Analítica (3), oct. de 2023 – sept. de 2024, ISSN – L 2805 – 1815, pp. 39-63
ANALÍTICA
Revista de Filosofía
SEMANTICS OF GALILEO’S GRAVITY (THOUGHT)
EXPERIMENTS
SEMÁNTICA DE LOS EXPERIMENTOS (MENTALES) DE
GRAVEDAD DE GALILEO
C. P. Hertogh
Free University Brussels – (VUB-BE/EU)
noromyxo2005@gmail.com
https://orcid.org/0000-0002-6778-4837
DOI https://doi.org/10.48204/2805-1815.4310
INFORMACIÓN DEL
ARTÍCULO ABSTRACT/RESUMEN
Recibido el: 5/08/2023
Aceptado el: 1/09/203
Keywords:
Semantics, thought experiment
(TE), gravity, falling bodies,
compound bodies, surface
structure (multiple TE),
(logical) deep structure
Palabras clave:
Semántica, experimento mental
(TE), gravedad, cuerpos en caída,
cuerpos compuestos, estructura
superficial (múltiples TE),
estructura profunda (lógica)
:
Abstract:
Galileo Galilei's Gravity TE Falling Bodies may be analyzed as a
(series of) elementary ideal Trial and Error TE (thought
experiments) analogous to experiments (E) in science. We
consider these TE from classical induction the basic TE of natural
sciences. As to bridge the (hermeneutical) gap between E and
TE in Galileo and its comments of Aristotle, we introduce two
types of TE, Experience TE, and Experiment TE.
The Falling Bodies TE appear in 1638 Dialogues concerning Two
New Sciences, and they have recently been updated by Apollo
15's The Hammer and The Feather, a falling experiment
conducted onthe surface of the moon (Scott, 1971). In recent TE
literature it is remarked that they have long been mistaken for a
real experiment (Galileo throwing two objects from Tower of
Pisa), and it is currently analyzed as a counter-Aristotelian TE of
Compound or Strapped Bodies (Gendler, 1996/2000; Brown
1991a, 1991b; Sorensen, 1992; Brown & Fehige, 2019).
In the logical deep analyses we show with help of mathematical
predicate logic (1) that the transitive Aristotelian falling theory is
replaced by the simpler for symmetrical Galilean gravity theory (as
in the second case all objects fall independent of their masses with
the same speed relative to gravitation constant of the heavenly
body under investigation) and (2) that in accordance with, e.g.,
Carnapian assumptions inductive and deductive protocols may be
considered complementary, that is, translatable into each other,
C.P. Hertogh 40
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
which may explain how Trial and Error TE may be interpreted as
Ideal(ized) Experiments.
Resumen:
Los TE de los cuerpos en caída aparecen en el Diálogo sobre los
Dos Nuevos Principios de 1638, y recientemente han sido
actualizados por el experimento del martillo y la pluma de la misión
Apollo 15, una prueba de caída realizada en la superficie de la luna
(Scott, 1971). En la literatura reciente sobre TE se destaca que
durante mucho tiempo se les ha considerado erróneamente como
un experimento real (Galileo lanzando dos objetos desde la Torre
de Pisa), y que actualmente se analizan como un TE antagónico a
Aristóteles, de cuerpos compuestos o atados (Gendler, 1996/2000;
Brown, 1991a, 1991b; Sorensen, 1992; Brown & Fehige, 2019).
En los análisis lógicos profundos mostramos, con la ayuda de la
lógica matemática de predicados, que (1) la teoría transitiva
aristotélica de la caída es reemplazada por la teoría galileana, más
simple, de la gravedad simétrica (ya que en el segundo caso, todos
los objetos caen independientemente de sus masas con la misma
velocidad relativa a la constante de gravedad del cuerpo celeste
bajo investigación) y (2) que, de acuerdo con, por ejemplo, las
suposiciones carnapianas, los protocolos inductivos y deductivos
pueden considerarse complementarios, es decir, traducibles entre
sí, lo que puede explicar cómo los TE de ensayo y error pueden
interpretarse como experimentos Ideales.
Introduction
Galileo Galilei's Falling Bodies experiment as from top of Leanng Tower of Pisa has
recently got renewed attention as a TE instead of an E (e.g. Brown, 1991a, 1991b;
Sorensen, 1992; Gendler, 1996/2000; Brown & Fehige, 2019). Close reading of the
original Galilean TE text may yield the same conclusion. But it may lead to another
formalization of the TE as after the many more (T)E in this Galilean text. Difference
between TE and E is not always completely sure from the original phrasings of e.g.
Aristotle and Galileo (especially not if we may read some phrases metaphorically), and
we may suppose that Aristotle, among more ancient Greeks, such as Archimedes and
Pythagoras, just like e.g. Chinese scientists and philosophers, such as Mozi, already
conducted real E, which may breach the traditional historical dichotomy between the
Ancient and Medieval Period and the herald of the New Period in western science and
philosophy, of which Galileo is one of the best known representatives. Moreover, on
close reading it may appear that Galileo, like Aristotle, may have conducted many more
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
which may explain how Trial and Error TE may be interpreted as
Ideal(ized) Experiments.
Resumen:
Los TE de los cuerpos en caída aparecen en el Diálogo sobre los
Dos Nuevos Principios de 1638, y recientemente han sido
actualizados por el experimento del martillo y la pluma de la misión
Apollo 15, una prueba de caída realizada en la superficie de la luna
(Scott, 1971). En la literatura reciente sobre TE se destaca que
durante mucho tiempo se les ha considerado erróneamente como
un experimento real (Galileo lanzando dos objetos desde la Torre
de Pisa), y que actualmente se analizan como un TE antagónico a
Aristóteles, de cuerpos compuestos o atados (Gendler, 1996/2000;
Brown, 1991a, 1991b; Sorensen, 1992; Brown & Fehige, 2019).
En los análisis lógicos profundos mostramos, con la ayuda de la
lógica matemática de predicados, que (1) la teoría transitiva
aristotélica de la caída es reemplazada por la teoría galileana, más
simple, de la gravedad simétrica (ya que en el segundo caso, todos
los objetos caen independientemente de sus masas con la misma
velocidad relativa a la constante de gravedad del cuerpo celeste
bajo investigación) y (2) que, de acuerdo con, por ejemplo, las
suposiciones carnapianas, los protocolos inductivos y deductivos
pueden considerarse complementarios, es decir, traducibles entre
sí, lo que puede explicar cómo los TE de ensayo y error pueden
interpretarse como experimentos Ideales.
Introduction
Galileo Galilei's Falling Bodies experiment as from top of Leanng Tower of Pisa has
recently got renewed attention as a TE instead of an E (e.g. Brown, 1991a, 1991b;
Sorensen, 1992; Gendler, 1996/2000; Brown & Fehige, 2019). Close reading of the
original Galilean TE text may yield the same conclusion. But it may lead to another
formalization of the TE as after the many more (T)E in this Galilean text. Difference
between TE and E is not always completely sure from the original phrasings of e.g.
Aristotle and Galileo (especially not if we may read some phrases metaphorically), and
we may suppose that Aristotle, among more ancient Greeks, such as Archimedes and
Pythagoras, just like e.g. Chinese scientists and philosophers, such as Mozi, already
conducted real E, which may breach the traditional historical dichotomy between the
Ancient and Medieval Period and the herald of the New Period in western science and
philosophy, of which Galileo is one of the best known representatives. Moreover, on
close reading it may appear that Galileo, like Aristotle, may have conducted many more
41 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
experiments and thought experiments, an amazing variety of series of multiple fall
(thought) experiments of objects of different materials, from different distances, in
different media as air, (hypothetical) void, water, wine, mercury etc.
However, there is a significant breach in gravity theories between the
Ancient/Medieval Period and the New Period, which could indeed be considered as a
paradigm shift (see e.g. Kuhn, 1962/1996), and which may be understood more fully by
hindsight as from Albert Einstein's work and definition of idealized experiments, which
per definition can't be real E, and so are necessarily TE, and necessarily ideal concepts
as (movement in) vacuum (which can't be realized on Planet Earth).
We will first show that the text of Aristotle and Galileo discuss many more
experiments and thought experiments (surface analyses show a series of multiple TE)
and, next, that we may formalize the TE in the same way as the E, namely as classical
induction (T)E, applying traditional inductive logical formulas, inferring, first, inductive
universal instantiation, which appears translatable in second deductive universal
instantiation.
We conclude by returning to the notion of ideal experiment and understand
classical physics as an exemplification of mathematics just because physics is
expressed in mathematical formulas, and notice that the theoretical distance to
understanding by intuition--traditional explanans of dynamics of thought experiments--
has got wider and wider throughout the history of physics, since Aristotle's theory may
still seem most intuitively plausible (as after conducting of real E), and Einstein's relativity
theory can hardly be demonstrated anymore by Es on Planet Earth.
Thought Experiments (TE) and Experiments (E) . Experience and
Experiment TE (TEEI, TEEX)
SIMP. His [Aristotle's] language would seem to indicate that he [Aristotle] had
tried the experiment, because he [Aristotle] says: We see the heavier; now the
word see shows that he [Aristotle] had made the experiment. (Galileo,
1638/1914, p. 106, italics in original, bracketed explanation added)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
experiments and thought experiments, an amazing variety of series of multiple fall
(thought) experiments of objects of different materials, from different distances, in
different media as air, (hypothetical) void, water, wine, mercury etc.
However, there is a significant breach in gravity theories between the
Ancient/Medieval Period and the New Period, which could indeed be considered as a
paradigm shift (see e.g. Kuhn, 1962/1996), and which may be understood more fully by
hindsight as from Albert Einstein's work and definition of idealized experiments, which
per definition can't be real E, and so are necessarily TE, and necessarily ideal concepts
as (movement in) vacuum (which can't be realized on Planet Earth).
We will first show that the text of Aristotle and Galileo discuss many more
experiments and thought experiments (surface analyses show a series of multiple TE)
and, next, that we may formalize the TE in the same way as the E, namely as classical
induction (T)E, applying traditional inductive logical formulas, inferring, first, inductive
universal instantiation, which appears translatable in second deductive universal
instantiation.
