On Phenomenology - Discipline and Method

by Maria Odete Madeira

Phenomenology is a branch of philosophy, applied to the study of the phenomena.

Phenomenon (phainomenon) is that which reveals itself, by itself and in itself. Thus, all existing things can be considered to be phenomena.

Phenomenology is not a method, it is a disciplinary area constituted by a theoretical body, available as fundament for the construction of methods and methodologies aimed at the study of any existing reality that, genetically, by itself and in itself, reveals itself as position rooted in the world.

Criticizing the positivism as a mere construction of facts, Husserl (1907) held that the so-called crisis of the sciences had to do with a reduction of humans to constructed facts. In the positivistic model, humans, as such, were alienated in the human facticity, derooted from that which constituted them as beings that are intentionally inscribed in the world, from which they received the sense of themselves and of the things with which they related.

For Husserl, the world was the originary datum, that was turned towards humans and towards which they, themselves, turned self-reflexively, in order to determine and distinguish the sense of the things.

Protesting against the reduction of human reason to mere exercises of calculation, Husserl defended phenomenology as the science of the phenomena. In Husserl, the phenomenon is an eidos that reveals itself in an intuition that is defined by an intentionality that assigns a plenitude of presence to the eidos (phenomenon) that is aimed at. Each eidos is accessible, only, to a certain type of intuition: the intuition that refers and identifies it in an immediate way and that, because of that, captures it in all its totality.

Intuition has its origin in the Latin terms tueri (to see) and in (in, within) that conjointly mean the action of seeing directly within the things, thus, signaling a mode of immediate knowledge of an existing object that, because it exists, shows itself, as such, to the consciousness that aims at it, and, because it shows itself, it also demonstrates itself in its modes of existence, so that it can be described from its fundament (eidos).

The experience, in Husserl, assumes the sense of lived world (Lebenswelt), as that which is in the origin of the knowledge and that is before any reflexive activities. That is, the objects present themselves to the consciousness, giving themselves in their completeness (eidos) in order to be, only after, and through a conscious act of radical reflexivity, on the part of the subject, actively apprehended by the consciousness that intentionally signaled them as existents in themselves, and by themselves, and, in this way, as autonomies.

The noumenon, that was impossible to be categorized in Kant, appears, in Husserl, as that which is immediately intuited. Thus, Husserl turned away from the criteria that transcended the experience, to be able to, in the same experience (Lebenswelt) and in a direct way, capture that which, in the phenomena, was their noumenic sense.

In Heidegger, the notion of experience lost the theoretical sense present in Husserl, to mix itself with the notion of existence. The author considered that, originarily, the things do not “make their apparition” and do not “appear to be” to the humans as phenomena or objects of thought, but, instead, as entities that (co)exist in a complex system of references that constitutes the world where each human exists, understands and interprets himself as being-the-there (dasein), projectively launched to a future that he existentially anticipates.

This perspective, of a gnoseology, as activity rooted in the worldly experience, was, also, developed by Merleau-Ponty (1945), who considered that all the universe of science is constituted upon the lived world. The notions of subjectivity and objectivity are synthesized in the notion of the world, lived and understood by subjects incarnated in it. The phenomenological perception is, thus, considered as an originary pre-reflexive experience of each subject with an own body (corps propre), that body, understood, as a node of living significations that is incorporated by an operating intentionality that links it to the world of life.

In this way, the phenomenological perception constitutes itself as the ground that is previous to all reflexive activity. Assuming that knowledge is, always, the apprehension of an ontologically constituted structure, an ontologically constituted structure that, as such, is given to any originary human consciousness, (a consciousness) which is fully rooted in a world that is previous to it, exterior to it and autonomous.

On Individuation

by Maria Odete Madeira

Individuation is a philosophical term that designates the intrinsic, constitutive, genetic and autopoietic event of separation of each individual within a same species.

It is a systemic principle of separation that operates from the first causes and the first principles that were involved in the genesis of each individual, be these principles entities, situations, processes or events.

In methodological terms, it constitutes an ontological principle used as a classificative criterion of identity.

On Penrose's Argument Against Density Operators

by Carlos Pedro Gonçalves

What is a quantum state?

Should we speak of a quantum state at all?

Should we speak of quantum states or of quantum processes?

These questions can be raised from the work of Baugh, Finkelstein and Galiautdinov (http://arxiv.org/abs/hep-th/0206036) and from the results obtained by Gonçalves and Madeira (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1438013), about the connection between a stationary quantum state and the consistent histories formalism, these results being obtained from the relational structure of the different bases in which a stationary quantum state can be expanded.

