Auguste Comte: Course of positive philosophy 2 – Sound, light and electricity

With little to no explanation, Comte places acoustics as the next physical discipline after thermology. Indeed, one might even doubt if acoustics deserves a place on the list, because it seems more of an applied science, which Comte has usually excluded from his account of abstract physics. Yet, what he conceives as the topic of acoustics is not so much sound, but all vibrations. This topic has been studied positively, Comte thinks, at least as long as weight, although it is far less known. It seems that it is only the highly intricate mathematical analysis of heat by Fourier that has given reason for Comte to put thermology before acoustics.

Comte sees the importance of acoustics in that sonorous vibrations have revealed – and might be the only method to reveal – the internal molecular structure on inorganic bodies. Thus, he insists, it is through these vibrations that we know the inorganic bodies can acquire dispositions, just like living things. Acoustics is also important for physiology, Comte thinks, for the study of hearing and vocalisation, excluding what happens in nerves and brains. Yet, he emphasises, the study of these phenomena should not be left to physicists, who do not understand the peculiarities of physiology.

According to Comte acoustics is, after barology, physical science using mathematics most. It investigates, he explains, minute molecular oscillations near a state of equilibrium, where perturbation of the order is immediately followed by a return to the original state. Now, since these oscillations can be transmitted through an elastic medium, like waves on water, acoustics become an application of mechanics. Still, Comte notes, acoustics is far more difficult to study than barology, since it requires much more complicated mathematical tools: for instance, we can calculate only movement of vibrations in one dimension, but not in three dimensions. Even so, he assures the reader mathematical theory gives at least guidance for finding approximations and allows use of analogies in calculations.

Comte divides acoustics into three different topics, although he mentions also fourth, the timbre of each peculiar body, but then quickly discards it, because it is more a part of concrete physics. The first topic of acoustic proper, according to Comte, is the propagation of the sound. He notes that the velocity of the sound in air is known, but propagation in other substances or such intricate questions like the behaviour of echo have not been studied conclusively.

The second topic of acoustics would be the intensity of the sound. Yet, Comte thinks, we have not advanced much beyond what we know by common observation, the only fact he considers scientific being the effect of the density of the atmosphere on the intensity. The main reason for this poor state, according to him, is that we have not yet been able to measure this intensity.

The most satisfying part of acoustics, for Comte, are the laws regulating the musical tones. Yet, even here he sees insufficiency, since only the one-dimensional case has been studied, while the behaviour of a full three-dimensional instrument has not yet been investigated.

In an even worse condition Comte sees optics, which he regards as being plagued by the two hypotheses about the nature of light, whether it is supposed to be a material emission or a vibration. Comte thinks that both hypotheses try to reduce optics to a different science: emission theory to barology and vibration theory to acoustics. He is not enthusiastic about such an attempt to unify sciences: even physiology proves that vision is quite different from hearing and feeling weight and pressure. Since both hypotheses work as well, Comte suggests rejecting both of them and concentrating in a description of the laws governing optical phenomena.

Just like acoustics does not explain the physiological phenomena of hearing, Comte insists that optics does not explain vision. Furthemore, he thinks, optics – and indeed, no science – can explain the natural colours that different objects have: any explanation would be metaphysical and always more complicated to understand than what is to be explained. Somewhat ironically, Comte thinks it would be equally ridiculous to attempt to explain why different substances have different specific gravities of substances (periodic table had not yet been discovered).

Comte’s division of optics is quite traditional. First part should study direct light, and just like with acoustics, Comte mentions that we still have no tool for measuring the intensity of light. The second part is catoptrics that deals with reflection, while the third part, dioptrics, studies refraction, and the topic of the fourth part is diffraction. Beyond these general topics, Comte also mentions double refraction and polarisation as important particular issues.

The final physical discipline, in Comte’s opinion, is electrology. It is the most complex and thus had to be developed last, he explains, and due to this late blooming it is the least developed as science: although it has many curious facts, it still lacks laws to make the facts into a scientific system. Comte sees a clear sign of its unscientific nature in the abundance of hypotheses about various fluids that should explain electric phenomena. He thinks they are not as detrimental as in optics, since no true scientist takes them seriously and uses them as mere mnemonic devices. Still, Comte warns, they have had bad influence especially on physiology, where they have inspired such ridiculous notions as animal magnetism.

