[5]Take the following example: A generous person is worthy of honour. Who would expect to recognize here a case of coexistence between phenomena? But so it is. The attribute which causes a person to be termed generous, is ascribed to him on the ground of states of his mind, and particulars of his conduct: both are phenomena; the former are facts of internal consciousness, the latter, so far as distinct from the former, are physical facts, or perceptions of the senses. Worthy of honour, admits a similar analysis. Honour, as here used, means a state of approving and admiring emotion, followed on occasion by corresponding outward acts. "Worthy of honour" connotes all this, together with our approval of the act of showing honour. All these are phenomena, states of internal consciousness, accompanied or followed by physical facts. When we say, A generous person is worthy of honour, we affirm coexistence between the two complicated phenomena connoted by the two terms respectively. We affirm, that wherever and whenever the inward feelings and outward facts implied in the word generosity have place, then and there the existence and manifestation of an inward feeling, honour, would be followed in our minds by another inward feeling, approval.
[5]Take the following example: A generous person is worthy of honour. Who would expect to recognize here a case of coexistence between phenomena? But so it is. The attribute which causes a person to be termed generous, is ascribed to him on the ground of states of his mind, and particulars of his conduct: both are phenomena; the former are facts of internal consciousness, the latter, so far as distinct from the former, are physical facts, or perceptions of the senses. Worthy of honour, admits a similar analysis. Honour, as here used, means a state of approving and admiring emotion, followed on occasion by corresponding outward acts. "Worthy of honour" connotes all this, together with our approval of the act of showing honour. All these are phenomena, states of internal consciousness, accompanied or followed by physical facts. When we say, A generous person is worthy of honour, we affirm coexistence between the two complicated phenomena connoted by the two terms respectively. We affirm, that wherever and whenever the inward feelings and outward facts implied in the word generosity have place, then and there the existence and manifestation of an inward feeling, honour, would be followed in our minds by another inward feeling, approval.
[6]Selon les logiciens idéalistes, on démêle cet être en consultant cette notion, et l'idée décomposée met l'essence à nu. Selon les logiciens classificateurs, on atteint cet être en logeant l'objet dans son groupe, et l'on définit cette notion en nommant le genre voisin et la différence propre. Les uns et les autres s'accordent à croire que nous pouvons saisir l'essence.
[6]Selon les logiciens idéalistes, on démêle cet être en consultant cette notion, et l'idée décomposée met l'essence à nu. Selon les logiciens classificateurs, on atteint cet être en logeant l'objet dans son groupe, et l'on définit cette notion en nommant le genre voisin et la différence propre. Les uns et les autres s'accordent à croire que nous pouvons saisir l'essence.
[7]An essential proposition, then, is one which is purely verbal; which asserts of a thing under a particular name only what is asserted of it in the fact of calling it by that name; and which therefore either gives no information, or gives it respecting the name, not the thing. Non-essential, or accidental propositions, on the contrary, may be called Real Propositions, in opposition to Verbal. They predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it; some attribute not connoted by that name.
[7]An essential proposition, then, is one which is purely verbal; which asserts of a thing under a particular name only what is asserted of it in the fact of calling it by that name; and which therefore either gives no information, or gives it respecting the name, not the thing. Non-essential, or accidental propositions, on the contrary, may be called Real Propositions, in opposition to Verbal. They predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it; some attribute not connoted by that name.
[8]The definition, they say; unfolds the nature of the thing: but no definition can unfold its whole nature; and every proposition in which any quality whatever is predicated of the thing, unfolds some part of its nature. The true state of the case we take to be this. All definitions are of names, and of names only; but, in some definitions, it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word.
[8]The definition, they say; unfolds the nature of the thing: but no definition can unfold its whole nature; and every proposition in which any quality whatever is predicated of the thing, unfolds some part of its nature. The true state of the case we take to be this. All definitions are of names, and of names only; but, in some definitions, it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word.
[9]The definition above given of a triangle, obviously comprises not one, but two propositions, perfectly distinguishable. The one is, "There may exist a figure bounded by three straight lines;" the other, "And this figure may be termed a triangle". The former of these propositions is not a definition at all; the latter is a mere nominal defition, or explanation of the use and application of a term. The first is susceptible of truth or falsehood, and may therefore be made the foundation of a train of reasoning. The latter can neither be true nor false; the only character it is susceptible of is that of conformity to the ordinary usage of language.
[9]The definition above given of a triangle, obviously comprises not one, but two propositions, perfectly distinguishable. The one is, "There may exist a figure bounded by three straight lines;" the other, "And this figure may be termed a triangle". The former of these propositions is not a definition at all; the latter is a mere nominal defition, or explanation of the use and application of a term. The first is susceptible of truth or falsehood, and may therefore be made the foundation of a train of reasoning. The latter can neither be true nor false; the only character it is susceptible of is that of conformity to the ordinary usage of language.
[10]The mortality of John, Thomas and company is, after all, the whole evidence we have for the mortality of the duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical form into which we choose to throw it can make greater than it is; and since that evidence is either sufficient in itself, or, if insufficient for the one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the shortest cut from these sufficient premisses to the conclusion, and constrained to travel the "high priori road", by the arbitrary fiat of logicians.
[10]The mortality of John, Thomas and company is, after all, the whole evidence we have for the mortality of the duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical form into which we choose to throw it can make greater than it is; and since that evidence is either sufficient in itself, or, if insufficient for the one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the shortest cut from these sufficient premisses to the conclusion, and constrained to travel the "high priori road", by the arbitrary fiat of logicians.
[11]All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulae for making more: The major premiss of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawnfromthe formula, but an inference drawnaccordingto the formula: the real logical antecedent, or premisses, being the particular facts from which the general proposition was collected by induction. Those facts, and the individual instances which supplied them, may have been forgotten; but a record remains, not indeed descriptive of the facts themselves, but showing how those cases may be distinguished respecting which the facts, when known, were considered to warrant a given inference. According to the indications of this record we draw our conclusion, which is, to ail intents and purposes, a conclusion from the forgotten facts. For this it is essential that we should read the record correctly: and the rules of the syllogism are a set of precautions to ensure our doing so.
