homepages.ius.edu/kforinas/K/pdf/Galileo.pdf
acceleration, in which he uses geometry instead of algebra to represent quantities ... Galileo argues that natural acceleration (the acceleration of falling bodies}.
But Galileo’s theorem, stating that force is proportional to acceleration, does not come immediately from experience; logically considered, it is a free statement. It comes from the intuitively acquired knowledge that the phenomena of motion can be easily understood if acceleration is regarded as the fundamental phenomenon whose causes are sought. That this is not obvious in itself – to be precise, that it is not necessary – can be seen by looking at the
history of mechanics before Galileo.
history of mechanics before Galileo.
Honorable Rector, Honorable Professors, and Students of this University: In these times of
political and economic struggle and nationalistic fragmentation, it is a particular joy for me to
see people assembling here to give their attention exclusively to the highest values that are
common to us all. I am glad to be in this blessed land before a small circle of people who are
interested in topics of science to speak on those issues that, in essence, are the subject of my
own meditations.
In science, there are always two opposite and complementary goals that, owing to
their mutual complementarity, constitute the essence of its progress. On the one hand, there is
the quest for enlargement and enrichment of our understanding of some particular area of
knowledge; and on the other hand, there is the endeavor to achieve a systematic unity of
knowledge. In my work I have always attempted the latter; therefore, I wish to communicate
here more accurate observations on this goal, the systematic unity of knowledge.
Using as few hypothetical laws as possible, science attempts to explain relations
between observable facts, arriving at them in a deductive manner, that is, in a purely logical
way. Physics is customarily referred to as an empirical science and it is believed that its
fundamental laws are deduced from experiments, so as to indicate how it differs from
speculative philosophy. However, in truth the relationship between fundamental laws and
facts from experience is not that simple. Indeed, there is no scientific method to deduce
inductively these fundamental laws from experimental data. The formulation of a
fundamental law is, rather, an act of intuition which can be achieved only by one who
watches empirically with the necessary attention and has sufficient empirical understanding of
the field in question. The sole criteria for the truth of a fundamental law is only that we can be
sure that the relations between observable events can be logically deduced from it. It follows
then that a fundamental law can be refuted in a definite manner, but can never be definitely
shown to be correct, as one must always bear in mind the possibility of discovering a new
phenomenon that contradicts the logical conclusions arising from a fundamental law.
Experience is, therefore, the judge, but not the generator of fundamental laws. The
transition from the facts of experience to a fundamental law often requires an act of free
creativity from our imagination, as well as an act of creation of concepts and relations; it
would not be possible to replace this act with a necessary and conclusive method.3
The fact that a concept in the presence of experience, even if originated from
experience, has a certain logical independence is appreciated by considering extra-scientific
thought. The observation of the existence of similar objects has given rise to the notion of
number, but has not created it. In fact, people in some cultures have not gone any further than
an understanding of only the smallest of numbers.
Returning to the ideas and fundamental laws of physics, it is easy to show that
starting from the facts of experience there is no fixed road taking us back to those ideas and
fundamental laws. Let us consider, for example, the laws of motion on which classical
astronomy rests. Using logical and mathematical methods we can deduce from Kepler’s laws
Newton’s law on the inverse proportionality of force on the square of the distances. But Galileo’s theorem, stating that force is proportional to acceleration, does not come immediately from experience; logically considered, it is a free statement. It comes from the intuitively acquired knowledge that the phenomena of motion can be easily understood if acceleration is regarded as the fundamental phenomenon whose causes are sought. That this is not obvious in itself – to be precise, that it is not necessary – can be seen by looking at the
history of mechanics before Galileo. The logical arbitrariness of this point of view is revealed
by the fact that the general theory of relativity has found it necessary to modify it.
Not only are fundamental laws the result of an act of imagination that can not be
controlled, but so are their ingredients, the ideas derived from those laws. Thus, the concept
of acceleration was in itself an act of free creation of the mind which, even if supported by the
observation of the motion of solid bodies, assumes as a precondition nothing less than the infinitesimal calculus. It follows from here that fundamental laws can be refuted not only by showing that
the consequences attributed to them are wrong, inexact, or not generally applicable, but also
can be refuted by showing that the concepts introduced for them do not suit the observed
facts.
