The Sensation and the - Ricerca sull'intelligenza artificiale specializzata al MIT

The Sensation and the
Stimulus: Psychophysics
and the Prehistory of
the Marburg School

Marco Giovanelli
University of Tübingen

This paper analyzes the role played by Fechner’s psychophysics—the new science
meant to measure sensation as a function of the stimulus—in the development of
Marburg Neo-Kantianism. It will show how Cohen, in the early 1870s, In
order to make sense of Kant’s obscure principle of the Anticipations of Perception,
resorted to psychophysics’ parlance of the relation between stimulus and sensation.
By the end of the decade, Cohen’s remarks encouraged the early ‘Cohen circle’
(Stadler, Elsas, Müller) to pursue what were often sophisticated analyses of
the problem of the measurability of sensation. This paper argues that in reaction
to these contributions, Cohen shifted his interests towards the history of the in-
ﬁnitesimal calculus in his controversial 1883 monograph, Das Princip der
Inﬁnitesimal-Methode. This book, with its characteristic amalgam of tran-
scendental philosophy and history of science, paved the way to what, around
1900, would become the “Marburg school” (Natorp, Cassirer, Görland and
others). Tuttavia, it also interrupted a promising discussion in Marburg on the
problem of measurability in science.

introduzione

1.
In 1912, Ernst Cassirer (1912) contributed to the special issue of the Kant-
Studien that honored Hermann Cohen’s retirement—his mentor and teacher,
and the recognized founding father of the so-called ‘Marburg school’ of
Neo-Kantianism (Poma [1989] 1997). In the context of an otherwise rather
conventional presentation of Cohen’s interpretation of Kant, Cassirer made
a remark that is initially surprising. It is “anything but accurate,” he wrote,
to regard Cohen’s philosophy as focused “exclusively on the mathematical

I would like to thank Michael Heidelberger for many useful suggestions concerning the
ﬁrst draft of the manuscript.

Perspectives on Science 2017, vol. 25, NO. 3
© 2017 by The Massachusetts Institute of Technology

doi:10.1162/POSC_a_00244

287

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

288

Sensation and Stimulus

theory of nature," (Cassirer 1912, P. 256) as is usually done. A reconstruc-
tion of the genesis of Cohen’s thought, Cassirer continued, would already
refute this interpretation. Actually, “[T]he conditions of the problem, as they
were presented to Cohen at that time [die Cohen vorfand], lay at least as
much in the critique of physiology as in the critique of physics” (1912,
P. 256).1 From the “concept of sensation,” Cassirer went on, Cohen was ini-
tially led to investigate “the [concept] of ‘stimulus’," (1912, P. 256) Quale
was regarded only in the second instance as a possible object of physics. IO
suspect that this allusion to the relation between sensation and stimulus,
made only in passing, might escape the attention of most readers. Tuttavia,
Cassirer alluded to an over ten year debate initiated by Cohen and continued
by a small group of early sympathizers—a little “Cohen circle” as it might
be called, to distinguish it from what only later would become the “Marburg
school.” Surprisingly, this debate has been completely neglected by histo-
rians of Neo-Kantianism, despite being an important line in the develop-
ment of the history of 19th century philosophy and science.

At the beginning of the 1860s, the nearly sixty-year-old physicist
Gustav Theodor Fechner (1860) claimed to have established a new science,
which he called psychophysics. Psychophysics sought to measure sensation on
the basis of its functional dependency on the “stimulus,” and, at the same
time, to present in rigorous form the problem of the relation between the
mental and the physical. Starting from Ernst Heinrich Weber’s experimental
risultati (Weber 1834, 1846), Fechner suggested that inﬁnitesimal increments
of sensation were directly proportional to inﬁnitesimal increments in stimu-
lus and inversely proportional to the amount of the original stimulus. Così,
the function relating sensation to the stimulus would be logarithmic (Fechner
1860, vol. 2, pag. 9–14). In the successive decades, a debate was sparked
among philosophers, psychologists, physicists, and mathematicians over
whether sensations could be measured at all (Heidelberger [1993] 2004;
Michell 1999). Many, if not most, of the writings of the members of the
Cohen circle—nearly forgotten ﬁgures like August Stadler, Adolf Elsas and
Ferdinand August Müller—were meant to contribute to this debate. These
sometimes-sophisticated analyses were in turn inspired by Cohen’s early
attempt to use psychophysics’ conceptual tools to make sense of some of
Kant’s obscure remarks about the intensive magnitude of sensation in the
Kritik der reinen Vernunft.

Michael Heidelberger, in his classic 1993 Fechner monograph (Heidelberger
[1993] 2004, Ch. 6), was the ﬁrst to take the Marburg debate on psycho-
physics into consideration and to suggest its importance for the formation
of the early Cohen circle (Heidelberger [1993] 2004, P. 124f.). Tuttavia,

1. Henceforth the emphasis in the original has been rendered as italics.

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

Perspectives on Science

289

Heidelberger’s contribution, which is “hidden” in a monumental investiga-
tion of Fechner’s work and its reception, seems to have completely escaped
the attention of historians of philosophy. The aim of this paper is to ﬁll what
I think is a serious gap in the historical literature on Neo-Kantianism,
which has recently been enjoying a renewed interest, especially in the
English-speaking world (Beiser 2014; Makkreel and Luft 2009; Luft 2015).
Elsewhere (Giovanelli 2016), I have analyzed in detail the role played by
Cohen’s 1883 “unsuccessful” book on the history of the inﬁnitesimal method,
Das Princip der Inﬁnitesimal-Methode (Cohen 1883), in shaping some of the
fundamental tenets of the school (in particular the intimate relation between
transcendental philosophy and the history of science). In the present paper,
I aim to show that it was the early Marburg debate on psychophysics that,
in a sort of heterogony of ends, prompted Cohen’s interest in the history of
higher analysis. This paper is of course very much indebted to Heidelberger’s
path-breaking contributions. Tuttavia, by considering the Marburg debate
on psychophysics from the perspective of the history of the Marburg school,
rather than of Fechner’s reception, I hope I will throw a different light on the
matter. In particular, in my opinion, there is a missing piece in Heidelberger’s
reconstruction of the puzzle: Kant’s principle of the Anticipations of
Perception (UN, pag. 166–176; B, pag. 207–218). In my view, this is the key
element to understanding the entire debate. The Marburg interest in psycho-
physics arose from Cohen’s early attempt at providing a psychophysical inter-
pretation of Kant’s principle, and then faded away when Cohen became
convinced that this attempt had failed. It was at this point that he ventured
himself into a new interpretation exposed in Das Princip der Inﬁnitesimal-
Methode. It was the stance towards Cohen’s “paradigm switch” that deter-
mined the Cohen circle’s internal dynamics, Quale, as we shall see, was more
turbulent than it appears in Heidelberger’s presentation.

The narrative structure of the paper will be as follows. In the early
1870S, Cohen, in order to make sense of Kant’s obscure principle of the
Anticipations of Perception, initially resorted to psychophysics’ parlance of
the relation between stimulus and sensation (sec. 1). The few remarks that
Cohen made on the subject encouraged his early followers (Stadler, Elsas
and Müller) to pursue an often-technical analysis of Fechner’s psycho-
physics (sec. 2). In turn, Cohen, inspired by these critiques, realized that
psychophysics was not the proper framework for understanding Kant’s
Anticipations of Perception, Quale, he claimed, should be interpreted
against the background of the history of the inﬁnitesimal calculus (sec. 3).
On the one hand, Cohen’s inﬁnitesimal turn divided the early Cohen circle
into those ready to follow his new course and those who were taken aback
by his unorthodox approach to the calculus (sec. 4). D'altra parte,
Cohen’s Das Princip der Inﬁnitesimal-Methode paved the way for the Marburg

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

290

Sensation and Stimulus

school’s interest in the historical ﬁeri of science (Natorp 1912b). At the same
time, Tuttavia, this new course abruptly interrupted a promising discussion
in Marburg on the issue of “measurability” in science, a discussion that
Cohen himself had somehow unwittingly inspired (sec. 5).

2. Anticipations of Perception and Psychophysics: Cohen and Stadler
In the ﬁrst edition of Kants Theorie der Erfahrung (Cohen 1871), his ﬁrst
Kant monograph, Cohen dedicates several lines to the principle of Antici-
pations of Perception, the second of the synthetic principles enumerated by
Kant in his Kritik der reinen Vernunft. In the second 1787 edition of the
Kritik, the principle somewhat cryptically attributes an intensive magni-
tude to the realitas phaenomenon—the “real” that is the object of sensation.
In the ﬁrst 1781 edition the wording was slightly different. Kant attri-
butes an intensive magnitude to the sensation and to the real that corre-
sponds to it (UN, P. 166). Noticing the difference between these two
formulations of the principle, Cohen commented: “What is the real as an
object of simple sensation, as an intensive quantity, in antithesis to an
extensive?": “it is the unity of the stimulus in which we objectify sensation”
(1871, pag. 215–16). Kant of course did not use the expression “unity of
the stimulus” (1871, P. 217). Tuttavia, Cohen was convinced that Kant’s
insistence in the second edition of his opus magnus on the “real” that is the
object of sensation, rather than on sensation itself, was motivated by the
need to ﬁnd an objective correlate of sensation: “the intention […] of clar-
ifying the real as a simple unity of the objectiﬁed stimulus seems to me to
be the reason for modifying this afﬁrmation in the second edition” (1871,
P. 216).

The language of the “physiology of the senses” used by Cohen (1871, P. 215)
might not mean much to today’s Kant scholar. In contrasto, Cohen’s insight
was enormously inﬂuential among his early acolytes, a point that is rarely
mentioned in the literature. Cohen’s readers at the time probably imme-
diately understood that Cohen’s parlance was a reference to Fechner’s con-
troversial attempt to measure the intensive magnitude of sensation in terms
of its functional relation to the stimulus (Fechner 1860). Similar wordings
can be found in Cohen’s previous “Herbartian” writings (1868, P. 420).
Tuttavia, Cohen might have learned about this issue from Friedrich Albert
Lange’s Geschichte des Materialismus (Lange 1866). Lange, by discussing the
relation between form and content in Kant’s philosophy, mentions Fechner’s
logarithmic formula for the relation between the sensation as the internal
content of consciousness, and the “external (physical) stimulus” (Lange 1866,
P. 251).

From 1870 A 1872 Lange was professor of inductive philosophy in
Zurich. It was one of his Zurich students, August Stadler (1850–1910), who

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

Perspectives on Science

291

took up Cohen’s insights a few years later. Lange himself had recommended
Stadler to Cohen, the latter of which being an unknown Privatdozent in Berlin
at the time (cf. Cohen 1910a). In Berlin, Stadler broadened his scientiﬁc
outlook by following the lectures of some of the great scientists of his time:
Hermann von Helmholtz, Emil Du Bois Reymond and Ernst Engel; in addi-
zione, he attended Cohen’s small seminar on the Kritik der reinen Vernunft
(Cohen to Lange, May 14, 1873; Lange 1968, P. 372). This seminar deeply
inﬂuenced him. At the end of 1873, Stadler ﬁnished writing a short but
inﬂuential monograph on Kant’s teleology (Stadler 1874), and by October
1875 had already ﬁnished a second book, in which he developed Cohen’s
insight on the transcendental meaning of the a priori (Stadler 1876). Cohen,
who in the meantime had succeeded the prematurely deceased Lange in
Marburg, immediately elaborated on Stadler’s contributions in his 1876/77
book on Kant’s ethics (Cohen 1877).

Nel suo 1876 book, Stadler took an original stance towards Kant’s Antici-
pations of Perception. Stadler, like Cohen, also read Kant’s second principle
as a claim about the psychology of sensation. Tuttavia, Stadler was not con-
vinced of the success of Kant’s attempt to deduce a priori the continuity of
the degree of sensation. Così, he preferred to reformulate Kant’s second
principle as what he called the “principle of material connection” (Prinzip
der materiellen Verknüpfung) (Stadler 1876, Ch. VIII). The principle indicates
as an a priori condition the weaker claim that “all sensations must possess
an intensive magnitude” (Stadler 1876, P. 65). All sensations must be “over
the zero-point of consciousness” (Stadler 1876, P. 65) (that is there are
no negative sensations), otherwise the succession of sensations would be
interrupted; as a consequence, the unity and identity of consciousness
would be compromised and no objectively valid experience would be pos-
sible. “Beyond this,” Stadler pointed out, Kant took a further step “that I
cannot follow” (1876, P. 145). Kant claimed that the increase and decrease
of the intensive magnitude of sensation is continuous. Stadler “tried in vain
to ﬁnd a transcendental reason” for this claim, but he had to conclude that
“the Kritik leaves it unproven” (1876, P. 145). Whether or not the degree of
sensation varies continuously can at most be decided a posteriori, “through
the investigation of the single sensations” (1876, P. 72). Tuttavia, Stadler
would soon show that empirical investigations about sensations, far from
supporting Kant’s claim, actually refuted it.

