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An Introduction to the Philosophy of Science” alıntıları – Rudolf Carnap adlı yazardan

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observation is ever completely precise. There is always an element of uncertainty. All laws of science are, in this sense, statistical
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The law does not predict what will happen on any one roll, nor does it say what is certain to happen on sixty rolls. It asserts that, if a great many rolls are made, each face can be expected to appear about as often as any other face. Because there are six equally probable faces, the probability of rolling any one face is %. Probability is used here in a statistical sense, to mean relative frequency in the long run, and not in the logical or inductive sense, which I call degree of confirmation
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For example, a statistical law states that, if a cubical die is rolled sixty times, a given face may be expected to be uppermost on about ten of the rolls.
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A statistical law, however, states only a probability distribution for the values of a magnitude in individual cases.
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assertion that, when the bar is heated to a certain temperature, its length increases by a certain amount, is a quantitative assertion. A quantitative deterministic law always states that, if certain magnitudes have certain values, another magnitude (or one of the former magnitudes at a different time) will have a certain value. In brief, the law expresses a functional relation between the values of two or more magnitudes
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I object to this reasoning, because I think it involves a confusion between determination in the theoretical sense, in which an event is determined by a previous event according to laws (which means no more than predictability on the basis of observed regularities), and compulsion.
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Predictability and compulsion are two entirely different things
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CAUSALITY” and “causal structure of the world” are terms I prefer to use in an extremely wide sense. Causal laws are those laws by which events can be predicted and explained. The totality of all these laws describes the causal structure of the world.
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Neurath, for instance, said that it would be a sin against empiricism to speak of laws as true
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But this is not, I suspect, what scientists mean when they speak of a basic law of nature. By “basic law”, they mean something that holds in nature regardless of whether any human being is aware of it.
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In many fields—biology, sociology, anthropology, economics—there are laws that seem at first to hold generally, but only because the author did not look beyond the limits of his country, or his continent, or his period of history. Laws thought to express a universal moral behavior or universal forms of religious worship turned out to be limited laws when it was discovered that other cultures behaved differently. Today, it is suspected that there may be life on other planets. If so, many laws of biology, which are universal with respect to living things on earth, may not apply to life elsewhere in the galaxy. Apparently, then, there are many laws that are not accidental, but that hold only in certain limited regions of space-time and not universally.
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We think we have a choice, that we make up our minds; actually, every event is predetermined by what happened before, even before we were born.
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Can a man choose between different possible actions, or is his feeling that he has freedom of choice a delusion
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Free will is an illusion.
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The problem of determinism is, of course, closely connected in the history of philosophy with the problem of free will.
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that most physicists and philosophers of science would describe as not deterministic
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is, so to speak, weaker than the structure of classical physics because it contains basic laws that are essentially probabilistic; they cannot be given a deterministic form like: “If certain magnitudes have certain values, then certain other magnitudes have exactly specified other values
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In the context of this point of view, what can be said about the meaning of the term “determinism”? In my opinion, determinism is a special thesis about the causal structure of the world. It is a thesis that maintains that this causal structure is so strong that, given a complete description of the entire state of the world at one instant in time, then with the help of the laws, any event in the past or future can be calculated.
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In present-day physics, quantum mechanics has a causal structure
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Geometry, therefore, is completely certain in a way that does not demand justification by experience
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