Since all bodies are not at all times electrical, the first topic investigated in electrology, Comte says, should be the investigation of methods to introduce bodies into an electric state. He also includes in this part the recognition and measurement of an electric state in a body. The second part of electrology, for Comte, is electrostatics, by which he means what he describes a state of an electric equilibrium: this part includes e.g. study of distribution of electrical state in a single body or in a set of contiguous bodies. The third part is then, naturally, electrodynamics, which studies movements generated by an electrical state, for instance, repulsions and attractions of two electrified bodies. Fourth part, finally, studies magnetism and its connection to electricity.

Auguste Comte: Course of positive philosophy 2 – Weight and heat

Comte begins his study of the concrete parts of physics from what he calls barology, that is, the study of terrestrial phenomena involving weight. He regards it as the most complete part of physics, because it is based on nothing more than observations and sound use of mathematics. Yet, he adds, barology has still been in a state of dispersed fragments, with Comte’s own account as the first attempt to unite them into a single doctrine.

Comte divides barology into two parts: static and dynamic barology. Static barology investigates the effects of weight with bodies in a state of equilibrium. In the case of solid bodies, Comte notes, this investigation began already with the discovery of the Archimedian principle.

In the case of liquids, static barology, Comte thinks, did not begin until modern times. He divides this part of barology into two studies. First of them concerns the case of a small portion of liquid within a vessel: here Comte emphasises especially Stevin’s investigation of the pressure of liquid on the vessel. The second study concerns great amounts of liquid, like oceans, where we have to take into account that the direction of gravity varies significantly from one place to another. This study, Comte thinks, is intrinsically linked with the more astronomical questions of the shape of the Earth and of the theory of tides.

Static barology of gases, Comte continues, has the added difficulty of determining the weight of the gas in case. This was first made possible, he explains, by the invention of a method for creating vacuum, which allowed measuring the difference in the weight of a container with gas and without any gas at all. This discovery made it possible to apply methods of static barology of liquids to gases.

Comte notes that an important addition to static barology would be a study of capillary phenomena, especially as they are important to explaining organic processes. Unfortunately, he laments, this part of barology is still hindered by the metaphysical notion of attraction,

Dynamic barology, Comte states, should then investigate the involvement of weight in the movement of bodies. This investigation began, in his opinion, with Galileo’s study of freely falling bodies and curves of projectiles. Comte thinks that this part of barology is still far from perfect, since the laws governing air resistance are still not determined. Even more insufficient dynamic barology becomes, when we move from solid bodies to liquids and gases.

Heat, Comte suggests, is after gravity the most universal phenomena in physics. He backs up this claim with the statement that heat affects organic and inorganic nature as much as gravity, being the foremost agent acting against the effects of gravity. While gravity affects geometry and mechanics of bodies, Comte continues, heat affects the constitution of molecules and especially living organisms. Indeed, he continues, heat is the primary method by which humans affect nature. Thus, after barology, Comte concludes, thermology is the next part of physics.

Although the investigation of heat began around the time of Galileo with the invention of the thermometer, Comte notes, it was always many steps behind barology. The greatest difference between the two disciplines, according to him, was that while barology already investigated laws of weight, thermology still concentrated on metaphysical questions like the nature of fire. Comte still sees vestiges of metaphysics especially in the so-called caloric theory of heat, which assumes the existence of a fluid causing thermal phenomena.

Comte divides his account of thermology to physical and mathematical thermology, the former of which provides the basis for the latter. He then divides physical thermology into two parts, first of which studies interaction of bodies influencing their temperature, that is, warmer body warming the cooler and the cooler body cooling the warmer. He notes that there are two different cases of this interaction, in the first of which bodies radiate their heat and thus affect one another at distance, while in the other the bodies are in contact with one another.

The other part of physical thermology, Comte says, studies reversible changes in the physical constitution of the body through heat – thus, all chemical changes and inconvertible changes, like a body losing its elasticity due to heat, are excluded from this investigation. Such changes include changes in the volume of the body and changes between solid, liquid, and gaseous states of a substance. Comte also suggests the study of evaporation and hygrometry as an appendix to this part of thermology.