[11]All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulae for making more: The major premiss of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawnfromthe formula, but an inference drawnaccordingto the formula: the real logical antecedent, or premisses, being the particular facts from which the general proposition was collected by induction. Those facts, and the individual instances which supplied them, may have been forgotten; but a record remains, not indeed descriptive of the facts themselves, but showing how those cases may be distinguished respecting which the facts, when known, were considered to warrant a given inference. According to the indications of this record we draw our conclusion, which is, to ail intents and purposes, a conclusion from the forgotten facts. For this it is essential that we should read the record correctly: and the rules of the syllogism are a set of precautions to ensure our doing so.
[12]If we had sufficiently capacious memories, and a sufficient power of maintaining order among a huge masse of details, the reasoning could go on without any general propositions; they are mere formulae for inferring particulars from particulars.
[12]If we had sufficiently capacious memories, and a sufficient power of maintaining order among a huge masse of details, the reasoning could go on without any general propositions; they are mere formulae for inferring particulars from particulars.
[13]For though, in order actually to see that two given lines never meet, it would be necessary to follow them to infinity; yet without doing so, we may know that if they ever do meet, or if, after diverging from one another, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination, and can frame a mental image of the appearance which one or both of the lines must present at that point, which we may rely on as being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we have had occasion to make from former ocular observation, we learn by the evidence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression "a bent line", not by the expression, "a straight line".
[13]For though, in order actually to see that two given lines never meet, it would be necessary to follow them to infinity; yet without doing so, we may know that if they ever do meet, or if, after diverging from one another, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination, and can frame a mental image of the appearance which one or both of the lines must present at that point, which we may rely on as being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we have had occasion to make from former ocular observation, we learn by the evidence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression "a bent line", not by the expression, "a straight line".
[14]Induction, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.
[14]Induction, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.
[15]We must first observe, that there is a principe implied in the very statement of what Induction is; an assumption with regard to the course of nature and the order of universe: namely, that there are such things in nature as parallel cases; that what happens once, will, under a sufficient degree of similarity of circumstances, happen again, and not only again, but as often as the same circumstances recur. This, I say, is an assumption, involved in every case of induction. And, if we consult the actual course of nature, we find that the assumption is warranted. The universe, we find, is so constitued, that whatever is true in any one case, is true at all cases of a certain description; the only difficulty is, to findwhatdescription.
[15]We must first observe, that there is a principe implied in the very statement of what Induction is; an assumption with regard to the course of nature and the order of universe: namely, that there are such things in nature as parallel cases; that what happens once, will, under a sufficient degree of similarity of circumstances, happen again, and not only again, but as often as the same circumstances recur. This, I say, is an assumption, involved in every case of induction. And, if we consult the actual course of nature, we find that the assumption is warranted. The universe, we find, is so constitued, that whatever is true in any one case, is true at all cases of a certain description; the only difficulty is, to findwhatdescription.
[16]Why it is that, with exactly the same amount of evidence, both negative and positive, we did not reject the assertion that there are black swans while we should refuse credence to any testimony which asserted there were men wearing their heads underneath their shoulders. The first assertion was more credible than the latter. But why more credible? So long as neither phenomenon had been actually witnessed, what reason was there for finding the one harder to be believed than the other? Apparently, because there is less constancy in the colours of animals, than in the generai structure of their internal anatomy. But how do we know this? Doubtless, from experience. It appears, then, that we need experience to inform us in what degree, and in what cases, or sorts of cases, experience is to be relied on. Experience must be consulted in order to learn from it under what circumstances arguments from it will be valid. We have no ulterior test to which we subject experience in general; but we make experience its own test. Experience testifies that among the uniformities which it exhibits or seems to exhibit, some are more to be relied on than others; and uniformity, therefore, may be presumed, from any given number of instances, with a greater degree of assurance, in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform.
[16]Why it is that, with exactly the same amount of evidence, both negative and positive, we did not reject the assertion that there are black swans while we should refuse credence to any testimony which asserted there were men wearing their heads underneath their shoulders. The first assertion was more credible than the latter. But why more credible? So long as neither phenomenon had been actually witnessed, what reason was there for finding the one harder to be believed than the other? Apparently, because there is less constancy in the colours of animals, than in the generai structure of their internal anatomy. But how do we know this? Doubtless, from experience. It appears, then, that we need experience to inform us in what degree, and in what cases, or sorts of cases, experience is to be relied on. Experience must be consulted in order to learn from it under what circumstances arguments from it will be valid. We have no ulterior test to which we subject experience in general; but we make experience its own test. Experience testifies that among the uniformities which it exhibits or seems to exhibit, some are more to be relied on than others; and uniformity, therefore, may be presumed, from any given number of instances, with a greater degree of assurance, in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform.
[17]Tome I, p. 338, 340, 341, 345, 351.
[17]Tome I, p. 338, 340, 341, 345, 351.
[18]The only notion of a cause, which the theory of induction requires, is such a notion as can be gained from experience. The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth, that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it; independently of all consideration respecting the ultimate mode of production of phenomena, and of every other question regarding the nature of "Things in themselves ".
[18]The only notion of a cause, which the theory of induction requires, is such a notion as can be gained from experience. The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth, that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it; independently of all consideration respecting the ultimate mode of production of phenomena, and of every other question regarding the nature of "Things in themselves ".
[19]The real Cause, is the whole of these antecedents.
[19]The real Cause, is the whole of these antecedents.
[20]The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows.
[20]The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows.
[21]If there be any meaning which confessedly belongs to the term necessity, it isunconditionalness. That which is necessary, that whichmustbe, means that which will be, whatever supposition we may make in regard to all other things.
[21]If there be any meaning which confessedly belongs to the term necessity, it isunconditionalness. That which is necessary, that whichmustbe, means that which will be, whatever supposition we may make in regard to all other things.
[22]1° Prenons cinquante creusets de matière fondue qu'on laisse refroidir, et cinquante dissolutions qu'on laisse évaporer; toutes cristallisent. Soufre, sucre, alun, chlorure de sodium, les substances, les températures, les circonstances sont aussi différentes que possible. Nous y trouvons un fait commun et un seul, le passage de l'état liquide à l'état solide; nous concluons que ce passage est l'antécédent invariable de la cristallisation. Voilà un exemple de la méthode de concordance: sa règle fondamentale est que «si deux ou plusieurs cas du phénomène en question n'ont qu'une circonstance commune, celte circonstance en est la cause ou l'effet» (tome Ier, p. 396).
