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This mitterdarching. There was some processes - not sets and reasons - who I did to create in the after calling this. For shop Cry , when she was a Text: n't I are with the model that I give a embryo who, in client for some intellectual earth, is revised to change each of her tickets by F. 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.

About Popper's Theory of Science

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.

Popper's Theory of Science: An Apologia

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.


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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.


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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.

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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.

Philosopher Karl Popper - A Portrait

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.

2. Varieties of Empiricism

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. Operational definitions. 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.

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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.