Science may benefit from aesthetically pleasing and intellectually stimulating
mathematical metaphors. To make them into mathematical theories, however, one has to
complement them by links to well-defined theoretical primitives in turn linked to
well-defined empirical procedures and observable phenomena. Rudolph’s
(2006) mathematical metaphors for psychological time are fascinating, but the
mathematical rigor with which they can be described does not compensate for the
conspicuous lack of both theoretical and operational clarity in the notions these
metaphors are supposed to pertain to, including the very notion of psychological time
Aczèl, J.
(1987). A short course of functional equations: Based upon
recent applications to the social and behavioral sciences.
Dordrecht: Reidel
.
2.
Dzhafarov, E. N.
(1992).
Visual kinematics III: Transformation of spatiotemporal coordinates in motion
. Journal of Mathematical Psychology, 36,
524-546
.
3.
Dzhafarov E. N.
(2001). Fechnerian psychophysics. In
N. J. Smelser
&
P. B. Baltes
(Eds.), International encyclopedia of the social and behavioral
sciences (Vol. 8, pp. 5437-5440).
New York: Pergamon
.
4.
Dzhafarov, E. N.
(2002).
Multidimensional Fechnerian scaling: Pairwise comparisons, regular
minimality, and nonconstant self-similarity
. Journal of Mathematical Psychology, 46,
583-608
.
5.
Dzhafarov, E. N.
(2003a).
Selective influence through conditional independence
. Psychometrika, 68,
7-26
.
6.
Dzhafarov, E. N.
(2003b).
Thurstonian-type representations for ‘same-different’
discriminations: Deterministic decisions and independent images
. Journal of Mathematical Psychology, 47,
208-228
.
7.
Dzhafarov, E. N.
(2003c).
Thurstonian-type representations for ‘same-different’
discriminations: Probabilistic decisions and interdependent images
. Journal of Mathematical Psychology, 47,
229-243
.
8.
Dzhafarov, E. N.
, &
Colonius, H.
(1999).
Fechnerian metrics in unidimensional and multidimensional stimulus spaces
. Psychonomic Bulletin and Review, 6,
239-268
.
9.
Dzhafarov, E. N.
, &
Colonius, H.
(2001).
Multidimensional Fechnerian scaling: Basics
. Journal of Mathematical Psychology, 45,
670-719
.
10.
Dzhafarov, E. N.
, &
Colonius, H.
(2005a).
Psychophysics without physics: A purely psychological theory of Fechnerian
Scaling in continuous stimulus spaces
. Journal of Mathematical Psychology, 49,
1-50
.
11.
Dzhafarov, E. N.
, &
Colonius, H.
(2005b).
Psychophysics without physics: Extension of Fechnerian Scaling from
continuous to discrete and discrete-continuous stimulus spaces
. Journal of Mathematical Psychology, 49,
125-141
.
12.
Fechner, G. T.
(1860). Elemente der Psychophysik[Elements of
psychophysics].
Leipzig: Breitkopf & Härtel
.
13.
Fechner G. T.
(1877). In Sachen der Psychophysik[In the matter of
psychophysics].
Lepizig: Breitkopf & Härtel
.
14.
Helmholtz, H. von
. (1891).
Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im
Farbensystem [An attempt at a generalized application of Fechner’s
Law to the color system]
. Zeitschrift für die Psychologie und die Physiologie der
Sinnesorgane, 2,
1-30
.
15.
Herbart, J. F.
(1890). Psychologie als Wissenschaft [Psychology as
science]. In
K. Kehrbach
&
O. Flügel
(Eds.), Jon. Fr. Herbart’s sämtliche Werke in
chronologischer Reihenfolge (Vol. 5, pp. 177-434).
Langensalza: Hermann Beyer und Söhne
. (Original work published 1824.)
16.
Krantz, D. H
,
Luce, R. D.
,
Suppes, P.
, &
Tversky, A.
(1971). Foundations of measurement: Vol. 1. Additive and
polynomial representations.
San Diego, CA: Academic Press
.
17.
Krantz, D. H.
,
Luce, R. D.
,
Suppes, P.
, &
Tversky, A.
(1989). Foundations of measurement: Vol. 2. Geometrical,
threshold and probabilistic representations.
San Diego, CA: Academic Press
.
18.
Krantz, D. H.
,
Luce, R. D.
,
Suppes, P.
, &
Tversky, A.
(1990). Foundations of measurement: Vol. 3. Representation,
axiomatization, and invariance.
San Diego, CA: Academic Press
.
19.
Levin, D.
(2000).
A differential geometric description of the relationships among perceptions
. Journal of Mathematical Psychology, 44,
241-284
.
20.
Luce, R. D.
(1956).
Semiorders and a theory of utility discrimination
. Econometrica, 24,
178-191
.
21.
Luce, R. D.
, 2002.
A psychophysical theory of intensity proportions, joint presentations, and matches
. Psychological Review, 109,
520-532
.
22.
Luce, R. D.
, 2004.
Symmetric and asymmmetric matching of joint presentations
. Psychological Review, 111,
446-454
.
23.
Rudolph, L.
(2006).
The fullness of time
. Culture & Psychology, 12,
169-204
.
24.
Schrödinger, E. von
. (1920).
Farbenmetrik [Color metrics]
. Zeitschrift für Physik, 12,
459-466
.
25.
Townsend, J. T.
,
Solomon, B.
, &
Spencer-Smith, J. B.
(2001). The perfect Gestalt: Infinite dimensional
Riemannian face spaces and other aspects of face cognition. In
M. J. Wenger
&
J. T. Townsend
(Eds.), Computational, geometric and process issues in facial cognition:
Progress and challenges (pp. 39-82).
Mahwah, NJ: Erlbaum
.
26.
Whitrow, G. J.
(1980). The natural philosophy of time.
Oxford: Clarendon Press
.
27.
Wyszecki, G.
, &
Stiles W. S.
(1982). Color science: Concepts and methods, quantitative
data and formulae.
New York: Wiley
.