Comte singles out the mathematical study of thermology, because he thinks that it holds a unique position among the physical disciplines: barology and acoustics merely apply mechanics, while optics and electrology are still mired in the metaphysics of luminous and electric fluids. Comte refers especially to Fourier’s account of heat flux, the mathematical part of which he had already applauded in the first volume. Comte notes that Fourier’s work concerns only the first part of the physical thermology, that of transmission of heat, while the account of other physical changes involving heat still await their scientifically mathematical treatment. Comte also suggests the study of the global changes of temperatures as a more practical application of Fourier’s theory.

Auguste Comte: Course of positive philosophy 2 – Physics

Moving on from astronomy or the study of the large objects of our Solar System, Comte arrives at the study of objects on the surface of one of these large objects, namely, Earth. Within this study, he notes, it is easy to distinguish between the study of inorganic and organic objects, but it is difficult to note what distinguishes the two major parts of the former, namely, physics and chemistry.

Comte notes, firstly, that physics studies properties general to all matter, while chemistry studies only interactions of particular substances. Thus, weight, temperature, electricity and even acoustic and optic properties concern all bodies, and while magnetism seems to be an exception, Comte points out that it has been shown to be a mere type of electrical phenomena.

A further point of distinction Comte states is that physics studies masses, while chemistry studies molecules. He admits that this distinction is not completely general, since weight is also a property of molecules, and indeed, most physical phenomena are a result of molecular interactions, with the possible exception of acoustics and electricity. A more apt distinction, Comte suggests, is that in chemistry at least one of the interacting substances must be in a state of extreme division and fluidity, while such a division would hinder physical processes.

The final characteristic differentiating physics from chemistry, according to Comte, is that while in the former the arrangement of molecules may change, the nature of molecules themselves does not, although this happens all the time in chemistry. He admits this distinction is not rigid, since physical changes can sometimes result in chemical changes, where the molecules themselves change their nature. Still, Comte insists, even if all chemical phenomena would eventually be reduced to physical processes, the structural difference between the two disciplines would remain.

Having thus defined physics, Comte notes that it must follow astronomy in the hierarchy of sciences, since it is much more complex than the latter: while astronomy studied its objects only through vision and investigated only their form and motion, in physics we use all our senses. The complexity means, he adds, that physics is less perfect as a science, but admits more routes of investigation.

Indeed, while in astronomy we could only observe celestial objects and their movements, Comte notes, physics uses beside observationa also experimentation and is in fact a prime example of latter, since in physical studies we have the most possibility to put bodies in different circumstances. He thinks that physics outdoes even chemistry in this, since the latter allows only artificial experiments, while in physics we can also do experiments with bodies in their natural conditions.

Physics is not just less general than astronomy, but also presupposes the results of the latter, Comte thinks. Thus, in order to do physical investigations, we need to take into account various properties of the Earth itself – its shape, size and weight, for example – all of which are determined by astronomy.

Through astronomy, physics is connected to mathematics, Comte points out, but it also itself uses mathematics in its investigations: not as much as astronomy, but more than any other science. Sometimes physical investigations involve pure mathematical analysis, like in the study of heat, while in other cases they involve geometry and mechanics, like in the study of reflection and refraction. Comte suggests that physics gives an empirical foundation to pure mathematical speculations, while mathematics gives a rational structure to physics, which would otherwise be just a random collection of facts.

As has already been suggested by Comte, physics is a general study of Earthly matter and thus precedes sciences like chemistry and study of life. Indeed, he insists, these investigations presuppose the study of matter in general, and for instance, even living beings must follow the laws of physics.

Comte admits that astronomy as the study of the world and the study of life and human beings have been philosophically more inspiring than the intervening sciences. Still, he thinks that physics has its own interest as the current battlefield between properly scientific and metaphysical and theological theories. Thus, while astronomy is better at giving predictions and thus showing that we need not make supernatural assumptions, physics, according to Comte, is better at showing the human power to manipulate phenomena and thus alleviate any theological fears of e.g. lightning.

An important aspect of this role of physics as a battlefield is, Comte says, the use of hypotheses in it. Generally, he explains, scientific laws must be discovered either inductively from phenomena or deductively from more general laws. Yet, due to complexity of the phenomena investigated, we often cannot do induction or deduction straightaway, but we must assume some hypothesis as a preliminary explanation. Still, Comte insists, we should do so only if in setting up such a hypothesis we also suppose that we can at some point properly prove it through induction or deduction.