At the time, nearly two decades after the publication of the Elemente der
Psychophysik, the debate about Fechner’s result, that physical and subjective
intensity are related by a logarithmic function, was alive as ever. In 1877,
Fechner published In Sachen der Psychophysik (1877), in which he defended
himself from his numerous and often renowned critics: Hermann von
Helmholtz (1867), Ernst Mach (1863), Joseph Plateau (1872), Joseph

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

292

Sensation and Stimulus

Delbœuf (1873), Ewald Hering (1875), Franz Brentano (1874) and others.
Fechner’s attempt to measure sensation was based precisely on the assump-
tion that the degree of sensation varies continuously along with the con-
tinuous variation of the stimulus. It was this assumption that Stadler
wanted to challenge, Quale, he claimed, Fechner’s opponents had not called
into question. In February 1878, Stadler ﬁnished a brief paper entitled
“Über die Ableitung des Psychophysischen Gesetzes,” which was published
in Philosophische Monatshefte in the same year (Stadler 1878). In contrast to,
per esempio., Delbœuf (1878), Stadler did not want to deny the quantitative aspect
of sensation, but rather to challenge the empirical adequacy of Fechner’s
logarithmic formula. We shall roughly follow Stadler’s derivation of the lat-
ter. Although Stadler’s procedure is similar though not identical to Fechner’s,
it remained the model of similar derivations presented by the Marburg group.
Throughout this paper, I will follow Stadler (who in turn follows Fechner
himself ) and indicate the variable corresponding to sensation with γ, E
that corresponding to the stimulus with β.

Initially Fechner introduced his formula speculatively in the second
Appendix of his Zend-Avesta (Fechner 1851, pag. 373–86; cf. Scheerer
1987). Tuttavia, Dopo, in his Elemente der Psychophysik (Fechner 1860), he
presented it as based on Weber’s experimental results, in particular those
concerning the sensation of weight and touch (Weber 1834, 1846). On
the basis of numerous trials on pairwise comparisons of weights, Weber
found that subjects do not perceive the absolute difference between them
but the ratio of difference to the initial weight. If a one-ounce weight is
placed in our hand, we can easily perceive it; Tuttavia, if two weights of,
Dire, 32 E 33 ounces are compared, we do not perceive the one-ounce dif-
ference between them; the ratio 1/33 is too small to be discerned. The same
can be said for the difference between eye-estimated lengths, sound pitches,
eccetera. Weber’s ﬁndings can be summarized in the formula:

Δβ
β

¼ c

(io)

The constant c depends on the different senses (touch, hearing, eccetera). In this
formulation of Weber’s results, there is no mention of sensation. In order to
establish a functional relation between sensation and stimulus, Fechner
made a further assumption. He postulated that the “difference sensation”
(Unterschiedsemempﬁndung) or “contrast sensation” (Contrastempﬁndung)—which
arises when the difference of two stimuli becomes “just noticeable”—is
proportional to the “sensation difference” (Empﬁndungsunterschied), the dif-
ference between the two corresponding sensations (Fechner 1860, vol. 2,

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

Perspectives on Science

293

P. 85). This assumption is nothing but the psychophysical analogon of the
deﬁnition of equal temperature differences in terms of equal volumes of
expansion in the theory of heat (Tannery 1875a, 1875B). To put it more
precisely: if the just-noticeable stimulus-increase with respect to the original
stimulus is constant Δβ / β = c, then the corresponding “difference sensation”
is constant Δγ = c0. Setting c = kc0, the “just-noticeable differences” between
stimuli (j.n.d.) might be used as a unit of measurement; the number of
sensation differences Δγ between two stimuli is k times the number of j.n.d.
Δβ / β between them. In this way one can write Weber’s experimental ﬁnd-
ings in the form of a functional relation between stimulus and sensation:

Δγ ¼ k

Δβ

β where k ¼ c 0

(ii)

Notice that this equation does not appear in Fechner’s writings (Vedere
below in sec. 3). In Stadler’s reconstruction, Tuttavia, Fechner started from
this equation and postulated that it is valid for every change of sensation,
however small; questo è, it is also valid for the so-called “unconscious sen-
sations” that are caused by a stimulus which is not sufﬁcient to raise them
to consciousness (per esempio., the increase from 32 A 33 ounces). Fechner ap-
pealed to what he called an “a priori valid mathematical auxiliary principle
[Hülfsprincip]" (Fechner 1860, P. 40): what is true for ﬁnite differences
ought to also be true in the limit. Then he substituted the ﬁnite increments
Δβ and Δγ with the inﬁnitesimally small increments dβ and dγ. The simple
relation (ii) between two units of measure turned into an informative dif-
ferential equation, the so-called Fundamentalformel:

dγ ¼ k

dβ
β

(iii)

The next step was to derive an integral formula containing an expression
for the measurement of sensation. This is a matter of more or less elementary
differential and integral calculus. One ﬁrst calculates the indeﬁnite integral
of eq. (iii) (cioè., without upper and lower limits):

dγ ¼

dβ
β

þ Const

(iv)

By consulting a table of integrals one can easily ﬁnd that the integral of
a fraction whose numerator is the differential of the denominator is the

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

294

Sensation and Stimulus

natural logarithm (questo è, a logarithm with base e = 2.7182 …) del
denominator:

γ ¼ k lnβ þ Const

(v)

To eliminate the constant of integration one evaluates the integral be-
tween deﬁnite limits. Fechner chooses as the lower limit γ = 0, dove il
sensation begins (that is it becomes conscious) and disappears and the
correspondent β0, questo è, the threshold of stimulus below which there is
no perception:

Z γ

γ
0

dγ ¼

Z β

dβ
β

(vi)

D
o
w
N
o
UN
D
e
D

F
R
o
M
H

T
T

:
/
/

D
io
R
e
C
T
.

io
T
.

The sensation γ—or more precisely the difference of two sensations γ0 − γ
which corresponds to the differences of two stimuli β − β0—can be measured
as the deﬁnite integral, questo è, as a summation of inﬁnitesimally small
sensation increments dγ which corresponds to the summation of inﬁnitely
small stimuli increments dβ. According to eq. (v) this is of course equivalent
to γ − γ0 = lnβ − lnβ0. For a well-known logarithmic identity, the differ-
ence of the logarithms of two numbers is the logarithm of their ratio. Così
Fechner’s ﬁnal equation is the following:

γ ¼ k ln

β
β
0

(vii)

Sensation γ is not simply the logarithm of the stimulus β, but of the
latter expressed in terms of its threshold value β0, the ﬁrst unit stimulus,
from which the zero point where the sensation begins and disappears
(Fechner 1860, vol. 2, P. 13). After the initial value (β0) and the unit of
measurement (β0 = 1) have been speciﬁed, sensation can then be measured
as an accumulation of j.n.d. Così, Fechner’s formula is both a law of nature
and a measurement formula at the same time (cf. Heidelberger [1993]
2004, P. 206; Heidelberger 1993).

After roughly presenting Fechner’s derivation in this way, Stadler pointed
to a simple but serious conceptual difﬁculty that it entails. According to
Weber’s ﬁndings, if one imagines the stimulus gradually increasing from
a weight of, Dire, 32 ounces to twice that, then not all of the inﬁnite possible
values between 32 E 64 ounces can be perceived, rather only those for

e
D
tu
P
o
S
C
/
UN
R
T
io
C
e
–
P
D

F
/

2
5
3
2
8
7
1
7
9
0
3
0
8
P
o
S
C
_
UN
_
0
0
2
4
4
P
D

B
sì
G
tu
e
S
T

o
N
0
7
S
e
P
e
M
B
e
R
2
0
2
3

Perspectives on Science

295

which the eq. (io) or Δβ = cβ holds. We can perceive the difference between,
Dire, 32 E 42 ounces, but not between 32 E 33 ounces: “not every Δβ
corresponds to a variation of the sensation, rather Δγ remains zero for all values >
c ⋅ β ” (Stadler 1878, P. 219). When Fechner, relying on his mathematical
auxiliary principle, introduced eq. (iii)—that is, he substituted ﬁnite differ-
ences Δβ and Δγ with inﬁnitesimally small ones dβ and dγ—he contra-
dicted Weber’s results rather than building on them.