[22]1° Prenons cinquante creusets de matière fondue qu'on laisse refroidir, et cinquante dissolutions qu'on laisse évaporer; toutes cristallisent. Soufre, sucre, alun, chlorure de sodium, les substances, les températures, les circonstances sont aussi différentes que possible. Nous y trouvons un fait commun et un seul, le passage de l'état liquide à l'état solide; nous concluons que ce passage est l'antécédent invariable de la cristallisation. Voilà un exemple de la méthode de concordance: sa règle fondamentale est que «si deux ou plusieurs cas du phénomène en question n'ont qu'une circonstance commune, celte circonstance en est la cause ou l'effet» (tome Ier, p. 396).
[23]Prenons un oiseau qui est dans l'air et respire; plongeons-le dans l'acide carbonique, il cesse de respirer. La suffocation se rencontre dans le second cas, elle ne se rencontre pas dans le premier; du reste les deux cas sont aussi semblables que possible, puisqu'il s'agit dans tous les deux du même oiseau et presque au même instant; ils ne diffèrent que par une circonstance, l'immersion dans l'acide carbonique substituée à l'immersion dans l'air. On en conclut que cette circonstance est un des antécédents invariables de la suffocation. Voilà un exemple de la méthode de différence; sa règle fondamentale est que «si un cas où le phénomène en question se rencontre et un cas où il ne se rencontre pas ont toutes leurs circonstances communes, sauf une, le phénomène a cette circonstance pour cause ou pour effet.»
[23]Prenons un oiseau qui est dans l'air et respire; plongeons-le dans l'acide carbonique, il cesse de respirer. La suffocation se rencontre dans le second cas, elle ne se rencontre pas dans le premier; du reste les deux cas sont aussi semblables que possible, puisqu'il s'agit dans tous les deux du même oiseau et presque au même instant; ils ne diffèrent que par une circonstance, l'immersion dans l'acide carbonique substituée à l'immersion dans l'air. On en conclut que cette circonstance est un des antécédents invariables de la suffocation. Voilà un exemple de la méthode de différence; sa règle fondamentale est que «si un cas où le phénomène en question se rencontre et un cas où il ne se rencontre pas ont toutes leurs circonstances communes, sauf une, le phénomène a cette circonstance pour cause ou pour effet.»
[24]Prenons deux groupes, l'un d'antécédents, l'autre de conséquents. On a lié tous les antécédents, moins un, à leurs conséquents, et tous les conséquents, moins un, à leurs antécédents. Ou peut conclure que l'antécédent qui reste est lié au conséquent qui reste. Par exemple, les physiciens, ayant calculé, d'après les lois de la propagation des ondes sonores, quelle doit être la vitesse du son, trouvèrent qu'en fait les sons vont plus vite que le calcul ne semble l'indiquer. Ce surplus ou résidu de vitesse est un conséquent et suppose un antécédent; Laplace trouva l'antécédent dans la chaleur que développe la condensation de chaque onde sonore, et cet élément nouveau introduit dans le calcul le rendit parfaitement exact. Voilà un exemple de la méthode des résidus. Sa règle est que «si l'on retranche d'un phénomène la partie qui est l'effet de certains antécédents, le résidu du phénomène est l'effet des antécédents qui restent.»
[24]Prenons deux groupes, l'un d'antécédents, l'autre de conséquents. On a lié tous les antécédents, moins un, à leurs conséquents, et tous les conséquents, moins un, à leurs antécédents. Ou peut conclure que l'antécédent qui reste est lié au conséquent qui reste. Par exemple, les physiciens, ayant calculé, d'après les lois de la propagation des ondes sonores, quelle doit être la vitesse du son, trouvèrent qu'en fait les sons vont plus vite que le calcul ne semble l'indiquer. Ce surplus ou résidu de vitesse est un conséquent et suppose un antécédent; Laplace trouva l'antécédent dans la chaleur que développe la condensation de chaque onde sonore, et cet élément nouveau introduit dans le calcul le rendit parfaitement exact. Voilà un exemple de la méthode des résidus. Sa règle est que «si l'on retranche d'un phénomène la partie qui est l'effet de certains antécédents, le résidu du phénomène est l'effet des antécédents qui restent.»
[25]Prenons deux faits: la présence de la terre et l'oscillation du pendule, ou bien encore la présence de la lune et le mouvement des marées. Pour joindre directement ces deux phénomènes l'un à l'autre, il faudrait pouvoir supprimer le premier, et vérifier si cette suppression entraînerait l'absence du second. Or cette suppression est, dans l'un et l'autre de ces cas, matériellement impossible. Alors nous employons une voie indirecte pour joindre les deux phénomènes. Nous remarquons que toutes les variations de l'un correspondent à certaines variations de l'autre; que toutes les oscillations du pendule correspondent aux diverses positions de la terre; que toutes les circonstances des marées correspondent aux positions de la lune. Nous en concluons que le second fait est l'antécédent du premier. Voilà un exemple de la méthode des variations concomitantes: sa règle fondamentale est que «si un phénomène varie d'une façon quelconque toutes les fois qu'un autre phénomène varie d'une certaine façon, le premier est une cause ou un effet direct ou indirect du second.»
[25]Prenons deux faits: la présence de la terre et l'oscillation du pendule, ou bien encore la présence de la lune et le mouvement des marées. Pour joindre directement ces deux phénomènes l'un à l'autre, il faudrait pouvoir supprimer le premier, et vérifier si cette suppression entraînerait l'absence du second. Or cette suppression est, dans l'un et l'autre de ces cas, matériellement impossible. Alors nous employons une voie indirecte pour joindre les deux phénomènes. Nous remarquons que toutes les variations de l'un correspondent à certaines variations de l'autre; que toutes les oscillations du pendule correspondent aux diverses positions de la terre; que toutes les circonstances des marées correspondent aux positions de la lune. Nous en concluons que le second fait est l'antécédent du premier. Voilà un exemple de la méthode des variations concomitantes: sa règle fondamentale est que «si un phénomène varie d'une façon quelconque toutes les fois qu'un autre phénomène varie d'une certaine façon, le premier est une cause ou un effet direct ou indirect du second.»