We conclude by returning to the notion of ideal experiment and understand
classical physics as an exemplification of mathematics just because physics is
expressed in mathematical formulas, and notice that the theoretical distance to
understanding by intuition--traditional explanans of dynamics of thought experiments--
has got wider and wider throughout the history of physics, since Aristotle's theory may
still seem most intuitively plausible (as after conducting of real E), and Einstein's relativity
theory can hardly be demonstrated anymore by Es on Planet Earth.
Thought Experiments (TE) and Experiments (E) . Experience and
Experiment TE (TEEI, TEEX)
SIMP. His [Aristotle's] language would seem to indicate that he [Aristotle] had
tried the experiment, because he [Aristotle] says: We see the heavier; now the
word see shows that he [Aristotle] had made the experiment. (Galileo,
1638/1914, p. 106, italics in original, bracketed explanation added)
C.P. Hertogh 42
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Both the fall experiments and discussion on Aristotelian gravity theory are in the
dialogue of the first day between Salviati, Sagredo and Simplicio (resp. usually
Galilean, neutral, and Aristotelian view) in Galileo/Crew (1638/1914) Mathematical
Discourses and Demonstrations, relating to Two New Sciences, treatise on the
behavior of bodies in motion, the nature of acceleration, etc. (which book title is often
abbreviated to Dialogues concerning Two New Sciences or The Two New Sciences).
As we will see later, it is about examples of singular, elementary, or basic TE, Ideal
Experiments that chain a series of Trial and Error TE.
As clarified by the bracketed explanation the motto quote does not refer to Galileo
but to Aristotle and it is Simplicio's reply to Salviati's doubt if Aristotle may ever have
tested by experiment whether two stones of unequal weight may fall at the same
speed.
It may seem obvious that the ancients already performed experiments as
according to some experimental methodology of ceteris paribus and it can even be
inferred from Salviati's statement about Aristotle:
… Aristotle declares that bodies of different weights, in the same medium, travel
(in so far as their motion depends upon gravity) with speeds which are
proportional to their weights; this he illustrates by use of bodies in which it is
possible to perceive the pure and unadulterated effect of gravity, eliminating other
considerations, for example, figure as being of small importance [minimi
momenti], influences which are greatly dependent upon the medium which
modifies the single effect of gravity alone. … (Galileo, 1638/1914, p.109, brackets
in original text, italics added)
Some of Galileo's (T)E are clearly stated as an experiment e.g., Sagredo
emphasizing
But I, Simplicio, who have made the test can assure you that a cannon ball
weighing one or two hundred pounds, or even more, will not reach the ground by
as much as a span ahead of a musket ball weighing only half a pound, provided
both are dropped from a height of 200 cubits. (Galileo 1638/1914, p. 106-107,
italics added)
Some passages, however, have the form of a TE including TE indicators as
'Consider...', 'Imagine...' e.g.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Both the fall experiments and discussion on Aristotelian gravity theory are in the
dialogue of the first day between Salviati, Sagredo and Simplicio (resp. usually
Galilean, neutral, and Aristotelian view) in Galileo/Crew (1638/1914) Mathematical
Discourses and Demonstrations, relating to Two New Sciences, treatise on the
behavior of bodies in motion, the nature of acceleration, etc. (which book title is often
abbreviated to Dialogues concerning Two New Sciences or The Two New Sciences).
As we will see later, it is about examples of singular, elementary, or basic TE, Ideal
Experiments that chain a series of Trial and Error TE.
As clarified by the bracketed explanation the motto quote does not refer to Galileo
but to Aristotle and it is Simplicio's reply to Salviati's doubt if Aristotle may ever have
tested by experiment whether two stones of unequal weight may fall at the same
speed.
It may seem obvious that the ancients already performed experiments as
according to some experimental methodology of ceteris paribus and it can even be
inferred from Salviati's statement about Aristotle:
… Aristotle declares that bodies of different weights, in the same medium, travel
(in so far as their motion depends upon gravity) with speeds which are
proportional to their weights; this he illustrates by use of bodies in which it is
possible to perceive the pure and unadulterated effect of gravity, eliminating other
considerations, for example, figure as being of small importance [minimi
momenti], influences which are greatly dependent upon the medium which
modifies the single effect of gravity alone. … (Galileo, 1638/1914, p.109, brackets
in original text, italics added)
Some of Galileo's (T)E are clearly stated as an experiment e.g., Sagredo
emphasizing
But I, Simplicio, who have made the test can assure you that a cannon ball
weighing one or two hundred pounds, or even more, will not reach the ground by
as much as a span ahead of a musket ball weighing only half a pound, provided
both are dropped from a height of 200 cubits. (Galileo 1638/1914, p. 106-107,
italics added)
Some passages, however, have the form of a TE including TE indicators as
'Consider...', 'Imagine...' e.g.
43 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Salviati
Let us, in view of this, consider what takes place in air, where for the sake of a
definite figure and light material imagine an inflated bladder. The air in this
bladder when surrounded by air will weigh little or nothing, since it can be only
slightly compressed; its weight then is small being merely that of the skin which
does not amount to the thousandth part of a mass of lead having the same size
as the inflated bladder. Now, Simplicio, if we allow these two bodies to fall from
a height of four or six cubits, by what distance do you imagine the lead will
anticipate the bladder? You may be sure that the lead will not travel three times,
or even twice, as swiftly as the bladder, although you would have made it move a
thousand times as rapidly. (Galileo 1638/1914, p. 117, italics added)
We would need more proof to falsify such an established paradigm as the rise of
the experimental method in western science, but there are surely indications that
experiments have been performed many ages before the Renaissance, including
ancient Greece of Aristotle's days, and that both the ancients and representatives of
the New Period used thought experiments.
Quite a few TE philosophers, such as Rescher (1991) and Lakatos (1976), detect
TE in texts of Greek ancients as pre-Socratic philosophers and pre-Euclidean
mathematicians.
In favor of the established view of Galileo's new experimental method we quote
Salviati where he tells about some sort of a crucial experiment defeating the results of
Aristotle's (supposed) mere reasoning
Aristotle says that 'an iron ball of one hundred pounds falling from a height of
one hundred cubits reaches the ground before a one-pound ball has fallen a
single cubit.' I say that they arrive at the same time. You find, on making the
experiment, that the larger outstrips the smaller by two finger-breadths, that is,
when the larger has reached the ground, the other is short of it by two finger-
breadths; …. (Galileo, 1638/1914, 109, italics added)
However, it does not contradict the importance of the manifold of additional (T)E to
both Aristotle's and Galileo's scientific methodology for--as our surface analyses may
show--just one TE or E is not sufficient to develop a new theory.
We guess that at least some of Aristotle's and Galileo's TE can be categorized as
Experience-like TE instead of Experiment-like TE, or possibly as a blend of these two
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Salviati
Let us, in view of this, consider what takes place in air, where for the sake of a
definite figure and light material imagine an inflated bladder. The air in this
bladder when surrounded by air will weigh little or nothing, since it can be only
slightly compressed; its weight then is small being merely that of the skin which
does not amount to the thousandth part of a mass of lead having the same size
as the inflated bladder. Now, Simplicio, if we allow these two bodies to fall from
a height of four or six cubits, by what distance do you imagine the lead will
anticipate the bladder? You may be sure that the lead will not travel three times,
or even twice, as swiftly as the bladder, although you would have made it move a
thousand times as rapidly. (Galileo 1638/1914, p. 117, italics added)
We would need more proof to falsify such an established paradigm as the rise of
the experimental method in western science, but there are surely indications that
experiments have been performed many ages before the Renaissance, including
ancient Greece of Aristotle's days, and that both the ancients and representatives of
the New Period used thought experiments.
Quite a few TE philosophers, such as Rescher (1991) and Lakatos (1976), detect
TE in texts of Greek ancients as pre-Socratic philosophers and pre-Euclidean
mathematicians.
In favor of the established view of Galileo's new experimental method we quote
Salviati where he tells about some sort of a crucial experiment defeating the results of
Aristotle's (supposed) mere reasoning
Aristotle says that 'an iron ball of one hundred pounds falling from a height of
one hundred cubits reaches the ground before a one-pound ball has fallen a
single cubit.' I say that they arrive at the same time. You find, on making the
experiment, that the larger outstrips the smaller by two finger-breadths, that is,
when the larger has reached the ground, the other is short of it by two finger-
breadths; …. (Galileo, 1638/1914, 109, italics added)
However, it does not contradict the importance of the manifold of additional (T)E to
both Aristotle's and Galileo's scientific methodology for--as our surface analyses may
show--just one TE or E is not sufficient to develop a new theory.
We guess that at least some of Aristotle's and Galileo's TE can be categorized as
Experience-like TE instead of Experiment-like TE, or possibly as a blend of these two
C.P. Hertogh 44
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
taxonomies, as they often refer not to a supposed experimental setting, but to daily
experiences, that is, they call to memory what we are supposed to know from daily life.
The call to imagination is partly a call to memory from past experiences. The Experience
feature of Galileo's TE is obvious in Galileo's Ship, where the thought experimenter recalls
common experiences from water travel by ship.
Experiment TE may resemble the description of a real experiment, but in Aristotle
and Galileo we can't be sure if the experiment has actually been conducted in reality. The
constraints of what an experiment or experimental setting may amount to, have got stricter
and more elaborate last centuries, and may include repetition of E, control E, use of
laboratorium and special equipment, from telescope in classical physics to cyclotron in
modern physics.
Surface Analyses
Galileo's Gravity TE of Falling Bodies, one of the most famous TE in the history of
science was sometimes mistakenly thought to be a real experiment (see e.g. Lodge,
1960, p. 90, recounted in Sorensen,1992, pp. 224-225, who discusses it as an
example of a 'mythical experiment'), and even today it is misleadingly accompanied
by illustrations of a tower representing the famous Leaning Tower of Pisa, and two
objects falling down from it as the I don't even have to look Galileo cartoon in Stanford
Encyclopedia of Philosophy (Brown & Fehige, 2019, fig. 6). In The Two New Sciences
there are no illustrations in this section, none of all 126 figures in the book shows a
tower with falling bodies, and while (T)E of bodies falling from a tower are described
some two or three times, there is no reference to Pisa's Leaning Tower. We must add
that part of mystery, magic and fame of the TE may have been brought about because
of association with Leaning Tower and Renaissance Italian culture and art in general
and Galileo in particular. Galileo (1564 – 1642) is considered one of the great creators
of the Renaissance as well as the founder of western (experimental) science as
prefaces and introductions don't forget to tell.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
taxonomies, as they often refer not to a supposed experimental setting, but to daily
experiences, that is, they call to memory what we are supposed to know from daily life.