Of course this objection is valid only if one equates sensation with con-
scious sensations, as Stadler explicitly does. In this case one can claim that
Weber’s experiments have shown that no sensation change Δγ corresponds
to a very small stimulus variation Δβ = dβ: “Weber’s law is an empirical
law and it is valid only for the real, empirically given sensations, and not
so-called unconscious ones” (Stadler 1878, P. 220). As a consequence, we
are not allowed to “represent the reciprocal correlation of the stimulus and
of the sensation through a continuous function or a curve” (1878, P. 220).
In Fechner’s conception, stimulus and sensation are related by the natural
β
exponential function γ = e
. Such a function can be plotted on a Cartesian
coordinate system by a smooth curve (looking like half a parabola) Quale
increases dramatically over its domain, since γ increases faster as β increases:
equal units on a sensation scale correspond to progressively greater units
on an external physical scale. Tuttavia, according to Weber’s ﬁndings, if
we represent a small variation of the stimulus (Δβ < c) on the x-axis, then no variation of the sensation (Δγ) would correspond on the y-axis: “The sensation progression,” in Stadler’s words, “then has the form of a stair with steps of increasing width” (1878, p. 220). “The essence of the relation between Δβ and Δγ,” as Stadler summa- rized his critique of psychophysics, “is discontinuity. The logarithmic curves, with which one attempts to represent the psycho-physical law, lack empirical truth” (1878, p. 223). However one might judge this technical result, its philosophical implications seem hard to fathom at ﬁrst. How- ever, the philosophical intent of Stadler’s critique of Fechner became more perspicuous in a paper Stadler ﬁnished in June of 1880 and published in the same year in the Philosophische Monatshefte, “Das Gesetz der Stetigkeit bei Kant” (Stadler 1880). Stadler showed that Kant had an ambiguous attitude on the question of the continuity of the intensive magnitude. In the Anticipations of Perception, Kant claims that the intensive magnitude of sensation is continuous only in the weak sense, that between every degree and nothing, one can always think of another arbitrary possible smaller degree. Nothing can be said about the continuous increasing or decreasing of the variation of degree, which is an empirical question (B, pp. 212–13). However, in the Beweis of the second Analogy of Experience, Kant seems to defend the stronger claim, that the intensive magnitude of sensation l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 296 Sensation and Stimulus arises from 0 to a certain degree in a continuous manner, running through all actual intermediate degrees (B, pp. 255–56). At ﬁrst sight, Stadler’s paper seems to lack theoretical ambition, and it is based on a detailed textual analysis of Kant’s passages on continuity. However, though “only in passing,” he does note “that modern psychology has not offered any reason to reshape Kant’s concept of the degree of sen- sation” (Stadler 1880, p. 585). Modern psychophysics does not permit any a posteriori demonstration of what Kant attempted in vain to demonstrate a priori. Psychophysics postulates that the process of the emergence of a sensation runs through all intermediate degrees, even if this passage is so rapid that it remains unnoticed. However—and this was the result of Stadler’s 1878 paper—this postulate, far from being valid a priori as Fechner claimed, can probably be proven wrong a posteriori: “as far as intensity is concerned, in my opinion, psycho-physical research has instead shown the discontinuity in psychical transition in relation to the continuous growth of the stimulus” (Stadler 1880, pp. 585–6). Experience seems to show that the stimulus, e.g., a weight, can be increased to a certain degree without causing any change in the corresponding conscious sensation. Cohen seems to have immediately appreciated Stadler’s result. In a letter to Stadler on February 24, 1881 Cohen claimed that he now “fully agreed” with his “‘Stetigkeit’” (that is, Stadler 1880). However, he added: “I have out- lined a formulation of the Anticipation in which your previous concerns seem to be acknowledged and at the same time eliminated” (Cohen to Stadler, February 24, 1881; Cohen 2015, pp. 128–9; my emphasis). This only re- cently published letter is central to my account. It shows that a fundamental “paradigm shift” happened at this point. On the one hand, Cohen recognized that Stadler’s objections were justiﬁed against Kant’s a priori deduction of the continuity of the degree of sensation. On the other hand, one can surmise that at that time Cohen probably started to realize that Kant’s Anticipations of Perception should be understood from a quite different perspective, out- side the framework of psychophysics. We do not have further information on what exactly Cohen had in mind. His next letter to Stadler is dated months later in October and includes the ﬁrst mention of “our new Privatdozent Dr. Natorp”; in particular, Cohen announced the latter’s new writing “which is thorough a[nd] clear” (Cohen to Stadler, October 30, 1881; Cohen 2015, p. 131). Paul Natorp’s habilitation thesis on Descartes (later published as Natorp 1882a) had just been accepted and he had given his inaugural lecture on Leibniz a few days earlier (Natorp 1881). Natorp’s early works in Marburg revealed that Cohen was reorienting the interests of his circle towards the “prehistory of criticism” and its connection to the his- tory of science (Natorp 1882b, 1882c). In particular, Cohen might have al- ready realized that the Anticipations of Perception should be understood not l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 297 in the context of the epistemology of empirical psychology, but by investi- gating the historical roots of Kant’s principle in the development of modern mathematics and physics. 3. Elsas, Müller and the Early Cohen Circle in Marburg That Cohen initially attempted to interpret Kant’s second principle against the background of Fechner’s psychophysics might surprise today’s Kant scholars. However, this approach was part of a vast research program that Cohen put forward just after he succeeded the deceased Lange in Marburg, becoming the ﬁrst Jewish philosophy full professor at a German university. According to the guideline of the Prussian Kultusministerium, the philosophy faculty in Marburg used to offer scientiﬁc Preisaufgaben (essay prizes) with the intent of supporting students (Sieg 1994, p. 130). The call for papers launched by Cohen for the 1880/1881 prize (cf. Holzhey 1986, vol.1, p. 381) required the candidate to “[e]xplain Kant’s mathematical principles”; the ﬁrst principle, the Axioms of Intuition with reference to “the new science of space,” that is, non-Euclidean geometry; “the second principle,” the Antici- pations of Perception, “should be evaluated with respect to the problem of psycho- physics” (cited in Holzhey 1986, vol.1, p. 382; my emphasis). The recipient of the prize was the physicist Adolf Elsas (1855–1895), who, after his dissertation written under Helmholtz’s guidance in Berlin (Elsas 1881), was working as an assistant at the Marburg physical-mathematical institute. In his referee report, Cohen praised Elsas’ secure knowledge of Kant’s philosophy (Sieg 1994, p. 131). Concerning the treatment of Kant’s ﬁrst principle, Cohen appreciated Elsas’ ability to grasp the philosophical implications of “the Riemmann-Helmholtz speculations” beyond technicali- ties; with regard to the second principle, Cohen recognized that Elsas pre- sented “the correct point of view for the appreciation of the psychophysical problem” (Holzhey 1986, p. 23n86). The question of the measurability of psychical magnitudes was hotly debated among philosophers at that time. An inﬂuential scholar like the great historian of Greek philosophy (and proto-neo-Kantian) Eduard Zeller, had just published a discussion of the issue in the proceedings of the Prussian Academy of Science (Zeller 1881). The dissertation of Ferdinand August Müller (1858–1888), of which Cohen was the main supervisor, further tes- tiﬁes that this was one of the main philosophical concerns in Marburg. In his Gutachten, Cohen emphasized that, after Stadler’s technical objection against Fechner’s law, Müller was able to show “that in the very problem of estab- lishing a functional relation between stimulus and sensation there is an epistemological mistake” (Holzhey 1986, vol.1, p. 22). In October 1881, Müller ﬁnished transforming his dissertation into the booklet Das Axiom der Psychophysik (Müller 1882). The title refers to the fact l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 298 Sensation and Stimulus that Müller distinguished the “axiom of psychophysics,” that is, Fechner’s claim that there is a functional relationship between stimulus and sensation, and the “problem of psychophysics,” the search for the particular form that such a functional relationship actually assumes (e.g., logarithmic law, power law, etc.). Instead of attacking Fechner’s solution of the problem as Stadler had done, Müller wanted to strike the heart of Fechner’s enterprise by ques- tioning the very idea that a functional relationship exists at all. Müller recognized the importance of Stadler’s critique of Fechner’s law. “Such a sharp objection,” he wrote “would alone be capable of overthrow- ing Fechner’s entire construction of formulas [Formelgebäude]” (Müller 1882, p. 23), if the latter were based exclusively on Weber’s result, that is, only on the “method of just-noticeable differences”. However, Müller argued, “[t]his is not the case” (Müller 1882, p. 23). Beyond the experi- ments that concern the just-noticeable differences, one must take into account the “method of more-than-noticeable differences,” or the method of bisection. Müller showed that Delbœuf’s (1873) repetition of Joseph Plateau’s (1872) experiments on color differences allow dividing an initial interval between two largely different perceived magnitudes of a sensation into equal subintervals. Once equally-appearing intervals are deﬁned, accord- ing to Müller, Fechner could introduce the hypothesis expressed by Weber’s fraction (ii). Müller argued that if one accepts this hypothesis, as Stadler did, then “the passage to the fundamental formula containing the inﬁnitely small values dβ and dγ is irreproachable” (Müller 1882, p. 25). Müller’s defense of Fechner’s derivation (see however Heidelberger [1993] 2004, p. 215) was of course meant to strategically shift the attention to a more fundamental question. The shortcomings of psychophysics are not physical-mathematical, but, as Müller put it, “transcendental.” Müller uses the term transcendental according to the interpretation that Cohen had laid down a few years earlier in the ﬁrst part of his book on Kant’s ethics (Cohen 1877). As is well known, in Cohen’s view, Kant’s transcen- dental method proceeds bottom-up from the fact of the mathematical science of nature as it is historically given in the “printed books,” to the conditions of its possibility (cf. Cohen 1877, p. 77). The same approach must be applied to psychophysics. Quantitative psychologists assumed as a fact that the psychological attributes that they aspired to measure are quantitative. How- ever, this alleged fact must be transformed into a “problem”, and its possi- bility must be carefully evaluated. Müller’s considerations, unfortunately, presuppose that the reader has already bought into quite a lot of Kant’s philosophy. In particular, not sur- prisingly, Cohen’s early interpretation of the Anticipations of Perception plays a major part in Müller’s line of argument. Müller conceded that Kant’s two formulations of the principle are confusing to say the least. Does Kant l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 299 claim that sensation has intensive magnitude, or the real, which is the object of sensation, or both? “The relations between sensation and the real, which corresponds to it in the object, is not expressed with full clarity” (Müller 1882, p. 51). In Müller’s view, Cohen had made a fundamental step toward solving the riddle: “by deﬁning the real that corresponds to sensation in the object as ‘stimulus’, Cohen developed in a highly signiﬁcant way Kant’s doctrine of the intensive magnitudes” (Müller 1882, p. 55). On the one hand, Cohen obtained a hermeneutic elucidation of Kant’s different formulation of the Anticipations of Perception in the two editions of the Kritik der reinen Vernunft; on the other hand, he provided an epistemological clariﬁcation of the ambiguous notion of stimulus. The stimulus does not arouse or cause sensation, the stimulus is the object of sensation or it is the objectiﬁed sen- sation (Müller 1882, p. 53). The main consequence of Cohen’s approach, in Müller’s view, is that it is not the sensation that has intensive magnitude, nor the sensation and the stimulus, but only the stimulus. According to Müller, “physics measures intensive magnitudes and it is therefore the task of physics to measure the magnitude of the stimulus” (Müller 1882, p. 55). Using a Bunsen’s grease-spot photometer, for instance, one can establish that the illuminance of the photometer screen due to the source S located a distance d from the photometer is equal to the illuminance of the screen due to the source S 0 located a distance d0 from the screen when the grease spot on the photometer’s screen becomes invisible (S:d2 = S 0:d 02). After choosing a luminous intensity of a standard candle (Normalkerze) as a unit, it is possible to construct the luminous intensity scale with equally spaced units along the scale. Then one can establish “how many standard candles at the same distance one would need to obtain the same effect as the light that we want to measure” (Müller 1882, p. 54). Using a Kantian terminology (B, pp. 201n), Müller claimed that intensive magnitudes can be measured through a coalition of parts, rather than through aggregation as in the case of extensive magnitudes (Müller 1882, p. 54). In Müller’s reconstruction, Fechner attempted to achieve something anal- ogous for the intensity of sensation. As we have mentioned, the trick was to postulate that the difference sensation or contrast sensation (Contrastempﬁndung) for two stimuli (the just-noticeable relative increase in stimulus), was pro- portional to the sensation difference (Empﬁndungsunterschied) (the difference between the two corresponding sensations). However, Müller objected, this has the “absurd” implication that equal stimuli would produce no sensation (Müller 1882, p. 106); but even if one sets aside this issue, there is still no proof that the proportionality postulated by Fechner holds (Müller 1882, p. 18). However, without this assumption sensation intensities cannot be transformed into a class of measurable intensities. Instead of speaking of contrast sensations that vary according to their intensity, Müller concluded, l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 300 Sensation and Stimulus we can at most speak of contrast feelings (Contrastgefühle) that vary according to their character (Müller 1882, pp. IV, 104, 106). In other terms, the equal- ity and difference among, say, luminosities can be organized only in a nom- inal scale assigning different names to different types of contrast feelings (say, dark, shadowy, bright, luminescent, etc.; cf. Philippi 1883, p. 585ff. See Müller 1882, pp. 106–115, for more sophisticated examples). Thus, contrary to Fechner’s ambitions, Müller believed himself to have shown that “sensation cannot be expressed in numbers at all,” i.e., it cannot be measured (Müller 1882, p. 58). The stimulus can be measured, but one can speak of the magnitude of sensation only in a ﬁgurative sense. As a consequence, no functional relationship can be established between them. Fechner’s indirect scaling method, in which the sensation differences are measured by putting j.n.d in a row between stimuli becomes powerless (Müller 1882, p. 58). The conclusion is of course that the axiom of psycho- physics, the very claim that a functional relationship exists between the magnitude of sensation and the magnitude of the stimulus, is ﬂawed: “sen- sation is not a function of the stimulus, but the stimulus is the object of sensation” (Müller 1882, p. 56). Müller’s epistemological reﬂections constitute only a relatively small por- tion of the book. The latter includes further detailed analyses of Weber’s and Charles Delezenne’s (1826) experiments (II.1 and II.2), of Helmholtz’s (1877) analysis of sound sensations (II.3–5), of Georg Elias Müller’s (1878) devel- opment of the right or wrong cases method (III.1), Delbœuf ’s (1873) measurement of fatigue (III.2), and Hering’s (1875) work on spatial and temporal sensations (III.1). This material cannot be considered here. What is relevant in this context is that Müller displayed a solid technical knowledge of the topic. Thus, Fechner himself took the time to reply to the “mathemat- ically as well as philosophically trained author” (Fechner 1882, p. 324). In 1882, Fechner published Revision der Hauptpuncte der Psychophysik (Fechner 1882), a newly articulated defense of psychophysics against an apparently never-ending series of new critics, including several philoso- phers like Zeller (1881, 1882) and Johannes von Kries (1882). If Zeller insisted that sensation magnitudes cannot be measured in practice, von Kries thought that they cannot be measured in principle; Müller, as we have seen, raised the more radical “quantity objection” that there are no sen- sation magnitudes at all (cf., e.g., Michell 1999, p. 40ff.). Against Müller’s argument “from Kantian principles” (Fechner 1882, p. 325), Fechner pointed out that no one can deny that sensations of the same type (light, acoustic, etc.) can be said to become stronger or weaker. Müller can regard contrast sensations or sensation differences as mere contrast feelings, if he wants to. However, Fechner believed himself to have shown that if one deﬁnes sensa- tion differences as proportional to “difference sensations,” one can achieve l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 301 measurements that are empirically correct. “What should I care about Kantian deﬁnitions” (Fechner 1882, p. 325), he concluded.2 Müller is correct in claiming that quantities can be compared only via a unit of measure: “and exactly in this way my measurement formula measures sensation, even if not directly, but through the mediation of its functional relations with the stimuli” (Fechner 1882, p. 326). In his review of Müller’s book, Elsas (1883a)—who in the meantime had become Privatdozent in Marburg (Elsas 1882)—defends his Marburg colleague on this point. If sensation intensities are ordinal (weaker and stronger), this does not mean that they are measurable, that a certain sen- sation is ﬁve or six times stronger than another one. Neither this measur- ability of a quantity can be inferred from the fact that it is set in functional relation to a measurable quantity. For instance, the welfare of a nation depends, say, on its morality (Sittlichkeit); if one concedes that the former is measurable, this does not mean that the latter is too (Elsas 1883a, pp. 130–31). Fechner’s objection to Müller, according to Elsas, reveals that the problem was much deeper. Fechner and his followers should undertake a serious discussion to establish what a “measurable magnitude” is in general (1883a, p. 131). Physics could be successful for a long time without raising this question, but empirical psychology made an epistemological analysis of the issue unavoidable. Elsas’s review is worth mentioning because it reveals the background against which this issue was understood within the Cohen circle. According to Elsas—who was probably summarizing the results of his prize essay— Kant’s transcendental question about the possibility of mathematics and physics should be extended to the new sciences that were gaining ground in the second half of the 19th century. “Is metageometry, is psychophysics a possible science?” (Elsas 1883a, p. 127). The issue, as Cohen has shown, is not a physio-psychological one; neither the origin of the representation of space nor the organization of our sensibility are at stake. The question is, “on which transcendental foundations (that is, on which conditions making the knowledge possible) is the necessity of mathematical knowledge based?” Müller, embracing “Cohen’s conception of the transcendental” (Elsas 1883a, p. 127), has ventured to submit psychophysics to such a critical investigation. In mathematics and physics we establish functional relationships among magnitudes. The stimulus is clearly a magnitude that can be measured. “Can the sensation also be measured? Yes or no? The answer to this simple question decides the possibility of psychophysics” (Elsas 1883a, p. 130). Despite providing an overall positive review of the book, Elsas however did 2. For the importance of Fechner’s answer to Müller, cf. Heidelberger [1993] 2004, p. 240. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 302 Sensation and Stimulus not fully agree with Müller’s philosophical conclusions. Elsas, like Müller, subscribed to Cohen’s identiﬁcation of Kant’s “real which corresponds to sensation” with the stimulus. However, Elsas denied that one can attribute an intensive magnitude to the stimulus: “Physics measures intensities only as extensive magnitudes; the intensity of a physical phenomenon, e.g., of sound, of a light source, of a force is never an intensive magnitude” (1883a, p. 133). Intensive magnitudes are measurable only indirectly through their extensive effects.3 4. Cohen: From Psychophysics to the History of the Inﬁnitesimal Method When Elsas published his review of Müller’s book, Cohen had already come to the conclusion that his interpretation of the Anticipations of Perception, in which the real was identiﬁed with the stimulus of psycho- physics, was not satisfying. Psychophysics was simply not the right frame- work for making sense of Kant’s Anticipations of Perception. As we have mentioned, at the beginning of 1881, Cohen wrote to Stadler that he envisaged a way to acknowledge, and at the same time overcome, the latter’s objection that, contrary to Kant’s claim, the degree of sensation probably var- ies discontinuously. The most reliable, though indirect, source at our disposal for concretely understanding what Cohen had in mind is probably Stadler’s then-new monograph, Kants Theorie der Materie (Stadler 1883)—possibly the ﬁrst monograph on Kant’s Metaphysische Anfangsgründe der Naturwissenschaft (Kant 1786). Stadler still fully works within the framework built by Cohen and dis- cussed by the early Cohen circle. As Stadler writes, “Cohen, very happily, called ‘stimulus’ the objective correlate of the intensive magnitude” (1883, p. 60). The magnitude that corresponds to the stimulus of the intensive magnitude of sensation would thus be called the “magnitude of the stim- ulus” (1883, p. 60). Stadler agreed with Müller that “only the stimulus can be measured, not sensation”; however, this did not mean that “intensive mag- nitude can only be attributed to the stimulus,” as Müller claimed (Stadler 1883, p. 248n24). For Stadler, only sensation has intensive magnitude, but this is an internal psychological determination, which “in its own nature is not measurable” (Stadler 1883, p. 61). Stadler agreed with Elsas that in- tensive magnitudes are measurable only through their causal product of extensive ones. Stadler attempted to apply these conceptual tools to Kant’s work, giving of a sort of psychophysical interpretation of some of the key elements of his philosophy. Kant’s Gegebenwerden and the Afﬁcirtwerden can be interpreted 3. This is, by the way, a quite Kantian point of view, see, e.g. Ak., 18:322; 28:425. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 303 as, in a ﬁrst approximation, the “representation of the dependence of the change of sensation on the outside” (Stadler 1883, p. 53); more precisely this dependence—“which today one would call psychophysical” (1883, p. 58)—means “the emergence of a degree of consciousness, an intensive magnitude” (1883, p. 59). The objective correlate of the intensive magni- tude, as suggested by Cohen, is the stimulus. In Stadler’s view, the stimulus of sensation should ultimately be thought of as motion. This is what Kant meant when he claimed that the object of the external senses must be motion “because only thereby [through motion] can these senses be affected” (Ak., vol. 4, p. 477). The differences between sense qualities should be ulti- mately dissolved in the differences between motions. In Stadler’s reading, this is nothing but “the principle of physiology that all external stimuli of the sensations must be motions” (1883, p. 8), which, through the peripheral nervous system are passed to the central nervous system (cf. Stadler 1878, p. 223; see also Wundt 1874, p. 277). Stadler notices further that, in the Beweis of the Anticipations of Percep- tion, Kant used the expression “moment” to indicate the “reality as cause” and, in particular, as the “cause of sensation,” as something that exerts an inﬂuence on the senses (B, p. 211). “Moment” is for Kant the moment of acceleration, an inﬁnitely small variation of velocity. According to Stadler, the term moment reveals that what Kant called “‘inﬂuence on the senses’, the ‘stimulus’” (1883, p. 60) is nothing but the effect on what in physics we call force. The “moment is the magnitude of the force that corresponds to the intensive magnitude of the sensation” (1883, p. 60). The magnitude of the force and intensive magnitude are correlated, but not identical. Force can be measured only through its extensive effects. The intensive magnitude is given in consciousness, it is a “subjective evaluation” of the stimulus, and cannot be measured (Stadler 1883, p. 61). Stadler conceded that there are passages where Kant seems to attribute intensive magnitude not to sensation, but to physical determinations like velocity (cf. Ak., vol. 4, p. 540–41). However, he claimed, one should re- sist confusing this intensive magnitude with the intensive magnitude of sensation. According to Stadler, Kant “did not want to identify it [the intensive magnitude of velocity] at all with the intensive magnitude, which corresponds to reality” (1883, p. 37; in the sense of the category of reality). The deﬁnition of the velocity as an intensive magnitude, Stadler pointed out, was only an analogy used to emphasize that the magnitude of velocity is not composed of parts, as the magnitude of space and time is. Stadler took some pains to interpret away the passages that could sup- port the opposite reading. E.g., he comments on Kant’s reﬂection with the title ‘Über das Moment der Geschwindigkeit im Anfangsaugenblick des Falls’ (Ak.,vol. 14: Reﬂ. 67; 1788–1791). Here Kant attributes an intensive l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 304 Sensation and Stimulus magnitude to the moment of velocity—that is, the tendency to fall down- ward at the beginning of a falling