The Logic of Experimental Phenomenology

Musatti (1958) argues that there is an analogy between mathematical and perceptual problems such that the logic of some fundamental questions of mathematical geometry can be used to account for the logic of experimental demonstrations in the phenomenology of perception. The rules of perception are derived from such evidence that the more it differs from the metric, me­chanical and geometric properties of the stimulation, the more compelling it is. In most experiments it has been found that the more the experimental de­vices are at variance with appearances, the more their ordered and systematic behaviour is reasonably accounted for in terms of self-sufficient phenomenal features and structures. For example, the perception of movement is studied through stroboscopic movement, the constancy of shape through deforma­tions. Likewise, perceptual identity can be studied through the “tunnel effect” (see Burke, 1952). In this research paradigm, two elements are presented. The first moves until it stops and disappears at the edge of an occluder, while the second appears at and begins to move from the opposite edge of the occluder. The perceived values of speed, trajectory, “entry-exit” interval, size and width of the occluder are the factors that allow the identity of one and the same ele­ment to appear (for earlier evidence, seeWertheimer (1912a: 224), where this effect is obtained with apparent movement). In such conditions, the appear­ances of movement, of constant form and identity occur in spite of the succes­sion, the deformations and the diversity that should have been expected on the basis of the designed mechanical, geometric and projective properties of the devices that are set to control the experimental conditions.

Musatti claims that this procedure corresponds to the following general scheme:

• designing experimental devices whose physical properties differ from the particular perceptual feature ϕ
• observing that appearances show ϕ or that the description “that ϕ” is true of what is systematically perceived in the experimental conditions.

Musatti remarks that this scheme satisfies the logic of Poincare (1902) proof of the fundamental principle of free mobility that cannot be reduced to anything else. Suppose that a particular world is embedded within our world, which is contained in a sphere with the center O and the radius R. In this world, the bodies change dimensions as they move from place to place, so that they get smaller as they approach the surface of the sphere according to a coefficient of contraction R² – r² in which “r” denotes the distance of any point from O. The beings living in this world don’t perceive a bounded world, because as they move away from O the dimensions of their bodies become increasingly smaller so that the space they have to cover to reach the boundary will increase corre­spondingly. Therefore, they perceive their own world as we perceive ours. The sphere appears boundless, because its boundary is never reached and there­fore does not exist for them, as well as infinite, because it allows them to pro­ceed endlessly along a given direction without ever finding the same positions occupied earlier. Poincare maintains that in such a world, the shortest path to transpose a material body from point A to point B does not lie on the straight line connecting A and B but on the arc passing through them and orthogonal to the surface, because the lengthening of the path with respect to the line that appears straight from the outside of this world is offset by the increasing size of the body as it approaches O. If a measurement unit, for instance a metallic rod, is transposed on the straight line and on the arc, the distance between A and B is smaller in the arc than in the line. Hence, it could be determined that all the orthogonal arcs to the surface of the sphere are minimizing length lines, just as the straight lines in our world are. Moreover, if the light is propagated with a refractive index that varies locally and proportionally to the coefficient of contraction, the light rays also travel along the orthogonal arcs. Thus the arcs correspond to the straight lines of our world in all relevant respects so that for the beings living in this world they are their straight lines. Poincare emphasizes a seemingly paradoxical consequence. If the inhabitants tried to discover the physical structure of this spherical world, they would arrive at a law of deformation of all bodies. In fact, from their standpoint the world would be found to obey the principle of rigidity that yet predicts the opposite to what it is the case. If the inhabitants looked for direct measures to control the hy­pothesis of universal deformation, they would not be able to observe its effects because the standard unit of measurement undergo the same deformations when transposed through space and time as any other body. Musatti remarks that the law of universal deformations of all bodies in this world confirms just the “principle of free mobility” that it violates. On the one hand, the validity of the law still has to be proved through measurements. On the other hand, any measurement needs the “principle of free mobility” that states that any change in space and time, that is any transposition, is indifferent to the physical di­mensions of bodies. If a standard unit did not preserve its dimensions through transpositions, no congruence could be observed.

Musatti claims that this demonstration of the principle of free mobility fol­lows the scheme of:

(a1) constructing a conjecture about a world in which the principle of free mobility is not valid;
(b1) observing that within this world this principle needs to be valid.