The call to imagination is partly a call to memory from past experiences. The Experience
feature of Galileo's TE is obvious in Galileo's Ship, where the thought experimenter recalls
common experiences from water travel by ship.
Experiment TE may resemble the description of a real experiment, but in Aristotle
and Galileo we can't be sure if the experiment has actually been conducted in reality. The
constraints of what an experiment or experimental setting may amount to, have got stricter
and more elaborate last centuries, and may include repetition of E, control E, use of
laboratorium and special equipment, from telescope in classical physics to cyclotron in
modern physics.
Surface Analyses
Galileo's Gravity TE of Falling Bodies, one of the most famous TE in the history of
science was sometimes mistakenly thought to be a real experiment (see e.g. Lodge,
1960, p. 90, recounted in Sorensen,1992, pp. 224-225, who discusses it as an
example of a 'mythical experiment'), and even today it is misleadingly accompanied
by illustrations of a tower representing the famous Leaning Tower of Pisa, and two
objects falling down from it as the I don't even have to look Galileo cartoon in Stanford
Encyclopedia of Philosophy (Brown & Fehige, 2019, fig. 6). In The Two New Sciences
there are no illustrations in this section, none of all 126 figures in the book shows a
tower with falling bodies, and while (T)E of bodies falling from a tower are described
some two or three times, there is no reference to Pisa's Leaning Tower. We must add
that part of mystery, magic and fame of the TE may have been brought about because
of association with Leaning Tower and Renaissance Italian culture and art in general
and Galileo in particular. Galileo (1564 – 1642) is considered one of the great creators
of the Renaissance as well as the founder of western (experimental) science as
prefaces and introductions don't forget to tell.
45 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
However, study of Galileo's authentic Gravity TE text shows that these
eurocentric connotations aren't, in fact, in the TE text. Theoretically speaking, one of
its precursors was Mozi (墨子Mo Tzu or Mo Ching, ca. 470 – ca. 391 BCE), founder
of Mohism in the Chinese Hundred Schools of Thought Period, who already wrote on,
e.g., forces and motion, e.g., reminding Galileo's law of inertia, Isaac Newton's first
law of motion “The cessation of motion is due to the opposing force ... If there is no
opposing force ... the motion will never stop …”. (e.g., Needham, 1962, p. 56)1
The Hammer and The Feather
Galileo's Gravity TE has a brilliant update in Galileo's Gravity Experiment The Hammer
and The Feather, a sci story that could look quite sci-fi. It is a video of an experiment by
an astronaut on the moon (name of astronaut and date of video go alas unmentioned).
The astronaut is shown to drop both a hammer and a falcon feather from chest height
and one can witness clearly how they fall at the same speed and hit the surface of the
1 From Needham (1962) on physics. After Joseph Needham's decease his work on science and civilization
in China continues under name of Needham Research Institute. Cf. Smith (2016)
.... Few histories of physics consider developments outside Europe; and of those that do, non-
Western physics is often presented as ‘derivative’ of European work. However, recent scholarship
has made it clear that this European view is incomplete, and that numerous non-Western cultures,
including those of China, India, the Islamic world, and others, developed sophisticated physical
theories independently of Europe. In this expanded view, physics began in prehistoric times”.
Contrarily, western science is often derivative of eastern science, e.g., West and East now acknowledge
China was the first to invent or discover (woodblock, movable type) printing press, gunpowder, fireworks,
paper, paper money, compass, smallpox inoculation, mechanical clock, suspension bridge, alcohol, tea,
soy sauce, tofu, toothbrush, silk, umbrella, kite, acupuncture, chopsticks, go (board game), playing cards,
(hand, hanging) scroll, ink, porcelain, bronze, iron smelting, seed drill, row crop farming, earthquake
detector, rocket, etc. (see e.g. Wikipedia on (list of) Chinese inventions). Wrt ancient Chinese logic. Liu and
Zhang (2010) show e.g.
First, the Moist theory of classifying names had the same spirit as Aristotle’s account of “genus and
differentia.” Indeed, their view on the relationship between names and objects suggests that they
already realized the distinction between syntax and semantics, as found in modern authors like
Frege. (Liu & Zhang, 2010, p. 619)
We will discuss Galilean gravity theory and (T)E etc. as global cross-cultural, i.e., like they may have been
invented, discovered, and applied in non-western cultures, too.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
However, study of Galileo's authentic Gravity TE text shows that these
eurocentric connotations aren't, in fact, in the TE text. Theoretically speaking, one of
its precursors was Mozi (墨子Mo Tzu or Mo Ching, ca. 470 – ca. 391 BCE), founder
of Mohism in the Chinese Hundred Schools of Thought Period, who already wrote on,
e.g., forces and motion, e.g., reminding Galileo's law of inertia, Isaac Newton's first
law of motion “The cessation of motion is due to the opposing force ... If there is no
opposing force ... the motion will never stop …”. (e.g., Needham, 1962, p. 56)1
The Hammer and The Feather
Galileo's Gravity TE has a brilliant update in Galileo's Gravity Experiment The Hammer
and The Feather, a sci story that could look quite sci-fi. It is a video of an experiment by
an astronaut on the moon (name of astronaut and date of video go alas unmentioned).
The astronaut is shown to drop both a hammer and a falcon feather from chest height
and one can witness clearly how they fall at the same speed and hit the surface of the
1 From Needham (1962) on physics. After Joseph Needham's decease his work on science and civilization
in China continues under name of Needham Research Institute. Cf. Smith (2016)
.... Few histories of physics consider developments outside Europe; and of those that do, non-
Western physics is often presented as ‘derivative’ of European work. However, recent scholarship
has made it clear that this European view is incomplete, and that numerous non-Western cultures,
including those of China, India, the Islamic world, and others, developed sophisticated physical
theories independently of Europe. In this expanded view, physics began in prehistoric times”.
Contrarily, western science is often derivative of eastern science, e.g., West and East now acknowledge
China was the first to invent or discover (woodblock, movable type) printing press, gunpowder, fireworks,
paper, paper money, compass, smallpox inoculation, mechanical clock, suspension bridge, alcohol, tea,
soy sauce, tofu, toothbrush, silk, umbrella, kite, acupuncture, chopsticks, go (board game), playing cards,
(hand, hanging) scroll, ink, porcelain, bronze, iron smelting, seed drill, row crop farming, earthquake
detector, rocket, etc. (see e.g. Wikipedia on (list of) Chinese inventions). Wrt ancient Chinese logic. Liu and
Zhang (2010) show e.g.
First, the Moist theory of classifying names had the same spirit as Aristotle’s account of “genus and
differentia.” Indeed, their view on the relationship between names and objects suggests that they
already realized the distinction between syntax and semantics, as found in modern authors like
Frege. (Liu & Zhang, 2010, p. 619)
We will discuss Galilean gravity theory and (T)E etc. as global cross-cultural, i.e., like they may have been
invented, discovered, and applied in non-western cultures, too.
C.P. Hertogh 46
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
moon at the same time. The astronaut concludes “So, Mr. Galileo was correct in his
findings.” 2
Although one might say it is not a TE but a real experiment (E), one may, firstly,
question what is real. Is living on the moon as real as living on Planet Earth? Do the same
background assumptions apply as oxygen air, gravity etc.? Clearly not (on the moon there
is hardly any atmosphere and only a sixth part of Earth's gravitation)! Secondly, as it is a
modern-day registration of an experiment that can't be easily reperformed (when
scientists would like to do so, they would have to travel to the moon first), it may fit in with
classical TE feature of being essentially unperformable (as on Planet Earth). Thirdly, it
could easily be considered a crucial TE showing a paradigm shift--from paradigm of
experiments solely performed on Planet Earth to paradigm of experiments performed in
space, on the moon, on Mars etc. And, lastly, as it is a visual, video description of an
experiment it fits in with one more—but rather weak— feature of TE i.e., that is a
description of an experiment instead of an experiment itself.
Two New Sciences (Galileo/Crew 1638/1914)Series of TE
Returning to 17th century text by Galileo--The famous TE is introduced by Salviati to
Simplicio on the First Day of the Dialogues between Salviati, Sagredo and Simplicio
(Galileo, 1638/1914, p. 117) “Our problem is to find out what happens to bodies of
different weight moving in a medium devoid of resistance, so that the only difference in
speed is that which arises from inequality of weight”.
Not just falling bodies in air -fall experiment as we imagine it could have taken
place from Leaning Tower of Pisa- are discussed, but many more as relating to density of
medium -among more factors- and Sagredo and Salviati bring up for discussion many
alternate (T)E that not only vary mass (e.g. cannon ball of 200 pounds, musket ball of
only half a pound, stones of 20 pounds, 2 pounds, bird- shots), but also falling distance
(height – e.g. 1, 4-6, 12, 20, 50, 100, 200, 1,000, 'some thousands of cubits', 'from the
distance of the moon or from the upper regions of the atmosphere'), force, momentum,
2 See references, Top 10 Most Famous TE (on the net). It is about astronaut David Scott of Apollo 15
project in 1971.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
moon at the same time. The astronaut concludes “So, Mr. Galileo was correct in his
findings.” 2
Although one might say it is not a TE but a real experiment (E), one may, firstly,
question what is real. Is living on the moon as real as living on Planet Earth? Do the same
background assumptions apply as oxygen air, gravity etc.? Clearly not (on the moon there
is hardly any atmosphere and only a sixth part of Earth's gravitation)! Secondly, as it is a
modern-day registration of an experiment that can't be easily reperformed (when
scientists would like to do so, they would have to travel to the moon first), it may fit in with
classical TE feature of being essentially unperformable (as on Planet Earth). Thirdly, it
could easily be considered a crucial TE showing a paradigm shift--from paradigm of
experiments solely performed on Planet Earth to paradigm of experiments performed in
space, on the moon, on Mars etc. And, lastly, as it is a visual, video description of an
experiment it fits in with one more—but rather weak— feature of TE i.e., that is a
description of an experiment instead of an experiment itself.