motion—and conceives of the ﬁnite motion as a summation of inﬁnitely many “moments” (Ak., vol. 14, p. 495; Reﬂ. 67). Stadler warned that one should not try to read passages like these as Kant’s attempt to provide a foundation for the “objective validity of the differential calculus” (1883, p. 39). Interpreters committed to such a reading “would be in contradiction with the view that Kant expressed of the inﬁnitesimal method” (1883, p. 39). In general, in Kant’s work, continuity means inﬁnite possibility of division, not composition from actual, though inﬁnitely small parts. Stadler concludes polemically that, “those who make the intensive magnitude correspond with the differential confuse the form with the con- tent” (1883, p. 39). Although Stadler never mentioned Cohen explicitly, Cohen himself later read this last claim in particular as being directed towards his upcoming book (Cohen 1910a). Stadler’s monograph was ﬁnished in March (Stadler 1883, p. IV). According to Cohen’s later recollections, Stadler stayed in Marburg in the summer of 1883 while Cohen was working on his Das Princip der Inﬁnitesimal-Methode (Cohen 1883). The Vorwort of Cohen’s book is dated August 1883 (Cohen 1883), but the book was sent to print only in mid- October (Cohen to Natorp, September 27, 1883; CN, Br. 1, 148). Reading the drafts of their books, Stadler and Cohen probably realized that one of them put forward precisely what the other vehemently rejected. Edited by that time, Cohen had completely abandoned the framework of psycho- physics, which had enjoyed so much success among his acolytes. He became convinced that Kant’s second principle could be understood precisely by looking at the connection between the concepts of moment, intensive mag- nitude and reality, which was suggested by the Kant passages mentioned by Stadler. According to Cohen, by establishing this connection, Kant had expressed philosophically in his principle of Anticipations of Perception the problem that Galileo, Leibniz and Newton had tried to answer mathemati- cally when they introduced a new type of quantities, namely, inﬁnitesimally small quantities. I cannot enter into the details here of this highly obscure book and its tormented reception, which I have described elsewhere (Giovanelli 2016). What I would like to emphasize is that Cohen explicitly recognized that it was Stadler’s critique of a possible psychophysical reading of Kant’s Anticipations of Perception that changed his mind: to understand “what was new and valuable in Kant’s conception of the intensive magnitude,” Cohen wrote, it was necessary to become aware of “the deﬁciencies in its foundation and presentation, which A. Stadler had ﬁrst emphasized” (Cohen 1883, p. 105). Stadler showed the failure of psychophysics’ attempt to present the intensive magnitude of sensation as the differential dγ (Cohen 1883, l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 305 pp. 159–60).4 Cohen, however, at the turn of the 1880s, must have come to realize that what psychophysics had failed to achieve in the case of sensation could still be established on another basis. The intensive magnitude of sen- sation was not at stake in Kant’s Anticipations of Perception, but rather the intensive magnitude of physical determinations such as velocity. It was in the attempt to give a mathematical counterpart to the intensive magnitude of velocity that the differential was introduced. Kant’s principle was the philo- sophical expression of this historical fact. The passage from one interpretative framework to the other seems to be based more on an association of ideas than on a proper argument. However, the role played by the discussion of psychophysics is conﬁrmed by Cohen’s own reconstruction of the path that led him to rethink the interpretation of Kant’s second principle in the revised and greatly augmented edition of his Kants Theorie der Erfahrung (Cohen 1885), which was ﬁnished in August 1885. Cohen recalls that “[i]n the ﬁrst edition of this book” (cf. Cohen 1871, p. 46), he had attempted to identify the real that corresponds to sensation with “the ‘unity of stimulus, in which we objectify sensation’” (1885, p. 436). However, he now recognized that “this expression, although useful to encourage further reﬂections, was too psychological to be main- tained” (1885, p. 436). What is at stake is not “the unit of stimulus,” but the “the unit of motion” (1885, p. 436). It is precisely in those passages mentioned by Stadler that Kant, by establishing a relation between reality, intensive magnitude, and the mathematical/physical concept of moment, expresses the very problem that the discoverers of the inﬁnitesimal calculus had to solve to make motion an object of scientiﬁc inquiry: “Consequently Galilei and Leibniz talk of the inﬁnitely small as an intensive magnitude” (Cohen 1885, p. 427). Kant, Cohen claims, does not even have to emphasize this connection since it was obvious to his readers (Cohen 1883, p. 105). Again Cohen recognized that it was Stadler’s work on psychophysics that led him to completely rethink his own interpretation of the Antici- pations of Perception. In Cohen’s words, Stadler “rightly opposes the con- tinuity of sensation as an a priori determination” (Cohen 1885, p. 437). Not only is there no pure transcendental foundation for the continuity of sensation; Stadler also demonstrated that empirical studies on the psy- chology of sensation are even less capable of demonstrating a posteriori that sensation grows in a continuous way. However, Stadler “only looks for the pure transcendental foundation he is missing in the sensation” (Cohen 1885, p. 437). He did not realize that “the ‘pure transcendental 4. See cf. Heidelberger [1993] 2004, p. 222 for more on Cohen’s critique of psycho- physics in Das Princip der Inﬁnitesimal-Methode. In my perspective, the interesting part of the story is the role psychophysics played in Cohen’s work before this book was written. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 306 Sensation and Stimulus foundation’” he was looking for cannot be found “in the sensation, but only for the sensation” (Cohen 1885, p. 437; my emphasis). That transcen- dental ground should be found “in the new and autonomous mode of mag- nitude, which in the inﬁnitesimal method reveals itself to be fruitful for the constitution of the object in his mechanical meaning” (Cohen 1885, p. 437). In other words, Stadler still thought that psychophysics offered the conceptual framework for understanding the problem Kant was facing. According to Cohen, however, this framework was inadequate for under- standing Kant’s concept of the “intensive”: “the so-called intensity of sensa- tion must absolutely be distinct from the intensive magnitude or reality of sensation” (1883, p. 156). Elsas, in his 1885 review of Stadler’s 1883 book (1885b), points out clearly where Stadler was no longer in accordance with Cohen’s new ap- proach to Kant’s second principle. Stadler considered “motion as the stim- ulus of sensation” (1885b, p. 146); according to Elsas, however—even if there is some textual evidence to apply this psychological interpretation to Kant—the central point is different: transcendental philosophy should try to explain what makes general mechanics a science and thus what makes motion a legitimate object of scientiﬁc inquiry: “The task is to explain the fact of science, the fact of general mechanics” (1885b, p. 146). The relation between motion and sensation is philosophically secondary, if not irrelevant. “Maybe the author should have further developed the concept of intensive magnitude and its relation to the category of reality” (1885b, p. 146); “the elementary concepts of mechanics,” Elsas continues alluding to Cohen’s work, “already offer some indication in this direction” (1885b, p. 146). The Dissolution of the Cohen Circle 5. Stadler’s publication rate fell drastically in the ensuing years, possibly for health reasons, and we do not have textual evidence of his possible counter- objections. However, we know that he never agreed with Cohen’s new course, even if he himself unwittingly had brought it about; their friend- ship, however, never suffered (Cohen 1910a). Elsas continued to publish, as a physicist (Elsas 1883b, 1885a, 1886c, 1887), a reviewer of philo- sophical publications (1884, 1885b) and as a high quality science popu- larizer (1886a). Moreover, after Fechner’s 1882 Revision der Hauptpuncte der Psychophysik (1882), Elsas returned to psychophysics; in 1886 he published his philosophical reﬂections on the topic in a little pamphlet, Über die Psychophysik (1886b). Elsas continued the early Marburg debate on the measurability of sensation and at the same time made some timid attempts to integrate it into the new approach taken by Cohen in his 1883 monograph. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 307 5.1. Elsas’ Über die Psychophysik Elsas organized his book around two questions: 1. “Are Fechner’s measur- ing formulas mathematically and physically correct and derived from the data?” (Elsas 1886b, p. VI). 2. “Is psychophysics in the sense of Fechner possible in general?” (1886b, p. VI). Elsas answered both these questions with a resounding “no.” In this sense Elsas was more radical than both Stadler and Müller. In the language introduced by the latter, he intended to criticize both the problem and axiom of psychophysics. In what follows, for reasons of brevity I will concentrate on the third and ﬁnal part of the book, in which Elsas dealt with question 2., which is of course the one richer in philosophical implications (see also Heidelberger [1993] 2004, p. 229ff ). After a long digression on du Bois-Reymond’s (1882) theory of quantity (Elsas 1886b, pp. 50–61; cf. Darrigol 2003, p. 540)—Elsas argued against the very possibility of measuring the sensation via its functional relation with the stimulus. Elsas deﬁned the concept of function as the production of quantity from other quantities. For instance, the area of a triangle is a function of two variables, base and altitude (Elsas 1886b, p. 61). However, something different is meant when one says that, according to Ohm’s law, the current through a conductor between two points is a function of the voltage across the two points and a constant of proportionality, the resis- tance (Bois-Reymond 1882). According to Elsas, in the latter case we as- sume, at least implicitly, that there is a causal connection that serves as the basis of the functional relationship (Elsas 1886b, p. 61; cf. Heidelberger 2010). The volume of Knallgas or oxyhydrogen that can be produced by water electrolysis in a given amount of time measures the electric current because the current causes the electrolysis; or, to take a simpler example, the thermometer measures temperature because equal temperature differ- ences cause equal expansions of the mercury column, etc. No such causal connection can be found between stimulus and sensa- tion. Thus, Fechner has no real reason to claim that equal difference sensations are proportional to equal sensation differences. The question is not merely epistemological; Elsas showed that, without having a causal connection as a guide, it is easy to lose grasp of the mathematical deri- vation. Let’s grant Fechner that his “constant k has the same meaning as the practical measuring unit for sensation” (Elsas 1886b, p. 17); then inconsistencies arise in his system of formulae. According to eq. (ii), k is the value of the sensation difference Δγ that corresponds to Δβ:β = 1, that is, to a doubling of the initial stimulus β; according to eq. (v), k is the value of the sensation difference Δγ that corresponds to β = e, where e is the base of the natural logarithm (the natural logarithm of e is 1); according to eq. (vii), Δγ = k when β0:β = 1:e (the natural logarithm of 1 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 308 Sensation and Stimulus is 0).5 Thus, without an underlying causal connection, a mere functional relation is not sufﬁcient to establish a quantitative comparison. It is true that, as Fechner points out, even in physics a functional rela- tionship does not always imply a causal relationship (Fechner 1882, p. 227); the frequency of a pendulum is a function of the pendulum’s length, the orbital velocity of a planet of its distance from the sun, etc.; however, no causal relationship between these pair of quantities is im- plied (Elsas 1886b, p. 65). However, according to Elsas, at a deeper level, there must always be “a causal condition at the basis of the functional con- nection” (1886b, p. 65); in the cases just mentioned, it is the gravitational force (cf. Heidelberger [1993] 2004, p. 230ff ). Thus there are only two alternatives. If, as Fechner claims, there is no causal relationship between the body and the mind, then the connection between stimulus and sen- sation cannot be expressed through a mathematical equation; the latter is not measurable. What Fechner constructed is only “pseudo-physics [Scheinphysik]” (Elsas 1886b, p. 67). If Weber’s law were really an ex- pression of the causal connection between stimulus and sensation, then Fechner’s psychophysics would be a “real physics of the soul” (Elsas 1886b, p. 64). However, the existence of a causal relationship between stimulus and sensation, the body and soul, seems to be incompatible with energy conservation. Thus, Elsas did not seem to allow for any appeal against his draconian statement: “Mathematical psychology, psychophysics and physiological psychology—three absurd expressions [Bezeichnungen]!” (Elsas 1886b, p. 79). The only escape, in Elsas’ view—as Stadler had already suggested (Stadler 1878, p. 223; cf. Elsas 1886b, p. 74n20)—is to consider the causal relationship not between stimulus and sensation, but between stimulus and the peripheral/central nervous system: “then psychophysics becomes nothing but common physiology” (Elsas 1886b). As Elsas put it in the opening of a contemporary semi-popular introduction to acoustics, “[t]he object of sensations is always motion, which is transmitted to the nerves of our sense organs and through them is transported to our brain” (1886a, p. 1). We can say that hearing is different from sight, but we are not able to express in words this difference between sound and color. The only difference is in the types of motion that excite our sense organs; this difference is investigated by physics, “the task of which is to reduce the natural phenomena to motion” (1886a, p. 1). If one cannot make use of the concepts of force and motion, Elsas concludes rather narrow-mindedly, then no mathematics can be applied (1886b, p. 70). Sensation is not an object of scientiﬁc knowledge; it is not a part of nature; it has no reality 5. Recall that eq. (vii) is derived from γ0 − γ = klogβ0 − logβ. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 309 for the mathematical physicist; it cannot be treated mathematically as a measurable quantity (Elsas 1886b, p. 70). 5.2. With or Against Cohen The role of sensation, Elsas concluded in his book, is epistemological. Sensation expresses the need to go beyond measurable extended quantities, to look at that something which is extended, and provides physical content to extension. This is, in Cohen’s interpretation, what Kant had tried to express in the Anticipations of Perception, by connecting sensation, reality and intensive magnitude (Elsas 1886b, pp. 75f ). E.g., as Elsas put it, velocity as a physical concept cannot be reduced to the differential quotient of space and time: it “is an intensive magnitude; the extensive quotient is only the mathematical expression of it but not an adequate one” (1886b, p. 68). In this way Elsas attempted to rephrase Cohen’s infamously obscure prose in a language more familiar to science practitioners: “At least I hope that I have not changed something essential in this translation from the scholastic language of the philosophers into the one of the physicists” (Elsas 1886b, p. 76). These remarks seem to be tacked on at the end of the book, rather than part of its main line of argument.6 However, they show that, in contrast to Stadler, Elsas had at least tried to embrace Cohen’s new course. This was far from obvious. In contrast, Müller’s attitude towards Cohen’s work dramat- ically changed after the latter’s 1883 book. In his 1886 habilitation writing, Das Problem der Continuität im Mathematik und Mechanik (Müller 1886), Müller became highly critical of Cohen’s connection of the differential and the intensive magnitude. Interestingly, according to Müller, the “difﬁculties which Cohen got tangled up in the development of his thought” should be traced to the fact that he was misled by the analogy with psychophysics. Cohen, in Müller’s view, “committed the same mistake that psycho-physics fell into” (1886, p. 96n.); he attributed “to something which, like the differ- ential, is not a real object […], a magnitude, indeed an intensive magnitude” (1886, p. 96n). Müller’s remark is important insofar as it conﬁrms that Cohen, more or less consciously, tried to transfer the approach that psycho- physics had applied to the intensive magnitude of psychological quantities to the intensive magnitude of physical ones. Just as psychophysics wanted to 6. I disagree with Heidelberger’s claim that Elsas “associates this [his critique of psy- chophysics] with Cohen’s theory of inﬁnitesimals” (Heidelberger [1993] 2004, p. 230). I suspect that Elsas’s emphasis on “role that causality plays in measurement” (Heidelberger [1993] 2004, p. 229) was formulated before (possibly already in the answer to the 1881 Preisaufgabe) and independently from Cohen’s 1883 book; only as an afterthought Elsas tried to give some Cohenian ﬂavor to his line of argument. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 310 Sensation and Stimulus measure sensation as the accumulation of inﬁnitesimally small sensation in- crements, Cohen wanted to present the production of ﬁnite quantities in physics as the inﬁnite summation of inﬁnitesimal quantities. However, as Müller pointed out, this is “a complete misunderstanding of the method of limits” (1886, p. 96n). Müller’s attacks, who “for some years was part of our restricted circle,” came as a surprise (Elsas to Lasswitz, January 7, 1887; CN, Br. 11, 171). Elsas pointed this out in a letter to Kurd Lasswitz at the beginning of 1887, when he thanked the latter for the positive review (Lasswitz 1887a) of his psycho- physics booklet in the Deutsche Literaturzeitung—Germany’s most important general review journal. Elsas did not want to inﬂuence Lasswitz’s judgment, whom Natorp had asked to review Müller’s book for the Philosophische Monatshefte (Natorp to Lasswitz, September 24, 1886; CN, Br. 10, 170). However, he did not hide his disappointment towards Müller’s behavior, after all Cohen had done for him (Elsas to Lasswitz, January 7, 1887; CN, Br. 11, 171). Nevertheless, he also had to admit the difﬁculties of fully embracing Cohen’s approach: “Often I myself am not sure if Cohen really means and says what I read off or hear from his elliptic remarks” (Elsas to Lasswitz, January 7, 1887; CN, Br. 11, 172). Elsas expressed a similar uneasiness a month later in another letter to Lasswitz (Elsas to Lasswitz, Febuary 8, 1887; CN, Br. 12, 182). Lasswitz (1848–1910) was a high school teacher from Gotha who was working on the history and philosophy of atomism (Lasswitz 1878, 1884). He became interested in Cohen’s work on the history of the inﬁnitesimal calculus (Lasswitz 1885a, 1885b), possibly after a correspondence (Eccarius 1985) with one of Cohen’s most renowned mathematician critics, Georg Cantor (Cantor 1884). Lasswitz’s review of Müller’s book became a long paper entitled “Das Problem der Continuität” (Lasswitz 1888). Besides addressing some of Müller’s criticisms (Lasswitz 1888, pp. 24–8; see also Lasswitz 1887b), Lasswitz mostly gave his take on Cohen’s connection between the differential and intensive magnitudes. Motion, he explained, as a change of space extension in a certain time span, has no physical reality. In every instant, there is no change of position, thus no motion. The physical reality of motion has to be searched for in something that is beyond extension, but possesses a greater or smaller ability to generate a determinate motion (Lasswitz 1888, p. 19ff ). However, this intensity of motion ﬁnds mathe- matical expression in the differential function dy = f0(dx), and not in the dif- ferential dx, as Cohen misleadingly claimed (Lasswitz 1888, pp. 29–31). Yet Müller remained unconvinced. He replied to Lasswitz in October 1887, call- ing Cohen’s work on the inﬁnitesimal method “one of the most monstrous births in the entire history of philosophy” (Müller to Lasswitz, Octtober 26, 1887; CN, Br. 13, 172). Müller died a few months later of a severe lung dis- ease, so that no further discussion was possible. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 311 5.3. The Fechner-Elsas Debate Toward the end of 1887, Elsas sent Lasswitz detailed comments on the latter’s “essay on the problem of continuity” (Elsas to Lasswitz, Nov. 9, 1887; CN, Br. 14, 179). He also took the opportunity to announce that he had ﬁnished another paper on psychophysics for the Philosophische Monatshefte: “Even though I’m very busy with accumulators and galva- nometers, I did not want to hesitate too long in answering Fechner’s paper in the Philos. Studien” (Elsas to Lasswitz, Nov. 9, 1887; CN, Br. 14, 182). In fact, the indefatigable Fechner again made the effort to answer some of his critics, Elsas himself and Alfred Köhler (1886), in Wilhelm Wundt’s journal (Fechner 1888), which in spite of the title, mainly dealt with em- pirical psychology. Fechner was 86 years old, and as he recognized half- jokingly, this may have been the last time that he was able to defend his own scientiﬁc creature (Fechner 1888, p. 163). Fechner’s reply to Elsas is too long and detailed to be dealt with here. However, a point is worth noticing. Here Fechner repeated, even more clearly than in Müller’s review, that the assumption that difference sen- sations are proportional to sensation differences was merely the “simplest hypothesis” (Fechner 1888, pp. 171, 174) from which he could choose (cf. also Fechner 1888, pp. 147ff for more details). Fechner calls it the Unterschiedshypothese, the difference hypothesis (j.n.d.s are proportional to sensation differences). Such a hypothesis is acceptable inasmuch as it is im- plied by the empirically conﬁrmed logarithmic law. Fechner claims that there is at least one other simple alternative one can think of, which he calls the Verhältnishypothese, the ratio hypothesis (j.n.d.s are proportional to sensation ratios). This hypothesis, which was adopted by Plateau and Brentano (and supported by Elsas himself ), leads however to a power law which, Fechner claimed, is empirically wrong (but see of course Stevens 1961). However, Fechner had to concede Elsas’ point that, if one assumes the difference hypothesis, eqs. (ii), (v) and (vii) are indeed incompatible “as the author [Elsas] has correctly shown on p. 17” (Fechner 1888, p. 167). However, Fechner had a quite interesting response. He claimed that the proportionality between sensation differences and difference sensations applies only to the differential equation (iii), and not to the ﬁnite equation (ii), an equation that he actually never wrote: “where for God’s sake did I ever put forward equation [ii]?” (Fechner 1888, p. 168). Thus, in the reply to Elsas, Fechner may have revealed a quite astonishing fact, which, Neo- Kantianism aside, is relevant to Fechner scholarship in general (cf. Scheerer 1987). Fechner did not regard eq. (iii) as an approximation derived from the empirically veriﬁed eq. (ii), but vice versa: he saw eq. (ii) as the approxima- tion of the exact eq. (iii) (cf. Dzhafarov and Colonius 1999). After all, this is l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 312 Sensation and Stimulus conﬁrmed by the fact that, in the Zend-Avesta, he had introduced the dif- ferential equation as an exact equation before he knew about Weber’s ﬁnd- ings (Fechner 1851). Thus Fechner’s rebuttal to Elsas reveals that, in contrast to what most of Fechner’s critics had assumed, the passage from Weber’s law (ii) to the differential equation (iii) via the infamous mathe- matical auxiliary principle was not the spine of Fechner’s derivation of the logarithmic formula. In his reply, Elsas (1888a) had to admit that he could not ﬁnd eq. (ii) in any of Fechner’s writings (Elsas 1888a, p. 132n1). However, he was not particularly impressed. Even if I cannot do full justice of Elsas’ thirty-page defense here, I suspect that he did not fully realize the importance of Fechner’s counter-move. Elsas went on to criticize Fechner’s derivation starting from a more general ﬁnite formula, again attacking the mathemat- ical auxiliary principle, that, he claimed, Fechner used more as the wand of a magician rather than the tool of a craftsman (Elsas 1888a, p. 134). Elsas showed that one can actually obtain the logarithmic equation (vii) without magically deriving it from the ﬁnite formula via the auxiliary principle. In this setting, the proportionality factor k becomes something that has to be obtained by differentiation of the logarithmic equation (v) and not intro- duced from the outset in Weber’s eq. (ii) (Elsas 1888a, p. 136). Thus, the proportionality between j.n. difference sensations and sensation differences is strictly valid only “when the change of [γ] and [β] are inﬁnitesimally small” (Elsas 1888a, p. 137). This, however, might have been the exact point Fechner wanted to make. The constant k is derived from the loga- rithmic law and not taken from the empirical Weber law. It is the loga- rithmic law itself, taken as measurement formula that deﬁnes the relation between two units of measure (Heidelberger [1993] 2004, p. 206). Elsas did not seem to realize that this might have fended off many neo-Kantian objections. However, for Elsas, the essential philosophical point has not changed. Let’s concede to Fechner that the number of sensation differences becomes approximately proportional to the number of difference sensations, the smaller the stimuli difference becomes. Still, Fechner uncritically assumed that one can measure sensation by adding up sensation differences. How- ever, it is far from obvious that sensation has such an additive structure (Elsas 1888a, p. 139ff ). Musical intervals are certainly quantitatively com- parable (a 4th is smaller than a 5th), but cannot be meaningfully added (a 5th plus a 4th equals an octave) (Elsas 1888a, p. 140). Fechner, Elsas points out, wants us to believe that sensation is “something spiritual, psy- chical, and nevertheless has magnitude that can be connected additively with other magnitudes of the same types”; but Elsas simply could not under- stand this: “[f]undamental epistemological views prevent me from doing so” l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 313 (1888a, p. 143). The epistemological difference between Fechner and Elsas, I think, boils down to the following: the transformation of a class of inten- sities into a class of measurable