A different, but related, problem arises from Penrose’s Road to Reality (Penrose, 2004), where the author questions the mathematical structure that should be used to formalize what is usually called a quantum state.

Thinking about these two threads, one is lead to the following question:


What is the most fundamental mathematical structure that should be used to describe the quantum system, and, what is the nature of the physical semantics that this structure formalizes?


This is the main question to which we shall return, recurrently, during this article.

Looking at Penrose's (2004) work, and regarding the first part of the question, we find that Penrose (2004) raised the problem of formalizing the quantum state by:

A) The density operator, whose entropy zero space (using von Neumann’s notion of entropy) is comprised of the density operators for the so-called "pure states".

B) The normalized kets (for the "pure states")

It is clear that the density operator is more general, since it can be used for statistical mixtures, but is it more fundamental than the ket for pure states? And, should we call these states at all?

The notion of a zero entropy density operator is effectively equivalent to a projective notion of a (pure) quantum state, as Penrose noticed. Therefore, one might take the position that such density operators appropriately describe a “physical quantum state”, taking the perspective that only that which has an impact in measurement problems can be considered to be physical.

About this, however, Penrose (2004, p.796) argues that:

“(…) I feel uncomfortable about regarding such a ‘pure-state density matrix’ as the appropriate mathematical representation of a ‘physical state’. The phase factor (…) is only ‘unobservable’ if the state under consideration represents the entire object of interest. When considering some state as part of a larger system, it is important to keep track of these phases (…)”

Penrose’s main issue is related to the superposition principle. As Penrose puts it, the basic quantum linearity is obscured in the density operator description. Indeed, an objection of Penrose against the density operator is that the density operator makes complex the simpler linearity of the ket formalism.

So far, Penrose’s arguments equally apply to the density operator and to the density matrix. In pages 797 to 800 of Road to Reality, however, Penrose proceeds discussing what he considers to be the “confused ontological status of the density matrix”, in this case, the argument centers itself in the matrix and not in the operator. Indeed, some of the statements, used as counter-argumens apply correctly to the density matrix but not to the operator.

The major argument refers to the inability of the density matrix to distinguish between different kinds of entangled pairs. For instance, consider the following scheme/example:




Even though we have two different kinds of entangled pairs, the density matrix is the same, that is, the density matrix does not seem to distinguish the bases.

However, this is not the case if we take into account the density operator. The density operators are, not only, different, but if we determine the projection, for instance, of the second density operator with respect to the basis in which the first is represented, we obtain:

Indeed, the second operator is a statistical mixture between two pure states of superposition of 0> and 1> (+> and ->).

What the above results show is that the projections of the second density operator to the basis {0>, 1>} and to the basis {+>,->}, differ, with respect to the probabilities assigned to the quantum events formalized by these projections.

We can use a density matrix for reading probabilities, however, one must never confuse the matrix with the operator, and one must always use the operator, for the fundamental description.

The problems of ontological confusion, raised by Penrose, can be raised with respect to the density matrix but not with respect to the density operator.

This stresses the importance of precision of language, and the issue of the generalized practice of calling the density operator a density matrix (a practice followed by Penrose, and called into attention by Feynman in his Lectures on Physics, as a practical but mathematically imprecise simplification). This must be considered as a simplification of language, as Feynman stressed, but, nonetheless, it is a mathematical imprecision in the usage of the terminology, and, when dealing with fundamental arguments, one must take into account the distinction between the density matrix and the density operator.

However, Penrose’s argument about the phase seems to stand for both operator and matrix, quoting Penrose (2004, p.803):

“Under normal circumstances, moreover, one must regard the density matrix as some kind of approximation to the whole quantum truth. For there is no general principle providing an absolute bar to extracting detailed information from the environment. Maybe a future technology could provide means whereby quantum phase relations can be monitored in detail, under circumstances where present-day technology would simply ‘give up’. It would seem that the resort to a density-matrix description is a technology-dependent prescription! With better technology, the state-vector could be maintained for longer, and the resort to a density matrix put off until things get really hopelessly messy! It would seem to be a strange view of physical reality to regard it to be ‘really’ described by a density matrix (…)”

Although these arguments may seem compelling, one may place a question regarding the statement on the approximation to the whole quantum truth, the question is: what about the so-called 'impure states'?

As Penrose notices, one cannot discard that, at the quantum level, detailed phase relations may get “lost”, because of some deep overriding basic principle. It is still too soon to discard such a hypothesis, and this, indeed, may be likely, if one considers a foamy Planck scale space-time (quantum foam) (Penrose, 2004).