He argues, then, that there is an analogy between the scheme of this demon­stration and that of the experiments on the autonomous rules of perception. This analogy satisfies the logical form:

(a2) assuming that either “p” or “¬p,” then positing “¬p”;
(b2) deducing the consequences of “¬p” and proving that “¬p” is false; hence, “p.”

Musatti concedes that this logic seems inconsistent at first glance because it is evident that it is impossible to deduce false propositions from a true proposi­tion. Yet, it is consistent to derive the negation of a proposition that is proved false through the deduction of its consequences. Stating “-p” allows deriving directly its negation if the deduction of its consequences proves that it is self­contradictory or inconsistent with the propositions that must be admitted in the demonstration. The seeming inconsistency of this logic stems from the fact that the contradiction between “-p” and the admitted propositions can be ascer­tained solely at the end of the conclusion of the proof. Musatti remarks that this demonstration is equivalent to the so-called Saccheri’s “consequentia mirabilis” (cf. Kneale and Kneale, 1962: 347; Hoorman, 1976; Angelelli, 1975). It is interesting because it was conceived as a “direct and ostensive” proof of the fundamental principles that by definition cannot be derived from other propositions (Vailati, 1904). It is different from the proof by contradiction, whose scheme is

where S is a set of admitted necessary propositions and C is a contradiction. The scheme of the consequentia mirabilis is

where the negation of “p” is the rule of inference.³ Musatti argues that the proof of fundamental principles of mathematics must rest on this logic of a di­rect and ostensive demonstration of one principle through its negation. Since the rules of perception have an equivalent epistemological autonomy, the ex­perimental proof of the self-sufficient rules discovered by the phenomenology of perception satisfies the same logic. As the principle of free mobility cannot be derived from other principles, so the rules of perception cannot be derived from the stimulation. As the principle of free mobility is proved directly and ostensively through the universal deformations, so the phenomenological structures and rules are proved directly and ostensively through devices and conditions that deny them from a mechanical and geometric standpoint.

Musatti acknowledges the importance of the objections that have been raised against Poincare’s thought experiment. The argumentation is restrict­ed to the linear dimensions of the bodies in the spherical world. In fact, the change of size involves a change of surface and volume as well, which must be proportional respectively to the square and the cube of the size variation. If one supposes that the mass varies according to the volume, the mass of a body moving away from O has to decrease more steeply than the decrease of the square of its distance from O. This should enable the inhabitants to ob­serve that the gravitation is locally variable and to determine the position of O as the point of maximum attraction, whence they could reconstruct the actually bounded and finite structure of the world. However, Musatti claims that the objection neither refutes Poincare’s epistemological argument nor rules out the implications of the analogy for the study of perception. From a general epistemological standpoint, it does not regard the possibility of a di­rect measurement through a standard unit, rather of an indirect control. Still, the inhabitants could assume that their world has the structure that it would present to subjects observing it from the outside. As regards the analogy with perception, this case might correspond to the perception of things reflected in a convex mirror. Yet this is not a model of perception, unless the deformation of the convex mirror is extended to the entire world surrounding the subjects. Besides, when this condition is artificially obtained, the perception is progres­sively adapted to the distortions that disappear while the constant appear­ances of things are restored (see I. Kohler, 1964). Another objection is that the inhabitants could deceptively judge that their world is boundless and infinite as it seems, because it obeys additional physical laws according to which the deformations of the standard unit of measurement vary locally. For example, a metallic rod could experience a contraction in a given direction with respect to the transposition, which offsets the deformations in other directions. The rigidity of the standard unit would turn out to be an illusion, because the struc­ture of the world appears homogeneous, while it is governed in reality by laws that vary locally. Accordingly, as the principle of free mobility is not proven, so the evidence of the self-sufficient structures and rules of perception is not conclusive. However, why are these additional laws not ad hoc adjustments of the theory? Moreover, this additional control is again indirect, so why trust it more than the direct observations of appearances? Musatti argues that one should prove that it is not more parsimonious to trust the evidence provided by appearances before assuming that their ordered and systematic course is ruled by laws whose effects cannot be directly controlled.

