Chapter 8

Santayana,46.Scepticism,66,67.Seeing double,86.Self,73.Sensation,25,75,123.and stimulus,139.Sense-data,56,63,67,75,110,141,143,213.and physics,v,64,81,97,101ff.,140.infinitely numerous?149,159.Sense-perception,53.Series,49.compact,132,142,178.continuous,131,132.Sigwart,187.Simplicius,170 n.Simultaneity,116.Space,73,88,103,112ff.,130.absolute and relative,146,159.antinomies of,155ff.perception of,68.of perspectives,88ff.private,89,90.of touch and sight,78,113.Spencer,4,12,236.Spinoza,46,166.Stadium, Zeno's argument of,134 n.,175ff.Subject-predicate,45.Synthesis,157,185.

Santayana,46.

Scepticism,66,67.

Seeing double,86.

Self,73.

Sensation,25,75,123.and stimulus,139.

Sense-data,56,63,67,75,110,141,143,213.and physics,v,64,81,97,101ff.,140.infinitely numerous?149,159.

Sense-perception,53.

Series,49.compact,132,142,178.continuous,131,132.

Sigwart,187.

Simplicius,170 n.

Simultaneity,116.

Space,73,88,103,112ff.,130.absolute and relative,146,159.antinomies of,155ff.perception of,68.of perspectives,88ff.private,89,90.of touch and sight,78,113.

Spencer,4,12,236.

Spinoza,46,166.

Stadium, Zeno's argument of,134 n.,175ff.

Subject-predicate,45.

Synthesis,157,185.

Tannery, Paul,169 n.Teleology,223.Testimony,67,72,82,87,96,212.Thales,3.Thing-in-itself,75,84.Things,89ff.,104ff.,213.Time,103,116ff.,130,155ff.,166,215.absolute or relative,146.local,103.private,121.

Tannery, Paul,169 n.

Teleology,223.

Testimony,67,72,82,87,96,212.

Thales,3.

Thing-in-itself,75,84.

Things,89ff.,104ff.,213.

Time,103,116ff.,130,155ff.,166,215.absolute or relative,146.local,103.private,121.

Uniformities,217.Unity, organic,9.Universal and particular,39 n.

Uniformities,217.

Unity, organic,9.

Universal and particular,39 n.

Volition,223ff.

Whitehead,vi,207.Wittgenstein,vii,208 n.Worlds, actual and ideal,111.possible,186.private,88.

Whitehead,vi,207.

Wittgenstein,vii,208 n.

Worlds, actual and ideal,111.possible,186.private,88.

Zeller,173.Zeno,129,134,136,165ff.

Zeller,173.

Zeno,129,134,136,165ff.