Furthermore, there is still a division in the community in what regards the information loss in black holes. Even if many believe, including, more recently, Hawking (http://arxiv.org/abs/hep-th/0507171), that information may not be lost, we cannot yet reject this possibility.

It seems that, accepting Penrose's argument, leads to the position that if we wish to use a fundamental mathematical description of physical reality, we must use two different formalisms, a ket for the pure states and a density operator for all the other cases, and we cannot discard the need for the usage of the density operator.

Thus, to the first part of our main question (what is the most fundamental mathematical structure that should be used to describe the quantum system?)The arguments seem to point towards using the density operator only when necessary, as a technological tool.

But is this sustainable? Do the phases matter?

The answers to these questions cannot be entirely solved by appealing to mathematics alone.

Indeed, a mathematician might be divided between: (a) a choice where one would work with what can be argued to be a more fundamental structure with respect to the information conserved in the description (the phase information), but two formalisms would be used for two different situations (pure vs impure states); (b) a choice where one works with a single formalism but part of the information (the phase) is lost.

Since we are dealing with physics, all that matters is whether or not the phase is physically relevant, or, even, whether or not the density operator expresses, formally, the most fundamental physical nature, the normalized ket just being a useful representation, that can be shown to be equivalent to the density operator up to a global phase factor.

In effect, so far, all that we can get from the system is the information contained in the density operator. The question of whether or not there might be some technology to recover the phase from a measurement, is still open to discussion.


One may argue that, physically, the phase is irrelevant, one may alternatively argue that the phase is not physically irrelevant. However, to do the latter would demand the mathematical formulation of what might constitute a measurement procedure for the phase, leading inevitably to the problem of the physical meaning and measurability of a complex number.

If one chooses to spend some time with this issue, one is led to this bifurcation of perspectives, where the choice depends less on mathematics and more on physics, in particular, our main question «what is the most fundamental mathematical structure that should be used to describe the quantum system, and what is the nature of the physical semantics that this structure formalizes?» should be considered as a whole, since one cannot really consider the formalism, independently from the object of intentionality of the formalization (that which the formalization is about and that justifies the development of the formalization itself). What is fundamental for the mathematical structures of the formalism, may not be so for the object of formalization.

In the end, the interpretation of quantum mechanics that one follows may decide the choice between the two paths, if one wishes to make such a choice at all, or if, and until, a fundamental thinking about physics demands such a choice.

An interpretation of quantum mechanics that thinks about the nature of quantum processes, inevitably restricts our choices about what is fundamental due to the ontological and epistemological commitments that we assume, along the way of the construction of a scientifically grounded interpretation.

In the interpretations that assign a physical nature to the wave function as corresponding to a pilot wave, the phases are relevant, even if they cannot be measured, since the fundamental object of formalization is that pilot wave.

For a follower of Bohr, on the other hand, the whole discussion would be pointless, since the quantum formalism is just a useful tool used to predict results of experiments, whether we use a ket, a wave function or a density operator is irrelevant.


Furthermore, Bohr was “suspicious” of complex numbers, these could be useful tools, but, in the end, all that mattered were the predictions, and if a phase is unobservable by current technology it is a waste of time to think about it or to assign it a physical significance.


In the Aristotle-based realist interpretation, followed by Heisenberg, the density operator should be taken as the formalization of the fundamental physical structure, since what the formalism “formalizes” is the tendency of a potential alternative to be actualized, this intensity of the dynamis corresponds is quantifiable in terms of a degree, a degree with which probabilities coincide numerically, when these probabilities are interpreted as being proportional to the physical propensity of the potential alternative to be actualized, which is nothing but the intensity of the dynamis associated with that alternative.

Taking this into account, the diagonal terms of the density operator are the fundamental structure, since they are in the direct correspondence with the object of formalization of the theory, i.e., they formalize the most fundamental physical structure, and their interpretation is naturally processual, a processual nature that is obscured by the ket representation.

A closely related mathematical argument can be found in Bohm, Davies and Hiley's paper Algebraic Quantum Mechanics and Pregeometry (http://arxiv.org/abs/quant-ph/0612002), where the authors built quantum theory from the primitive idempotents that are directly related to the different entries of the density operator. Bohm et al. show that the ket notation hides the fact that each ket represents an object with two labels.

Thus, in the end, one’s solution to the phase problem and the answer to the central question placed here, depends on one’s choice of interpretation of quantum mechanics.

On Situation

By Maria Odete Madeira

The term situation comes from the Latin situs that means relational position or relational disposition of some thing.

