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Tractatus Logico-Philosophicus (English): Difference between revisions
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<p style="text-align: center;">''Preface''</p> | <p style="text-align: center;">''Preface''</p> | ||
This book will perhaps only be understood by those who have | This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts. It is therefore not a text-book. Its object would be attained if there were one person who read it with understanding and to whom it afforded pleasure. | ||
The book deals with the problems of philosophy and shows, as I believe, that the method of formulating these problems rests on the | The book deals with the problems of philosophy and shows, as I believe, that the method of formulating these problems rests on the misunderstanding of the logic of our language. Its whole meaning could be summed up somewhat as follows: What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent. | ||
The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought). | The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought). | ||
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Absence of this mark means disagreement. | Absence of this mark means disagreement. | ||
4.431 The expression of the agreement and disagreement with the truth-possibilities of the elementary-propositions expresses the truth-conditions of the proposition. The proposition is the expression of its truth- conditions. | 4.431 The expression of the agreement and disagreement with the truth-possibilities of the elementary-propositions expresses the truth-conditions of the proposition. The proposition is the expression of its truth-conditions. | ||
(Frege has therefore quite rightly put them at the beginning, as explaining the signs of his logical symbolism. Only Frege's explanation of the truth-concept is false: if "the true" and "the false" were real objects and the arguments in ~''p'' etc., then the sense of ~''p'' would by no means be determined by Frege's determination.) | (Frege has therefore quite rightly put them at the beginning, as explaining the signs of his logical symbolism. Only Frege's explanation of the truth-concept is false: if "the true" and "the false" were real objects and the arguments in ~''p'' etc., then the sense of ~''p'' would by no means be determined by Frege's determination.) | ||
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5.1 The truth-functions can be ordered in series. That is the foundation of the theory of probability. | 5.1 The truth-functions can be ordered in series. That is the foundation of the theory of probability. | ||
5.101 The truth-functions of every number of | 5.101 The truth-functions of every number of elementary propositions can be written in a schema of the following kind: | ||
{| style="margin: 0 auto 0 auto;" | {| style="margin: 0 auto 0 auto;" | ||
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5.11 If the truth-grounds which are common to a number of propositions are all also truth-grounds of some one proposition, we say that the truth of this proposition follows from the truth of those propositions. | 5.11 If the truth-grounds which are common to a number of propositions are all also truth-grounds of some one proposition, we say that the truth of this proposition follows from the truth of those propositions. | ||
5.12 In particular the truth of a proposition ''p'' follows from that of a proposition ''q'', if all the truth- grounds of the second are truth-grounds of the first. | 5.12 In particular the truth of a proposition ''p'' follows from that of a proposition ''q'', if all the truth-grounds of the second are truth-grounds of the first. | ||
5.121 The truth-grounds of ''q'' are contained in those of ''p''; ''p'' follows from ''q''. | 5.121 The truth-grounds of ''q'' are contained in those of ''p''; ''p'' follows from ''q''. | ||
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Contradiction is the external limit of the propositions, tautology their substanceless centre. | Contradiction is the external limit of the propositions, tautology their substanceless centre. | ||
5.15 If ''T<sub>r</sub>'' is the number of the truth-grounds of the proposition "''r''", ''T<sub>r</sub>'' the number of those truth-grounds of the proposition "''s''" which are at the same time truth-grounds of "''r''", then we call the ratio ''T<sub>rs</sub>:T<sub>r</sub>'' the measure of the ''probability'' which the proposition "''r''" gives to the proposition "''s''". | 5.15 If ''T<sub>r</sub>'' is the number of the truth-grounds of the proposition "''r''", ''T<sub>r</sub>'' the number of those truth-grounds of the proposition "''s''" which are at the same time truth-grounds of "''r''", then we call the ratio {{nowrap|''T<sub>rs</sub> : T<sub>r</sub>''}} the measure of the ''probability'' which the proposition "''r''" gives to the proposition "''s''". | ||
5.151 Suppose in a schema like that above in No. 5.101 ''T<sub>r</sub>'' is the number of the "T"'s in the proposition ''r'', ''T<sub>rs</sub>'' the number of those "T"'s in the proposition ''s'', which stand in the same columns as "T"'s of the proposition ''r''; then the proposition ''r'' gives to the proposition ''s'' the probability ''T<sub>rs</sub>: T<sub>r</sub> | 5.151 Suppose in a schema like that above in No. 5.101 ''T<sub>r</sub>'' is the number of the "T"'s in the proposition ''r'', ''T<sub>rs</sub>'' the number of those "T"'s in the proposition ''s'', which stand in the same columns as "T"'s of the proposition ''r''; then the proposition ''r'' gives to the proposition ''s'' the probability {{nowrap|''T<sub>rs</sub> : T<sub>r</sub>''}}. | ||
5.1511 There is no special object peculiar to probability propositions. | 5.1511 There is no special object peculiar to probability propositions. | ||
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So ''this'' is not a mathematical fact. | So ''this'' is not a mathematical fact. | ||
If then, I say, It is equally probable that I should draw a white and a black ball, this means, All the circumstances known to me (including the natural laws hypothetically assumed) give to the occurrence of the one event no more probability than to the occurrence of the other. That is they give — as can easily be | If then, I say, It is equally probable that I should draw a white and a black ball, this means, All the circumstances known to me (including the natural laws hypothetically assumed) give to the occurrence of the one event no more probability than to the occurrence of the other. That is they give — as can easily be understood from the above explanations — to each the probability ½. | ||
What I can verify by the experiment is that the occurrence of the two events is independent of the circumstances with which I have no closer acquaintance. | What I can verify by the experiment is that the occurrence of the two events is independent of the circumstances with which I have no closer acquaintance. | ||
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5.2 The structures of propositions stand to one another in internal relations. | 5.2 The structures of propositions stand to one another in internal relations. | ||
5.21 We can bring out these internal relations in our manner of expression, by presenting a | 5.21 We can bring out these internal relations in our manner of expression, by presenting a proposition as the result of an operation which produces it from other propositions (the bases of the operation). | ||
5.22 The operation is the expression of a relation between the structures of its result and its bases. | 5.22 The operation is the expression of a relation between the structures of its result and its bases. | ||
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5.3 All propositions are results of truth-operations on the elementary propositions. | 5.3 All propositions are results of truth-operations on the elementary propositions. | ||
The truth - operation is the way in which a truth - function arises from elementary propositions. | The truth-operation is the way in which a truth-function arises from elementary propositions. | ||
According to the nature of truth-operations, in the same way as out of elementary propositions arise their truth-functions, from truth-functions arises a new one. Every truth-operation creates from truth-functions of elementary propositions another truth-function of elementary propositions, ''i.e.'', a proposition. The result of every truth-operation on the results of truth-operations on elementary propositions is also the result of ''one'' truth-operation on elementary propositions. | According to the nature of truth-operations, in the same way as out of elementary propositions arise their truth-functions, from truth-functions arises a new one. Every truth-operation creates from truth-functions of elementary propositions another truth-function of elementary propositions, ''i.e.'', a proposition. The result of every truth-operation on the results of truth-operations on elementary propositions is also the result of ''one'' truth-operation on elementary propositions. | ||