intensities was for Fechner a matter of deﬁ- nition, whereas for Elsas it was a matter of physics. Thus, for Fechner the difference hypothesis was a better deﬁnition than the alternative, whereas Elsas spent the rest of the paper trying to prove that the ratio hypothesis was physically superior. When Elsas’ rebuttal appeared in the 1888 issue of the Philosophische Monatshefte, Fechner had already passed away. “The previous remarks,” Elsas acknowledged in a short postscript to his paper, “are no laurel wreath and no palm branches worth being placed on Fechner’s fresh grave” (1888a, p. 155). They were written as Fechner was still alive and still speak as if he were alive, “since Fechner’s contribution to science will never die” (1888a, p. 155). Elsas’ note was not simply rhetorical. In the same year, Elsas dedicated a long homage to the great scientist in the national-liberal magazine Die Grenzboten (1888b). Granting Fechner the honors of war, Elsas now celebrated Fechner’s work as the ﬁrst serious critical reﬂection on the measurability of mental contents (cf. 1888a, p. 114). However, Elsas’ con- ciliatory remarks could not and probably were not meant to bridge the wide philosophical divide that separated him from Fechner. For Fechner, mea- suring sensations was a worthy enterprise, because as Heidelberger has pointed out, he ultimately conceived of physical measurement itself as nothing but the reﬁnement of the resolution power of sensations via mea- suring apparatuses (Heidelberger [1993] 2004, sec. 6.5 and in particular pp. 246); but this point of view was fundamentally foreign to Elsas, who, like most 19th century physicists, regarded sensations as nothing but anthropomorphic slags that physical measurement was meant to get rid of. 6. Conclusion: From the Cohen Circle to the Marburg School In those years, the Marburg critique of scientiﬁc psychology was taking a more philosophically sophisticated form in Natorp’s hands (Natorp 1887, 1888, 1893; cf. Luft 2009); Elsas’ technical objections against psycho- physics were largely forgotten. They are mentioned, albeit rarely, in the his- torical literature on psychophysics and measurement theory (Heidelberger [1993] 2004; Darrigol 2003), though, surprisingly, never in the literature on Marburg Neo-Kantianism. Yet Elsas’ work on the topic was respected in the scientiﬁc community. Beside Fechner’s own detailed reply, Elsas’ booklet deserved the mention (alongside Paul du Bois-Reymond’s Allgemeine Functionentheorie [Bois-Reymond 1882]) of his teacher Helmholtz in his 1887 paper, Zählen und Messen (Helmholtz 1887). The reference to Elsas reveals that Helmholtz’s paper—which is now regarded as a classic contribution l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 314 Sensation and Stimulus to the philosophical/mathematical reﬂection on the notion of measure- ment in science (Darrigol 2003)—was probably occasioned by the ques- tion of the measurability of sensation (Heidelberger 1993). Thus, the publications of the early Cohen circle were perceived as contributions to this debate. By contrast, Cohen’s commentaries on Helmholtz’s 1887 paper (Cohen 1888)—which appeared in the same 1888 volume of the Philosophische Monatshefte as Elsas’ rebuttal to Fechner—give the impression that he did not fully recognize the philosophical importance of the issue at stake. Elsas’ causal theory of measurement is not even mentioned; most of all, Cohen, intent on attacking Helmholtz’s naive empiricism, does not seem to appreciate the im- plications of the latter’s analysis of the conditions governing extensive magni- tudes; similarly he quickly passed over Helmholtz’s deﬁnition of intensive magnitude as coefﬁcients (measurable only as ratios between extensive mag- nitudes) (Helmholtz 1887, p. 47). Instead, Cohen concluded the paper by plugging his own work on the intensive magnitude as inﬁnitesimals (Cohen 1888, p. 273), which seems rather out of context. In the following years, Elsas, a close friend of Heinrich Hertz (Fölsing 1997, p. 423), published extensively on the new Maxwell-Hertz theory; he introduced an autonomous circuit breaker, alternative to the Wagner hammer (Elsas 1889b), suggested methods to measure electric resistance (Elsas 1891c) and the dielectric constants (Elsas 1891b), etc. However— despite Hertz’s advice not to go astray “in swampy borderlands” like psy- chophysics (Hertz to Elsas, February 10, 1889; cited in Fölsing 1997, p. 423)—he did not forgo some interesting philosophical escapades (Elsas 1889a). After Hertz failed to ﬁnd a position for him in Bonn (Fölsing 1997, pp. 429), he became an extraordinary professor without salary in Marburg. In a difﬁcult ﬁnancial situation (Lasswitz to Natorp, June 4, 1895; cited in Holzhey 1986, p. 24n89), he died prematurely in 1895 of pulmonary tuberculosis. Cohen’s funeral oration (Cohen 1895) in his honor is also a recollection of the interdisciplinary atmosphere of the early Marburg circle. If it was Cohen’s early interest in psychophysics that contributed to gathering this small group around his Marburg chair, it was Cohen’s inﬁnitesimal turn that had fragmented and eventually dissolved this group. It was not just the traitor Müller that did not follow Cohen’s approach, but also the sincere friend Stadler—since 1892 a professor at the ETH Zurich (Beller 2000)—; Elsas attempted to translate it for non-philosophically-trained readers, but ultimately he was himself not fully convinced. It was the newcomer Lasswitz, though never an ofﬁcial member of the Marburg group, who was the ﬁrst to try to implement a watered-down version of Cohen’s connection between the intensive and inﬁnitesimal in his own successful work as a historian of science (Lasswitz 1890; see Natorp 1891; Elsas 1891a), even if his efforts were not to Cohen’s complete satisfaction (Cohen 1896, p. XLVII). l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 315 Precisely this combination of transcendental philosophy and history of sci- ence became the trademark of the Marburg community at the turn of century. At the end of 1890s—after Natorp became full professor—Cohen started to talk cautiously of a little school that was forming in Marburg (Cohen to Natorp, April 19, 1897; CN, Br. 42, 243 and Cohen to Althoff, May 8, 1897; CN, Br. 43, 244). The titles of the Preisaufgaben launched in those years testify to the historical interests that dominated this group: Aristotle and mathematics in 1894/95 (Albert Görland), Leibniz’s foundation of mathematics and natural science in 1896/97 (Ernst Cassirer), Galileo’s Mechanics in 1900/1901 (Enrico DePortu), and Faraday’s concept of matter in 1901/1903 (Otto Buek) (cf. Holzhey 1986, vol. 1, p. 382). The prize essays were transformed into often excellent dissertations and monographs (Görland 1899; Cassirer 1902; Portu 1904; Buek 1904) which represent some early examples of the Marburg-style integration of history of philosophy and history of science which soon found its most successful expression in Cassirer’s Erkenntnisproblem (Cassirer 1906a). The interests in psychophysics—the attempt “to make sensation arise and increase till it comes to consciousness and becomes integral” (Cohen 1902, p. 441)—faded in the background. However, interestingly, it did not completely disappear. The Preisaufgabe suggested by Natorp in 1904/1906 concerned the problem of sensation in modern psychology. The prize re- mained unassigned. However, in 1906 Johannes Paulsen ﬁnished a disser- tation on Fechner’s concept of sensation under the guidance of Cohen and Natorp (Paulsen 1906–1907). A longer version of it was published as a booklet (Paulsen 1907) in the ﬁrst volume of the Philosophische Arbeiten, the series edited by Cohen and Natorp that was meant to represent (Cassirer 1906b, pp. I–III) what people began to call the Marburg school (cf. Cohen 1913–1914). Even if Paulsen’s work does not add anything new to the pre- vious neo-Kantian criticisms of psychophysics (see also Natorp 1912a), it shows that the issue was still considered part of the legacy of the Marburg community. After all, as Cohen himself recognized in his Nachruf for Stadler, it was the latter’s critique of Fechner’s logarithmic formula that led him to take a new course in his 1883 book (Cohen 1910a). It is probably not just by chance that a contribution of Paulsen’s (1912) was included in the 1912 Festshrift for Cohen’s seventieth birthday, testifying to the role that psychophysics played in the evolution of the latter’s thought. As we mentioned at the opening of the present paper, this was precisely what Cassirer suggested in his article (Cassirer 1912) for the 1912 special issue of the Kant-Studien that was prepared for the celebration of Cohen’s retirement. Cohen’s interest in the problem of sensation in Kant’s Anticipa- tions of Perception, Cassirer explained, led to the notion of stimulus as ob- jectiﬁed sensation; the latter in turn must be ultimately thought of as a motion. It was the question of the possibility of motion as an object of l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 316 Sensation and Stimulus scientiﬁc knowledge that ultimately led to Cohen’s interest in the history of the inﬁnitesimal method (Cassirer 1912, p. 260). Cohen’s Das Princip der Inﬁnitesimal-Methode, despite being unsuccessful as a scholarly work on the inﬁnitesimal calculus, exempliﬁed that peculiar amalgam of history and phi- losophy of science that became one of the trademarks of the Marburg school (cf. Giovanelli 2016). However, as we have tried to show, the appearance of that book also interrupted a fruitful discussion on measurability in science that the Cohen circle had initiated. This discussion seems to have left no trace in the major Marburg contributions to philosophy of science (Cassirer 1910; Natorp 1910). It was only in the 1930s, that Cassirer returned, although brieﬂy, to the issue of measurement in physics in his “Determinismus und Indeterminismus” (Cassirer 1936). However, he could resume the discussion from the exact point where the 19th century had left it: physical measure- ment, Cassirer insisted, is not simply the emancipation of sensation from the limits imposed by “the fundamental psychophysical law”, “the Fechner- Weber law” (Cassirer 1936, p. 42; trans. 1956, p. 32) by means of measuring apparatuses. The physical world, Cassirer claimed, is not a mere quantitative reﬁnement of the sensible world; it is a qualitatively different world, a world of shadows, a symbolic construction that takes the place of the fullness and color of the sensible world (Cassirer 1936, p. 41; trans. 1956, p. 43). Abbreviations A Ak. B CN CW Immanuel Kant. Critik der reinen Vernunft. 1st ed. Riga: Johann Friedrich Hartknoch, 1781. Repr. in Ak., 4. Immanuel Kant. Kant’s gesammelte Schriften. Edited by Preussische Akademie der Wissenschaften, Berlin- Brandenburgische Akademie der Wissenschaften, and Akademie der Wissenschaften in Göttingen. 29 vols. Berlin: Reimer, 1900–. Immanuel Kant. Critik der reinen Vernunft. 2nd ed. Riga: Johann Friedrich Hartknoch, 1787. Repr. in Ak., 3. Helmut Holzhey. Cohen und Natorp. Vol. 2. Basel: Schwabe, 1986. Hermann Cohen. Werke. Edited by Helmut Holzhey. 15 vols. Hildesheim: Olms, 1977–. ECW Ernst Cassirer. Gesammelte Werke. Hamburger Ausgabe. Edited by Birgit Recki. 26 vols. Hamburg: Meiner, 1998–. References Beiser, Frederick C. 2014. The Genesis of Neo-Kantianism, 1796–1880. Oxford: Oxford University Press. Beller, Mara. 2000. Kant’s Impact on Einstein’s Thought. Pp. 83–106 in Einstein: The Formative Years 1879–1909. Edited by Don Howard and John Stachel. Boston: Birkhäuser. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 317 Bois-Reymond, Paul Du. 1882. Allgemeine Functionentheorie. Tübingen: Laupp. Brentano, Franz. 1874. Psychologie Vom Empirischen Standpunkt. Leipzig: Duncker & Humblot. Buek, Otto. 1904. “Die Atomistik und Faradays Begriff der Materie.” Archiv für Geschichte der Philosophie 18: 65–139. Cantor, Georg. 1884. “Review of Cohen, Das Princip der Inﬁnitesimal-Methode (Cohen 1883).” Deutsche Literaturzeitung 5: 266–8. Cassirer, Ernst. 1902. Leibniz’ System in seinen wissenschaftlichen Grundlagen. Marburg: Elwert. Repr. in ECW, Vol. 1. Cassirer, Ernst. 1906a. Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit. Vol. 1. Berlin: B. Cassirer. Repr. in ECW, Vol. 2. Cassirer, Ernst. 1906b. Der kritische Idealismus und die Philosophie des “gesunden Menschenverstandes.” Giessen: Töpelmann. Cassirer, Ernst. 1910. Substanzbegriff und Funktionsbegriff: Untersuchungen über die Grundfragen der Erkenntniskritik. Berlin: Bruno Cassirer. Repr. in ECW, Vol. 6. Cassirer, Ernst. 1912. “Hermann Cohen und die Erneuerung der Kantischen Philosophie”. Kant-Studien 17: 252–273. Repr. in ECW, Vol. 9, 119–138. Cassirer, Ernst. 1936. “Determinismus und Indeterminismus in der moder- nen Physik: Historische und systematische Studien zum Kausalproblem”. Göteborgs Högskolas Årsskrift 42 (3). Repr. in ECW, Vol. 19. Cassirer, Ernst. 1956. Determinism and Indeterminism in Modern physics: Historical and Systematic Studies of the Problem of Causality. New Haven: Yale University Press. Cohen, Hermann. 1868. “Mythologische Vorstellungen von Gott und Seele.” Zeitschrift Völkerpsychologie und Sprach- wissenschaft 5: 396–434. Repr. in CW, Vol. 12, pp. 271–343. Cohen, Hermann. 1871. Kants Theorie der Erfahrung. 1st ed. Berlin: Dümmler. Repr. in in CW, vol. 1/III. Cohen, Hermann. 1877. Kants Begründung der Ethik. 1st ed. Berlin: Dümmler. The 2nd edition (Cohen 1910b) is reprinted in CW, vol. 2. Cohen, Hermann. 