The notion of situation has been largely worked upon by philosophy. Besides the scholastic authors, other authors such as Jaspers, Sartre, Merleau-Ponty, Kierkegaard and Heidegger were some of the philosophers that developed philosophical criteria called situationists, in which the situation is thought upon as a concrete and objective reality that underlies all existing things.

Any existent is considered an existent-in-situation, because any existent is one among other contingent existents, situationally launched in the world.

The term world is genetically related to the term nature, that comes from the Latin natura (gnatura, natus, gnatus, nasci), which means to be born. This term has its Greek equivalent in ousia, which means to produce, to give origin to (fazer nascer, faire naître).

Both terms (natura and ousia) are equivalent to the Greek term gignomai, which means to come to be.

Natura and ousia are both related to the Greek term genesiz (birth). All that exists, exists as presence and existence (natura, ousia, dasein).

The Production of Judgments in Kant

by Maria Odete Madeira

For Kant, the production of judgments consists in thinking the diverse of the empirical experience as if it was contained in a universal.

If the universal is previously given, as a rule, principle or law, indicating, a priori, the conditions in which the empirical diverse can be subsumed, then the judgment is said to be determinant and it is objective. However, if only the empirical diverse is given, the faculty of judgment (existent in all subjects capable of thought and reason) has to find the universal to that empirical diverse, then, the judgment is said to be reflexive, indeterminate and subjective.

For Kant, to judge is, always, an exercise of subsuming the empirical diverse in unifying rules. Be it a subjective or an objective judgment, that judgment has, always, its foundation and its condition of possibility in general rules of unity of synthesis of the diverse of the experience. These rules are considered, by Kant, rules a priori, without which no possible experience could be thought or known.

Thus, in Kant, every general unity of synthesis has its condition of possibility in a reflexive capability, dispositionally existent in all the subjects capable of thought and reason.

On Transdisciplinarity

by Maria Odete Madeira

No researcher can rigorously identify the border that separates the interdisciplinary from the transdisciplinary work. In question are matters such as individual and collective experiences, processual and methodological convergences and integration of the disciplinary knowledge.

The plurality of the senses and meanings, synthesized by each concept, trigger self-referent systemic lines of fugue that can oscillate between the interdisciplinarity and the transdisciplinarity.

Thus, any transdisciplinary exercise is conditioned by a structuring systemic uncertainty, in regards to the interpretation, comprehension and verbalization of the signs and respective meanings that emerge from the borders of each system involved in the processes.

The great challenge that is placed to the transdisciplinary work is, precisely, the development of techniques and technologies that allow the researchers to capture, in the systems, all the available information about the identity of each of these systems, as well as to capture the respective autopoietic processes involved in the systems’ development, evolution and growth.

on observation and experience

During the Renaissance, the impulse towards observation trajected and projected new criteria based upon the notion of experience, from the Latin experientia, that signals a sense of proof through which some thing is acquired or learned.

The observation and experience, during this same period, became the basic elements of a new and compulsive rationality, that tried to apprehend quickly the laws of nature, in order to apply them to fundamental methodologies.

The notion of experience became a fundamental notion that oriented itself by criteria of true/objective knowledge, conditioned by two proposals: a notion of experience linked to the empirism, and a notion of experience linked to the critical rationalism.

Linked to the empirism, the experience is defined as individual living experience/action, accumulation of information and evidence of the immediate/qualitative observation.

Linked to the critical rationalism, experience is approached from criteria of quantitative/repeated qualitative, compared, transmissible with fundamentation and pluripersonal observation. The accumulation of information does not constitute evidence/certainty and the individual experience is considered only in terms of specific information.

On Transcendental - Aristotle, Aquinas, Kant and Husserl

By: Maria Odete Madeira

The notion of transcendental assumed, in Aristotle, a metaphysical sense of characterization of attributes, such as, the unity, the true and the bene.

Thomas Aquinas assumed Aristotle’s transcendental attributes and added other two: res and aliquid.

Kant introduced a new sense to the notion of transcendental, relating it to the Copernican Revolution, thus, this notion that, until Kant, was taken in a "formal-logical" sense that fundamented the things in themselves, after Kant, came to constitute the condition a priori of the possibility of something to constitute itself as a phenomenon and object for any subject capable of thought and knowledge, in this way, concepts or categories assumed the value of transcendentals and, because of that, existed, according to Kant, a priori (dispositionally) in each human subject.

The transcendental no longer operated at the fundament of the things in themselves, but, only, at the fundament of the phenomena and respective objects of knowledge for any subject capable of knowing.

Husserl maintained the Kantian sense of the term, but radicalized it by making the reduction to subjectivity (epoché) as the ultimate fundament of the sense and validity of the experience.