Two New Sciences (Galileo/Crew 1638/1914)Series of TE
Returning to 17th century text by Galileo--The famous TE is introduced by Salviati to
Simplicio on the First Day of the Dialogues between Salviati, Sagredo and Simplicio
(Galileo, 1638/1914, p. 117) “Our problem is to find out what happens to bodies of
different weight moving in a medium devoid of resistance, so that the only difference in
speed is that which arises from inequality of weight”.
Not just falling bodies in air -fall experiment as we imagine it could have taken
place from Leaning Tower of Pisa- are discussed, but many more as relating to density of
medium -among more factors- and Sagredo and Salviati bring up for discussion many
alternate (T)E that not only vary mass (e.g. cannon ball of 200 pounds, musket ball of
only half a pound, stones of 20 pounds, 2 pounds, bird- shots), but also falling distance
(height – e.g. 1, 4-6, 12, 20, 50, 100, 200, 1,000, 'some thousands of cubits', 'from the
distance of the moon or from the upper regions of the atmosphere'), force, momentum,
2 See references, Top 10 Most Famous TE (on the net). It is about astronaut David Scott of Apollo 15
project in 1971.
47 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
figure (e.g. gold leaf, inflated bladder, stone), material of bodies (e.g. gold, lead, copper,
porphyry, ivory, ebony balls, bladder, wood, knots, roots), resistance of medium (e.g.
vacuum, air, water, wine, quicksilver). This array of (T)E is not only about falling (e.g.,
stones through air), but also about sinking (e.g., ball of lead through water, gold through
quicksilver) or drifting (e.g., knots and roots resting on water). The (T)E touch on
seemingly unrelated matters as cohesion of fluids (water, wine) and fish maws.
The (T)E are set to counter persistent doubts and critical questions by Simplicio
“Perhaps the result would be different if the fall took place not from a few cubits but from
some thousands of cubits” (Galileo 1638/1914, p. 110) or “Your discussion is really
admirable; yet I do not find it easy to believe that a bird-shot falls as swiftly as a cannon
ball” (Galileo, 1638/1914, p. 109) which are indeed justified as Aristotle's theory is more
in accordance with daily experience than Galileo's theory which seems counter-intuitive,
unnecessarily abstract etc.
Instead of just one E or TE we find in Galileo's text a multitude of a variety of series
of multiple TE, either mentioned by Galileo's interlocutors, or in Aristotle—as paraphrased
by Galileo. Some TE seem necessarily TE as they can't be performed in reality, certainly
in those days they could not, as falling bodies in vacuum, from 'some thousands of cubits',
'from the distance of the moon or from the upper regions of the atmosphere' etc.
The Hammer and the Feather (T)E fits in perfectly with this discussion as a whole,
as it is not just about falling in air – “this vapor-laden atmosphere of ours” (Galileo,
1638/1914, p. 122)-but about many more media, and changing the medium to the
atmosphere of the moon fits in with Galileo's line of argument. We may conclude that
neither Aristotle nor Galileo based their theories on just one E or TE, but that both have
performed many more (T)E, and, so, the authentic TE text in Two New Sciences suggests
an analysis of a series of basic or elementary (T)E instead of only one conclusive TE as
suggested in secondary TE literature as (Brown, 1991a, 1991b; Brown & Fehige, 2019).
The (T)E as mentioned in e.g. (Brown,1991a, 1991b; Brown & Fehige, 2019;
Sorensen, 1992 and Gendler, 1996/2000) is not a report of one of the many elementary
(T)E, but an argumentative reply by Galileo to a passage in Aristotle's text.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
figure (e.g. gold leaf, inflated bladder, stone), material of bodies (e.g. gold, lead, copper,
porphyry, ivory, ebony balls, bladder, wood, knots, roots), resistance of medium (e.g.
vacuum, air, water, wine, quicksilver). This array of (T)E is not only about falling (e.g.,
stones through air), but also about sinking (e.g., ball of lead through water, gold through
quicksilver) or drifting (e.g., knots and roots resting on water). The (T)E touch on
seemingly unrelated matters as cohesion of fluids (water, wine) and fish maws.
The (T)E are set to counter persistent doubts and critical questions by Simplicio
“Perhaps the result would be different if the fall took place not from a few cubits but from
some thousands of cubits” (Galileo 1638/1914, p. 110) or “Your discussion is really
admirable; yet I do not find it easy to believe that a bird-shot falls as swiftly as a cannon
ball” (Galileo, 1638/1914, p. 109) which are indeed justified as Aristotle's theory is more
in accordance with daily experience than Galileo's theory which seems counter-intuitive,
unnecessarily abstract etc.
Instead of just one E or TE we find in Galileo's text a multitude of a variety of series
of multiple TE, either mentioned by Galileo's interlocutors, or in Aristotle—as paraphrased
by Galileo. Some TE seem necessarily TE as they can't be performed in reality, certainly
in those days they could not, as falling bodies in vacuum, from 'some thousands of cubits',
'from the distance of the moon or from the upper regions of the atmosphere' etc.
The Hammer and the Feather (T)E fits in perfectly with this discussion as a whole,
as it is not just about falling in air – “this vapor-laden atmosphere of ours” (Galileo,
1638/1914, p. 122)-but about many more media, and changing the medium to the
atmosphere of the moon fits in with Galileo's line of argument. We may conclude that
neither Aristotle nor Galileo based their theories on just one E or TE, but that both have
performed many more (T)E, and, so, the authentic TE text in Two New Sciences suggests
an analysis of a series of basic or elementary (T)E instead of only one conclusive TE as
suggested in secondary TE literature as (Brown, 1991a, 1991b; Brown & Fehige, 2019).
The (T)E as mentioned in e.g. (Brown,1991a, 1991b; Brown & Fehige, 2019;
Sorensen, 1992 and Gendler, 1996/2000) is not a report of one of the many elementary
(T)E, but an argumentative reply by Galileo to a passage in Aristotle's text.
C.P. Hertogh 48
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
We can reconstruct this complex (T)E—one or two bodies and a compound body
falling through Planet Earth's atmosphere from considerable height as 200 cubits (i.e., 200
x 46 cm, 92 m)3—as both inductive and deductive universal instantiation (UI) of Galileo's
general physical law that objects (of same material, in same medium etc.) fall at the same
speed.
But, again, James Brown (and more philosophers) have not firstly reconstructed a
(T)E proving Galileo's law of gravity, but foremost Galileo's argument of refutation of
Aristotle's view that falling speed of objects depends on mass of the objects as illustrated
by an argument why a compound body falls with the same speed as its components.4
That is, their analyses don't represent the structure of the classical induction TE or Trial
and Error TE, that abound in Galileo's text, and many of which may have been real
3 A cubit is an ancient unit of length. 1 Cubit is 46 cm, 'based on the length of the forearm ...' (according to
Webster's 11th). The Leaning Tower of Pisa is about 56 m, so also proposed falling distance of 92 m does
not match Tower of Pisa.
4 This is indeed noticed by Tamar Gendler who unfolds something like a surface analysis in her 1996
dissertation. Although Gendler's discussion focuses on the famous TE of two bodies strapped together, her
introduction acknowledges that this TE only poses a weaker conclusion than the main one discussed in
Galileo's section aimed at challenging and falsifying the preeminent Aristotelian gravity view of linear
proportionality 'a moveable ten times as heavy as another is moved ten times as fast' as the other. Our
discussion does not neglect the many more E or TE (it is not always sure if they are E or TE) that are
mentioned in the text, in which, e.g., material of falling bodies, falling distance and (density of) medium is
changed. Gendler (1996, pp. 55-56):
Perhaps the most famous thought experiment in the history of western science is the thought
experiment with which Galileo is credited with having refuted the Aristotelian view that the speed
with which a body falls is directly proportional to its weight [...]. The thought experiment appears in
his last and most mature work, the Discourse Concerning Two New Sciences [...], in the context of
a more general discussion of the possibility and nature of motion in a void. Galileo's goal in the
section as a whole is to establish that 'if one were to remove entirely the resistance of the medium,
all materials would descend with equal speed' (Galileo 1638/1914, 116); the thought experiment in
question leads to the weaker conclusion that “both great and small bodies, of the same [material],
are moved with like speeds”. (Galileo, 1638/1914, p. 109, italics added).
The view that Galileo is challenging is that 'movables differing in heaviness are moved in the same
medium with unequal speeds, which maintain to one another the same ratio as their weights
[gravità]' (Galileo 1638/1914, p. 106). That is, he is challenging the view that heavier bodies fall
faster than lighter ones, and that they do so in direct proportion to their heaviness. On the version
Galileo takes himself to be opposing, the proportionality is linear; 'a moveable ten times as heavy
as another is moved ten times as fast' as the other. (Galileo, 1638/1914, p. 106)
Sorensen describes 'the Pisa experiment' as an example of a “mythical experiment” that “probably never
occurred” (Sorensen, 1992, pp. 224-225), and calls the argumentative refutation of Aristotle's theory of
motion by “having us suppose that a heavy falling object is joined to a lighter one”, (p. 126) what Brown
and Fehige calls Compound Bodies and Gendler Strapped Bodies, “fused-descent” TE. (p. 316)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
We can reconstruct this complex (T)E—one or two bodies and a compound body
falling through Planet Earth's atmosphere from considerable height as 200 cubits (i.e., 200
x 46 cm, 92 m)3—as both inductive and deductive universal instantiation (UI) of Galileo's
general physical law that objects (of same material, in same medium etc.) fall at the same
speed.
But, again, James Brown (and more philosophers) have not firstly reconstructed a
(T)E proving Galileo's law of gravity, but foremost Galileo's argument of refutation of
Aristotle's view that falling speed of objects depends on mass of the objects as illustrated
by an argument why a compound body falls with the same speed as its components.4
That is, their analyses don't represent the structure of the classical induction TE or Trial
and Error TE, that abound in Galileo's text, and many of which may have been real
3 A cubit is an ancient unit of length. 1 Cubit is 46 cm, 'based on the length of the forearm ...' (according to
Webster's 11th). The Leaning Tower of Pisa is about 56 m, so also proposed falling distance of 92 m does
not match Tower of Pisa.