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[1]Delivered as Lowell Lectures in Boston, in March and April 1914.[2]London and New York, 1912 (“Home University Library”).[3]The first volume was published at Cambridge in 1910, the second in 1912, and the third in 1913.[4]Appearance and Reality, pp. 32–33.[5]Creative Evolution, English translation, p. 41.[6]Cf.Burnet,Early Greek Philosophy, pp. 85 ff.[7]Introduction to Metaphysics, p. 1.[8]Logic, book iii., chapter iii., § 2.[9]Book iii., chapter xxi., § 3.[10]Or rather a propositional function.[11]The subject of causality and induction will be discussed again inLecture VIII.[12]See the translation by H. S. Macran,Hegel's Doctrine of Formal Logic, Oxford, 1912. Hegel's argument in this portion of his “Logic” depends throughout upon confusing the “is” of predication, as in “Socrates is mortal,” with the “is” of identity, as in “Socrates is the philosopher who drank the hemlock.” Owing to this confusion, he thinks that “Socrates” and “mortal” must be identical. Seeing that they are different, he does not infer, as others would, that there is a mistake somewhere, but that they exhibit “identity in difference.” Again, Socrates is particular, “mortal” is universal. Therefore, he says, since Socrates is mortal, it follows that the particular is the universal—taking the “is” to be throughout expressive of identity. But to say “the particular is the universal” is self-contradictory. Again Hegel does not suspect a mistake but proceeds to synthesise particular and universal in the individual, or concrete universal. This is an example of how, for want of care at the start, vast and imposing systems of philosophy are built upon stupid and trivial confusions, which, but for the almost incredible fact that they are unintentional, one would be tempted to characterise as puns.[13]Cf.Couturat,La Logique de Leibniz, pp. 361, 386.[14]It was often recognised that there wassomedifference between them, but it was not recognised that the difference is fundamental, and of very great importance.[15]Encyclopædia of the Philosophical Sciences, vol. i. p. 97.[16]This perhaps requires modification in order to include such facts as beliefs and wishes, since such facts apparently contain propositions as components. Such facts, though not strictly atomic, must be supposed included if the statement in the text is to be true.[17]The assumptions made concerning time-relations in the above are as follows:—I. In order to secure that instants form a series, we assume:(a) No event wholly precedes itself. (An “event” is defined as whatever is simultaneous with something or other.)(b) If one event wholly precedes another, and the other wholly precedes a third, then the first wholly precedes the third.(c) If one event wholly precedes another, it is not simultaneous with it.(d) Of two events which are not simultaneous, one must wholly precede the other.II. In order to secure that the initial contemporaries of a given event should form an instant, we assume:(e) An event wholly after some contemporary of a given event is wholly after someinitialcontemporary of the given event.III. In order to secure that the series of instants shall be compact, we assume:(f) If one event wholly precedes another, there is an event wholly after the one and simultaneous with something wholly before the other.This assumption entails the consequence that if one event covers the whole of a stretch of time immediately preceding another event, then it must have at least one instant in common with the other event;i.e.it is impossible for one event to cease just before another begins. I do not know whether this should be regarded as inadmissible. For a mathematico-logical treatment of the above topics,cf.N. Wilner, “A Contribution to the Theory of Relative Position,”Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449.[18]The above paradox is essentially the same as Zeno's argument of the stadium which will be considered in ournext lecture.[19]Seenext lecture.[20]Monist, July 1912, pp. 337–341.[21]“Le continu mathématique,”Revue de Métaphysique et de Morale, vol. i. p. 29.[22]In what concerns the early Greek philosophers, my knowledge is largely derived from Burnet's valuable work,Early Greek Philosophy(2nd ed., London, 1908). I have also been greatly assisted by Mr D. S. Robertson of Trinity College, who has supplied the deficiencies of my knowledge of Greek, and brought important references to my notice.[23]Cf.Aristotle,Metaphysics, M. 6, 1080b, 18sqq., and 1083b, 8sqq.[24]There is some reason to think that the Pythagoreans distinguished between discrete and continuous quantity. G. J. Allman, in hisGreek Geometry from Thales to Euclid, says (p. 23): “The Pythagoreans made a fourfold division of mathematical science, attributing one of its parts to the how many,τὸ πόσον, and the other to the how much,τὸ πηλίκον; and they assigned to each of these parts a twofold division. For they said that discrete quantity, or thehow many, either subsists by itself or must be considered with relation to some other; but that continued quantity, or thehow much, is either stable or in motion. Hence they affirmed that arithmetic contemplates that discrete quantity which subsists by itself, but music that which is related to another; and that geometry considers continued quantity so far as it is immovable; but astronomy (τὴν σφαιρικήν) contemplates continued quantity so far as it is of a self-motive nature. (Proclus, ed. Friedlein, p. 35. As to the distinction betweenτὸ πηλίκον, continuous, andτὸ πόσον, discrete quantity, see Iambl.,in Nicomachi Geraseni Arithmeticam introductionem, ed. Tennulius, p. 148.)”Cf.p. 48.