this, the latter, and
Husserl blamed him for “naturalization”).
5 Thus logic & mathematics,
philosophy, and psychology need and would share a relevant method of research,
which should be independent of the hypothesis (or axiom) of reality. In
particular, that method cannot be experimental or ground on any experience in
reality.
6 Logic and mathematics as the
most advanced ones in that kind of cognition can suggest its extended model and
interpretation where “intension” would correspond to “intention”, and
“extension” to some area of reality relevant to that intension at issue.
7 Then “attension” is the
“extension” with reality added secondarily as far as reality cannot be
presupposed in phenomenological research.
The presentation also as a PDF or a video; furthermore as slides @ EasyChair
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