4 This is indeed noticed by Tamar Gendler who unfolds something like a surface analysis in her 1996
dissertation. Although Gendler's discussion focuses on the famous TE of two bodies strapped together, her
introduction acknowledges that this TE only poses a weaker conclusion than the main one discussed in
Galileo's section aimed at challenging and falsifying the preeminent Aristotelian gravity view of linear
proportionality 'a moveable ten times as heavy as another is moved ten times as fast' as the other. Our
discussion does not neglect the many more E or TE (it is not always sure if they are E or TE) that are
mentioned in the text, in which, e.g., material of falling bodies, falling distance and (density of) medium is
changed. Gendler (1996, pp. 55-56):
Perhaps the most famous thought experiment in the history of western science is the thought
experiment with which Galileo is credited with having refuted the Aristotelian view that the speed
with which a body falls is directly proportional to its weight [...]. The thought experiment appears in
his last and most mature work, the Discourse Concerning Two New Sciences [...], in the context of
a more general discussion of the possibility and nature of motion in a void. Galileo's goal in the
section as a whole is to establish that 'if one were to remove entirely the resistance of the medium,
all materials would descend with equal speed' (Galileo 1638/1914, 116); the thought experiment in
question leads to the weaker conclusion that “both great and small bodies, of the same [material],
are moved with like speeds”. (Galileo, 1638/1914, p. 109, italics added).
The view that Galileo is challenging is that 'movables differing in heaviness are moved in the same
medium with unequal speeds, which maintain to one another the same ratio as their weights
[gravità]' (Galileo 1638/1914, p. 106). That is, he is challenging the view that heavier bodies fall
faster than lighter ones, and that they do so in direct proportion to their heaviness. On the version
Galileo takes himself to be opposing, the proportionality is linear; 'a moveable ten times as heavy
as another is moved ten times as fast' as the other. (Galileo, 1638/1914, p. 106)
Sorensen describes 'the Pisa experiment' as an example of a “mythical experiment” that “probably never
occurred” (Sorensen, 1992, pp. 224-225), and calls the argumentative refutation of Aristotle's theory of
motion by “having us suppose that a heavy falling object is joined to a lighter one”, (p. 126) what Brown
and Fehige calls Compound Bodies and Gendler Strapped Bodies, “fused-descent” TE. (p. 316)
49 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
experiments, either already performed by Aristotle, or by Galileo.
We call these TE classical induction TE or Trial and Error TE after their real
analogues of classical physics which are called Trial and Error E as part of the
methodology of classical induction. We are aware that our analyses could be considered
overcomplex, but they are not. Only a close reading of the authentic TE text and its
manifold of (T)E can reveal it is about a chain of basic or elementary TE of (classical)
physics, which are often performed in series of Trial and Error TE, trying, checking, and
balancing out a multitude of possible variables and constants, which is a procedure typical
for classical induction. These procedures are fallible, and one may need many heuristic
guesses to arrive at a subsequent Ideal TE, which we will discuss under a separate
heading later on.
Because it is foremost about series of many classical induction (T)E, the procedure
of Trial and Error (T)E is empiricist, and we don't need recourse to mysterianism of
Platonist TE, through which we may 'see' the laws of nature in a Platonist sense (see e.g.,
Brown 1991a, b). Instead, we rebaptize this type of TE that destruct, falsify an old (e.g.,
Aristotelian) paradigm and construct, verify a new (e.g., Galilean) paradigm,
Deconstructive TE, and we hold on to an empiricist and argumentative view of TE, which
is defended in e.g., Norton (1996, 2004a, 2004b).
Deep Analyses - Inductive and Deductive UI
Galileo's argument as retold in e.g., Brown (1991a, 1991b), is not a mere TE but rather
like a calculation. It is also considered an argument as based on a supposed
experiment of Compound or Strapped Bodies, of which it is not clear if it has indeed
been performed by Aristotle or Galileo, but the argument seems to make execution of
the (T)E superfluous:
But, even without further experiment, it is possible to prove clearly, by means of
a short and conclusive argument, that a heavier body does not move more rapidly
than a lighter one provided both bodies are of the same material and in short such
as those mentioned by Aristotle. (Galileo, 1638/1914, p. 107, see Section 3.3)
In our analyses of the many Falling Bodies (T)E, we have concluded to a sequence
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
experiments, either already performed by Aristotle, or by Galileo.
We call these TE classical induction TE or Trial and Error TE after their real
analogues of classical physics which are called Trial and Error E as part of the
methodology of classical induction. We are aware that our analyses could be considered
overcomplex, but they are not. Only a close reading of the authentic TE text and its
manifold of (T)E can reveal it is about a chain of basic or elementary TE of (classical)
physics, which are often performed in series of Trial and Error TE, trying, checking, and
balancing out a multitude of possible variables and constants, which is a procedure typical
for classical induction. These procedures are fallible, and one may need many heuristic
guesses to arrive at a subsequent Ideal TE, which we will discuss under a separate
heading later on.
Because it is foremost about series of many classical induction (T)E, the procedure
of Trial and Error (T)E is empiricist, and we don't need recourse to mysterianism of
Platonist TE, through which we may 'see' the laws of nature in a Platonist sense (see e.g.,
Brown 1991a, b). Instead, we rebaptize this type of TE that destruct, falsify an old (e.g.,
Aristotelian) paradigm and construct, verify a new (e.g., Galilean) paradigm,
Deconstructive TE, and we hold on to an empiricist and argumentative view of TE, which
is defended in e.g., Norton (1996, 2004a, 2004b).
Deep Analyses - Inductive and Deductive UI
Galileo's argument as retold in e.g., Brown (1991a, 1991b), is not a mere TE but rather
like a calculation. It is also considered an argument as based on a supposed
experiment of Compound or Strapped Bodies, of which it is not clear if it has indeed
been performed by Aristotle or Galileo, but the argument seems to make execution of
the (T)E superfluous:
But, even without further experiment, it is possible to prove clearly, by means of
a short and conclusive argument, that a heavier body does not move more rapidly
than a lighter one provided both bodies are of the same material and in short such
as those mentioned by Aristotle. (Galileo, 1638/1914, p. 107, see Section 3.3)
In our analyses of the many Falling Bodies (T)E, we have concluded to a sequence
C.P. Hertogh 50
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
of Trial and Error (T)E from classical induction, which we may formalize with help of
inductive logic and generalize to inductive universal instantiation. Since induction and
deduction may be considered logically complementary (see e.g., Carnap, 1966), we may
next translate inductive universal instantiation into deductive UI.
Inductive Universal Instantiation
for all x it holds that x falls at speed y (given a certain material and medium)
a falls at speed s
b falls at speed s
c falls at speed s
…
- - - - - - - - - - - - - - - - - - - - - - - - - -
all objects fall at speed s
Suppose
Fx x Falls
xF'y x Falls at speed y
a, b, c … objects with different masses (constants for variable x)
s (a certain) speed (constant for variable y)
x universal quantifier
conjunction
x (Fx xF'y) Fa aF's
Fb bF's
Fc cF's
….
- - - - - - - - - - - - induction
x (Fx xF's)
Suppose
(1)
(2)
(3)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
of Trial and Error (T)E from classical induction, which we may formalize with help of
inductive logic and generalize to inductive universal instantiation. Since induction and
deduction may be considered logically complementary (see e.g., Carnap, 1966), we may
next translate inductive universal instantiation into deductive UI.
Inductive Universal Instantiation
for all x it holds that x falls at speed y (given a certain material and medium)
a falls at speed s
b falls at speed s
c falls at speed s
…
- - - - - - - - - - - - - - - - - - - - - - - - - -
all objects fall at speed s
Suppose
Fx x Falls
xF'y x Falls at speed y
a, b, c … objects with different masses (constants for variable x)
s (a certain) speed (constant for variable y)
x universal quantifier
conjunction
x (Fx xF'y) Fa aF's
Fb bF's
Fc cF's
….
- - - - - - - - - - - - induction
x (Fx xF's)
Suppose
(1)
(2)
(3)
51 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Fx x Falls
Sx x has Speed s
Fa Sa
Fb Sb
Fc Sc
…
- - - - - - - - - - - - induction
x (Fx Sx)
In these formulas, constants a, b and c represent objects with different masses. In
formula (2) supposed relation F' turns out to be property S in formula (3) as all objects fall
at the same speed.5
It is counter-intuitive to many people, that is why it makes sense to pay some
attention to it as by (thought) experiments. And foremost it is contradicting Aristotle's
theory saying that heavier bodies fall faster than lighter bodies, which is in accordance
with intuition of many people.
Please, compare, Ptolemaic-Aristotelian geocentric sun-rotates-around-earth
universe, which is in accordance with everyday living experience and language (e.g. 'the
sun rises at 7 AM today', see Gadamer, 1960) and Galilean-Copernican heliocentric
earth-turns-around-sun theory (please, see Galileo, 1632/1967 Two Chief World
Systems), which is not easily understood from daily experience and language, so, it could
be considered counter-intuitive, too.
The TE debate is not just about elementary inductive universal instantiation, but
5 More alternate formalizations and analyses are possible e.g., suppose:
F''x x Falls at speed s (given a certain material and medium)
a, b, c … objects of different weights (constants for variable x)
F'' a
F'' b
F'' c …
- - - - - - - -
∀x F'' x
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Fx x Falls
Sx x has Speed s
Fa Sa
Fb Sb
Fc Sc
…
- - - - - - - - - - - - induction
x (Fx Sx)
In these formulas, constants a, b and c represent objects with different masses. In
formula (2) supposed relation F' turns out to be property S in formula (3) as all objects fall
at the same speed.5
It is counter-intuitive to many people, that is why it makes sense to pay some
attention to it as by (thought) experiments. And foremost it is contradicting Aristotle's
theory saying that heavier bodies fall faster than lighter bodies, which is in accordance
with intuition of many people.
Please, compare, Ptolemaic-Aristotelian geocentric sun-rotates-around-earth
universe, which is in accordance with everyday living experience and language (e.g. 'the
sun rises at 7 AM today', see Gadamer, 1960) and Galilean-Copernican heliocentric
earth-turns-around-sun theory (please, see Galileo, 1632/1967 Two Chief World
Systems), which is not easily understood from daily experience and language, so, it could
be considered counter-intuitive, too.
