Chapter 2 discusses two basic functions of theories. The distinction between prediction and explanation constituted a hot topic in the debate between instrumentalist and realist astronomers. Chapter 3 demonstrates the emergence of four mutually irreducible principles of explanation in the physical sciences, concerning quantitive, spatial, kinetic, and interactive relations. Chapter 5 is concerned with the problem solving and problem generating function of theories. Chapter 6 discusses how in the history of optics many problem shifts occurred, mostly made possible by the parallel and often independent development of the arts and crafts.
The success of experimental research into infrared and ultraviolet light interacting with matter led to the downfall of mechanism, and the end of classical physics. Chapter 7 on the unification of the physical sciences first discusses the Newtonian synthesis of the Copernican achievements, next the idea of the unity of physical science as promoted by 19th-century romantic philosophers. It led to the discovery of the law of conservation of energy, the development of thermodynamics, and — despite romantic and instrumentalist objections — to atomic theories. Chapter 8 returns to the structure of theories, discussing the distinction between hypotheses and axioms, and the idea of natural law.
Chapter 9 is involved with the heuristics of experimental philosophers, how they searched for and found natural laws. The mathematical method and its complement, successive approximation, were both applied by Newton in his Principia. The method of analogy was most effectively used by Maxwell in finding the laws called after him. The application of technology is a condition for experimental science, to be illustrated by the investigation of gases at a very low pressure, culminating in the discovery of the electron and of X-rays.
Applying the philosophical distinction between immanent, transcendent, and transcendental critique, the final chapter 10 reflects on the former chapters. The critical approach is elaborated in the companion volume, Nature and freedom The logic of theories and the significance of language. Theory and experiment. The Copernican revolution. The introductory chapter 1 is a synopsis of what I consider to be a theory , to be studied in the context of the Copernican era, when a modern view of theories arose 1. It concerns the artificial character of a theory 1.
For various reasons, the time-honoured expression Copernican revolution has a strong appeal. The term Copernican revolution was probably first used in by Immanuel Kant, who coined it to emphasize a radically new point of view in his own epistemology. Like Thomas Kuhn in his book The Copernican revolution , I shall apply the expression Copernican revolution to the historical period from to The division of history into well-defined eras is unavoidably arbitrary. More aesthetic than logical, it indicates various styles of investigation. The Copernican revolution overlaps the scientific revolution , starting with Galileo and Kepler.
Besides physics and astronomy, it includes alchemy, geography, medicine, and the life sciences, if not mathematics. This revival was caused by the downfall of Aristotelian philosophy, largely due to Copernicanism. During the Copernican era, atomism was a common yet speculative world view. Only in the 19th century it became an experimentally well-founded theory in chemistry and physics. However, more than mechanism or atomism, for Kepler and Galileo the Copernican thesis of the moving earth was the driving force.
In science, the Platonic-Pythagorean Renaissance indicates the period between circa and The humanist Renaissance, starting circa with Francesco Petrarch, contributed to the rise of natural science by its renewed interest in classical texts purged from translation errors , by its criticism of scholastic Aristotelian science, and its call to return to ancient, especially Platonic, views. It was succeeded by classical physics, about dominated by mechanical and experimental philosophy. The latter two, translated into Italian by Nicolo Tartaglia, marked a neo-Platonic interest in mathematics, and would strongly influence classical physics.
Kepler and Galileo started their careers as Renaissance scientists, but their most mature work is classical in spirit. They crossed the watershed between ancient and early modern science. Indeed, the Copernican ideology of the moving earth was the motor of the transition from Renaissance to classical physics. Copernicus started it, Kepler, Galileo and Descartes were its chief advocates, and Newton brought it to completion. This period is called Copernican because almost all its heroes considered themselves Copernicans. Their common creed was that the earth moves, and their common aim was to explain this.
The Copernican revolution concerned astronomy and physics, mechanics, magnetism, and optics. Simultaneously it saw a battle between several philosophies. Christianized during the Middle Ages, Aristotelian philosophy dominated the universities, and was mostly defended by conservative professors.
It included a realist view of physics and cosmology, in contrast to an instrumentalist view of observational astronomy. Up till Galileo, most Copernicans were under the spell of this philosophy. It was a reaction to Aristotelian philosophy as well. It saw a revival during the 19th century.
Finally, empirism came to life, a new philosophy opposing the rationalistic trends of the preceding ones. Traces of it can be found in Kepler, Galileo, and Huygens.
Francis Bacon was its prophet, and Blaise Pascal, Robert Boyle, and Isaac Newton propagated it under the flag of experimental philosophy. The artificial character of a theory. Would it be possible to distinguish theoretical thought from non-theoretical thought?
Let me try to answer this question without discussing the far more difficult problem about the nature of thought itself. Natural, non-theoretical thought is spontaneous.
It is characterized by an immediate relation between the thinking person, the subject , and the object of their thought. In theoretical thought this direct relation is interrupted, because people put theories between themselves and their object of thought. A theory is like a medium, mediating between subject and object, it is an instrument. I shall elaborate this, without committing myself to instrumentalism.
Natural and artificial seeing. In order to clarify the instrumental character of theories, let us compare these with instruments to improve human vision. Seeing is a natural activity of men, and of all animals having eyes. We see objects in our environment — a tree, a tower, a car. Occasionally, we also look at a picture of a tree. In an artificial manner, we see a tree, whereas in a natural manner, we see a picture. In a natural way, we cannot see our own face, or the phases of Venus.
Using a mirror, we see naturally a picture, but artificially our own face. Using a telescope, we see naturally an image, but artificially the phases of Venus. Artificial seeing is not contrary to natural seeing, but depends on it. Optical instruments are invented in order to see better than would be possible in a natural way. In Holland, one cannot see the Eiffel tower directly.
But one can see a picture of it, a photo, a miniature, or a TV-picture. This kind of artificial seeing seems to be an exclusively human activity. Animals do not see the Eiffel tower, if they see its picture — they only see a piece of paper. Nor do animals invent instruments to improve on their seeing.