In this respect the history of modern theoretical physics offers beautiful examples. In
the kinetic theory of heat, temperature is an elementary concept that stands out in a discussion
on fundamental relations in that science. The development of thermodynamics showed that, in
a body isolated from exchanges with its surroundings for any length of time, energy fluctuates
permanently around a fixed average value; the smaller the portion of the body considered, the
larger the fluctuations. If we observe parts that are sufficiently smaller, a precise distinction
between its thermal and mechanical energy loses its meaning. The apparent incongruence of
all these ideas is dispelled if we consider microscopically observable motions, such as those
of very small particles suspended in liquids, as in the case of Brownian motion.
The process of progress in theoretical science finds its expression not only in the fact
that the relations expressed by elementary laws are replaced by others that are more precise,
but also in the circumstance that elementary concepts that are associated with the most
immediate perceptions of reality need to be replaced by newer ones, better suited to the
complex data provided by experience.
The Physics of Galileo
Aristotle taught that the substances making up the Earth were different from the substance making up the heavens. He also taught that dynamics (the branch of physics that deals with motion) was primarily determined by the nature of the substance that was moving.
In addition, Galileo's extensive telescopic observations of the heavens made it more and more plausible that they were not made from a perfect, unchanging substance. In particular, Galileo's observational confirmation of the Copernican hypothesis suggested that the Earth was just another planet, so maybe it was made from the same material as the other planets. Thus, the groundwork was laid by Galileo (and to a lesser extent by others like Kepler and Copernicus) to overthrow the physics of Aristotle, in addition to his astronomy. It fell to Isaac Newton to bring these threads together and to demonstrate that the laws that governed the heavens were the same laws that governed motion on the surface of the Earth.
political and economic struggle and nationalistic fragmentation, it is a particular joy for me to
see people assembling here to give their attention exclusively to the highest values that are
common to us all. I am glad to be in this blessed land before a small circle of people who are
interested in topics of science to speak on those issues that, in essence, are the subject of my
own meditations.
In science, there are always two opposite and complementary goals that, owing to
their mutual complementarity, constitute the essence of its progress. On the one hand, there is
the quest for enlargement and enrichment of our understanding of some particular area of
knowledge; and on the other hand, there is the endeavor to achieve a systematic unity of
knowledge. In my work I have always attempted the latter; therefore, I wish to communicate
here more accurate observations on this goal, the systematic unity of knowledge.
Using as few hypothetical laws as possible, science attempts to explain relations
between observable facts, arriving at them in a deductive manner, that is, in a purely logical
way. Physics is customarily referred to as an empirical science and it is believed that its
fundamental laws are deduced from experiments, so as to indicate how it differs from
speculative philosophy. However, in truth the relationship between fundamental laws and
facts from experience is not that simple. Indeed, there is no scientific method to deduce
inductively these fundamental laws from experimental data. The formulation of a
fundamental law is, rather, an act of intuition which can be achieved only by one who
watches empirically with the necessary attention and has sufficient empirical understanding of
the field in question. The sole criteria for the truth of a fundamental law is only that we can be
sure that the relations between observable events can be logically deduced from it. It follows
then that a fundamental law can be refuted in a definite manner, but can never be definitely
shown to be correct, as one must always bear in mind the possibility of discovering a new
phenomenon that contradicts the logical conclusions arising from a fundamental law.
Experience is, therefore, the judge, but not the generator of fundamental laws. The
transition from the facts of experience to a fundamental law often requires an act of free
creativity from our imagination, as well as an act of creation of concepts and relations; it
would not be possible to replace this act with a necessary and conclusive method.3
The fact that a concept in the presence of experience, even if originated from
experience, has a certain logical independence is appreciated by considering extra-scientific
thought. The observation of the existence of similar objects has given rise to the notion of
number, but has not created it. In fact, people in some cultures have not gone any further than
an understanding of only the smallest of numbers.
