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Tractatus Logico-Philosophicus (English): Difference between revisions
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<p style="text-align:center;"><math>(\Omega ' \Omega)^{\prime} (\Omega ' \Omega)^{\prime} x = \Omega ' \Omega ' \Omega ' \Omega ' x = \Omega^{1 + 1 + 1 + 1 \prime} x = \Omega^{4 \prime} x</math></p> | <p style="text-align:center;"><math>(\Omega ' \Omega)^{\prime} (\Omega ' \Omega)^{\prime} x = \Omega ' \Omega ' \Omega ' \Omega ' x = \Omega^{1 + 1 + 1 + 1 \prime} x = \Omega^{4 \prime} x</math></p> | ||
6.3 Logical research means the investigation of all regularity. And outside logic all is accident. | 6.3 Logical research means the investigation of ''all regularity''. And outside logic all is accident. | ||
6.31 The so-called law of induction cannot in any case be a logical law, for it is obviously a significant proposition.—And therefore it cannot be a law a priori either. | 6.31 The so-called law of induction cannot in any case be a logical law, for it is obviously a significant proposition.—And therefore it cannot be a law a priori either. | ||
6.32 The law of causality is not a law but the form of a law. | 6.32 The law of causality is not a law but the form of a law. | ||
6.321 "Law of Causality" is a class name. And as in mechanics there are, for instance, minimum-laws, such as that of least action, so in physics there are causal laws, laws of the causality form. | 6.321 "Law of Causality" is a class name. And as in mechanics there are, for instance, minimum-laws, such as that of least action, so in physics there are causal laws, laws of the causality form. | ||
6.3211 Men had indeed an idea that there must be a "law of least action", before they knew exactly how it ran. (Here, as always, the a priori certain proves to be something purely logical.) | 6.3211 Men had indeed an idea that there must be ''a'' "law of least action", before they knew exactly how it ran. (Here, as always, the a priori certain proves to be something purely logical.) | ||
6.33 We do not believe a priori in a law of conservation, but we know a priori the possibility of a logical form. | 6.33 We do not ''believe'' a priori in a law of conservation, but we ''know'' a priori the possibility of a logical form. | ||
6.34 All propositions, such as the law of causation, the law of continuity in nature, the law of least expenditure in nature, etc. etc., all these are a priori intuitions of possible forms of the propositions of science. | 6.34 All propositions, such as the law of causation, the law of continuity in nature, the law of least expenditure in nature, etc. etc., all these are a priori intuitions of possible forms of the propositions of science. | ||
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(As with the system of numbers one must be able to write down any arbitrary number, so with the system of mechanics one must be able to write down any arbitrary physical proposition.) | (As with the system of numbers one must be able to write down any arbitrary number, so with the system of mechanics one must be able to write down any arbitrary physical proposition.) | ||
6.342 And now we see the relative position of logic and mechanics. (We could construct the network out of figures of different kinds, as out of triangles and hexagons together.) That a picture like that instanced above can be described by a network of a given form asserts nothing about the picture. (For this holds of every picture of this kind.) But this does characterize the picture, the fact, namely, that it can be completely described by a definite net of definite fineness. | 6.342 And now we see the relative position of logic and mechanics. (We could construct the network out of figures of different kinds, as out of triangles and hexagons together.) That a picture like that instanced above can be described by a network of a given form asserts ''nothing'' about the picture. (For this holds of every picture of this kind.) But ''this'' does characterize the picture, the fact, namely, that it can be ''completely'' described by a definite net of ''definite'' fineness. | ||
So too the fact that it can be described by Newtonian mechanics asserts nothing about the world; but this asserts something, namely, that it can be described in that particular way in which as a matter of fact it is described. The fact, too, that it can be described more simply by one system of mechanics than by another says something about the world. | So too the fact that it can be described by Newtonian mechanics asserts nothing about the world; but ''this'' asserts something, namely, that it can be described in that particular way in which as a matter of fact it is described. The fact, too, that it can be described more simply by one system of mechanics than by another says something about the world. | ||
6.343 Mechanics is an attempt to construct according to a single plan all true propositions which we need for the description of the world. | 6.343 Mechanics is an attempt to construct according to a single plan all ''true'' propositions which we need for the description of the world. | ||
6.3431 Through their whole logical apparatus the physical laws still speak of the objects of the world. | 6.3431 Through their whole logical apparatus the physical laws still speak of the objects of the world. | ||
6.3432 We must not forget that the description of the world by mechanics is always quite general. There is, for example, never any mention of particular material points in it, but always only of some points or other. | 6.3432 We must not forget that the description of the world by mechanics is always quite general. There is, for example, never any mention of ''particular'' material points in it, but always only of ''some points or other''. | ||
6.35 Although the spots in our picture are geometrical figures, geometry can obviously say nothing about their actual form and position. But the network is purely geometrical, and all its properties can be given a priori. | 6.35 Although the spots in our picture are geometrical figures, geometry can obviously say nothing about their actual form and position. But the network is ''purely'' geometrical, and all its properties can be given a priori. | ||
Laws, like the law of causation, etc., treat of the network and not of what the network describes. | Laws, like the law of causation, etc., treat of the network and not of what the network describes. | ||
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But that can clearly not be said : it shows itself. | But that can clearly not be said : it shows itself. | ||
6.361 In the terminology of Hertz we might say: Only uniform connexions are thinkable | 6.361 In the terminology of Hertz we might say: Only ''uniform'' connexions are ''thinkable''. | ||
6.3611 We cannot compare any process with the "passage of time"—there is no such thing—but only with another process (say, with the movement of the chronometer). | |||
Hence the description of the temporal sequence of events is only possible if we support ourselves on another process. | Hence the description of the temporal sequence of events is only possible if we support ourselves on another process. | ||
It is exactly analogous for space. When, for example, we say that neither of two events (which mutually exclude one another) can occur, because there is no cause why the one should occur rather than the other, it is really a matter of our being unable to describe one of the two events unless there is some sort of asymmetry. And if there is such an asymmetry, we can regard this as the cause of the occurrence of the one and of the non-occurrence of the other. | It is exactly analogous for space. When, for example, we say that neither of two events (which mutually exclude one another) can occur, because there is ''no cause'' why the one should occur rather than the other, it is really a matter of our being unable to describe ''one'' of the two events unless there is some sort of asymmetry. And if there ''is'' such an asymmetry, we can regard this as the ''cause'' of the occurrence of the one and of the non-occurrence of the other. | ||
6.36111 The Kantian problem of the right and left hand which cannot be made to cover one another already exists in the plane, and even in one-dimensional space; where the two congruent figures ''a'' and ''b'' cannot be made to cover one another without moving them out of this space. The right and left hand are in fact completely congruent. And the fact that they cannot be made to cover one another has nothing to do with it. | |||
6.36111 | [[File:TLP 6.36111.png|330px|center|link=]] | ||