Contrary to natural seeing, artificial seeing has a history. Medieval painting, Renaissance and modern art differ widely from each other. Photography was invented in the 19th, television in the 20th century. It is more than a coincidence that the telescope and the microscope were invented during the Copernican revolution. The new movement made these discoveries possible, and needed them all the same. Galileo was the first to use the telescope for astronomical observations — it is a historical event.
He used these discoveries in his propaganda for the Copernican theory. Natural and artificial thought. There is no need to define seeing — everyone knows what it is. Similarly, natural thinking is familiar. It is a natural activity of men and women, and perhaps of all animals having brains. Natural thought concerns trees, towers, or stars, good or evil deeds, families and churches, colours and paintings.
All thought is characterized by dissociation and association, by logic. Thinking beings are logical subjects , and they think about logical objects. The logical objects of natural thought are concrete, everyday things, events, and their relations. The thinker distinguishes and relates them. A theory, too, is an object. It is certainly not a thinking subject, as it does not think. But it is not a logical object. Except for philosophers, nobody thinks about theories. A theory is an artefact. Theories are used as instruments in human thought.
Theoretical thinking is natural thinking, opened up by the use of instruments. People form concepts of concrete things, of events, and of relations, and they think theoretically about these. Contrary to natural thought, theoretical thought has a history, the history of ideas. It is generally assumed that theoretical thought originated with the Greeks, about BC.
The theories of the Greeks differ from the medieval theories, from those of the 17th century, and from the present. Theoretical thought is concerned with statements, and statements concern concrete things, events, and relations. This constitutes a problem, the problem of the relation between artificially conceived theories, statements, and concepts on the one hand, and concrete things, events, and relations on the other hand. This problem is related to the fact that by using an instrument people enlarge their power of seeing or thinking, but simultaneously diminish their field of vision or attention.
Using a microscope one can see much better than without, but at the same time one sees much less. Moreover, the other senses are eliminated. Looking at a real dog, one does not only see him, but also smell him, and hear him. This continuity of sensory experience is interrupted when looking at a picture of a dog. Therefore, a dog can see another dog, but if shown a picture of a dog, he may not recognize it.
In theoretical thought people make abstractions, restricting their conceptual activity, and switching off their other modes of experience — for instance, their feelings. Often, theoretical thought is at variance with natural thought. An example is the Copernican leading idea of the moving earth, which is counter-intuitive. Whether this is possible and to what extent will be discussed later on.
The three worlds of Karl Popper. The correspondence is not perfect, however. Popper seems to think that his classification is complete and exhaustive, that everything belongs to one of his worlds. My classification is merely logical ; it has merely a logical function. There are more subjects than logical subjects: mathematical subjects like numbers and spatial figures, physical subjects like atoms and stars, biological subjects like plants and animals.
Theye have feelings, they act, they love, they believe. Philosophically speaking, something is a subject if it is directly and actively subjected to a given law. An object is passively and indirectly via a subject subjected to a law. Therefore, whether something is a subject or an object depends on the nomic context. If one wants to discuss individual subjects or objects, one needs typical laws in order to distinguish them from each other. These laws also determine typical relations between subjects and between subjects and objects. However, individual things and events have non-typical relations to each other as well.
Next, there are more objects than logical objects. The magnitude of a spatial figure, its length or volume, is a spatial object. A road is a kinetic object, it does not move, but is indispensable for traffic. Food is a biological object; it does not live, but is a condition for life. A painting is an object of art. There are also far more artefacts than theories and ideas — telescopes, houses, cars, clothing. Hence, distinguishing logical subjects, logical objects, and theories as logical instruments concerns only one of our fundamental modes of experience.
The logical aspect of human experience is only one of its segments. Other aspects, like the quantitative, the spatial, the kinetic, and the physical, have played equally important parts in the history of the Copernican revolution, as will be seen in due course chapter 3. The logical character of a theory. A human mode of experience and relations, logic implies making distinctions and connections.
One of the most important logical distinctions to be made is that between the truth and falsity of statements. Hence, the most general logical function of a theory is to prove a statement, to establish its truth content relative to other statements. Omitting statements which are more or less probable, I shall restrict myself to propositions which are hold either false or true. Logical distinctions are made by people. As a logical subject, a person is actively subjected to logical laws, which they apply in their arguments, and which they have to obey if wishing to argue correctly.
The most important logical law is the law of non-contradiction. Within a certain context a statement and its negation cannot both be true. It points out that theoretical reasoning has a relative value.
A statement can be true in one context, false in another one. But a theory is inconsistent if it simultaneously contains a statement and its negation. In addition to the law of non-contradiction several other logical rules or tools of proof are available, such as syllogisms, modus tollens, modus ponens, and argumentum ad absurdum. Brouwer and other intuitionists accepted a proof only if it is finite. Proof by complete induction is therefore rejected. Brouwer also rejected reductio ad absurdum as proof.
The logical definition of a theory. What is a theory? The Greek word theoria means something like contemplation our word theatre is related , but already the earliest Greek philosophers connected theoria with proof, or deductive reasoning. I shall take for granted that a theory invariantly implies logical deduction. It is often assumed that a theory should start from well-known and accepted truths, in order to arrive at new statements or theorems.
Other people maintain that scientific theories start from the unknown, from hypotheses which should explain the observable. In this case, theories are even identified with hypotheses,  but I shall consider hypotheses to be statements, not theories. Leaving room for both approaches, from the known to the unknown, or from the unknown to the known, I propose the following provisional definition of a theory, as far as its logical character is concerned.
A theory is a deductively ordered collection of statements accepted or proved to be true. Hence, a theory is not just a set of statements, but a qualified collection. It only concerns the formal structure of a theory. A theory is a deductively ordered set of statements, meaning that each statement is directly or indirectly connected with each other statement by way of a deductive argument, a deduction.