1883. Das Princip der Inﬁnitesimal-Methode und seine Geschichte: Ein Kapitel zur Grundlegung der Erkenntnis-skritik. Berlin: Dümmler. Repr. in in CW, vol. 5/I. Cohen, Hermann. 1885. Kants Theorie der Erfahrung. 2nd ed. Berlin: Dümmler. Repr. in in CW, vol. 1/I. Cohen, Hermann. 1888. “Jubiläums-Betrachtungen.” Philosophische Monatshefte 24: 257–291. Repr. in Cohen 1928, 1:397–431. Cohen, Hermann. 1895. “Worte an der Bahre von Adolf Elsas, Professor der Physik an der Universität Marburg.” Gesprochen im Trauerhause am 16. Mai 1895. In Cohen 1928, pp. 396–397. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 318 Sensation and Stimulus Cohen, Hermann. 1896. “Einleitung mit kritischem Nachtrag.” In Geschichte des Materialismus und Kritik seiner Bedeutung in der Gegenwart, 5th edited by Friedrich Albert Lange. Leipzig: Baedeker. Repr. in CW, Vol. 5/2. Cohen, Hermann. 1902. Logik der reinen Erkenntnis. Berlin: B. Cassirer. Repr. in CW, vol. 6. Cohen, Hermann. 1910a. “August Stadler: Ein Nachruf.” Kant-Studien 15: 403–420. Repr. in CW, vol. 15, 513–542. Cohen, Hermann. 1910b. Kants Begründung der Ethik: nebst ihren Anwendungen auf Recht, Religion und Geschichte. 2nd edn. Berlin: B. Cassirer. Cohen, Hermann. 1913–1914. Paul Natorp: Zu seinem 60. Geburtstag. Pp. 466–470 in Cohen 1928. Cohen, Hermann. 1928. Schriften zur Philosophie und Zeitgeschichte, eds. Albert Görland and Ernst Cassirer. Berlin: B. Cassirer. Cohen, Hermann. 2015. Briefe an August Stadler. Edited by Hartwig Widebach. Basel: Schwabe. Darrigol, Olivier. 2003. “Number and Measure: Hermann Von Helmholtz at the Crossroads of Mathematics, Physics, and Psychology.” Studies in the History of the Philosophy of Science 34: 515–73. Delbœuf, Joseph. 1873. Études psychophysiques sur la mesure des sensations. Bruxelles: Muquardt. Delbœuf, Joseph. 1878. “La loi psychophysique et le nouveau livre de Fechner.” Revue philosophique de la France et de l’etranger 5: 34–63. Delezenne, Charles Edouard Joseph. 1826. “Mémoire sur les valeurs numériques des notes de la gamme.” Recueil des travaux de la Societè des Sciences de l’Agriculture et des Arts de Lille 1826 et premier semestre 1827 4: 1–56. Dzhafarov, Ehtibar N., and Hans Colonius. 1999. “Fechnerian Metrics in Unidimensional and Multidimensional Stimulus Spaces.” Psychonomic Bulletin & Review 6 (2): 239–268. Eccarius, Wolfgang. 1985. “Georg Cantor und Kurd Laßwitz: Briefe zur Philosophie des Unendlichen.” NTM – Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin 22 (1): 29–52. Elsas, Adolf. 1881. Ueber erzwungene Schwingungen weicher Fäden. Würzburg: Elberfeld / Fassbender. Elsas, Adolf. 1882. Untersuchungen über erzwungene Membranschwingungen. Marburg: Blochmann & Sohn. Elsas, Adolf. 1883a. “Review of Müller, Das Axiom der Psychophysik (Müller 1882).” Zeitschrift für Philosophie und Philosophische Kritik 83: 126–134. Elsas, Adolf. 1883b. “Untersuchungen über erzwungene Schwingungen von Platten.” Annalen der Physik und Chemie new 20 (11): 468–484. Elsas, Adolf. 1884. “Review of Cohen, Das Princip der Inﬁnitesimal-Methode (Cohen 1883).” Philosophische Monatshefte 20: 556–560. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 319 Elsas, Adolf. 1885a. “Bemerkungen zu der Abhandlung des Herrn F. Melde: Akustische Experimentaluntersuchungen.” Annalen der Physik und Chemie new 25 (8): 676–677. Elsas, Adolf. 1885b. “Review of Stadler, Kants Theorie der Materie (Stadler 1883).” Philosophische Monatshefte 21: 144–160. Elsas, Adolf. 1886a. Der Schall: Eine populäre Darstellung der physikalischen Akustik mit besonderer Berücksichtigung der Musik. Leipzig/Prag: Freytag / Tempsky. Elsas, Adolf. 1886b. Über die Psychophysik: Physikalische und erkenntnisstheor- etische Betrachtungen. Marburg: Elwert. Elsas, Adolf. 1886c. “Ueber die Nobili’schen Farbenringe und verwandte electrochemische Erscheinungen.” Annalen der Physik und Chemie new 29 (10): 331–343. Elsas, Adolf. 1887. “Ueber die Nobili’schen Farbenringe und verwandte electrochemische Erscheinungen.” Annalen der Physik und Chemie new 30 (4): 620–630. Elsas, Adolf. 1888a. “Die Deutung der psychophysischen Gesetze.” Philosophische Monatshefte 24: 129–155. Elsas, Adolf. 1888b. “Zum Andenken Gustav Theodor Fechners.” Die Grenzboten: Zeitschrift für Politik, Literatur und Kunst 47 (2): 73–80, 113–124. Elsas, Adolf. 1889a. “Kritische Betrachtungen über die Wahrscheinlich- keitsrechnung.” Philosophische Monatshefte 25: 557–584. Elsas, Adolf. 1889b. “Ueber einen selbstthätigen Stromunterbrecher.” Annalen der Physik und Chemie new 37 (8): 675–680. Elsas, Adolf. 1891a. “Review of Lasswitz, Geschichte der Atomistik (Lasswitz 1890).” Zeitschrift für Philosophie und Philosophische Kritik 99: 290–303. Elsas, Adolf. 1891b. “Ueber eine neue Methode zur Bestimmung von Dielectricitätsconstanten.” Annalen der Physik und Chemie new 280 (12): 654–665. Elsas, Adolf. 1891c. “Ueber Widerstandsmessungen mit Hülfe des Telephons.” Annalen der Physik und Chemie 44 (12): 666–680. Fechner, Gustav Theodor. 1851. Zend-Avesta oder über die Dinge des Himmels und des Jenseits: Vom Standpunkt der Naturbetrachtung 3 vols. Hamburg: Voss. Fechner, Gustav Theodor. 1860. Elemente der Psychophysik. 2 vols. Leipzig: Breitkopf & Härtel. First volume translated in Fechner 1966. Fechner, Gustav Theodor. 1877. In Sachen der Psychophysik. Leipzig: Breitkopf und Härtel. Fechner, Gustav Theodor. 1882. Revision der Hauptpuncte der Psychophysik. Leipzig: Breitkopf & Härtel. Fechner, Gustav Theodor. 1888. “Ueber die psychischen Maßprincipien und das Weber’sche Gesetz: Discussion mit Elsas und Köhler.” Edited l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 320 Sensation and Stimulus by Wilhelm Wundt. Philosophische Studien 4: 161–230. Partially translated in Fechner 1987. Fechner, Gustav Theodor. 1966. Elements of Psychophysics, ed. Davis H. Howes and Edwin G. Boring, trans. Helmut E. Adler. With an Introduction by Edwin G. Boring. Vol. 1. New York: Holt, Rinehart / Winston. Fechner, Gustav Theodor. 1987. “My Own Viewpoint on Mental Mea- surement (1887),” trans. Eckart Scheerer. Psychological Research 49 (4): 213–219. Fölsing, Albrecht. 1997. Heinrich Hertz: eine Biographie. Hamburg: Hoffmann und Campe. Giovanelli, Marco. 2016. “Hermann Cohen’s Das Princip der Inﬁnitesimal- Methode: The History of an Unsuccessful Book.” Studies in History and Philos- ophy of Science Part A 58: 9–23. Görland, Albert. 1899. Aristoteles und die Mathematik. Marburg: Elwert. Heidelberger, Michael. 1993. “Fechner’s Impact for Measurement Theory.” Behavioral and Brain Sciences 16 (1): 146–148. Heidelberger, Michael. [1993] 2004. Nature from Within: Gustav Theodor Fechner and His Psychophysical Worldview. Pittsburgh: University of Pittsburgh Press. Heidelberger, Michael. 2010. “Functional Relations and Causality in Fechner and Mach.” Philosophical Psychology 23 (2): 163–172. Helmholtz, Hermann von. 1867. Handbuch der physiologischen Optik. Leipzig: Voss. Helmholtz, Hermann von. 1877. Die Lehre von den Tonempﬁndungen als physio- logische Grundlage für die Theorie der Musik. Braunschweig: Vieweg. Helmholtz, Hermann von. 1887. Zählen und Messen, erkenntnisstheoretisch betrachtet. Pp. 17–52 in Philosophische Aufsätze, Eduard Zeller zu seinem fünfzigjährigen Doctorjubiläum gewidmet. Leipzig: Fues. Hering, Ewald. 1875. Zur Lehre von der Beziehung zwischen Leib und Seele: I. Mittheilung: Über Fechner’s psychophysisches Gesetz. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien 72 (III Abt.): 310–348. Holzhey, Helmut. 1986. Cohen und Natorp. 2 vols. Basel: Schwabe. Kant, Immanuel. 1786. Metaphysische Anfangsgründe der Naturwissenschaft. Riga: Johann Friedrich Hartknoch. Repr. in Ak. 4:465–565. Köhler, Alfred. 1886. “Ueber die hauptsächlichen Versuche einer mathe- matischen Formulirung des psychophysischen Gesetzes von Weber.” Philosophische Studien 3: 572–642. Kries, Johannes von. 1882. “Ueber die Messung intensiver Grössen und über das sogenannte psychophysische Gesetz.” Vierteljahrsschrift für wissenschaftliche Philosophie 4 (3): 257–294. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 321 Lange, Friedrich Albert. 1866. Geschichte des Materialismus und Kritik seiner Bedeutung in der Gegenwart, 1st edn. Iserlohn: Baedeker. Lange, Friedrich Albert. 1968. Über Politik und Philosophie: Briefe und Leitartikel 1862 bis 1875. Edited by Georg Eckert. Duisburg: Braun. Lasswitz, Kurd. 1878. Atomistik und Kriticismus: Ein Beitrag zur erkenntnistheoretischen Grundlegung der Physik. Vieweg: Braunschweig. Lasswitz, Kurd. 1884. “Giordano Bruno und die Atomistik.” Vierteljahrsschrift für wissenschaftliche Philosophie 8: 18–55. Lasswitz, Kurd. 1885a. “Review of Cohen, Das Princip der Inﬁnitesimal- Methode (Cohen 1883).” Vierteljahrsschrift für wissenschaftliche Philosophie und Soziologie 9: 494–503. Lasswitz, Kurd. 1885b. “Zur Rechtfertigung der kinetischen Atomistik.” Vierteljahrsschrift für wissenschaftliche Philosophie 9: 137–161. Lasswitz, Kurd. 1887a. “Review of Elsas, Über die Psychophysik (Elsas 1886b).” Deutsche Literaturzeitung 8: 3–4. Lasswitz, Kurd. 1887b. “Review of Müller, Das Problem der Continuität im Mathematik und Mechanik (Müller 1886).” Deutsche Literaturzeitung 28: 1003–1004. Lasswitz, Kurd. 1888. “Das Problem der Continuität.” Philosophische Monatshefte 24: 9–36. Lasswitz, Kurd. 1890. Geschichte der Atomistik 2 vols. Hamburg/Leipzig: Voss. Luft, Sebastian. 2009. “Reconstruction and Reduction: Natorp and Husserl on Method and the Question of Subjectivity.” Pp. 59–91 in Makkreel and Luft 2009. Luft, Sebastian. ed. 2015. The Neo-Kantian Reader. London/New York: Routledge. Mach, Ernst. 1863. Vorträge über Psychophysik. Wien: Sommer. Makkreel, Rudolf A., and Sebastian Luft, eds. 2009. Neo-Kantianism in Contemporary Philosophy. Bloomington: Indiana University Press. Michell, Joel. 1999. Measurement in Psychology: Critical History of a Method- ological Concept. Cambridge: Cambridge University Press. Müller, Ferdinand August. 1882. Das Axiom der Psychophysik und die psychologische Bedeutung der Weber’schen Versuche. Marburg: Elwert. Müller, Ferdinand August. 1886. Das Problem der Continuität im Mathematik und Mechanik: Historische und systematische Beiträge. Elwert: Marburg. Müller, Georg Elias. 1878. Zur Grundlegung der Psychophysik: Kritische Beiträge. Berlin: Grieben. Natorp, Paul. 1881. “Leibniz und der Materialismus.” First pub. in Helmut Holzhey, “Paul Natorp. Leibniz und der Materialismus (1881).” Studia Leibnitiana 17 (1): 3–14. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 322 Sensation and Stimulus Paulsen, Johannes. 1906–1907. “Der Begriff der Empﬁndung bei Fechner.” Inauguraldissertation, Universität Marburg. Paulsen, Johannes. 1907. Das Problem der Empﬁndung. Töpelmann: Giessen. Paulsen, Johannes. 1912. “Ueber das empirische Verhältnis von Reiz und Empﬁndung.” Pp. 123–135 in Philosophische Abhandlungen: Hermann Cohen zum 70. Geburtstag (4. Juli 1912) dargebracht, Berlin: B. Cassirer. Philippi, E. 1883. “Review of Müller, Das Axiom der Psychophysik (Müller 1882).” Philosophische Monatshefte 19: 574–587. Plateau, Joseph. 1872. “Sur la mesure des sensations physiques et sur la loi qui lie l’intensité de ces sensations à l’intensité de la cause excitante.” Bulletins de l’Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 2me Serie 34: 141–142. Poma, Andrea. [1989] 1997. The Critical Philosophy of Hermann Cohen. Albany, NY: State University of New York Press. Portu, Enrico Stefano Maria de. 1904. Galileis Begriff der Wissenschaft. Scheerer, Eckart. 1987. “The Unknown Fechner.” Psychological Research 49 (4): Marburg: Elwert. 197–202. Sieg, Ulrich. 1994. Aufstieg und Niedergang des Marburger Neukantianismus: Die Geschichte einer philosophischen Schulgemeinschaft. Würzburg: Königshausen und Neumann. Stadler, August. 1874. Kants Teleologie und ihre erkenntnisstheoretische Bedeutung: Eine Untersuchung. Berlin: Dümmler. Stadler, August. 1876. Die Grundsätze der reinen Erkenntnisstheorie in der Kantischen Philosophie: Kritische Darstellung. Leipzig: Hirzel. Stadler, August. 1878. “Über die Ableitung des Psychophysischen Gesetzes.” Philosophische Monatshefte 14: 215–23. Stadler, August. 1880. “Das Gesetz der Stetigkeit bei Kant.” Philosophische Monatshefte 16: 577–97. Stadler, August. 1883. Kants Theorie der Materie. Leipzig: Hirzel. Stevens, Stanley Smith. 1961. “To Honor Fechner and Repeal His Law.” Science 133 (3446): 80–86. Tannery, Jules. 1875a. “Correspondence: A propos du logarithme des sensations.” La Revue scientiﬁque 15: 876–877. Tannery, Jules. 1875b. “La mesure des sensations: Réponses à propos du logarithme des sensations.” La Revue scientiﬁque 8: 1018–1020. Weber, Ernst Heinrich. 1834. De pulsu, resorptione, auditu et tactu: Annotationes anatomicae et physiologicae. Leipzig: Koehler. Weber, Ernst Heinrich. 1846. Tastsinn und Gemeingefühl. In Handwörterbuch der Physiologie mit Rücksicht auf physiologische Pathologie, Edited by Rudolph Wagner, 3.2:481–588. Braunschweig: Vieweg. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Perspectives on Science 323 Wundt, Wilhelm. 1874. Grundzüge der physiologischen Psychologie. Leipzig: Engelmann. Zeller, Eduard. 1881. “Über die Messung psychischer Vorgänge.” Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin: Philosophisch-Historische Klasse 3: 1–16. Zeller, Eduard. 1882. Einige weitere Bemerkungen über die Messung psychischer Vorgänge. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin vol. 1:295–305. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u p o s c / a r t i c e - p d l f / / / / 2 5 3 2 8 7 1 7 9 0 3 0 8 p o s c _ a _ 0 0 2 4 4 p d . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3
Scarica il pdf