The TE debate is not just about elementary inductive universal instantiation, but
5 More alternate formalizations and analyses are possible e.g., suppose:
F''x x Falls at speed s (given a certain material and medium)
a, b, c … objects of different weights (constants for variable x)
F'' a
F'' b
F'' c …
- - - - - - - -
∀x F'' x
C.P. Hertogh 52
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
foremost about falsifying Aristotle's theory. This is a more complex part of the argument,
possibly requiring higher- order predicate logic involving relations to express relative
(falling) speed.
Deductive Universal Instantiation
As from modus ponens,
If an object x Falls, then it has Speed s
a Falls
- - - - - - - - - - - - deduction
a has Speed s
Suppose
Fx x Falls,
Sx x has Speed s
a object (constant for variable x)
x (Fx → Sx)
Fa
- - - - - - - - - - - - deduction
Sa
Again, alternate analyses are possible.6
6 Proposition logic: Modus ponens, p → q, p therefore q. Adding predicate logic:
p x Falls
q x has Speed s
Predicate logic is appropriate here for it is about propositions that predicate different properties of object(s)
that are related to each other as shown in modus ponens. Furthermore, predicate logical analysis may
demonstrate (deductive) universal instantiation.
Formula (5)] resembles Rudolf Carnap's generic scheme of scientific explanation or prediction, which is
also modus ponens (instantiation)
(x) (Px Qx)
Pa
———
Qa
(4)
(5)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
foremost about falsifying Aristotle's theory. This is a more complex part of the argument,
possibly requiring higher- order predicate logic involving relations to express relative
(falling) speed.
Deductive Universal Instantiation
As from modus ponens,
If an object x Falls, then it has Speed s
a Falls
- - - - - - - - - - - - deduction
a has Speed s
Suppose
Fx x Falls,
Sx x has Speed s
a object (constant for variable x)
x (Fx → Sx)
Fa
- - - - - - - - - - - - deduction
Sa
Again, alternate analyses are possible.6
6 Proposition logic: Modus ponens, p → q, p therefore q. Adding predicate logic:
p x Falls
q x has Speed s
Predicate logic is appropriate here for it is about propositions that predicate different properties of object(s)
that are related to each other as shown in modus ponens. Furthermore, predicate logical analysis may
demonstrate (deductive) universal instantiation.
Formula (5)] resembles Rudolf Carnap's generic scheme of scientific explanation or prediction, which is
also modus ponens (instantiation)
(x) (Px Qx)
Pa
———
Qa
(4)
(5)
53 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Next, there are some more examples of Falling Bodies added, that is the deductive
universal law is inductively confirmed by a set of examples or instantiations.
It is about a property that connects mass to speed as according to Aristotle's gravity
theory, so, a relation, and we could need a higher-order predicate logic to express it (see
formula (2)).
However, Galileo's TE argument shows that the property of mass relative
falling/gravity motion is not transitive as Aristotle may have concluded, but symmetrical,
that is to say: speed of falling objects is independent of mass of the objects (see formula
(3)).
If it is an important step in Renaissance development of physical theories that they
apply mathematical formulas, then Galileo's (T)E examples may prove that physical laws
of Galileo's classical mechanics hold on to symmetry feature of Euclidean mathematics,
not just transitivity like Aristotle's.
The transitive laws of Aristotle appear to be symmetrical as in accordance with
results of (T)E, and instantiation of Galileo's new universal law of gravity.7
Compound or Strapped Bodies TE (e.g., Gendler, Brown)
SIMP. But what if we should place the larger stone upon the smaller?
SALV. Its weight would be increased if the larger stone moved more rapidly; but
where (x) (Px Qx) is a scientific law; Pa is a description of the initial conditions; and Qa is the description
of the event we want to explain. The last statement is a logical consequence of the first and the second,
which are the premises of the explanation. A scientific explanation is thus a logical derivation of an
appropriate statement from a set of premises, which state universal laws and initial conditions. (Carnap
1966, pp. 7, 17)
Carnap’s scheme may read both as explanation and prediction -inductive UI may count as explanation
(emergence of a new event subsumes under an existing rule or law), deductive UI as prediction of the same
event (from an existing rule or law a new event may be predicted). Popper's falsificationism tries to replace
inductivism, which was unreliable according to Popper, by deductivism of critical rationalism (cf. e.g.,
Popper, 1959), another example of how induction may be translated into deduction.
7 That is, the new theory is simpler than the old one, a fact that advocates simplicity as an epistemological
maxim. Symmetry implies transitivity but transitivity does not (necessarily) imply symmetry i.e., symmetry
is stronger and simpler than transitivity. Change from Aristotle's to Galileo's theory is in accordance with
epistemological maxims as simplicity. (Cf. e.g., Ockham's razor, “Simplification of theory is a central motive
…”. (Quine,1960, p. 158) See also Sorensen (1992, pp. 194-195), in note 9, e.g., “an idealization is
supposed to be an effective simplification”.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
Next, there are some more examples of Falling Bodies added, that is the deductive
universal law is inductively confirmed by a set of examples or instantiations.
It is about a property that connects mass to speed as according to Aristotle's gravity
theory, so, a relation, and we could need a higher-order predicate logic to express it (see
formula (2)).
However, Galileo's TE argument shows that the property of mass relative
falling/gravity motion is not transitive as Aristotle may have concluded, but symmetrical,
that is to say: speed of falling objects is independent of mass of the objects (see formula
(3)).
If it is an important step in Renaissance development of physical theories that they
apply mathematical formulas, then Galileo's (T)E examples may prove that physical laws
of Galileo's classical mechanics hold on to symmetry feature of Euclidean mathematics,
not just transitivity like Aristotle's.
The transitive laws of Aristotle appear to be symmetrical as in accordance with
results of (T)E, and instantiation of Galileo's new universal law of gravity.7
Compound or Strapped Bodies TE (e.g., Gendler, Brown)
SIMP. But what if we should place the larger stone upon the smaller?
SALV. Its weight would be increased if the larger stone moved more rapidly; but
where (x) (Px Qx) is a scientific law; Pa is a description of the initial conditions; and Qa is the description
of the event we want to explain. The last statement is a logical consequence of the first and the second,
which are the premises of the explanation. A scientific explanation is thus a logical derivation of an
appropriate statement from a set of premises, which state universal laws and initial conditions. (Carnap
1966, pp. 7, 17)
Carnap’s scheme may read both as explanation and prediction -inductive UI may count as explanation
(emergence of a new event subsumes under an existing rule or law), deductive UI as prediction of the same
event (from an existing rule or law a new event may be predicted). Popper's falsificationism tries to replace
inductivism, which was unreliable according to Popper, by deductivism of critical rationalism (cf. e.g.,
Popper, 1959), another example of how induction may be translated into deduction.
7 That is, the new theory is simpler than the old one, a fact that advocates simplicity as an epistemological
maxim. Symmetry implies transitivity but transitivity does not (necessarily) imply symmetry i.e., symmetry
is stronger and simpler than transitivity. Change from Aristotle's to Galileo's theory is in accordance with
epistemological maxims as simplicity. (Cf. e.g., Ockham's razor, “Simplification of theory is a central motive
…”. (Quine,1960, p. 158) See also Sorensen (1992, pp. 194-195), in note 9, e.g., “an idealization is
supposed to be an effective simplification”.
C.P. Hertogh 54
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
we have already concluded that when the small stone moves more slowly it
retards to some extent the speed of the larger, so that the combination of the two,
which is a heavier body than the larger of the two stones, would move less rapidly,
a conclusion which is contrary to your hypothesis. We infer therefore that large
and small bodies move with the same speed provided they are of the same
specific gravity. (Galileo,1638/1914, pp. 108-109)
Introducing relative motion, a relation (higher-order predicate logic)
Suppose
Mxy x Moves faster than y
Mxy = Myx x Moves faster than y, and y Moves faster than x (i.e., x moves as fast as y
(and y moves as fast as x)
Fx x Falls
xy Fx, Fy Mxy = Myx
ab Fa, Fb Mab = Mba 8
The argument is reconstructed in Brown (1991a,1991b), Brown & Fehige (2019)
like this:
Suppose
H is Heavy body, L is Light body, HL is compound body
Suppose speed of movement of bodies depends on mass of bodies (when made of same
material and moving in same medium, etc.).
Compound HL body falls both faster and slower than L and compound HL body falls as
fast as both H and L. (Please, see Brown & Fehige (2019)
But consider Figure 6 [dropping two objects from Tower of Pisa], in which a heavy
cannon ball (H) and light musket ball (L) are attached together to form a
compound object (H+L); the latter must fall faster than the cannon ball alone. Yet
the compound object must also fall slower, since the light part will act as a drag on
the heavy part. Now we have a contradiction: H+L > H and H > H+L. That’s the
end of Aristotle’s theory. But there is a bonus, since the right account is now
8 More alternate formalizations, analyses are possible.
(6)
(7)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
we have already concluded that when the small stone moves more slowly it
retards to some extent the speed of the larger, so that the combination of the two,
which is a heavier body than the larger of the two stones, would move less rapidly,
a conclusion which is contrary to your hypothesis. We infer therefore that large
and small bodies move with the same speed provided they are of the same
specific gravity. (Galileo,1638/1914, pp. 108-109)
Introducing relative motion, a relation (higher-order predicate logic)
Suppose
Mxy x Moves faster than y
Mxy = Myx x Moves faster than y, and y Moves faster than x (i.e., x moves as fast as y
(and y moves as fast as x)
Fx x Falls
xy Fx, Fy Mxy = Myx
ab Fa, Fb Mab = Mba 8
The argument is reconstructed in Brown (1991a,1991b), Brown & Fehige (2019)
like this:
Suppose
H is Heavy body, L is Light body, HL is compound body
Suppose speed of movement of bodies depends on mass of bodies (when made of same
material and moving in same medium, etc.).
Compound HL body falls both faster and slower than L and compound HL body falls as
fast as both H and L. (Please, see Brown & Fehige (2019)
But consider Figure 6 [dropping two objects from Tower of Pisa], in which a heavy
cannon ball (H) and light musket ball (L) are attached together to form a
compound object (H+L); the latter must fall faster than the cannon ball alone. Yet
the compound object must also fall slower, since the light part will act as a drag on
the heavy part. Now we have a contradiction: H+L > H and H > H+L. That’s the
end of Aristotle’s theory. But there is a bonus, since the right account is now
8 More alternate formalizations, analyses are possible.
(6)
(7)
55 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
obvious: they all fall at the same speed (H = L = H+L).