In a technical sense, a theory is a partially ordered set, because it is never the case that each pair of statements is connected such that one is deduced from the other one. Because of this definition, a theory is called closed with respect to deduction, but it is quite open in other respects, as we shall see presently. Later on, various kinds of statements in a theory will be discussed 1.
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At present, I observe that in most if not all theories, data are indispensable for the deductive process. But data are exchangeable. A datum can be replaced by its negation, as long as this does not lead to contradictions. This means that a theory is an open system. With this criterion it can be decided at any moment which statements belong to the theory. Each theory consists of a number of independent axioms and data, and a number of theorems, which are derived from the axioms and data. Hence, in a theory two statements may be directly connected, if one is deduced from the other, or indirectly , either if both are deduced from the same set of axioms and data, or if both are used to deduce a third statement.
The deductive ordering in a theory ought to be non-circular: circular reasoning is a logical fallacy. A theory is a set of statements taken to be true within the context of the theory. This is the most intriguing part of our definition. It is a necessary part, because of the fact that a false statement allows of any conclusion. Put otherwise, a theory is required to be consistent , i. From a logical point of view, a statement asserted to be false is a contradiction.
From a couple of contradictory statements, any statement whatever can be validly inferred. Hence, if one admits both p and its negation, q is always true. Therefore, a statement asserted to be false cannot be used in a logical process. On the other hand, very often in a theory statements are used which are known to be false in a wider context. Theories of planetary motion now state that the earth is a point, then that it is a perfect sphere, although it is very well known that these statements contradict each other, and are both wrong.
The subjunctive method of using counterfactuals is so common, and so fruitful, that it cannot be ignored. Clearly, saying that only true statements in a theory are admitted is not meant to adhere to absolute truth in whatever sense. It is not even demanded that the statements are believed to be true — nobody believes the earth to be a point.
Theories as logical instruments are used by people, by logical subjects, in general not by a single person, but by a group of people, who want to use the theory together. These people must decide which statements they want to consider true, for the sake of the discussion. In other words: statements or propositions are true within a certain context — the context of the theory, and the context of the discussion between the people who use the theory. Outside this context the same statements may be false, or uncertain.
But to make the deductive process possible it has to be assumed that the starting points are true. Then, if no logical mistakes are made, all deduced statements are equally true. This leads to a most important conclusion: A theory is never able to prove a statement conclusively. The truth of any proved statement completely depends on the truth of the axioms and data from which the theory starts. A theory determines the truth of a statement relative to the truth of other statements. In how far the latter are true must be decided in a different way. A theory is an instrument to propagate truth, to transfer truth, but never to create truth.
Three logical relations. Clearly a theory functions in three logical relations:. In the logical subject-object relation , a theory is an instrument between subject and object. A theory is made and used by people individual or in groups , and is concerned with logical objects, the things or events about which people want to theorize. Each statement has a non-logical content, besides a logical form.
A theory has a function in an argument, a discussion, a logical debate between people who want to convince each other of the truth or falsity of statements. The participants in the debate must agree on the initial assumptions and the applied methods of proof, because otherwise a discussion would be impossible.
This intersubjective relation is a logical subject-subject relation. In using a theory, people are bound to logical rules or logical laws. Hence a theory is indirectly subjected to logical laws; it functions in a logical subject-law relation. Strictly speaking, it is not the theory which has to obey these laws, but the people who use the theory.
Only they can be responsible for any use or misuse of existing or new theories. In all three relations, logical subjects are involved. Theories cannot be considered apart from the people who make them and who use them. The functions of a theory. From the above definition it follows that a theory can never be intended to give a mere description of whatever state of affairs.
A description can be given with the help of words and sentences, and usually by a setof sentences, like a narrative. But a mere description is not an ordered deduction, and does not constitute a proof. As a narrative, it has more a lingual than a theoretical structure 1. A theory has other functions than to provide a description of reality. These functions: to predict, to explain, to solve problems, to systematize our knowledge, will be discussed in the next chapters. The distinction between a mere statement or set of statements and a theory as a deductive scheme may be illustrated by comparing Copernicus with his so-called precursor, Aristarchus of Samos, of whom little is known but his assumption that the earth moves around the sun.
Copernicus was aware of this difference, when he wrote:. Before starting the discussion of the functions of a theory, the logical character of a theory will be investigated in relation to the characters of concepts and statements. Logical reasoning is based on meaningful distinctions and connections. Not only theories, but also concepts and statements have an instrumental, an intermediary function in reasoning. Distinctions and connections are made in our subjective thought, and they concern external, objective affairs.
As intermediary artefacts, explicit expressions of human thought, concepts have an objective character, but they are not the primary objects of thought. Hence, theories, statements, and concepts have a logical character as instruments of thought , and a non-logical meaning, referring to non-logical states of affairs.
In natural thought explicit concepts and statements are not much in need. In theoretical thought they are indispensable. Classification and conceptualization belong to the first phase of any field of theoretical thought. Because a concept is not a statement, it cannot be an element of a theory. But a definition is a statement, and can therefore be an element of a theory.
A definition is employed in order to introduce explicitly a new concept into a theory. Usually, however, concepts are tacitly or implicitly introduced. Any theory contains well-defined concepts alongside ill-defined concepts. Each user of a theory can be challenged to clarify his concepts, to distinguish them clearly from other concepts. However, it is impossible to define all concepts, because concepts are needed to define others. Each theory has a number of primitive concepts, which cannot be defined within the theory. It is sometimes said that a definition is free.
This is not entirely true, if one wants to introduce a new concept into an existing theory. Also definitions are subjected to the logical law of excluded contradiction. The definition of a new concept should not contradict the definitions of already accepted concepts in the theory. Any definition should avoid a contradiction in terms. Concepts may have an individual or a universal character.
In the first case they establish an identity, in the second case a species or class. By its identity each thing can be distinguished from every other thing, each event from every other event, or each individual relation from every other individual relation. Since ancient times, Mercury, Venus, Mars, Jupiter, and Saturn were identified as planets, as wandering stars.