[26]«La méthode de différence, dit Mill, a pour fondement, que tout ce qui ne saurait être éliminé est lié au phénomène par une loi. La méthode de concordance a pour fondement, que tout ce qui peut être éliminé n'est point lié au phénomène par une loi.» La méthode des résidus est un cas de la méthode de différence; la méthode des variations concomitantes en est un autre cas, avec cette distinction qu'elle opère, non sur les deux phénomènes, mais sur leurs variations.
[26]«La méthode de différence, dit Mill, a pour fondement, que tout ce qui ne saurait être éliminé est lié au phénomène par une loi. La méthode de concordance a pour fondement, que tout ce qui peut être éliminé n'est point lié au phénomène par une loi.» La méthode des résidus est un cas de la méthode de différence; la méthode des variations concomitantes en est un autre cas, avec cette distinction qu'elle opère, non sur les deux phénomènes, mais sur leurs variations.
[27]"We must separate dew from rain, and the moisture of fogs, and limite the application of the term to what is really meant, which is, the spontaneous appearance of moisture on substances exposed in the open air when no rain orvisiblewet is falling."
[27]"We must separate dew from rain, and the moisture of fogs, and limite the application of the term to what is really meant, which is, the spontaneous appearance of moisture on substances exposed in the open air when no rain orvisiblewet is falling."
[28]"Now, here we have analogous phenomena in the moisture which bedews a cold metal or stone when we breathe upon it; that which appears on a glass of water fresh from the well in hot weather; that which appears on the inside of windows when sudden rain or hail chills the external air; that which runs down our walls when, after a long frost, a warm moist thaw comes on." Comparing these cases, we find that they all contain the phenomenon which was proposed as the subject of investigation. Now "all these instances agree in one point, the coldness of the object dewed, in comparison with the air in contact with it." But there still remains the most important case of ail, that of nocturnal dew: does the same circumstance exist in this case?" Is it a fact that the object dewediscolder than the air? Certainly not, one would at first be inclined to say; for what is to make it so? But ... the experiment is easy; we have only to lay a thermometer in contact with the dewed substance, and hang one at a little distance above it, out of reach of its influence. The experiment has been therefore made; the question has been asked, and the answer has been invariably in the affirmative. Whenever an object contracts dew, itiscolder than the air."
[28]"Now, here we have analogous phenomena in the moisture which bedews a cold metal or stone when we breathe upon it; that which appears on a glass of water fresh from the well in hot weather; that which appears on the inside of windows when sudden rain or hail chills the external air; that which runs down our walls when, after a long frost, a warm moist thaw comes on." Comparing these cases, we find that they all contain the phenomenon which was proposed as the subject of investigation. Now "all these instances agree in one point, the coldness of the object dewed, in comparison with the air in contact with it." But there still remains the most important case of ail, that of nocturnal dew: does the same circumstance exist in this case?" Is it a fact that the object dewediscolder than the air? Certainly not, one would at first be inclined to say; for what is to make it so? But ... the experiment is easy; we have only to lay a thermometer in contact with the dewed substance, and hang one at a little distance above it, out of reach of its influence. The experiment has been therefore made; the question has been asked, and the answer has been invariably in the affirmative. Whenever an object contracts dew, itiscolder than the air."
[29]Here then is a complete application of the Method of Agreement, establishing the fact of an invariable connexion between the deposition of dew on a surface, and the coldness of that surface compared with the external air. But which of these is cause, and which effect? or are they both effects of something else? On this subject the Method of Agreement can afford us no light: we must call in a more potent method. We must collect more facts, or, which comes to the same thing, vary the circumstances; since every instance in which the circumstances differ is a fresh fact: and especially, we must note the contrary or negatives cases, i.e., where no dew is produced: for a comparison between instances of dew and instances of no dew is the condition necessary to bring the Method of Difference into play.
[29]Here then is a complete application of the Method of Agreement, establishing the fact of an invariable connexion between the deposition of dew on a surface, and the coldness of that surface compared with the external air. But which of these is cause, and which effect? or are they both effects of something else? On this subject the Method of Agreement can afford us no light: we must call in a more potent method. We must collect more facts, or, which comes to the same thing, vary the circumstances; since every instance in which the circumstances differ is a fresh fact: and especially, we must note the contrary or negatives cases, i.e., where no dew is produced: for a comparison between instances of dew and instances of no dew is the condition necessary to bring the Method of Difference into play.
[30]"Now, first, no dew is produced on the surface of polished metals, but itisvery copiously on glass, both exposed with their faces upwards, and in some cases the under side of a horizontal plate of glass is also dewed." Here is an instance in which the effect is produced, and another instance in which it is not produced; but we cannot yet pronounce, as the canon of the Method of Difference requires, that the latter instance agrees with the former in all its circumstances except in one; for the differences between glass and polished metals are manifold, and the only thing we can as yet be sure of, is, that the cause of dew will be found among the circumstances by which the former substance is distinguished from the latter.
[30]"Now, first, no dew is produced on the surface of polished metals, but itisvery copiously on glass, both exposed with their faces upwards, and in some cases the under side of a horizontal plate of glass is also dewed." Here is an instance in which the effect is produced, and another instance in which it is not produced; but we cannot yet pronounce, as the canon of the Method of Difference requires, that the latter instance agrees with the former in all its circumstances except in one; for the differences between glass and polished metals are manifold, and the only thing we can as yet be sure of, is, that the cause of dew will be found among the circumstances by which the former substance is distinguished from the latter.
[31]"In the cases of polished metal and polished glass, the contrast shows evidently that thesubstancehas much to do with the phenomenon; therefore let the substancealonebe diversified as much as possible, by exposing polished surfaces of various kinds. This done, ascale of intensitybecomes obvious. Those polished substances are found to be most strongly dewed which conduct heat worst, while those which conduct well, resist dew most effectually."
[31]"In the cases of polished metal and polished glass, the contrast shows evidently that thesubstancehas much to do with the phenomenon; therefore let the substancealonebe diversified as much as possible, by exposing polished surfaces of various kinds. This done, ascale of intensitybecomes obvious. Those polished substances are found to be most strongly dewed which conduct heat worst, while those which conduct well, resist dew most effectually."
