¹ Uexküll, J. von. “Umwelt und Innenwelt der Tiere,” 1st ed., Springer, Berlin, 1909. Also: Uexküll und Kriszat, G. “Streifzüge durch die Umwelten von Tieren und Menschen,” Springer, Berlin, 1934.

² Bertalanffy, L. von. “An Essay on the Relativity of Categories,” Phil. of Sci., Vol. 22, Oct. 1955, pp. 243–263. This supervivence ‘guarantees that there is sufficient correspondence between “appearance” and “reality” ‘… and that a certain degree of isomorphism exists between the experienced world and the “real” world’ (p. 257).

³ Cassirer, Ernst. “An Essay on Man,” 1944; 3rd ed., Yale Univ. Press, New Haven, 1945, pp. 23 ff., 33 ff.

⁴ La Barre, Weston. “The Human Animal,” Univ. of Chicago Press, 1955. La Barre is keenly aware of the integrative trend of twentieth century science (p. ix) but he does not wish to integrate in it the winged heads of cherubim (p. 70), aesthetical creatures in the hands of Murillo and other painters which, as such, have a kind of existence that has nothing to do with nutrition or circulation but that must be explained and integrated with other kinds of existence.

⁵ Jeans, Sir James. “The New Background of Science,” MacMillan, New York, 1933. The bridge of knowledge “involves ourselves as well as nature” (p. 67).

⁶ Valéry, Paul. Lecture given in 1932 and published in “Varieté IV,” Gallimard, Paris, 1938. He speaks of the “impossibilité de séparer l'observateur de la chose observée” (p. 130).

⁷ Broglie, Louis de. “Physique et Microphysique,” A. Michel, Paris, 1947, p. 150.

⁸ Uexküll, J. von. “Ideas para una Concepción Biológica del Mundo,” Bibl. de Ideas del Siglo XX, Madrid, 1922. The Spanish edition contains a foreword of José Ortega y Gasset whose philosophy of “vital reason” supports a perspectivist point of view (“I am I and my circumstance”) coherent with these manifold perceptible worlds.

⁹ Humboldt, Wilhelm von. “Gesammelte Schriften,” Berlin Acad., 1836–39. Cf. Stenzel, Julio. “Filosofía del Lenguaje,” Rev. de Occidente, Madrid, 1935, pp. 11, 13, 27–28. The main difference among languages for von Humboldt consists in their “world perspectives” (Weltansichten).

¹⁰ Sapir, Edward. “Language and Environment,” lecture to American Anthropological Assn., 1911. Publ. 1912 in “American Anthropologist” Also: “Selected Writings of E. S. in Language, Culture and Personality,” ed. David G. Mendelbaum, Univ. of Calif. Press, 1951.

¹¹ Whorf, Benjamin Lee. “Collected Papers on Metalinguistics,” Washington D. C., Foreign Service Inst., Dept. of State, 1952.

¹² Kluckhohn, Clyde. “Mirror for Man,” Whittlesey, New York, 1949.

¹³ Xenophanes, Diels-Krantz, Frag. 32. Aristotle, “Meteorologica,” Oxford Trans.: 373∗32-375∗28. Strong theoretical developments mixed very curiously in Aristotle with the empirical perception of three colors: red, yellow and green. His abstract assumptions caused Aristotle to say that the rainbow necessarily had these three colors and no others.

¹⁴ Lubbock, John, 1st Baron Avebury. “Prehistoric Times … and the Manners and Customs of Modern Savages,” Williams and Norgate, London-Edinburgh, 1865. Also: “Los Origenes de la Civilización,” ed. Albatros, Buenos Aires, 1943.

Also: Olea, Bonifacio M. de. “Ensayo Gramatical del Dialecto de los Indios Guaraúnos,” Impr. Gutenberg, Caracas, 1928. The “guarauno” “no saben distinguir bien las diversas clases de colores” (pp. 172–73). “Solo distinguen las diversas clases de flores por el color” (p. 375). But if they do not distinguish clearly among colors or flowers, they can differentiate a great number of insects and fish which are valuable for them. Also: Rodriguez Delgado, Rafael. “Estructuras Mentales y Lenguaje. El Ejemplo Guarauno. I,” Boletín Indigenista Venezolano, Caracas, (accepted for publ.).

¹⁵ The Heraclitean themes of the fundamental unity of all things, as everlasting fire that continuously changes in absolute fluence of forms and in relative oppositions, submitted to “metron” or rhythm, represents the philosophical intuition of change, later elaborated in Hegel's dialectics and in Bergson's elan vital.

Also: Spengler, Oswald. “Heráclito,” trans. by A. de Mondolfo, E-Calpe, Buenos Aires, 1947, and the foreword of Rodolfo Mondolfo on the interpretations of Heraclitus in the last half century.