This means, for instance, that last night and tonight one recognizes the same planet to be Mars, even though it has moved on meanwhile. A significant result of Greek astronomy, ascribed to Pythagoras, was the identification of the morningstar and the eveningstar as the same planet, Venus. The idea of identity is subjected to the logical law of identity. Each thing is identical with itself. In the course of a logical argument it is not allowed to change the identity of the things about which one argues.
A common fallacy of identity is equivocation, to identify what is not identical. Classes and species may refer to things, like minerals, plants, animals; to events; to human acts, artefacts and associations; and much more. For instance, Aristotle distinguished four classes of change: variation of essence, of quality, of quantity, and of position.
Change of position, also called local motion, was further divided into natural and violent motion. Natural motion was divided into motion towards the centre of the universe, away from the centre, or around the centre. A system of related classes and subclasses is called a taxonomic system. It constitutes the barest kind of theory, for if one states that a certain individual belongs to a certain subclass, it can be deduced that it does not belong to other subclasses, and that it belongs to one or more superclasses.
A class concept points to things or events of the same kind, and are often indicated by a noun , like stars, planets, motions, dogs, lightings, birthdays. Properties, on the other hand, point to quite different things or events, which have something in common. In our language they are often indicated by an adjective , such as red, heavy, light-reflecting. Properties connect and disconnect classes.
They are used to define classes. The property light-reflecting connects planets with houses, and distinguishes planets from stars. Properties serve to mark distinctions and similarities. Aristotle distinguished between essential and accidental properties of an individual thing. Its essential properties indicate its nature, its essence, the species to which it belongs. Uniform circular motion around the centre of the universe is an essential property of a planet.
But it is accidental that Mars takes about two years, Jupiter about twelve years to complete one period. Intension and extension of the concept of a planet. A class concept involves both an intension meaning and an extension the number of things or events belonging to the class.
Extensional logic is restricted to the extension of concepts; predicate logic also concerns their intension. Consider, for example, the concept planet as conceived during the Copernican revolution. Before Copernicus, a planet was defined as a wandering star, a celestial body moving with respect to the fixed stars. Besides Mercury, Venus, Mars, Jupiter, and Saturn, both the sun and the moon were recognized as planets. In his heliocentric theory, a planet is a celestial body primarily moving around the sun.
Hence, the earth became a planet, and the sun and the moon ceased to be so. Not only the intension of the concept planet changed accordingly, but also its extension. The number of the planets decreased from seven to six. The Copernicans introduced the new concept of planetary system, namely a central body surrounded by one or more satellites. Copernicus knew two planetary systems, the solar system and the earth-moon system. It showed that the concept of a planetary system was not an arbitrary and improbable alternative for the geocentric systems of Aristotle and Ptolemy. Any theoretical definition has to take into account the character of planets as wandering stars.
Only with respect to the sun, the earth, and the moon the three theories differ. The difference with respect to intension implies a partial shift with respect to the extension. The extension of a concept can be changed without changing its intension, for example by the discovery of a new planet, like Uranus Such may be predicted with the help of a theory, as was the case with Neptune The recognition of Pluto as a planet was later undone, because it appeared not to fit into the intension of the concept planet as conceived in It has concealed the fact that there is another kind of concepts, namely relations.
A relation is not a property of a single individual, but a property of at least a pair of individuals, or a pair of classes. Aristotelian philosophy had hardly any place for relations. Something is large or small, heavy or light, warm or cold, moist or dry, moving or resting. Gradually, the Copernicans became aware that these binary contraries had better be replaced by relations, such as larger than, heavier than, warmer than. He rejected the contrary distinction between heavy and light bodies, by showing all bodies to be more or less heavy.
He emphasized that rest is not contrary to motion, but is only a gradation of motion, with zero speed. A falling body, starting from rest, has a continuously increasing speed, varying from zero to the final value. Aristotle distinguished between quantitative and qualitative properties, and he clearly valued the latter much higher than the former.
The Copernican revolution changed this radically. The question of how large something is will sooner be raised in a climate in which the relation larger than is more important than the contrary distinction of large and small. More and more the Copernicans became interested in measurable quantities, developing measuring instruments and standards, for instance, a yardstick, a thermometer scale, a standard weight. During the Copernican revolution, besides quantitative relations, also spatial, kinetic, and physical relations became increasingly important concepts for the physical sciences, as will be seen.
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The shift from qualitative to quantitative concepts is one of the most striking features of the scientific revolution of the 17th century. This shift has been of consequence for definitions. In Aristotelian physics, conceptual definitions concern the essence, the nature of things. Gravity is the tendency of heavy bodies to move towards the centre of the universe.
In their theories, Galileo and Newton attempted to describe gravity with the help of measurable properties like acceleration, mass, and weight. The distinction between heavy and light bodies, so important in Aristotelian physics, disappeared. Following Archimedes, both Giovanni Benedetti and Galileo Galilei stated that bodies only move upward spontaneously if their density is less than that of the surrounding water or air.
Definitions determining how a property can be measured are called operational. By an operational definition one does not define a magnitude, but its metric. Hence, a metric has both an experimental measuring and a theoretical aspect calculating. Because of the theoretical character of a metric the same metric may be connected to various measurement methods. As soon as a metric is established, a measuring instrument can be gauged , such that it satisfies the metric agreed upon.
If a metric is generally accepted, it serves as a standard. A coherent set of metrics forms a metrical system. In the 20th century, Percy Bridgman introduced operationism , saying that operational definitions only are fit to determine the meaning of concepts.
He thought that such a definition should unequivocally indicate how the property concerned should be measured. For instance, if several possibilities to measure the length of a thing are available, we should rather speak of different concepts of length, according to this somewhat extravagant view, which he later mitigated. The concepts of volume and density cannot be multiplied with another. He did not define density at all, apparently assuming this concept to be sufficiently known, contrary to mass.