[32]The conclusion obtained is, that,caeteris paribus, the deposition of dew is in some proportion to the power winch the body possesses of resisting the passage of heat; and that this, therefore (or something connected with this), must be at least one of the causes which assist in producing the deposition of dew on the surface."But if we expose rough surfaces instead of polished, we sometimes find this law interfered with. Thus, roughened iron, especially if painted over or blackened, becomes dewed sooner than varnished paper: the kind ofsurface,therefore, has a great influence. Expose, then, thesamematerial in very diversified states as to surface" (that is, employ the Method of Difference to ascertain concomitance of variations), "and another scale of intensity becomes at once apparent; thosesurfaceswhichpart with their heatmost readily by radiation, are found to contract dew most copiously."
[32]The conclusion obtained is, that,caeteris paribus, the deposition of dew is in some proportion to the power winch the body possesses of resisting the passage of heat; and that this, therefore (or something connected with this), must be at least one of the causes which assist in producing the deposition of dew on the surface.
"But if we expose rough surfaces instead of polished, we sometimes find this law interfered with. Thus, roughened iron, especially if painted over or blackened, becomes dewed sooner than varnished paper: the kind ofsurface,therefore, has a great influence. Expose, then, thesamematerial in very diversified states as to surface" (that is, employ the Method of Difference to ascertain concomitance of variations), "and another scale of intensity becomes at once apparent; thosesurfaceswhichpart with their heatmost readily by radiation, are found to contract dew most copiously."
[33]The conclusion obtained by this new application of the method is, that,caeteris paribus, the deposition of dew is also in some proportion to the power of radiating heat; and that the quality of doing this abundantly (or some cause on which that quality dépends) is another of the causes which promote the deposition of dew on the substance."Again, the influence ascertained to exist ofsubstanceandsurfaceleads us to consider that oftexture: and hère, again, we are presented on trial with remarkable differences, and with a third scale of intensity, pointing out substances of a close firm texture, such as stones, metals, etc., as unfavourable, but those of a loose one, as cloth, velvet, wool, eiderdown, cotton, etc., as eminently favourable to the contraction of dew. The Method of concomitant Variations is here, for the third time, had recourse to; and, as before, from necessity, since the texture of no substance is absolutely firm or absolutely loose. Looseness of texture, therefore, or something which is the cause of that quality, is another circumstance which promotes the deposition of dew; but this third cause resolves itself into the first, viz. the quality of resisting the passage of heat: for substances of loose texture are precisely those which are best adapted for clothing or for impeding the free passage of heat from the skin into the air, so as to allow their outer surfaces to be very cold, while they remain warm within."
[33]The conclusion obtained by this new application of the method is, that,caeteris paribus, the deposition of dew is also in some proportion to the power of radiating heat; and that the quality of doing this abundantly (or some cause on which that quality dépends) is another of the causes which promote the deposition of dew on the substance.
"Again, the influence ascertained to exist ofsubstanceandsurfaceleads us to consider that oftexture: and hère, again, we are presented on trial with remarkable differences, and with a third scale of intensity, pointing out substances of a close firm texture, such as stones, metals, etc., as unfavourable, but those of a loose one, as cloth, velvet, wool, eiderdown, cotton, etc., as eminently favourable to the contraction of dew. The Method of concomitant Variations is here, for the third time, had recourse to; and, as before, from necessity, since the texture of no substance is absolutely firm or absolutely loose. Looseness of texture, therefore, or something which is the cause of that quality, is another circumstance which promotes the deposition of dew; but this third cause resolves itself into the first, viz. the quality of resisting the passage of heat: for substances of loose texture are precisely those which are best adapted for clothing or for impeding the free passage of heat from the skin into the air, so as to allow their outer surfaces to be very cold, while they remain warm within."
[34]It thus appears that the instances in which much dew is deposited, which are very various, agree in this, and, so far as we are able to observe, in this only, that they either radiate heat rapidly or conduct it slowly: qualities between which there is no other circumstance of agreement, than that by virtue of either, the body tends to lose heat from the surface more rapidly than it can be restored from within. The instances, on the contrary, in which no dew, or but a small quantity of it, is formed, and which are also extremely various, agree (so far as we can observe) in nothing, except innothaving this same property.This doubt we are not able to resolve. We have found that, in every such instance, the substance must be one which, by its own properties or laws, would, if exposed in the night, become colder than the surrounding air. The coldness therefore, being accounted for independently of the dew, while it is proved that there is a connexion between the two, it must be the dew which depends on the coldness; or in other words, the coldness is the cause of the dew.
[34]It thus appears that the instances in which much dew is deposited, which are very various, agree in this, and, so far as we are able to observe, in this only, that they either radiate heat rapidly or conduct it slowly: qualities between which there is no other circumstance of agreement, than that by virtue of either, the body tends to lose heat from the surface more rapidly than it can be restored from within. The instances, on the contrary, in which no dew, or but a small quantity of it, is formed, and which are also extremely various, agree (so far as we can observe) in nothing, except innothaving this same property.
This doubt we are not able to resolve. We have found that, in every such instance, the substance must be one which, by its own properties or laws, would, if exposed in the night, become colder than the surrounding air. The coldness therefore, being accounted for independently of the dew, while it is proved that there is a connexion between the two, it must be the dew which depends on the coldness; or in other words, the coldness is the cause of the dew.
[35]The law of causation, already so amply established, admits, howewer, of efficient additional corroboration in no less than three ways. First, by deduction from the known laws of aqueous vapour when diffused through air or any other gas; and though we have not yet come to the Deductive Method, we will not omit what is necessary to render the speculation complete. It is known by direct experiment that only a limited quantity of water can remain suspended in the state of vapour at each degree of temperature, and that this maximum grows less and less as the temperature diminishes. From this it follows, deductively, that if there is already as much vapour suspended as the air will contain at its existing temperature, any lowering of that temperature will cause a portion of the vapour to be condensed, and become water. But, again, we know deductively, from the laws of heat, that the contact of the air with a body colder than itself, will necessary lower the temperature of the stratum of air immediately applied to its surface; and will therefore cause it to part with a portion of its water, which accordingly will, by the ordinary laws of gravitation or cohesion, attach itself to the surface of the body, thereby constituting dew. This deductive proof, it will have been seen, has the advantage of proving at once causation as well as coexistence; and it has the additional advantage that it also accounts for theexceptionsto the occurrence of the phenomenon, the cases in which, although the body is colder than the air, yet no dew is deposited; by shewing that this will necessarily be the case when the air is so under-supplied with aqueous vapour, comparatively to its temperature, that even when somewhat cooled by the contact of the colder body, it can still continue to hold in suspension all the vapour which was previously suspended in it: thus in a very dry summer there are no dews, in a very dry winter no hoar frost.