Returning to the ideas and fundamental laws of physics, it is easy to show that
starting from the facts of experience there is no fixed road taking us back to those ideas and
fundamental laws. Let us consider, for example, the laws of motion on which classical
astronomy rests. Using logical and mathematical methods we can deduce from Kepler’s laws
Newton’s law on the inverse proportionality of force on the square of the distances. But Galileo’s theorem, stating that force is proportional to acceleration, does not come immediately from experience; logically considered, it is a free statement. It comes from the intuitively acquired knowledge that the phenomena of motion can be easily understood if acceleration is regarded as the fundamental phenomenon whose causes are sought. That this is not obvious in itself – to be precise, that it is not necessary – can be seen by looking at the
history of mechanics before Galileo. The logical arbitrariness of this point of view is revealed
by the fact that the general theory of relativity has found it necessary to modify it.
Not only are fundamental laws the result of an act of imagination that can not be
controlled, but so are their ingredients, the ideas derived from those laws. Thus, the concept
of acceleration was in itself an act of free creation of the mind which, even if supported by the
observation of the motion of solid bodies, assumes as a precondition nothing less than the infinitesimal calculus. It follows from here that fundamental laws can be refuted not only by showing that
the consequences attributed to them are wrong, inexact, or not generally applicable, but also
can be refuted by showing that the concepts introduced for them do not suit the observed
facts.
In this respect the history of modern theoretical physics offers beautiful examples. In
the kinetic theory of heat, temperature is an elementary concept that stands out in a discussion
on fundamental relations in that science. The development of thermodynamics showed that, in
a body isolated from exchanges with its surroundings for any length of time, energy fluctuates
permanently around a fixed average value; the smaller the portion of the body considered, the
larger the fluctuations. If we observe parts that are sufficiently smaller, a precise distinction
between its thermal and mechanical energy loses its meaning. The apparent incongruence of
all these ideas is dispelled if we consider microscopically observable motions, such as those
of very small particles suspended in liquids, as in the case of Brownian motion.
The process of progress in theoretical science finds its expression not only in the fact
that the relations expressed by elementary laws are replaced by others that are more precise,
but also in the circumstance that elementary concepts that are associated with the most
immediate perceptions of reality need to be replaced by newer ones, better suited to the
complex data provided by experience.
The Physics of Galileo
Aristotle taught that the substances making up the Earth were different from the substance making up the heavens. He also taught that dynamics (the branch of physics that deals with motion) was primarily determined by the nature of the substance that was moving.
The Dynamics of Aristotle
For example, stripped to its essentials, Aristotle believed that a stone fell to the ground because the stone and the ground were similar in substance (in terms of the 4 basic elements, they were mostly "earth"). Likewise, smoke rose away from the Earth because in terms of the 4 basic elements it was primarily air (and some fire), and therefore the smoke wished to be closer to air and further away from earth and water. By the same token, Aristotle held that the more perfect substance (the "quintessence") that made up the heavens had as its nature to execute perfect (that is, uniform circular) motion. He also believed that objects only moved as long as they were pushed. Thus, objects on the Earth stopped moving once applied forces were removed, and the heavenly spheres only moved because of the action of the Prime Mover, who continually applied the force to the outer spheres that turned the entire heavens. (A notorious problem for the Aristotelian view was why arrows shot from a bow continued to fly through the air after they had left the bow and the string was no longer applying force to them. Elaborate explanations were hatched; for example, it was proposed that the arrow creating a vacuum behind it into which air rushed and applied a force to the back of the arrow!)Galileo vs. Aristotle
Thus, Aristotle believed that the laws governing the motion of the heavens were a different set of laws than those that governed motion on the earth. As we have seen, Galileo's concept of inertia was quite contrary to Aristotle's ideas of motion: in Galileo's dynamics the arrow (with very small frictional forces) continued to fly through the air because of the law of inertia, while a block of wood on a table stopped sliding once the applied force was removed because of frictional forces that Aristotle had failed to analyze correctly.In addition, Galileo's extensive telescopic observations of the heavens made it more and more plausible that they were not made from a perfect, unchanging substance. In particular, Galileo's observational confirmation of the Copernican hypothesis suggested that the Earth was just another planet, so maybe it was made from the same material as the other planets. Thus, the groundwork was laid by Galileo (and to a lesser extent by others like Kepler and Copernicus) to overthrow the physics of Aristotle, in addition to his astronomy. It fell to Isaac Newton to bring these threads together and to demonstrate that the laws that governed the heavens were the same laws that governed motion on the surface of the Earth.
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