Mass or quantity of matter was a completely new concept, introduced by Newton himself. For Descartes, the essence of matter was its extension 3. Being material meant being extended. Hence, the quantity of matter was its volume. For Newton, matter and space were completely different. Therefore, he needed a new definition of quantity of matter. Keeping silent about its essence, he defined how its quantity could be measured. In the context of his ensuing theory, he argued that mass is a real property of any body, independent of its position. Density could be measured independently of any operation related to the division of mass and volume.
Hence, for Newton it was obvious to define the new concept of mass using the well-known concepts of density and volume. However, his definition may very well have been influenced by the assumption that in denser matter atoms are more densely packed. Statements and their context. Statements may have various functions in a theory 5. The most simple statements are those connecting concepts via the copula is or equivalents.
In modern formal logic, the most important operations are negation, conjunction, disjunction, equivalence, and material implication. Propositions or statements are distinguished from propositional functions, in which variables occur. It is not a statement of which the truth can be established. It can only be ascribed a truth value if the free variables x , y , and z are bound, for instance by a so-called quantifier.
The use of variables, first in mathematics, and soon afterwards in physics, is a fruit of the Copernican revolution. The two quantifiers point to the important logical distinction between universal statements and existential ones. It reflects the ontological difference between the law side and the subject and object side of reality. Universal statements or law statements refer to lawful states of affairs. Existential statements refer to subjects or objects or their relations, or to data.
Only statements occur in a theory, and statements are human inventions. But the law determining the motion of the planets around the sun has been valid long before Newton, even long before human beings inhabited the earth and started theoretical thought. Similarly, the fact the Jupiter has moons was established by Galileo in But Jupiter having moons presumably preceded this statement for ages. Clearly not every all statement is a law statement. Therefore, the logical distinction between universal and existential statements is not identical with the ontological distinction between laws and what is subjected to laws 8.
Theory dependence and autonomy. The truth of a statement is only partially determined by the theoretical context. It is possible to have the same statement in different theoretical contexts, with the same truth content. This is highly fortunate, for otherwise one would be unable to compare different theories. This view expressing partial theory dependence and partial autonomy, both of concepts and statements, takes a middle course between two more extreme views, logical empiricism, and historical relativism. These were so-called observation statements or protocol statements, and observational or empirical concepts.
The empiricists strongly believed in observation, in which they found the certainty and trustworthiness of human experience. In particular, for the observations made in scientific observatories or laboratories, elaborate instruments are used, which are developed according to sometimes rather advanced theories. Criticism of empiricism was levelled by adherents of so-called historical-relativism. It makes no sense to say that the theory of Copernicus is better than that of Ptolemy, because these are incompatible, talking about different worlds.
The fact that sooner or later the Copernican theory was accepted is not the merit of the theory, but due to more or less accidental developments. Kuhn, Hanson, and Feyerabend believed discussions between adherents of competing theories to be quite fruitless. It may be doubted whether Galileo for instance would have accepted this view. Galileo became famous because of his two great books, Dialogo , and Discorsi These works of fiction describe discussions between three persons, Salviati, Sagredo, and Simplicio.
Although the opinions of Salviati the Copernican and Simplicio the Aristotelian differed strongly, Galileo presented them as able to discuss all problems put forward. Agreement with the view that observations cannot be made apart from any theoretical context should not blind us to the fact that observational results may be quite independent of some theories.
Hence theories, statements, and concepts are intimately interwoven. This is also the case with their respective structures or characters. Without any doubt, these characters are logically qualified. The main functions of theories, statements, and concepts is to mediate between logical subjective thought and its objects, and between the participants in any logical discourse. It is impossible to study theories, statements, and concepts as instruments of thought out of the context of logical laws and logical objects, and in particular apart from the logical subjects and their reasoning.
Logic might be considered a fundamental principle of human experience, not unlike the quantitative, spatial, kinetic, and physical principles, to be discussed in chapter 3. Because theories are characterized by deduction, their character has a typical kinetic aspect, deduction being the logical movement from one statement to another.
Similarly, statements have a typical spatial aspect, being dominated by the idea of logical connection. Statements invariably connect other statements or concepts. Finally, the character of a concept refers to the logical unity and multiplicity, hence to the quantitative relation frame or mode of human experience. In its turn, a theory has a function in a discussion, an argument. In a dispute, one does not only prove theorems from axioms and data, but the axioms and data themselves are discussed.
The force of the arguments is tested, convictions collide, data are weighed. Hence, a discussion in a logical sense has a physical foundation, because it is based in a logical interaction between arguments. The final section of the introductory chapter 1 is concerned with the art of the argumentative usage of language, the way people converse with each other when they use theories and other logical structures.
It is subject to the norm of clarity. It concerns the question of how theories are communicated, how they are made clear to various people. An important part of the philosophical discussions of the first half of the 20th century concerned the possibility of reducing theoretical language to observation language, of translating all theoretical statements into observation statements, supposed to be independent of any theory. Since the linguistic turn circa , analytical philosophy considers lingual analysis to be the nucleus, if not the whole of philosophy. It is a branch of logical empiricism, more influential in the humanities than in the natural sciences.
It considers concepts to be symbols, such that there is little difference between a word and a concept, between a logical statement and a lingual sentence, between a theory and a narrative. The aim of science is assumed to be hermeneutic, to translate reality, to interpret it, to clarify it. Because ordinary languages like Latin, German, or English are not suited for this purpose, logical-empiricist philosophers proposed that science should develop its own formal language, unequivocal, and interpretable in only one way, assuming the need of three vocabularies, a logical, a theoretical, and an empirical one.
In contrast, I shall assume that the logical aspect and the sign aspect of human experience are mutually irreducible, such that logical relations and structures presuppose the lingual ones. In order to find out whether the truth of a statement can be proved, first its semantic meaning has to be established. Metaphoric expressions are significant, but not logically true. They allow of nuances, of many ways to express the same thing. Though having semantic meaning, and providing insight, they cannot function in a proof.