[35]The law of causation, already so amply established, admits, howewer, of efficient additional corroboration in no less than three ways. First, by deduction from the known laws of aqueous vapour when diffused through air or any other gas; and though we have not yet come to the Deductive Method, we will not omit what is necessary to render the speculation complete. It is known by direct experiment that only a limited quantity of water can remain suspended in the state of vapour at each degree of temperature, and that this maximum grows less and less as the temperature diminishes. From this it follows, deductively, that if there is already as much vapour suspended as the air will contain at its existing temperature, any lowering of that temperature will cause a portion of the vapour to be condensed, and become water. But, again, we know deductively, from the laws of heat, that the contact of the air with a body colder than itself, will necessary lower the temperature of the stratum of air immediately applied to its surface; and will therefore cause it to part with a portion of its water, which accordingly will, by the ordinary laws of gravitation or cohesion, attach itself to the surface of the body, thereby constituting dew. This deductive proof, it will have been seen, has the advantage of proving at once causation as well as coexistence; and it has the additional advantage that it also accounts for theexceptionsto the occurrence of the phenomenon, the cases in which, although the body is colder than the air, yet no dew is deposited; by shewing that this will necessarily be the case when the air is so under-supplied with aqueous vapour, comparatively to its temperature, that even when somewhat cooled by the contact of the colder body, it can still continue to hold in suspension all the vapour which was previously suspended in it: thus in a very dry summer there are no dews, in a very dry winter no hoar frost.
[36]The second corroboration of the theory is by direct experiment, according to the canon of the Method of Difference. We can, by cooling the surface of any body, find in all cases some temperature (more or less inferior to that of the surrounding air, according to its hygrometric condition), at which dew will begin to be deposited. Here, too, therefore the causation is directly proved. We can, it is true, accomplish this only on a small scale; but we have ample reason to conclude that the same operation, if conducted in Nature's great laboratory, would equally produce the effect.And, finally, even on that great scale we are able to verify the result. The case is one of those rare cases, as we have shown them to be, in which nature works the experiment for us in the same manner in which we ourselves perform it; introducing into the previous state of things a single and perfectly definite new circumstance, and manifesting the effect so rapidly, that there is not time for any other material change in the pre-existing circumstances. It is observed that dew is never copiously deposited in situations much screened from the open sky, and not at all in a cloudy night, butif the clouds withdraw even for a few minutes, and leave a clear opening, a deposition of dew presently begins, and goes on increasing.... Dew formed in clear intervals will often even evaporate again, when the sky becomes thickly overcast. The proof, therefore, is complete that the presence or absence of an uninterrupted communication with the sky causes the deposition or non-deposition of dew. Now, since a clear sky is nothing but the absence of clouds, and it is a known property of clouds, as of all other bodies between which and any given object nothing intervenes but an elastic fluid, that they tend to raise or keep up the superficial temperature of the object by radiating heat to it, we see at once that the disappearance of clouds will cause the surface to cool; so that Nature, in this case, produces a change in the antecedent by definite and known means, and the consequent follows accordingly: a natural experiment which satisfies the requisitions of the Method of Difference.
[36]The second corroboration of the theory is by direct experiment, according to the canon of the Method of Difference. We can, by cooling the surface of any body, find in all cases some temperature (more or less inferior to that of the surrounding air, according to its hygrometric condition), at which dew will begin to be deposited. Here, too, therefore the causation is directly proved. We can, it is true, accomplish this only on a small scale; but we have ample reason to conclude that the same operation, if conducted in Nature's great laboratory, would equally produce the effect.
And, finally, even on that great scale we are able to verify the result. The case is one of those rare cases, as we have shown them to be, in which nature works the experiment for us in the same manner in which we ourselves perform it; introducing into the previous state of things a single and perfectly definite new circumstance, and manifesting the effect so rapidly, that there is not time for any other material change in the pre-existing circumstances. It is observed that dew is never copiously deposited in situations much screened from the open sky, and not at all in a cloudy night, butif the clouds withdraw even for a few minutes, and leave a clear opening, a deposition of dew presently begins, and goes on increasing.... Dew formed in clear intervals will often even evaporate again, when the sky becomes thickly overcast. The proof, therefore, is complete that the presence or absence of an uninterrupted communication with the sky causes the deposition or non-deposition of dew. Now, since a clear sky is nothing but the absence of clouds, and it is a known property of clouds, as of all other bodies between which and any given object nothing intervenes but an elastic fluid, that they tend to raise or keep up the superficial temperature of the object by radiating heat to it, we see at once that the disappearance of clouds will cause the surface to cool; so that Nature, in this case, produces a change in the antecedent by definite and known means, and the consequent follows accordingly: a natural experiment which satisfies the requisitions of the Method of Difference.
[37]Tome I, page 500.
[37]Tome I, page 500.
[38]Tome II, liv. vi, ch. 9. Tome I, p. 487. Explication, d'après Liebig, de la décomposition, de la respiration, de l'empoisonnement, etc. Il y a un livre entier sur la méthode des sciences morales; je ne connais pas de meilleur traité sur ce sujet.
[38]Tome II, liv. vi, ch. 9. Tome I, p. 487. Explication, d'après Liebig, de la décomposition, de la respiration, de l'empoisonnement, etc. Il y a un livre entier sur la méthode des sciences morales; je ne connais pas de meilleur traité sur ce sujet.
[39]Tome II, page 4.
[39]Tome II, page 4.
[40]There exist in nature a number of permanent causes, which have subsisted ever since the human race has been in existence, and for an indefinite and probably an enormous length of time previous. The sun, the earth, and planets, with their varions constituents, air, water, and the other distinguishable substances, whether simple or compound, of which nature is made up, are such Permanent Causes. They have existed, and the effects or consequences which they were fitted to produce have taken place (as often as the other conditions of the production met), from the very beginning of our experience. But we can give no account of the origine of the Permanent Causes themselves.