Bozzi (1961a) claims that the logic of the experimental demonstration studied by Musatti also shows the intersubjective meaning of the phenom­enological descriptions. One of the objections to phenomenology is that the descriptions of directly observable features of appearances cannot be univocal by their very nature. This objection rests on considering the propositions of physics as the standard of meaning for the theory of phenomena, because they are founded on measurements and can be set in mathematical relations that both interpret the observations and describe the structure of phenomena. This is the reason for the meaning ascribed in psychophysics to the measures of the physical properties of the stimulation. In psychophysics, perceptual expe­rience is accounted for according to the mapping between a physical scale of the stimulation and an estimation scale constructed from the sensory respons­es. The meaning of the physical scale is defined by the measurement opera­tions, and the physical values may hold mathematical relations among them. Instead, each sensory value may correspond to many physical values while the converse does not hold. Therefore, the agreement on the meaning of physical units like centimetres, grams and seconds set the meaning of estimations in the sensory scale. It is the corresponding physical magnitude that gives sen­sory magnitude a univocal meaning.

Bozzi argues that the agreement on the meaning of physical measurements plays a role also for phenomenological descriptions. Experimental phenom­enology does not deal with the mapping between two different scales, yet the observation of functional connections requires – as Musatti has shown – the design of conditions that can be described in mechanical and geometric terms. He cites as an example the so-called Korte’s laws. Korte (1915: 277, 291) formu­lated some “equalities” as generalizations of the observations for different con­ditions at which apparent movement is obtained:

whose symbols mean:

s = distance between the stimuli;

i = intensity of the stimuli;

t = inter-stimulation interval;

e = exposure time;

while “~” means that the equality does not denote a direct correlation so that the value on the right side increases if the value on the left side increases. These equalities show the structures of the perceptually optimal movement: (i) “s” increases as “i” increases with “e” and “t” constant; (ii) “i” decreases as “e” increases with “s” and “t” constant; (iii) “s” increases as “e” increases with “i” and “t” constant; (iv) “t” increases as “e” increases with “i” and “s” constant. The physical interpretation of the quantities in these equalities means the “physically objective conditions.” However, in such a case the measurement operations are carried out on the experimental device to set which values the functional connections between appearances must have in order to obtain the perception of movement. Physical magnitudes are neither the perceptual referent nor the meaning of phenomenological terms. They are the results of the measurements at which one discovers the functional connections that rest within the phenomenal domain. In Korte’s equalities, the index “opt.” refers indeed to a perceptual feature.

In this sense, Bozzi contends that the measurement operations applied to the experimental devices and the protocols of the transformations induced on the appearances share the same observable scale. If, for instance, the apparent motion is the phenomenon under scrutiny, one will need a perceptual speci­men of uniform motion. The experimenter will carry out some operations of measurement on the experimental devices that yet may not meet the accuracy and precision that are required in mechanics. It could happen that they only approximate the physical uniform motion. However, what matters is that for a definite range of measurement values a clear-cut appearance of uniform mo­tion is obtained. If some of these measures yielded irregular physical motions, this would not imply a presumed inaccuracy of perception with reference to the stimulation or of the experimental design. If in such a case the irregularity of physical motion is not directly observable, the values of the physical mea­sures play the same role as the physical deformations for the validity of free mobility. In addition, these values, together with the others encompassed by the relevant range for which the specimen of perceptual motion is obtained, give a contribution to the intersubjective understanding of the phenomenal functional connections themselves.

Although Bozzi does not cite him for this issue, the epistemological mean­ing of this argument is akin to Bridgman’s (1927: gf.) discussion of the obser­vational meaning of the concept of length. If length is measured by means of Johansson specimens, one needs to ensure that they are clean and actually in contact with each other. If length is measured at a smaller scale, one needs to ensure not only that there are no interleaving dust particles, but also to con­trol for humidity films and absorbable gaseous substances, as well as provide a higher void the smaller the dimension of the specimens. At the complete void, measurement has to deal with atomic structure. Because there are no stable contours, one will be obliged to average the observable positions of the contour at given times. Likewise, experimental phenomenology is carried out at the scale of directly observable effects of measurement operations and transformations of appearances. Physical terms denote the operations to bring about the conditions at which appearances are presented as repeatable data. Phenomenological terms are introduced through ostensive definitions, and their combination in descriptive propositions has a truth-value over the func­tional connections in this restricted domain. As far as the intersubjective un­derstanding of descriptions is concerned, it must be concluded that one who understands the meaning of the measurement units used in the mechanical and geometric descriptions of the designed conditions cannot deny under­standing the meaning of the functional connections in the phenomenological descriptions.