Thus, during and before the Middle Ages, the organistic world view required mechanical instruments like the lever to be made clear by comparing these to living systems. In a mechanistic world view, it is the other way round. Now the functioning of the human arm is explained by comparing it with a lever. Since the Copernican revolution, the clockwork metaphor became very popular in clarifying the new system of the world. The foundation of the logical mode of experience in the lingual one implies the possibility of expressing concepts in words, statements in verbal sentences, and theories in spoken or written texts.
In a logical argument one wants to establish whether a statement is or is not true, but that is only possible if the corresponding sentence is grammatically correct, having semantic significance. It can be true or false. They cannot play a part in a logical reasoning. We have seen that a theory cannot allow of statements supposed to be false. Similarly, a norm for the meaningful use of language is that people speak the truth.
In three respects argumentation needs a special kind of language. First, it requires its own logical indicators, words like therefore, thus, so, hence, consequently, because, since, for. Third, any science is in need of its own language. The logical requirement of having unequivocal concepts is at variance with the lingual variety of homonyms and synonyms, which, on the other hand, serves the needs of didactics very well. For instance, while acceptable in an Aristotelian context, the homonymic use of the word earth, meaning soil, the heaviest element, or the globe, became for Galileo an equivocation to be avoided.
In this process, science started to withdrew from common language.
Mathematics as language of physics. It is often stated that mathematics is the language of physics. This assumption is clearly contradicted by the view that physics itself is a language. If one rejects this, and mathematics is accepted as a science on a par with physics, one should also reject the idea that mathematics is a language. Only if one considers mathematics to be fundamentally different from science could one accept the statement that it is a vehicle of science.
In Il saggiatore Galileo seems to adhere to this view:. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.
In this passage, Galileo reveals his neo-Platonic background, according to which nature can only be explained with the help of mathematical ideas. In fact, Galileo laid the basis for a far more intricate relation between physics and mathematics. The possibility to project kinetic and physical relations onto quantitative and spatial relations allowed him to apply mathematics to physical states of affairs 9. This includes physics making use of the language of mathematics, which has been developed during the 17th century in a way that has been very important, also for physics.
This development, never foreseen by Galileo, concerns the introduction of the algebraic symbol system, the use of letters as symbols for numbers and variables. This is indeed an example of the introduction of a typical language into science, showing how important and fruitful a right and well-considered use of language can be. Another example is the introduction of decimal fractions by Simon Stevin, although a hundred years later Newton still applied ordinary fractions.
Finally, formulas as expressions of physical laws and relations came into use only very slowly. Started in the 17th century, it was commonly applied only in the 19th century. Levels of communication. The main function of language is communication, the transfer of feelings, thought and skills by means of symbols and metaphors. Another function is the preservation of scientific knowledge and its transfer to later generations, the historical formation of the collective memory of mankind, mostly in written texts.
Both private and public libraries have contributed significantly to this function. Since the 17th century, scientific communication  occurs at different levels: between specialists on the same subject; between specialist and non-specialist scientists; between scientists and non-scientists; and in the didactic communication between a teacher and their students.
Each has specific requirements with respect to the use of language. At the first level, communication took place in Latin, by means of books and letters. The distribution of books was much better organized than during the Middle Ages, thanks to the invention of movable type printing in the 15th century. But the number of copies of each printed book was relatively small, not more than a few hundred copies every edition.
Copyright did not exist, and often books were reprinted without permission of the author or the first publisher. Nevertheless, he indicates which parts of the book can be omitted at first reading. Opticks is a far less technical work, and was initially written in English, later also in Latin. Another channel of communication was the exchange of letters — by Kepler and Galileo, by Descartes and Mersenne, by Newton and Bentley, by Clarke and Leibniz.
Often, these letters were copied several times, and many of these have been preserved and form an impressive source of knowledge about 17th-century science. The second level is very important to make the results of one specialization available to the others. If this does not function satisfactorily, the network character of theories is endangered, and stagnation may follow. A novelty was the introduction of scientific journals, for instance, the Philosophical Transactions of the Royal Society at London.
Nowadays many of these journals have a specialist character and hence belong to the first category. But in the 17th century their aim was to inform non-specialists of the proceedings of science. Initially most papers were written in Latin, but gradually Latin had to give way to the common languages: Italian, French, English, Dutch, and German. At the third level, especially Galileo did pioneering work, by writing his most influential book in colloquial Italian, in such a style that it was readable by non-scientists, that is, for an intelligent public.
In the Netherlands, Galileo was preceded by Simon Stevin, who pleaded for writing scientific works in common language in a comprehensible way. According to Stevin,. An example is his Weeghconst The art of weighing, , a book about mechanics. After Galileo, Descartes wrote his influential Discourse on method in French. His scientific work is Meditationes de prima philosophia and Principia philosophiae , both written in Latin, though the latter was shortly afterwards translated into French.
Except for Galileo, no leading scientist of the 17th century wrote really popular works, leaving that to their disciples, usually scholars of high quality but lesser creativity. Thus Rohault popularized Descartes. The popularization of scientific results strongly influenced the common world view.
The Western world view has changed radically since the Copernican revolution, though it took a long time before the idea of a moving earth became commonly accepted. In the 17th century even the majority of the learned remained convinced of the geocentric world view, and discussions about the validity of the heliocentric system continued deep into the 18th century.
At the didactic level, pupils must be introduced to the science they want to learn. It is a didactic aim to clarify theories, to make students understand them. Because a theory is an instrument, for instance to solve problems, the use of a theory must be exercised, such that the mastering of the language used is enlarged. On the one hand, a student learns to apply his own language to new problems, and on the other hand he extends his language, by learning and applying new words and expressions.
In this way, a student not only gains clarity about a theory and its possible applications, but also about that part of reality with which the theory is concerned. For a large part, medieval scholastic education consisted of the citation of authorities.