Now, Comte notes, current physics has often leaped over these restrictions of hypotheses and made conjectures about e.g. special fluids or matters explaining heat, light or electricity. Such fluids do not really explain anything, Comte says, and they even lack the properties inherent in all real matter, like weight. Yet, such unfounded conjectures are normal for a science that is on the verge of transitioning away from metaphysics to proper science: he points out the example of Cartesian vortices as an example familiar from astronomy.

Before moving on to the concrete parts of physics, Comte suggests an ordering of these parts, although he at once admits that it is still somewhat arbitrary and only the best in the current state of scientific development. The premier part of physics, he insists, should be the most general and the closest to astronomy: this is the characteristic of barology or the study of weight, since weight is the most general property of all matter and connected with the universal gravity of astronomy. Similarly, Comte notes, the last part of physics should be the least general and the most connected with chemistry, in other words, electrology or the study of electricity and magnetism, which are intrinsically linked with chemical processes and occur only in very special circumstances. Between these two extremes he places thermology, acoustics and optics. Of these, Comte suggests, thermology or the study of heat is the most general, while acoustics are more general than optics.

Auguste Comte: Course of positive philosophy 2 – Celestial mechanics

From celestial geometry Comte moves to celestial mechanics, which he, naturally, interprets as the application of mechanics – part of mathematics in his classification – to celestial objects. It is important for Comte that there is no essential difference between earthly and celestial mechanics: there is only the arbitrary fact that we can directly observe the trajectories of earthly objects – e.g. thrown projectiles – but the trajectories of celestial objects we must at first determine through geometrical means. Thus, after Kepler had found the laws of planetary movement, the next step was to merely use mechanics to explain them.

Of course, the application presupposed that mechanics had to be developed into a ripe enough state, which is the reason why Kepler himself couldn’t do it, but had to rely on metaphysical notions like attraction, Comte explains. The notion of attraction, he insists, suggests that there is some agent actively pulling things toward the Sun. The Newtonian word gravity, on the other hand, should describe an intrinsic property of all matter in the Solar System, whether in the Sun or anywhere else – even the earthly objects, like the projectiles, have their own gravity.

Comte thinks that Newtonian notion of gravity is essentially based on the observed phenomena, and he goes into great lengths showing how Newton derived this idea from e.g. Kepler’s laws of motions. Importantly, Comte restricts the use of this notion to what he calls the world – our own Solar System – since we do not, and he thinks, probably will not have enough evidence to determine whether the Newtonian theory applies generally in the wider universe.

Having established Newtonian theory of gravitation, Comte notes that the rest of celestial mechanics is just application of this theory to various celestial phenomena. He divides this application into two disciplines, celestial statistics and celestial mechanics. Celestial mechanics regards some celestial object as not moving and tries to determine, for instance, the mass or shape of it. Comte considers an important part of celestial statistics the explanation of tides, which he also thinks as providing a transition from astronomy to earthly physics.

Celestial mechanics, Comte continues, considers the planets as moving and is especially involved in explaining perturbations in the trajectories or rotations of planets, satellites and moons (he notes also that in principle we could also apply celestial mechanics to the Sun, since it moves slightly around the mass centre of the Solar System, but since we do not know the exact position of this centre, this would be an impossible task). Comte divides the perturbations into two classes: sudden changes that involve collisions or explosions and continuous effects of the gravitation of other objects.

An important conclusion Comte makes is that the gravitational effect of other stars and solar systems to our Solar System are so insignificant and always nullified by the effect of other solar systems that this “world” of ours is effectively independent of other potential solar systems. This effectively makes any what he calls sidereal astronomy an impossible discipline, except as regards observations of movements of binary stars or even clusters of several stars. Thus, Comte says, although usually the disciplines with more general subject matter determine the disciplines with more particular disciplines, in case of astronomy this rule breaks down, since we observe no effect the universe as a whole has on our own Solar System.