¹⁶ “Source Book in Ancient Philosophy,” trans. of Diels “Die Fragmente der Vorsokratiker,” by Ch. M. Bakewell, Scribner, New York, 1907. The Parmenidean reality is a perfect and unlimited sphere, of identical weight in all its points, uncreated, indestructible, motionless, continuous and complete. It is an intuitive image, opposed to the Pythagorean discontinuity as stated by Bréhier in his “History of Philosophy.”

¹⁷ Kant, E. “Critique of Pure Reason.” The “a priori” intuition of Space and Time is for Kant an extensive quantity, but for him it is clearly differentiated from the intensive quantity of perception, this division being relevant to our study.

¹⁸ Bergson, H. “Essai sur les Données Immédiates de la Conscience,” doctoral thesis, 1889. “L'Intuition Philosophique,” lecture before the 4th Internatl. Congress of Philosophy, Bologna, 1911. “Matiére et Mémoire,” 1896. “The Introduction to a New Philosophy; Introduction à la Métaphysique,” Luce, Boston, 1912.

¹⁹ Rodriguez Delgado, Rafael. “Introducción a una Filosofía de la Era Atómica,” La Habana, 1950, pp. 237 ff. Also: “Esquema del Nuevo Pensamiento,” Rev. Venezolana de Síntesis. I, N, 1, Caracas, 1954, pp. 25–48, esp. pp. 44–45, for the complementarity between linear and scalar representations. The models for closed and open concepts were proposed for the first time in the cited paper, pp. 32–33.

²⁰ Helson, Harry. “Adaptation-level as Frame of Reference for Prediction of Psychophysical Data,” Amer. J. Psychol., LX, 1–29, 1947. “Fundamental to the theory is the assumption that effects of stimulation form a spatio-temporal configuration in which order prevails. For every excitation-response configuration there is assumed a stimulus which represents the pooled effect of all the stimuli and to which the organism may be said to be attuned or adapted” (p. 2). The adaptation-level “is a function of all the stimuli acting upon the organism at any given moment as well as in the past” (p. 3). See also: “Adaptation-level as a Basis for a Quantitative Theory of Frames of Reference,” Psychol. Rev., 55: 297–313, 1948.

²¹ Pitts, W., and McCulloch, W. S. “How We Know Universals: The Perception of Auditory and Visual Forms,” Bull. Math. Biophys., 9: 127–147, 1947.

²² Margenau, Henry. “The Competence and Limitations of Scientific Method,” J. of Operations Research Soc. of America, 3, no. 2, 1955, pp. 135–146. The term “construct” was first used by Pearson (The Grammar of Science; Part I, London, A. and C. Black, 1911) taking this use of the word from Lloyd Morgan. (Cf. Peter Caws, “The Functions of Definition in Modern Physical Science, pp. 48 and 72 of the ms). Margenau uses it also in “The Nature of Physical Reality.“

Also: See Notes 24 and 28.

²³ Cassirer, Ernst. “The Philosophy of Symbolic Forms,” trans. by R. Manheim. Preface and introduction by Charles W. Hendel, Vol. II, “Mythical Thought,” Yale Univ. Press, New Haven, 1955.

²⁴ Caws, Peter. “The Functions of Definition in Modern Physical Science,” dissertation for the degree of Ph.D., Graduate School, Yale University, 1950, unpub., pp. 48 and 52. The word “isolate” was used in somewhat different sense by Levy, H., “The Universe of Science,” New York, Century, 1933, passim. (Cf. Caws, p. 52.) The opinion of Caws: “There are many concepts out of which we do not attempt to make constructs at all, such as ‘squareness’.” (Op. cit. pp. 48–49); this fits our schema because “squareness”. is a concept of our second class, based in intuitions.

²⁵ Nicholas Krebs, Cardinal of Cusa. “De Docta Ignorantia,” 1440. Latin version of Paolo Rotta's “Classici della Filosofia Moderna,” G. Laterza, Bari, 1913, and “Nicolò Cusano” by Paolo Rotta, F. Bocca, Milano, 1942. For the practical impact of the abstract theories of Cusanus in the discovery of America see Rafael Rodriguez Delgado, “Nicolas de Cusa y el Descubrimiento de America,” Indice Literario de “El Universal,” Caracas, June 26, 1954.

²⁶ Bohr, Niels. “Quantum d'Action et Noyaux Atomiques,” Herman, Paris, 1939. Wave and corpuscle “apparaissent dans un rapport mutuel d'un genre, tout nouveau, que nous appelons complémentarité,” (p. 11). F. Gonseth has applied this principle in other fields. In “La Géometrie et le Problème de l'Espace” ed. du Griffon, Neuchâtel, 1946, he says: “en géometrie, l'aspect intuitif, l'aspect expérimental et l'aspect rationnel sont inséparables” (pp. 69–154). See also: “Déterminisme et Libre Arbitre,” entretiens presidées par F. Gonseth, ed. du Griffon, Neuchâtel, 1944.