In Gendler (1996/2000, 1998) it is emphasized that it is about the “possibility and
nature of motion is a void”, the counter-Aristotelian TE is called Strapped Bodies here, and
it is considered to prove only a weaker version of the new Galilean gravity theory
…. Galileo's goal in the section as a whole is to establish that 'if one were to
remove entirely the resistance of the medium, all materials would descend with
equal speed' (Galileo 1638/1914, 116); the thought experiment in question leads
to the weaker conclusion that “both great and small bodies, of the same [material],
are moved with like speeds” (Galileo, 1638/1914, 109, italics added). (Gendler
1996, p. 55-56, see note 4)
Compound or Strapped Bodies TE is in accordance with inductive UI analysis on Galilean
account of gravity as it is just one more instantiation of general inductive rule, e.g.,
suppose (e.g.) c to be equal to ab, that is a+b (c = ab = a+b).
Suppose
Fx x Falls
Sx x has Speed s
a, b, c objects of different masses (constants for variable x)
Additionally, suppose:
c = ab = a+b mass of object c equals mass of conjunction of objects a and b
x (Fx Sx)
Fa Sa
Fb Sb
Fc Sc
So, a, b and (compound) ab (c) fall at same speed s.
TE as Ideal Experiments
Although there may have been series of experiments that have been claimed by Salviati
and Salgredo in the text to have been performed in reality, the manifold of approaches
by varying variables makes one believe that all these endeavors sum up to a sort of ideal
(8)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
obvious: they all fall at the same speed (H = L = H+L).
In Gendler (1996/2000, 1998) it is emphasized that it is about the “possibility and
nature of motion is a void”, the counter-Aristotelian TE is called Strapped Bodies here, and
it is considered to prove only a weaker version of the new Galilean gravity theory
…. Galileo's goal in the section as a whole is to establish that 'if one were to
remove entirely the resistance of the medium, all materials would descend with
equal speed' (Galileo 1638/1914, 116); the thought experiment in question leads
to the weaker conclusion that “both great and small bodies, of the same [material],
are moved with like speeds” (Galileo, 1638/1914, 109, italics added). (Gendler
1996, p. 55-56, see note 4)
Compound or Strapped Bodies TE is in accordance with inductive UI analysis on Galilean
account of gravity as it is just one more instantiation of general inductive rule, e.g.,
suppose (e.g.) c to be equal to ab, that is a+b (c = ab = a+b).
Suppose
Fx x Falls
Sx x has Speed s
a, b, c objects of different masses (constants for variable x)
Additionally, suppose:
c = ab = a+b mass of object c equals mass of conjunction of objects a and b
x (Fx Sx)
Fa Sa
Fb Sb
Fc Sc
So, a, b and (compound) ab (c) fall at same speed s.
TE as Ideal Experiments
Although there may have been series of experiments that have been claimed by Salviati
and Salgredo in the text to have been performed in reality, the manifold of approaches
by varying variables makes one believe that all these endeavors sum up to a sort of ideal
(8)
C.P. Hertogh 56
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
experiment in favor of two competing theories or paradigms, the Aristotelian, and
Galilean(-Newtonian).
For Galilean gravity it is essential that the experiments are TE for as with regard
to the law Galileo wants to formulate, gravity is considered in vacuum, that is, without
effects of friction and air resistance. Exactly the latter factors make light bodies fall slower
than heavy bodies and his TE shows that these effects are not fundamental to gravity.
Einstein refers to his TE as idealized experiments that are experiments “created
by thought” (Einstein & Infeld 1938, p. 226) by which procedure there is abstracted from
friction, air resistance, etc., and he often mentions example of c, that is speed of light in
vacuum.
In Einstein & Infeld (1938) there are -next to the famous Elevator TE- many more
TE, from classical mechanics, electrodynamics ('repeating Faraday's experiment with a
circuit shrinking to a point', 'small sphere with an electrical charge') and quantum physics
involving electrons or photons.
Einstein & Infeld (1938) classical mechanics TE are about a 'cart on a perfectly
smooth road', 'wheels with no friction at all,' 'a perfect sphere rolls uniformly on a smooth
table', ' a body moving forever with no friction nor any other external forces acting', and
so on.
Einstein considers these TE necessarily unperformable in reality:
Imagine a road perfectly smooth, and wheels with no friction at all. Then there
would be nothing to stop the cart, so that it would run for ever. This conclusion is
reached only by thinking of an idealized experiment, which can never be actually
performed, since it is impossible to eliminate all external influences. The idealized
experiment shows the clue which really formed the foundation of the mechanics
of motion. (Einstein & Infeld, 1938, p. 8)
We have seen that this law of inertia cannot be derived directly from experiment,
but only by speculative thinking consistent with observation. The idealized
experiment can never be actually performed, although it leads to a profound
understanding of real experiments. (Einstein & Infeld 1938, pp. 8-9)
The division leads to an idealized experiment, for a physical process in which
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
experiment in favor of two competing theories or paradigms, the Aristotelian, and
Galilean(-Newtonian).
For Galilean gravity it is essential that the experiments are TE for as with regard
to the law Galileo wants to formulate, gravity is considered in vacuum, that is, without
effects of friction and air resistance. Exactly the latter factors make light bodies fall slower
than heavy bodies and his TE shows that these effects are not fundamental to gravity.
Einstein refers to his TE as idealized experiments that are experiments “created
by thought” (Einstein & Infeld 1938, p. 226) by which procedure there is abstracted from
friction, air resistance, etc., and he often mentions example of c, that is speed of light in
vacuum.
In Einstein & Infeld (1938) there are -next to the famous Elevator TE- many more
TE, from classical mechanics, electrodynamics ('repeating Faraday's experiment with a
circuit shrinking to a point', 'small sphere with an electrical charge') and quantum physics
involving electrons or photons.
Einstein & Infeld (1938) classical mechanics TE are about a 'cart on a perfectly
smooth road', 'wheels with no friction at all,' 'a perfect sphere rolls uniformly on a smooth
table', ' a body moving forever with no friction nor any other external forces acting', and
so on.
Einstein considers these TE necessarily unperformable in reality:
Imagine a road perfectly smooth, and wheels with no friction at all. Then there
would be nothing to stop the cart, so that it would run for ever. This conclusion is
reached only by thinking of an idealized experiment, which can never be actually
performed, since it is impossible to eliminate all external influences. The idealized
experiment shows the clue which really formed the foundation of the mechanics
of motion. (Einstein & Infeld, 1938, p. 8)
We have seen that this law of inertia cannot be derived directly from experiment,
but only by speculative thinking consistent with observation. The idealized
experiment can never be actually performed, although it leads to a profound
understanding of real experiments. (Einstein & Infeld 1938, pp. 8-9)
The division leads to an idealized experiment, for a physical process in which
57 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
only the mechanical aspect appears can be only imagined but never realized.
(Einstein & Infeld 1938, p. 47)
Although in Einstein's days, there were already vacuum pumps and suction
pumps (as there already were in ancient days of Pompeii) and philosophical speculation
of (e.g.) horror vacui had been replaced by empirical experiments to actually construct a
vacuum (like 1643 so-called first laboratory vacuum, Torricellian vacuum), one may say
that with the introduction of vacuum technology as vacuum tubes and later construction
of experimental ultra-high vacuum chambers and discovery of outer space with only a
few atoms per cubic meter, one has succeeded in creating or discovering a near-vacuum
as a near- approximation of a realization of what Einstein still considered actually
unperformable TE, so that we can relativize necessarily unperformable to a certain stage
in the progress of science.
Speculative nature of TE can be reduced in these experiments, that can be
performed as near-real E as well e.g., Galileo's TE of Falling Bodies executed on the
moon like above Hammer and Feather E.9
9 If one wants to hold on to emphasizing negligible or only theoretical differences, one may wonder which
entities and qualities do really exist in our world--Do numbers really exist? Which horse is a really (perfect)
essential, ideal, archetypal (etc.) horse? For us there is no reason to believe in (existence of), let's say,
Platonic ideals or Aristotelian essences in mathematics or physics or anywhere and we rather consider
mathematical laws and physical laws using mathematical symbols, operators and formulas abstractions,
idealizations from empirical regularities. Stating that TE can never be actually performed or realized or only
exist in imagination or in an ideal realm is reversing a possibly contrary naturalist process of thinking from
concrete to abstract, from empirical to rational, from real to 32 ideal instead of the other way around.
Nevertheless, there may be good methodological or conventional reasons to work with ideal or idealized
entities as numbers, formulas, physical laws, genera or DNA structures of organisms, concepts of I and
God etc. and, so, also with TE. Sorensen’s view accounts for both Galileo's simplification and idealization
.... Galileo engineered his methodology with the pragmatism of a physician who changes his
treatment of a patient.... Galileo found that nuisance variables could be eliminated by creating a
highly artificial setup. Some biases could be canceled by others. Small disturbances could be
ignored. Hard-to-reach values could be extrapolated by a trend from a series of easier-to-reach
values. All of these are empirical lessons learned about experiment, not a priori methodological
principles. When things get working, there is often a residue of uncertainty as to how the changes
succeeded, what the specific problem was, or whether a particular adjustment even had any real
impact at all. Hence, experimental design evolves in the uneven, half-blind manner of medical lore.
Theorists can come in later and rationally reconstruct many aspects of laboratory craft. They will
dismiss other features as vestigial or as superstitious pieties. Thought experiments are equally
dependent on their track records. After all, an idealization is supposed to be an effective
simplification—a shortcut that gets you most of the effect by concentrating on just a few variables.
(Sorensen, 1992, pp. 194-195)
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
only the mechanical aspect appears can be only imagined but never realized.