Physical and phenomenological terms are introduced by means of opera­tions and transformation at the same observable scale of a state of affairs. At this scale, the concepts of mechanics and Euclidean geometry can be consid­ered an idealization of phenomena with the same name taken at the limit. For example, many straight lines can pass for two points drawn by a pencil, but as their diameter becomes smaller and smaller these straight lines will tend progressively to coincide with one another. Bozzi acknowledges that the con­cepts of Euclidean geometry are valid, namely they enable one to construct ideal figures, to join a number of points and to find the intersection point of two or more straight lines, insofar as they are defined formally by defini­tions that establish in a consistent manner their relations with other concepts. However, he remarks also that the drawn figures that are an instance of the limit at which geometric figures are taken may satisfy at the same time the definitions of elementary geometry and the phenomenological descriptions of their visual properties. He cites the work of Rubin on the phenomenological conditions in which perceptual figures, lines and points occur, which might be the perceptual equivalent of the abstract concepts of mathematics and geometry (infra §5.6.2). In such cases, the stimulus error stems from neglect­ing the epistemological difference between the abstraction of geometry and phenomenology.

On the one hand, Musatti (1958) contended that the congruence, where­by the equivalence between figures is established, derives from the analysis of which perceivable quantitative features of things are preserved through physical transformations such as displacement, rotation and reversal. At the end of this kind of abstraction, the geometric concepts are defined to denote the incorporeal figures as idealized rigid objects that are transported with­out deformations for any condition. For this reason, it is not surprising that phenomena may provide formal concepts and operations at a certain level of idealization with visualization (infra §7.4 for the converse argument of per­ceptual properties as “phenomenal indicators” for measurement). Therefore, if the concepts of mechanics and geometry are applied to the experimental conditions and the description on the grounds of what subjects are expected to see in an observable state of affairs under a particular respect turns out to be false, their univocal meaning allows one to understand the phenomenological description that turns out to be true in that particular respect.

On the other hand, phenomenological descriptions are also introduced through successive abstractions. Musatti (1958) remarks that as the demon­stration of the principle of free mobility does not imply that every object is not deformable, so the demonstration of one phenomenological law does not imply that the physical properties of the stimulation are ineffectual under every respect. The principle of free mobility through space and time implies that the idea that any object is deformable is false. Indeed, it is established by means of successive abstractions through approximations to an ideal concept. For instance, it is conceivable that, first, all solid bodies are assumed to be not deformable. Then, solid bodies can be differentiated because some of them undergo deformations in given circumstances, and a more restricted class of bodies is identified as suitable for measurement, for instance metallic bodies. Yet, a new distinction is introduced in this class if differences of temperature or pressure are observed to induce deformations on some of them. Through such observations this abstraction leads successively from the standard sample of the unit of length made of platinum to the measurement devices at micro­scale precision level. Musatti maintains that these successive abstractions through approximations to the ideal rigidity imply that if a class of bodies is observed to undergo deformations, another class must be specified as not de­formable. Otherwise, the observed deformations would not be determinable. Likewise, a phenomenological law is the result of abstractions. For example, the phenomenology of shape constancy does not mean that every form is always perceived as constant. It precludes that any appearance undergoes de­formations unless the stimulation is constant. As the observation of deforma­tions of bodies due to temperature and pressure requires specifying a new class of rigid bodies, so deformations of the stimuli on the frontal-parallel plane di­vide the potential appearances into classes of constant shapes undergoing dis­placement in the three-dimensional space and of visual deformations on the two-dimensional space. As the deformations in the stimulation are brought about smoothly along a selected dimension, one might discover that for a class of appearances in which deformation is not converted into perceptually rigid displacement, there will be another class of invariant shape (see infra §5.5). The phenomenology of shape constancy through deformations on the frontal- parallel plane is developed by means of abstractions of perceptual structures according to which the deformations are converted in displacements of con­stant shapes or not.

Source: Calì Carmelo (2017), Phenomenology of Perception: Theories and Experimental Evidence, Brill.