²⁷ Richard von Mises in his “Positivism,” Brazilier, New York, 1956; (cf. his “Kleines Lehrbuch des Positivismus” 1939) distinguishes between Core Area and Area or Zone of Indeterminacy in words. Communication for him does not depend upon definitions but upon the use of linguistic expressions only within their cores of meaning, (See pp. 37–38.)

Paul Weiss (“The Real Art Object.” Rev. of Philosophy and Phenomenological Research, 16: 341–352, 1956) distinguishes between “the nucleus and the penumbrum of a being.” See also his “Reality,” Princeton Univ. Press, 1938.

Henry Margenau notices the “penumbra of meaning” of concepts (“The Nature of Physical Reality,” New York, McGraw Hill, 1950, p. 57), his “construct” being, therefore, a means for avoiding it.

²⁸ The Lewinian model that represents the individual as a dimensionless dot in a topological life-space would be a particular and extreme case of our model of ideas in which the idea that the subject has of itself is not explicit and the ideas about its environment are projected into a psychological (phenomenological) field. The model is a good picto-graphic representation of the imaginary projection of ideas in the case of motor reactions in an hodological field in relationship with a goal. But it suffers a distortion of perspective and its use is limited. Lewin, K. “A Dynamic Theory of Personality,” New York, McGraw Hill, 1935. “Principles of Topological Psychology,” Id., 1936. “Field Theory in Social Science,” New York, Harper, 1951.

Also: Floyd H. Allport, “Theories of Perception and the Concept of Structure,” New York, Wiley, 1955, pp. 148 ff.

²⁹ Tolman, E. C. “The Psychology of Social Learning,” J. Social Issues, Supp. 3, 1949, speaks of “cognitive maps.” Wallace, Anthony F. C., in “Mazeway Resynthesis,” Transact. N. Y. Acad. Sc, 18, May 1956, pp. 626–638, compares his “mazeway” or total complex of generalizations about the body, surrounding things “and sometimes the brain itself” to “a map of a gigantic maze.” But the concrete spots for mapping would be defined as actual ideas if we wish to give a factual sense to this abstract map.

³⁰ Rodriguez Delgado, Rafael. “Bioffsica de las Ideas. Estructuras Mentales,” Rev. Nac. de Cultura., no. 106–107, Caracas, 1954, pp. 148–157.

³¹ Kretschmer, Ernst. “Physique and Character,” trans. from 2nd German ed. by W. J. H. Sprott, New York, Harcourt, 1926; London, 1936, 2nd ed. rev.

³² Dilthey, Wilhelm. Gesammelte Schriften. Leipzig und Berlin 1914–36, 9 vols. 5–6 Bd., “Einleitung in die Philosophie des Lebens,” 1924. 8 Bd., “Weltanschauungslehre: Abhandlungen zur Philosophie der Philosophie,” 1931.

Also: Jung, in “Psychological Types,” (trans. by H. Godwin Baynes, Harcourt, New York, 1926) distinguishes between “general attitude types” as introverted and extra-verted, and “function-types.” The latter are named thinking, feeling, sensation and intuitive types (pp. 14 and 412). Thinking and feeling types are considered as “rational” and characterized by “the supremacy of the reasoning and the judging functions.” Sensation and intuition types are classed as “irrational” because their “commissions and omissions” are based “upon the absolute intensity of perception” (p. 468). Notwithstanding, he thinks that the intellect “proves incapable of formulating the real nature of feeling in abstract terms since thinking belongs to a category quite incommensurable with feeling” (p. 535). It seems, then, contradictory to classify them as rational and opposed to irrational sensation and intuition types.

³³ Spranger, Eduard. “Lebensformen: Geistes-wissenschaftlichen Psychologie und Ethik der Persönlichkeit,” Halle, Saale, M. Niemeyer, 1927. “Types of Men; the Psy, chology and Ethics of Personality,” trans. by P. J. W. Pigors, Halle, Salle, M. Niemeyer-1928.

³⁴ See Henri Poincaré “The Value of Science” in “The Foundations of Science,” trans. by G. B. Halsted, The Science Press, New York, 1929. He finds among mathematicians “two opposite tendencies, or rather two entirely different kinds of minds…” “It is the very nature of their mind which makes them logicians or intuitionalists” (p. 210). “The two sorts of minds are equally necessary for the progress of science; both … have achieved great things that others could not have done…” “Analysis and synthesis have then both their legitimate roles” (p. 212).