As a part of rejecting the sidereal astronomy, Comte denies the possibility of ever explaining where the stars have come from. On the contrary, he thinks that we can make reasonable, even if not completely proven conjectures about the generation of planets, satellites and comets within our own Solar System. Comte effectively assumes the Laplacian cosmogony, where the mass of our Sun originally extended to our whole Solar System, and in cooling down, broke down into masses that eventually developed into the system as it now exists, planets moving around the Sun and the satellites around their planets. Comte assumes that eventually the inobservably small, but necessarily existent resistance of the medium in which the planets float must slow the movement of the planets, which will mean their reabsorbment into the Sun. Thus, he concludes, the cosmogony again proves the independence of the Solar System, which has probably been varying between phases of a unified Sun and a diversified system innumerably many times before and will continue to do so no one knows how long.

Auguste Comte: Course of positive philosophy 2 – Celestial geometry

Although one would have assumed that celestial geometry concerns only such properties as the distance, figure and size of celestial objects, Comte defines these as only one class of phenomena in stellar geometry, namely, static phenomena. He spends considerable time explaining how astronomers can determine these static phenomena, that is, measure our distance from various stellar objects, recognise the figure of these objects, investigate their size and even note the density of their atmosphere. Comte also describes the history of attempts to determine the shape of the Earth, noting that even if there has always been room for making details more precise, this does not mean that the advance of science has been just replacing one error with another.

Comte is clearly more interested in the dynamic phenomena involving movement of celestial objects. He recounts in great detail the history of the discovery of Earth’s movement, both around its axis and around the Sun. What Comte finds philosophically interesting in this discovery is that it has forced us to abandon the theological idea of humans as the centre of the whole universe and also the teleological idea of planets moving for some purpose. This does not mean that astronomy has made the world meaningless, he soothes the reader, since through it we have found the lofty idea of humans as intelligences discovering the laws of the universe even from an insignificant vantage point.

A second important consequence of these discoveries is, Comte says, that we must distinguish the notions of world and universe. By world he means our region of universe, consisting of Earth and its nearby celestial objects – effectively, the Solar System. While people of earlier times could have thought that there is nothing beyond this world, modern astronomy must assume that the universe continues beyond our world, even if we cannot say anything certain about what happens beyond the confines of our world.

It is just to be expected that Comte still has much to say about the three laws of Kepler. He is especially keen to point out that Kepler had to overcome former mythological ideas, involving the notion of a circle as the perfect and thus the only suitable orbit for the supposedly divine stars. The great effect of these laws, Comte suggests, is that they allow us to make predictions about the orbits of planets, satellites and comets. Yet, he adds, even these laws are mere approximations of celestial mechanics – the topic of my next post.

Auguste Comte: Course of positive philosophy 2 (1835)

The second volume of Comte’s Cours de philosophie positive starts with the topic of astronomy. The position of this science is not arbitrary, since he thinks it to be the highest of all natural sciences. True, it is preceded by mathematics, because astronomy depends on geometry and mechanics, but these are more like methodology in comparison, while astronomy is the first science dealing with concrete objects.

Comte sees the importance of astronomy in its being the most perfect science. True, he admits, astronomy has its practical uses, for instance, in determining longitudes, but its premier importance lies in its purity from all theological and metaphysical considerations. Indeed, Comte suggests, astronomy frees us from all teleological considerations, since it shows that Earth is just one among planets and not the centre of the universe, with humans as the end of everything,

As a science, Comte says, it is not just a collection of facts about positions of stars, but its task is to determine laws, through which to predict these positions. Indeed, he adds, astronomy has been the only science that has reduced all the phenomena it describes into one law: gravity. It is thus, in a sense, the least complex of all concrete sciences.

The simplicity of astronomy, Comte suggests, is seen also in the fact that it has the least amount of methods it can use. We cannot do any astronomical experiments nor can we really compare our observations to analogical cases in other circumstances (no space travel yet in Comte’s time). The only methods available are then direct observation of celestial phenomena and mathematical calculations. Indeed, Comte adds, astronomy even uses proportionally more calculations than observations, being the most mathematical of concrete sciences.

Comte insists that astronomy is independent of all other concrete sciences. He does admit that an astronomer must know something about physics and even chemistry for the sake of perfecting their instruments and for making necessary corrections for such matters like refraction of the light of celestial objects. Yet, Comte insists, astronomy is independent in the sense that we have and even cannot have any idea of the chemical or mineralogical constitution of the stars and planets or even of their temperature (all of this, of course, has been proven wrong, since we nowadays do speak about these matters).