(Einstein & Infeld 1938, p. 47)
Although in Einstein's days, there were already vacuum pumps and suction
pumps (as there already were in ancient days of Pompeii) and philosophical speculation
of (e.g.) horror vacui had been replaced by empirical experiments to actually construct a
vacuum (like 1643 so-called first laboratory vacuum, Torricellian vacuum), one may say
that with the introduction of vacuum technology as vacuum tubes and later construction
of experimental ultra-high vacuum chambers and discovery of outer space with only a
few atoms per cubic meter, one has succeeded in creating or discovering a near-vacuum
as a near- approximation of a realization of what Einstein still considered actually
unperformable TE, so that we can relativize necessarily unperformable to a certain stage
in the progress of science.
Speculative nature of TE can be reduced in these experiments, that can be
performed as near-real E as well e.g., Galileo's TE of Falling Bodies executed on the
moon like above Hammer and Feather E.9
9 If one wants to hold on to emphasizing negligible or only theoretical differences, one may wonder which
entities and qualities do really exist in our world--Do numbers really exist? Which horse is a really (perfect)
essential, ideal, archetypal (etc.) horse? For us there is no reason to believe in (existence of), let's say,
Platonic ideals or Aristotelian essences in mathematics or physics or anywhere and we rather consider
mathematical laws and physical laws using mathematical symbols, operators and formulas abstractions,
idealizations from empirical regularities. Stating that TE can never be actually performed or realized or only
exist in imagination or in an ideal realm is reversing a possibly contrary naturalist process of thinking from
concrete to abstract, from empirical to rational, from real to 32 ideal instead of the other way around.
Nevertheless, there may be good methodological or conventional reasons to work with ideal or idealized
entities as numbers, formulas, physical laws, genera or DNA structures of organisms, concepts of I and
God etc. and, so, also with TE. Sorensen’s view accounts for both Galileo's simplification and idealization
.... Galileo engineered his methodology with the pragmatism of a physician who changes his
treatment of a patient.... Galileo found that nuisance variables could be eliminated by creating a
highly artificial setup. Some biases could be canceled by others. Small disturbances could be
ignored. Hard-to-reach values could be extrapolated by a trend from a series of easier-to-reach
values. All of these are empirical lessons learned about experiment, not a priori methodological
principles. When things get working, there is often a residue of uncertainty as to how the changes
succeeded, what the specific problem was, or whether a particular adjustment even had any real
impact at all. Hence, experimental design evolves in the uneven, half-blind manner of medical lore.
Theorists can come in later and rationally reconstruct many aspects of laboratory craft. They will
dismiss other features as vestigial or as superstitious pieties. Thought experiments are equally
dependent on their track records. After all, an idealization is supposed to be an effective
simplification—a shortcut that gets you most of the effect by concentrating on just a few variables.
(Sorensen, 1992, pp. 194-195)
C.P. Hertogh 58
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
However, the speculative TE with regard to General Relativity remain what we
will call Theoretical TE for they refer to micro- and macro-physics and can't be
persuasively reenacted on earth, although Einstein's Elevator TE was possibly devised
with this goal.
Trial and Error TE (Classical Induction)
It is true that if we analyze the TE instead of its use in a scheme as to falsify an old
theory and advance a new one, our analysis may as well like an inductive hypothetico-
deductive methodology. We also baptize one of our deep analyses as inductive ….
Indeed, we hold that in Galileo's text there is reference to many (T)E that are used to
inductively prove Galileo's new theory as falling (T)E in different media, trying different
materials of objects and different falling distances.
We see no problem in this likeness to induction nor in the fact that our TE are
formally indistinguishable from E analyses, particularly as from Galileo's text we can't
make sure if it is about TE or E and it is not necessary to employ modal logic in our
analyses as it is not about an essentially modal argument (as e.g. logical possibility of
Zombie TE in consciousness studies , see e.g. Chalmers (1996, 2017).
We will add some more examples wherein use of TE likes inductive use of E to a
high extent. Consider someone who wants to get a drifting ball from a pool and who can
choose out of three lengths of available sticks. Now we perform TE in the head as preps
to our actions, that is, we may first measure the lengths of the sticks in the head and try
in the mind the three sticks—one by one--before actually choosing a stick to try and
reach the ball. We are measuring the distance to the ball to the lengths of the sticks
before actually choosing a stick. In this case, we inductively perform TE as trial and
error in the head, and, after, possibly perform two or three inductive E if we don't pick
out a good stick at once.
We hold that these -and many more- sorts of TE are used in daily life very often
as by trial and error in the mind. It is about TE which we can perform in a split second,
and in many more rather abstract situations e.g., in algebra where this method is called
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
However, the speculative TE with regard to General Relativity remain what we
will call Theoretical TE for they refer to micro- and macro-physics and can't be
persuasively reenacted on earth, although Einstein's Elevator TE was possibly devised
with this goal.
Trial and Error TE (Classical Induction)
It is true that if we analyze the TE instead of its use in a scheme as to falsify an old
theory and advance a new one, our analysis may as well like an inductive hypothetico-
deductive methodology. We also baptize one of our deep analyses as inductive ….
Indeed, we hold that in Galileo's text there is reference to many (T)E that are used to
inductively prove Galileo's new theory as falling (T)E in different media, trying different
materials of objects and different falling distances.
We see no problem in this likeness to induction nor in the fact that our TE are
formally indistinguishable from E analyses, particularly as from Galileo's text we can't
make sure if it is about TE or E and it is not necessary to employ modal logic in our
analyses as it is not about an essentially modal argument (as e.g. logical possibility of
Zombie TE in consciousness studies , see e.g. Chalmers (1996, 2017).
We will add some more examples wherein use of TE likes inductive use of E to a
high extent. Consider someone who wants to get a drifting ball from a pool and who can
choose out of three lengths of available sticks. Now we perform TE in the head as preps
to our actions, that is, we may first measure the lengths of the sticks in the head and try
in the mind the three sticks—one by one--before actually choosing a stick to try and
reach the ball. We are measuring the distance to the ball to the lengths of the sticks
before actually choosing a stick. In this case, we inductively perform TE as trial and
error in the head, and, after, possibly perform two or three inductive E if we don't pick
out a good stick at once.
We hold that these -and many more- sorts of TE are used in daily life very often
as by trial and error in the mind. It is about TE which we can perform in a split second,
and in many more rather abstract situations e.g., in algebra where this method is called
59 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
guess and check and in decision theory when we want to choose from alternates. We
can then perform TE and go through all available alternates and possibilities in the head
as (e.g.) A, B and C by inductive trial and error, first trying A to situation S, next B, next
C, assessing possible consequences of A, B and C and, finally, make our choice
between A, B or C.
As we may see in analyses of Einstein's TE (see e.g., Hertogh, 2015, Pt. III,
2022a) this classical definition of TE can't hold anymore for Relativity TE, that are about
micro-physics (quantum mechanics) and macro-physics (astronomy) and engage so-
called Theoretical TE.
Acknowledgements
Identification, analysis and interpretation of Galileo Galilei's Gravity (Falling Bodies)
TE has been developed for PhD project 'Semantics of TE'. In provisional PhD text it
is Chapter 11, 1st chapter of Part III on TE in natural sciences, so-called Iconic TE
(as differentiated from Symbolic TE in mathematics and Indexical TE in philosophy
of mind and consciousness studies). Galileo's Falling Bodies is discussed, next to
Galileo's Ship, feat. principle of relativity, Albert Einstein's Magnet and Conductor,
feat. epistemological maxim of simplicity, Elevator and Chasing a Beam of Light, feat.
principle of relativity and, resp., light/mass equality and constancy of speed of light.
In 2013 seminar 'Thought Experiments—Capita Selecta' has been delivered at
Chongqing University (CQ/CN); in 2015 provisional PhD project at VUB Brussels
(BE/EU); in April 2022 presentation on Einstein's TE, particularly Elevator, at
conference Formal Methods and Science in Philosophy IV, Dubrovnik (HR/EU).
Special thanks to staff and students of Chongqing University.
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
guess and check and in decision theory when we want to choose from alternates. We
can then perform TE and go through all available alternates and possibilities in the head
as (e.g.) A, B and C by inductive trial and error, first trying A to situation S, next B, next
C, assessing possible consequences of A, B and C and, finally, make our choice
between A, B or C.
As we may see in analyses of Einstein's TE (see e.g., Hertogh, 2015, Pt. III,
2022a) this classical definition of TE can't hold anymore for Relativity TE, that are about
micro-physics (quantum mechanics) and macro-physics (astronomy) and engage so-
called Theoretical TE.
Acknowledgements
Identification, analysis and interpretation of Galileo Galilei's Gravity (Falling Bodies)
TE has been developed for PhD project 'Semantics of TE'. In provisional PhD text it
is Chapter 11, 1st chapter of Part III on TE in natural sciences, so-called Iconic TE
(as differentiated from Symbolic TE in mathematics and Indexical TE in philosophy
of mind and consciousness studies). Galileo's Falling Bodies is discussed, next to
Galileo's Ship, feat. principle of relativity, Albert Einstein's Magnet and Conductor,
feat. epistemological maxim of simplicity, Elevator and Chasing a Beam of Light, feat.
principle of relativity and, resp., light/mass equality and constancy of speed of light.
In 2013 seminar 'Thought Experiments—Capita Selecta' has been delivered at
Chongqing University (CQ/CN); in 2015 provisional PhD project at VUB Brussels
(BE/EU); in April 2022 presentation on Einstein's TE, particularly Elevator, at
conference Formal Methods and Science in Philosophy IV, Dubrovnik (HR/EU).
Special thanks to staff and students of Chongqing University.
C.P. Hertogh 60
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
List of abbreviations
Abbreviations of technical terms used in this paper :
TE: thought experiment(s)
E: experiment(s)
(T)E: (thought) experiment(s) e.g., TEs and Es, or E that looks like TE, or TE looking
like E, or event of which it is nor sure if it is a TE or E
UI: universal instantiation TEEI: Experience TE
TEEX: Experiment TE
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
List of abbreviations
Abbreviations of technical terms used in this paper :
TE: thought experiment(s)
E: experiment(s)
(T)E: (thought) experiment(s) e.g., TEs and Es, or E that looks like TE, or TE looking
like E, or event of which it is nor sure if it is a TE or E
UI: universal instantiation TEEI: Experience TE
TEEX: Experiment TE
61 Semantics of Galileo’s Gravity (Thougth) Experiments
Analítica (3), oct. 2023 sept. 2024, ISSN – L 2805 – 1815
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