[40]There exist in nature a number of permanent causes, which have subsisted ever since the human race has been in existence, and for an indefinite and probably an enormous length of time previous. The sun, the earth, and planets, with their varions constituents, air, water, and the other distinguishable substances, whether simple or compound, of which nature is made up, are such Permanent Causes. They have existed, and the effects or consequences which they were fitted to produce have taken place (as often as the other conditions of the production met), from the very beginning of our experience. But we can give no account of the origine of the Permanent Causes themselves.
[41]The resolution of the laws of the heavenly motions, established the previously unknown ultimate property of a mutual attraction between the bodies: the resolution, so far as it has yet proceeded, of the laws of crystallization, or chemical composition, electricity, magnetism, etc., points to various polarities, ultimately inherent in the particles of which bodies are composed; the comparative atomic weights of different kinds of bodies were ascertained by resolving, into more generai laws, the uniformities observed in the proportions in which substances combine with one another; and so forth. Thus although every resolution of a complex uniformity into simpler and more elementary laws has an apparent tendency to diminish the number of the ultimate properties, and really does remove many properties from the list; yet (since the result of this simplifying process is to trace up an ever greater variety of differents effects to the same agents), the further we advance in this direction, the greater number of distinct properties we are forced to recognise in one and the same object: the coexistences of which properties must accordingly be ranked among the ultimate generalities of nature.
[41]The resolution of the laws of the heavenly motions, established the previously unknown ultimate property of a mutual attraction between the bodies: the resolution, so far as it has yet proceeded, of the laws of crystallization, or chemical composition, electricity, magnetism, etc., points to various polarities, ultimately inherent in the particles of which bodies are composed; the comparative atomic weights of different kinds of bodies were ascertained by resolving, into more generai laws, the uniformities observed in the proportions in which substances combine with one another; and so forth. Thus although every resolution of a complex uniformity into simpler and more elementary laws has an apparent tendency to diminish the number of the ultimate properties, and really does remove many properties from the list; yet (since the result of this simplifying process is to trace up an ever greater variety of differents effects to the same agents), the further we advance in this direction, the greater number of distinct properties we are forced to recognise in one and the same object: the coexistences of which properties must accordingly be ranked among the ultimate generalities of nature.
[42]Why these particular natural agents existed originally and no others, or why they are commingled in such and such proportions, and distributed in such a manner throughout space, is a question we cannot answer. More than this: we can discover nothing regular in the distribution itself; we can reduce it to no uniformity, to no law. There are no means by which, from the distribution of these causes or agents in one part of space, we could conjecture whether a similar distribution prevails in another.
[42]Why these particular natural agents existed originally and no others, or why they are commingled in such and such proportions, and distributed in such a manner throughout space, is a question we cannot answer. More than this: we can discover nothing regular in the distribution itself; we can reduce it to no uniformity, to no law. There are no means by which, from the distribution of these causes or agents in one part of space, we could conjecture whether a similar distribution prevails in another.
[43]I am convinced that any one accustomed to abstraction and analysis, who will fairly exert his faculties for the purpose, will, when his imagination has once learnt to entertain the notion, find no difficulty in conceiving that in some one for instance of the many firmaments into which sidereal astronomy now divides the universe, events may succeed one another at random, without any fixed law; nor can anything in our experience, or in our mental nature, constitute a sufficient, or indeed any reason for believing that this is nowhere the case. The grounds, therefore, which warrant us in rejecting such a supposition with respect to any of the phenomena of which we have experience, must be sought elsewhere than in any supposed necessity of our intellectual faculties.
[43]I am convinced that any one accustomed to abstraction and analysis, who will fairly exert his faculties for the purpose, will, when his imagination has once learnt to entertain the notion, find no difficulty in conceiving that in some one for instance of the many firmaments into which sidereal astronomy now divides the universe, events may succeed one another at random, without any fixed law; nor can anything in our experience, or in our mental nature, constitute a sufficient, or indeed any reason for believing that this is nowhere the case. The grounds, therefore, which warrant us in rejecting such a supposition with respect to any of the phenomena of which we have experience, must be sought elsewhere than in any supposed necessity of our intellectual faculties.
[44]In distant parts of the stellar regions, where the phenomena may be entirely unlike those with which we are acquainted, it would be folly to affirm confidently that this general law prevails, any more than those special ones which we have found to hold universally on our own planet. The uniformity in the succession of events, otherwise called the law of causation, must be received not as a law of the universe, but of that portion of it only which is within the range of our means of sure observation, with a reasonable degree of extension to adjacent cases. To extend it further is to make a supposition without evidence, and to which, in the absence of any ground from experience for estimating its degree of probability, it would be idle to attempt to assign any.
[44]In distant parts of the stellar regions, where the phenomena may be entirely unlike those with which we are acquainted, it would be folly to affirm confidently that this general law prevails, any more than those special ones which we have found to hold universally on our own planet. The uniformity in the succession of events, otherwise called the law of causation, must be received not as a law of the universe, but of that portion of it only which is within the range of our means of sure observation, with a reasonable degree of extension to adjacent cases. To extend it further is to make a supposition without evidence, and to which, in the absence of any ground from experience for estimating its degree of probability, it would be idle to attempt to assign any.
[45]Voyez les seconds analytiques, si supérieurs aux premiers: [Greek: hoi aitioon kai protiroon]
[45]Voyez les seconds analytiques, si supérieurs aux premiers: [Greek: hoi aitioon kai protiroon]
[46]«Un fait, me disait un physicien éminent, est une superposition de lois.»
[46]«Un fait, me disait un physicien éminent, est une superposition de lois.»
[47]Die aufgehobene quantität.
[47]Die aufgehobene quantität.