On the other hand, Comte suggests, facts of all the other concrete sciences depend on facts of astronomy. Even sociology depends on astronomy, he insists, because even a slight variation on the orbit of Earth would change our societies enormously (considering that Comte insists that all concrete sciences should have some empirical basis, he does jump to this conclusion rather quickly).

Since all physical and chemical considerations are removed from astronomy, we are left with merely geometrical and mechanical properties of celestial bodies. Thus, Comte quite naturally divides astronomy into celestial geometry, studying forms and sizes of celestial objects, and celestial mechanics, studying their motions and forces.

In addition to these two disciplines, Comte suggests that we can also divide astronomy into solar astronomy, studying only our solar system, and sidereal astronomy, studying all celestial objects. He also adds that we should restrict our attention to solar astronomy, since other solar systems do not really affect us.

Théodore Simon Jouffroy: Course of natural right – Theoretical views

After reviewing a number of alternative theories about goodness, Jouffroy is finally ready to share his own ideas about it and thus to give a firm foundation to the (unpublished )future course of natural law. He starts in a Kantian fashion, distinguishing the immutable form of moral judgements – the good in itself – from the particular matter or variable circumstances, to which this form is applied. This difference, Jouffroy explains, makes it possible that natural law is immutable, but still is a science where we can make progress: we can always find new circumstances, where we have to decide what is good in them.

Now, an important feature of good in the case of particular individuals is that the good in this question should be the end or purpose of these individuals, Jouffroy insists. He immediately adds that this is no tautology, since it gives us a method for determining in each particular case what is good. Different beings have different natures or they are organised differently, thus, Jouffroy concludes, they must have different ends, indicated by their natures.

Jouffroy argues that since all things have an end – as clear and evident truth as causality, he thinks – their sum must also have an end, which is determined by the ends of the individual beings. In other words, the universe has an order that is moving toward a unified end. This final end is the good in itself we have been looking for, Jouffroy insists. As free and intelligent beings, he adds, we can understand that the universe has such an end and we have the capacity to contribute to this end by fulfilling our own portion in this whole: thus, we are obligated to do so.

Jouffroy asks still further what makes this end of the universe good. He answers that really nothing outside it, because as a total good, beyond it there can be nothing more good. Thus, Jouffroy argues, this goodness must be absolute and based on something necessary, that is, God, who is the source of the goodness of the universe: in other words, God does not make goodness good, but goodness is as immutable as God’s own nature, and God merely makes the universe conform to this goodness. This relation to God, Jouffroy things, makes goodness sacred and connects natural law with religion.

Jouffroy admits that not all humans can understand this final ingredient of sacredness in the notion of good. Indeed, our very view of the final end of the universe is limited by our standpoint: we can know there must be such an end, but we cannot say in detail what this end is like. Yet, Jouffroy insists, we can at least know something about the end of things we know best, that is, human beings. He will not go through this end in detail – this would be the topic of the whole natural law – but merely gives a very summarised overview of it.

An important aspect of Jouffroy’s idea of the human end is that humans have been provided with means by which to strive for their end, even if they lacked the full understanding of morality. Thus, our natural instincts and self-interest are not necessarily in contradiction with our final end and even contribute toward it most of the time. We want to, for instance, know things and associate with other human beings, because knowledge and communities are parts of human destiny.

Jouffroy notes that we can clearly never fully realise our natural tendencies in this life, because, for example, absolute knowledge and harmonious society of all humans are something we haven’t been able to reach. He concludes that the end of humans must be found in another life, which in a very Kantian manner requires that we must live after our seeming deaths. The end of this life, Jouffroy thinks, is to develop our personality by providing obstacles that make us virtuous and worthy of happiness.

All free and intelligent beings or persons strive toward their end, hence, Jouffroy insists, we must respect them and let them fulfill their own destinies. Yet, he adds, there are beings that are not free nor intelligent, in other words, that are mere things. Such mere things cannot have obligations, because they lack the tools for fulfilling them. Even these things must have ends, Jouffroy thinks, but their end is fulfilled by God, who uses them as mere instruments. In Jouffroy’s opinion, we humans can also use them as instruments, without a fear of violating them, and if our end requires altering or even destroying them, we are allowed to do so (a pretext for killing animals).