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 https://youtu.be/4V18eP4u8Rw

1. Intention and attention
Intension, extension, and “attension” of
a notion or set

2. Vasil Penchev
• Bulgarian Academy of Sciences: Institute for the Study of
Societies and Knowledge (Institute for Philosophical
Research)
• vasildinev@gmail.com
209 Bryant Hall at the University of Mississippi in Oxford, MS,
USA
11:00-11:50; 19 March 2016
The 2016 Meeting of the Mississippi Philosophical Association

3. Prehistory and background

4. Philosophical phenomenology
• Philosophical phenomenology starting from Brentano and
Husserl introduced (or restored from scholastic philosophy)
the conception about the 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”:
• Consciousness addresses always something beyond itself to
be able to constitute itself as what addresses

5. Mathematical cognition
• 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
• It needs only to address them consistently
• “Consistently” as it is used here means only a one-to-one
mapping between the set of addressees and the set of
addressers
• However, the addressers are often a finite number for
infinitely many addressees at least in mathematics

6. Attention and intention
• 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”

7. Reality
• 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”

8. Intention and intension
• 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

9. Thesis

10. “Attension”
• 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

11. • 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
“Attension”

12. A few main arguments:

13. • 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
Argument 1

14. • 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
Argument 2

15. • 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
• The contents of consciousness is only doubled in the manner
of mathematics as a one-to-one mapping of that contents
into … itself in the final analysis
Argument 3

16. • 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”)
Argument 4

17. • 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
• Indeed, any experimental method admits and even suggests
some mismatch of reality and consciousness unlike the
enumerated sciences
• Whether reality coincides with consciousness or not should
be a fundamental axiom, which generates two main
pathways of cognition: either “phenomenological” or
“naturalistic” (in Husserl)
Argument 5

18. • Logic and mathematics as the most advanced ones in that kind of
cognition can suggest the extended model and interpretation where
“intension” would correspond to “intention”, and “extension” to
some area of reality relevant to that intension at issue
• Both concepts of intension and extension just as well as that of
intentionality do not presuppose “reality”, but they are consistent to
it. Thus, the “property of reality” is able to be added or not
axiomatically to some entities postulated to possesses it
• Furthermore, the pair of intention and attention implies
a counterpart of “intension”, which is naturally to be called by t
he neologism “attension” as the missing member of both pair
“intention – attention” and pair “intension - ???”
Argument 6

19. • Then “attension” is the “extension” with reality added
secondarily as far as reality cannot be presupposed in
phenomenological research
• “Reality” can be interpreted as an additional bit of
information
• “Attension” is further definable by means of “extension”, to
which is added a bit more with values either “real” or
“unreal”
• “Attension” properly is the case where that additional bit is
obtained the value of “real”
Argument 7

20. Equating the transcendental to the naturalistic:
The unity of mind-brain as a quantum system

21. Husserl’s approach to transcendentalism
• Husserl, both mathematician and philosopher, was who offered a new
reading of transcendentalism, mathematical in essence
• The transcendental might be understood as the collection of all
possibilities therefore interpreting the “condition of possibility” in thus
• Mathematics accepts consistency seen as the possibility of existence as
mathematical existence as well.
• The collection of all possibilities might be defined as a certain invariant
shared by all possibilities at issue, obtainable by “eidetic reduction”,
which is phenomenological in the sense of Husserl’s psychology, or
transcendental in his philosophy

22. The reductions
• One might say that eidetic, phenomenological and
transcendental reduction are only different senses (or
contexts) of one and the same meaning mapping all
possibilities of a kind into their shared invariant
• Then Husserl’s opposition of the phenomenological
(transcendental) to the naturalistic might be further thought
as the opposition of the set of all possibilities, defined by
their invariant, to an arbitrary and therefore random
element of the same set

23. Mind-brain
• However, the system of mind-brain unifies somehow both aspects
allowing to be described as both mind (i.e. phenomenologically and
transcendentally) and brain (i.e. naturalistically)
• One might even postulate that kind of duality as the essential feature
of that system, necessary for its relevant definition
• If that is the case, and Husserl’s approach to the transcendental and
naturalistic is used, one would need a certain equation of the
transcendental and the naturalistic to define relevantly the system of
mind-brain

24. Mind-brain as a quantum system
• The interpretation of the mind-brain system as a quantum
system satisfies the condition for an element of a set to be
equated to the set, and therefore that of the reduction
whether eidetic or phenomenological, or transcendental in
Husserl’s sense
• Then a given mind state is associable only with the change of
the probability distribution of the brain as a whole
• In other words, any mind state corresponds to a certain state
of the brain as a whole, but not any true part of it

25. What is “quantum system”?
• Quantum mechanics being only an exemplification and
interpretation of a much more general set including it shares the
same property, namely, the equivalence of a set to its element
• Then, the term “quantum system” means it in the sense of both
quantum mechanics and generalization definable by that
equivalence of ‘set’ and ‘element’
• Furthermore, any element of the set is specified by the probability
distribution of all elements of the set
• Particularly, if all probabilities are always concentrated in an
element, one can obtain the classical sense of ‘set’ shared by finite
and infinite sets

26. Involving infinity
• No finite and constructive element can satisfy that kind of equivalence
• Even more, that equivalence is interpretable as a version of Dedekind’s
definition of infinity
• However if the axiom of choice is attached, a finite, though unknown in
principle, set equivalent one-to-one to each one infinite set should
exist “purely” and mathematically, i.e. only possibly, but not ever
actually
• That paradoxical corollary is implied by Skolem’s consideration of the
“relativeness of ‘set’” (1922)
• Thus infinity is decomposable to finiteness and randomness if
randomness be equated to “pure” (never actual) possibility

27. Bohr’s complementarity
• Then by interpreting in terms of mind-brain, a random element of
the one half of that duality would correspond to each one element
of the other
• This is equivalent to the suggested by Niels Bohr conception about
mind-brain complementarity as a generalization of complementarity
in quantum mechanics
• For example, given an element either of the brain or of the mind. All
other half of duality corresponds to it, but specified by a profile
(distribution) of probability for all elements of that half

28. Interpretation
• There is a gap (discrete jump) between ‘mind’ and ‘brain’ in mind-
brain, which involves complementarity, duality and holism
• The brain as a material macroscopic system can be seen as an
“apparatus” registering the state of mind as a probability distribution
• The mind in turn can be thought as a microscopic “quantum” system,
the state of which is what is registered by the brain
• The mind-brain relation is probabilistic “purely” due to the gap
between them without any hidden variables to determine the
probability distribution as a statistics in those variables
• Both mind and brain as well as both together can be interpreted as
the “substance of the gap and probability distribution” as the gap is
always and only a relation between them

29. Thank you for your kind
attention!
I am expecting for your questions
or comments