TABLE DES MATIÈRESPRÉFACE.I.La philosophie en Angleterre—Organisation de la science positive.—Absence des idées générales.II.Pourquoi la métaphysique manque.—Autorité de la religion.III.Indices et éclats de la pensée libre.—L'exégèse nouvelle.—Stuart Mill.—Ses oeuvres.—Son genre d'esprit.—A quelle famille de philosophes il appartient.—Valeur des spéculations supérieures dans la civilisation humain.§ I.—EXPOSITION.I.Objet de la logique.—En quoi elle se distingue de la psychologie et de la métaphysique.II.Ce que c'est qu'un jugement.—Ce que nous connaissons du monde extérieur et du monde intérieur.—Tout l'effort de la science est d'ajouter ou de lier un fait à un fait.III.Théorie de la définition.—En quoi cette théorie est importante.—Réfutation de l'ancienne théorie.—Il n'y a pas de définition des choses, mais des définitions des noms.IV.Théorie de la preuve.—Théorie ordinaire. Réfutation.—Quelle est dans un raisonnement la partie probante.V.Théorie des axiomes.—Théorie ordinaire.—Réfutation.—Les axiomes ne sont que des expériences d'une certaine classe.VI.Théorie de l'induction.—La cause d'un fait n'est que son antécédent invariable.—L'expérience seule prouve la stabilité des lois de la nature.—En quoi consiste une loi.—Par quelles méthodes on découvre les lois.—La méthode des concordances, la méthode des différences, la méthode des résidus, la méthode des variations concomitantes.VII.Exemples et applications.—Théorie de la rosée.VIII.La méthode de déduction.—Son domaine.—Ses procédés.IX.Comparaison de la méthode d'induction et de la la méthode de déduction.—Emploi ancien de la première.—Emploi moderne de la seconde.—Sciences qui réclament la première.—Sciences qui réclament la seconde.—Caractère positif de l'oeuvre de Mill.—Lignée de ses prédécesseurs.X.Limites de notre science.—Il n'est pas certain que tous les événements arrivent selon des lois.—Le hasard dans la nature.§ II.—DISCUSSION.I.Concordance de cette doctrine et de l'esprit anglais.—Liaison de l'esprit positif et de l'esprit religieux.—Quelle faculté ouvre le monde des causes.II.Qu'il n'y a ni substances ni forces, mais seulement des faits et des lois.—Nature de l'abstraction.—Rôle de l'abstraction dans la science.III.Théorie de la définition.—Elle est l'exposé des abstraits générateurs.IV.Théorie de la preuve.—La partie probante du raisonnement est une loi abstraite.V.Théorie des axiomes.—Les axiomes sont des relations d'abstraits.—Ils se ramènent à l'axiome d'identité.VI.Théorie de l'induction.—Ses procédés sont des éliminations ou abstractions.VII.Les deux grandes opérations de l'esprit, l'expérience et l'abstraction.—Les deux grandes apparences des choses, les faits sensibles et les lois abstraites.—Pourquoi nous devons passer des premiers aux secondes.—Sens et portée de l'axiome des causes.VIII.Il est possible de connaître les éléments premiers.—Erreur de la métaphysique allemande.—Elle a négligé la part du hasard et les perturbations locales.—Ce qu'une fourmi philosophe pourrait savoir.—Idée et limites d'une métaphysique.—Position de la métaphysique chez les trois nations pensantes.—Une matinée à Oxford.
TABLE DES MATIÈRES
PRÉFACE.
I.La philosophie en Angleterre—Organisation de la science positive.—Absence des idées générales.
II.Pourquoi la métaphysique manque.—Autorité de la religion.
III.Indices et éclats de la pensée libre.—L'exégèse nouvelle.—Stuart Mill.—Ses oeuvres.—Son genre d'esprit.—A quelle famille de philosophes il appartient.—Valeur des spéculations supérieures dans la civilisation humain.
§ I.—EXPOSITION.
I.Objet de la logique.—En quoi elle se distingue de la psychologie et de la métaphysique.
II.Ce que c'est qu'un jugement.—Ce que nous connaissons du monde extérieur et du monde intérieur.—Tout l'effort de la science est d'ajouter ou de lier un fait à un fait.
III.Théorie de la définition.—En quoi cette théorie est importante.—Réfutation de l'ancienne théorie.—Il n'y a pas de définition des choses, mais des définitions des noms.
IV.Théorie de la preuve.—Théorie ordinaire. Réfutation.—Quelle est dans un raisonnement la partie probante.
V.Théorie des axiomes.—Théorie ordinaire.—Réfutation.—Les axiomes ne sont que des expériences d'une certaine classe.
VI.Théorie de l'induction.—La cause d'un fait n'est que son antécédent invariable.—L'expérience seule prouve la stabilité des lois de la nature.—En quoi consiste une loi.—Par quelles méthodes on découvre les lois.—La méthode des concordances, la méthode des différences, la méthode des résidus, la méthode des variations concomitantes.
VII.Exemples et applications.—Théorie de la rosée.
VIII.La méthode de déduction.—Son domaine.—Ses procédés.
IX.Comparaison de la méthode d'induction et de la la méthode de déduction.—Emploi ancien de la première.—Emploi moderne de la seconde.—Sciences qui réclament la première.—Sciences qui réclament la seconde.—Caractère positif de l'oeuvre de Mill.—Lignée de ses prédécesseurs.
X.Limites de notre science.—Il n'est pas certain que tous les événements arrivent selon des lois.—Le hasard dans la nature.
§ II.—DISCUSSION.
I.Concordance de cette doctrine et de l'esprit anglais.—Liaison de l'esprit positif et de l'esprit religieux.—Quelle faculté ouvre le monde des causes.
II.Qu'il n'y a ni substances ni forces, mais seulement des faits et des lois.—Nature de l'abstraction.—Rôle de l'abstraction dans la science.
III.Théorie de la définition.—Elle est l'exposé des abstraits générateurs.
IV.Théorie de la preuve.—La partie probante du raisonnement est une loi abstraite.
V.Théorie des axiomes.—Les axiomes sont des relations d'abstraits.—Ils se ramènent à l'axiome d'identité.
VI.Théorie de l'induction.—Ses procédés sont des éliminations ou abstractions.
VII.Les deux grandes opérations de l'esprit, l'expérience et l'abstraction.—Les deux grandes apparences des choses, les faits sensibles et les lois abstraites.—Pourquoi nous devons passer des premiers aux secondes.—Sens et portée de l'axiome des causes.
VIII.Il est possible de connaître les éléments premiers.—Erreur de la métaphysique allemande.—Elle a négligé la part du hasard et les perturbations locales.—Ce qu'une fourmi philosophe pourrait savoir.—Idée et limites d'une métaphysique.—Position de la métaphysique chez les trois nations pensantes.—Une matinée à Oxford.