The best student was the one able to quote most citations, preferably from memory. Consequently, Kepler adopted the then usual form of question and answer, giving a systematic pedagogical order to his expositions, and avoiding biographical details. The turn of the tide came during the Copernican revolution. The French scholar Petrus Ramus advocated the educational value of visiting artisans, which he valued more than scholastic training. This means that he favoured the study of skills more than the study of bookish knowledge. Galileo also attacked the scholastic way of education.
This means that Galileo preferred to teach his students how to use theories, instead of teaching them accepted knowledge. Demonstration experiments. Based on experiments performed from his youth, Galileo showed the shape of a body to be irrelevant. Legend says Nanak went into a river at 28, proclaimed there is no Hindu or Muslim, only god and that he continued to bring Sikhism into the world. The 5th Guru, Arjan was a scholar and helped to build the Sikh religion by creating the first scripture. However, he was seen as a threat by the state and executed for his faith in The 6th Guru, Hargobind eventually moved to militarize the community and the Sikhs learned to fight to preserve their faith.
They became relatively peaceful until Tegh Bahadur, the 9th guru, was executed in by Aurangzeb, the Moghal Emperor. The 10th Guru, Gobind Singh, created the Khalsa as a military group so that they could forever defend their faith. The Sikhs continued to rebel against Muslim oppression and eventually became a state of their own. But then they were defeated by the British. Then they became peaceful for a while, until when there was a massacre of over dead and 1, wounded by British soldiers who fired on a crowd of protesters. A few historians signify this event as the beginning of the decline of the British Empire in India.
This spirit has no gender, is beyond time and space, is without form, beyond the comprehension of humans, but not completely unknowable. The religion prescribes meditation to allow for communication between god and man. It exists in all creation; it does not fear; it does not hate; it is timeless and universal and self-existent, you will come to know it through seeking knowledge and learning!
The ultimate goal of a Sikh is to be completely united with god. They achieve this state of liberation mukti by focusing on god rather than themselves. Maya is a spiritual concept that has evolved over time and crosses over nearly every eastern religion in one way or another.
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These worldly illusions are viewed as a direct opponent of realizing god in this lifetime the goal of the Sikh is to realize god. Once god is fully realized, the individual is considered jivanmukta and liberated in this lifetime, which is a belief also shared in Hinduism. Sikhs also believe in reincarnation and karma. The Khalsa is the collective body of all Sikhs. The Khalsa is responsible for all executive, military, and civil authority in the Sikh society. They are considered the pinnacle of Sikhism and perform no rituals and believe in no superstitions.
A Sikh is defined as any human being who faithfully believes in one immortal being; ten gurus, from Guru Nanak to Guru Gobind Singh, the teachings of the ten gurus and the baptism bequeathed by the tenth guru. Most Sikhs wake up early to meditate on the name of god. Then he chants the name of the lord. All sins, misdeeds, and negativity is erased through this process. When the sun rises, the Sikh is to meditate on the name of god again.
Sikhs are also very interested in music, many instruments were supposedly created by gurus. These instruments include the Rebab, the dilruba, the taus, the jori, and the sarinda. They would often play drums or Nagaras while marching into battle. Sikhs were some of the first to migrate to Britain from India and were used in the Indian Civil service and so were spread out over the entire British empire. Many have spread throughout Europe and Northern America. The caste system is still very prevalent within the Sikh religion, even though their gurus denounced the system.
Untouchables, or Dalits still face harsh discrimination. They are said to be often confused with Arabic or Muslim Middle Eastern men because of their turbans and CNN suggested an increase in hate Crimes against Sikh men after the attacks. So this is very real, and its happening right now. These are Americans that are discriminated against in our own country.
And in lots of cases the police turn a blind eye, refuse to investigate, or whatever nonsense racism and ignorance they can make up. But this seems to happen a lot and we, as a nation, should not allow this kind of intolerance or ignorance. This is the 5th largest religion in the world! Unfortunately, our world has over-complicated it with sexuality, superficiality, and our schedules for our selves. Yoga studios are some of the most interesting phenomenon in the past thirty years, in my opinion. The people who do yoga are not yoga.
We are called yogis for a reason. We grasp for yoga with our yoga practice. Even the supposed gurus are not yoga. They too must practice yoga to understand. Yoga is too simple for anyone to claim. You can start yoga right now. You only need your self. Yoga is about awareness of your breath. To start, you have to put your body into a comfortable position. Understand that the idea is to allow the body to stay in positions they call them asanas in yoga, which translates directly to posture for certain periods of time, so keep it reasonable.
If it feels like too much, it probably is too much. The real guide is your breath; if you lose your connection with your breath, lower the intensity of the posture for your body until your breath is flowing strongly through your nose again. If you practice and put some time into it. When you sprint and run, you are mostly trying to expel carbon dioxide which is why exhaling through your mouth feels so good. We can do this sometimes in yoga as well. But it is important to understand how powerful the force of your breath is to bring life back into your body.
This is what we are doing in yoga, breathing life and energy back into worn joints so that they can regenerate. We are simultaneously lengthening and strengthening our muscles with our breath, going back and forth like steel being smelted on an anvil to strengthen ourselves for the world around us. Our bones, ligaments, and joints become powerful machinations of efficiency when a yoga practice has been well-honed.
Everything flows easier, especially in your circulatory and digestive system. Now you are ready to start. Close your eyes and begin to breathe exclusively through your nose. It might be useful to take a few exaggerated exhales through your mouth to start, then shift all of the respiratory flow into the nose. If this is difficult, then spend some time during your day trying to breath through your nose; the more time you spent trying, the easier it will get. Your body should be comfortable, so you can focus. The idea behind a yoga practice is regeneration, healing, and awareness, so bring your mind into a peaceful place where you can focus completely on your breath.
Your breath is a healing force; your breath is also linked to your consciousness in ways that we do not fully understand.
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By focusing on your breath, you can give your entire attention to your body. A yoga practice can last a lifetime if practiced responsibly. You are already breathing through your nose, so the first and hardest part of this technique is already accomplished. Start to pay attention to the way air is flowing in the back of your throat. Can you restrict your throat muscles slightly to slow down the flow of air?
It should start to sound more and more like a wave, or the raspy sound of the ocean. Once you have spent a significant amount of time with the Ujjayi breathing technique, you will be able to variate and change the intensity of the breath with your postures in the yoga practice.
With more intense poses will come more intense breath, necessarily to keep your body sustained in the position. Equal inhales and exhales that are unceasing and complete will rejuvenate your body over 90 minutes, even if you are lying still on the floor. The breath is your yoga practice. The Ujjayi breath is powerful; there is also no reason to limit its use to the yoga room.
In stressful life situations, breathing techniques can help to keep you connected with your body and grounded in your thoughts. Your connection with your breath and the Ujjayi technique is the most vital aspect of the yoga practice. It is what allows the subconscious mind to integrate your thoughts and conscious feelings, soothes your bodily systems, and relaxes the central nervous system. If the pose gets too intense for the breath, lower the intensity of the posture in your body. When you are finished practicing, you lie down to rest with your back on the floor and your head on the floor.
The idea is to let your body sit completely still on the floor for about minutes, depending on how long your practice was. This is time where you let your breathing return to its normal state in a natural and easy way. You are set and ready to go. Closing your eyes always feels great. The magic starts to happen when you really start to let go of everything outside of your body and focus your attention completely inwards.
Here are a few more articles, in case you want to look at some additional information or more great resources:. Lao Tse is one of the great teachers and influencers of early eastern philosophy and helped to give foundation to the great traditions of the East. Many scholars argue that he was many people rather than one, but most ancient texts mention him in BCE. In any case, Lao Tse is said to have spent his life revealing the Tao. Much of his work after his death was used by anti-authoritarian establishments throughout history.
He was mentioned by several historical texts after his death. According to tradition, Laozi studied in the royal court of Zhou and attracted large numbers of people, legends tell of an encounter with Confucius , but Lao Tse never opened a school. One story says that Laozi is a hermit who lived in the woods until he was years old. One day he was stopped by Yinxi at a gate and Yinxi asked Laozi to record his wisdom.
He wrote the Tao Te Ching in response. Many stories then tell of Laozi traveling all the way to India to teach the Buddha. Some say that he was the Buddha. The Tao Te Ching is one of the most powerful works in Chinese history. It describes the Tao as the source and ideal of all existence and all of nature flows from it, so when humans defy their nature, they separate themselves from the flow of the Tao.
Laozi said that technology brings about a false sense of progress and taught about a method of existence called Wu-Wei, or non-action. What it really means is flowing with the moment, not forcing, acting spontaneously, not doing anything, or creating nothingness.
Some modern politicians think that Laozi was the first libertarian, believing that people should be allowed to govern themselves loosely and without much governmental structure. Raja means best, chief, or king; when used in yoga it means the highest state of yoga practice or striving for samadhi bliss. Hatha yoga is described as the way to achieve raja yoga when combined with the sutras of patanjali. Raja is a term that has undergone changes over time until it was most recently equated with the yoga sutras by Swami Vivekanada, but it has always referred to a style of yoga that attempts to make unison with the Brahman , or universal divinity.
Eight different steps have been mentioned numerous times and have also evolved over time as the usage of the word has evolved since it was used in the Bhagavad Gita. It has always been considered a type of yoga. Raja yoga is similar to a path of meditation towards the divine, assimilating the philosophy of samadhi and complete awareness into everyday life. Historically, there are three goals of Raja yoga: an altered state of higher consciousness, an uncovering of the soul, and the yogic traditions of isolation, meditation, and retrospection.
It is a term used to largely define the goal of the practices of hatha yoga. Mahadeva, or the supreme deity, also known as Shiva is the destroyer and transformer of all of life. He is limitless, unchanging, eternal, formless, and the ultimate yogi; one who has joined with the death of all things. Shiva is often displayed slaying demons with his trident. When not in battle, he is practicing yoga alone on Mount Kailash in his ascetic lifestyle of renunciation.
His third eye sees all and the Ganges river itself flows from his hair. Shiva is quite possibly the oldest god in history, dating back to the Indus Valley Civilization; however, his worship has lost none of its potency and he is worshipped across southeast Asia. Shiva is joined with the supreme self, the Brahman. Shiva powerfully deals destruction and death to make room for Brahma to create in the world. He smears his body with the ashes of the dead representing the impending death of all beings.
He dances to his drum bringing fiery and fierce death to all whose time has come to pass from this world. Shiva is a very fierce representation of what will eventually happen to all of us. A precedent to the grim-reaper, he represents what comes for life eventually and acceptance of this is the greatest freedom. Fear of death. If we can see past our own ego, we can realize that we never really existed in the first place.
It is an illusion to think that we matter more than the matter we are made up of. Even our idealisations of past figures in history are false representations. No one that is alive now actually knew who Jesus was. Nor Moses. Nor anyone else that has died over a hundred years ago.
It is important to remember that life is short. Make the most of each day. Gratitude for challenges, lessons, and difficulties that force us to grow. Once you let go of your ego, you can be free. Shiva, yoga, and ascetic practices will help you to let go. Freedom is in your mind, no one can give it to you or take it away from you.
Everything else is just an illusion. There is a certain point where I realized that there was nothing I could do to save anyone. And thinking otherwise is simply idealizing and overgeneralizing. Suffering is an unavoidable aspect of this world. You are not a victim, but instead an inhabitant; viewing suffering as against you or attacking you will only increase its power. Instead we should acknowledge our state of suffering and enjoy it; if everything was easy, life would be so boring, so monotonous, so pointless.
Accepting the state of suffering is the only freedom we have in the world. To enjoy the sun, a nice meal, the people around you, despite where you are, the ailments you have, or the desires that go unfulfilled. No one can do it for you. And the experiences of others are pretty irrelevant to you; you are a world in and of itself.
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