[25]Referred to by Burnet,op. cit., p. 120.[26]iv., 6. 213b, 22; H. Ritter and L. Preller,Historia Philosophiæ Græcæ, 8th ed., Gotha, 1898, p. 75 (this work will be referred to in future as “R. P.”).[27]The Pythagorean proof is roughly as follows. If possible, let the ratio of the diagonal to the side of a square bem/n, wheremandnare whole numbers having no common factor. Then we must havem2= 2n2. Now the square of an odd number is odd, butm2, being equal to 2n2, is even. Hencemmust be even. But the square of an even number divides by 4, thereforen2, which is half ofm2, must be even. Thereforenmust be even. But, sincemis even, andmandnhave no common factor,nmust be odd. Thusnmust be both odd and even, which is impossible; and therefore the diagonal and the side cannot have a rational ratio.[28]In regard to Zeno and the Pythagoreans, I have derived much valuable information and criticism from Mr P. E. B. Jourdain.[29]So Plato makes Zeno say in theParmenides, apropos of his philosophy as a whole; and all internal and external evidence supports this view.[30]“With Parmenides,” Hegel says, “philosophising proper began.”Werke(edition of 1840), vol. xiii. p. 274.[31]Parmenides, 128A–D.[32]This interpretation is combated by Milhaud,Les philosophes-géomètres de la Grèce, p. 140 n., but his reasons do not seem to me convincing. All the interpretations in what follows are open to question, but all have the support of reputable authorities.[33]Physics, vi. 9. 2396 (R.P. 136–139).[34]Cf.Gaston Milhaud,Les philosophes-géomètres de la Grèce, p. 140 n.; Paul Tannery,Pour l'histoire de la science hellène, p. 249; Burnet,op. cit., p. 362.[35]Cf.R. K. Gaye, “On Aristotle,Physics, Z ix.”Journal of Philology, vol. xxxi., esp. p. 111. Also Moritz Cantor,Vorlesungen über Geschichte der Mathematik, 1st ed., vol. i., 1880, p. 168, who, however, subsequently adopted Paul Tannery's opinion,Vorlesungen, 3rd ed. (vol. i. p. 200).[36]“Le mouvement et les partisans des indivisibles,”Revue de Métaphysique et de Morale, vol. i. pp. 382–395.[37]“Le mouvement et les arguments de Zénon d'Élée,”Revue de Métaphysique et de Morale, vol. i. pp. 107–125.[38]Cf.M. Brochard, “Les prétendus sophismes de Zénon d'Élée,”Revue de Métaphysique et de Morale, vol. i. pp. 209–215.[39]Simplicius,Phys., 140, 28D(R.P. 133); Burnet,op. cit., pp. 364–365.[40]Op. cit., p. 367.[41]Aristotle's words are: “The first is the one on the non-existence of motion on the ground that what is moved must always attain the middle point sooner than the end-point, on which we gave our opinion in the earlier part of our discourse.”Phys., vi. 9. 939B(R.P. 136). Aristotle seems to refer toPhys., vi. 2. 223AB[R.P. 136A]: “All space is continuous, for time and space are divided into the same and equal divisions…. Wherefore also Zeno's argument is fallacious, that it is impossible to go through an infinite collection or to touch an infinite collection one by one in a finite time. For there are two senses in which the term ‘infinite’ is applied both to length and to time, and in fact to all continuous things, either in regard to divisibility, or in regard to the ends. Now it is not possible to touch things infinite in regard to number in a finite time, but it is possible to touch things infinite in regard to divisibility: for time itself also is infinite in this sense. So that in fact we go through an infinite, [space] in an infinite [time] and not in a finite [time], and we touch infinite things with infinite things, not with finite things.” Philoponus, a sixth-century commentator (R.P. 136A,Exc. Paris Philop. in Arist. Phys., 803, 2. Vit.), gives the following illustration: “For if a thing were moved the space of a cubit in one hour, since in every space there are an infinite number of points, the thing moved must needs touch all the points of the space: it will then go through an infinite collection in a finite time, which is impossible.”[42]Cf.Mr C. D. Broad, “Note on Achilles and the Tortoise,”Mind, N.S., vol. xxii. pp. 318–9.[43]Op. cit.[44]Aristotle's words are: “The second is the so-called Achilles. It consists in this, that the slower will never be overtaken in its course by the quickest, for the pursuer must always come first to the point from which the pursued has just departed, so that the slower must necessarily be always still more or less in advance.”Phys., vi. 9. 239B(R.P. 137).[45]Phys., vi. 9. 239B(R.P. 138).[46]Phys., vi. 9. 239B(R.P. 139).[47]Loc. cit.[48]Loc. cit., p. 105.[49]Phil. Werke, Gerhardt's edition, vol. i. p. 338.[50]Mathematical Discourses concerning two new sciences relating to mechanics and local motion, in four dialogues.By Galileo Galilei, Chief Philosopher and Mathematician to the Grand Duke of Tuscany. Done into English from the Italian, by Tho. Weston, late Master, and now published by John Weston, present Master, of the Academy at Greenwich. See pp. 46 ff.[51]In hisGrundlagen einer allgemeinen Mannichfaltigkeitslehreand in articles inActa Mathematica, vol. ii.[52]The definition of number contained in this book, and elaborated in theGrundgesetze der Arithmetik(vol. i., 1893; vol. ii., 1903), was rediscovered by me in ignorance of Frege's work. I wish to state as emphatically as possible—what seems still often ignored—that his discovery antedated mine by eighteen years.[53]Giles,The Civilisation of China(Home University Library), p. 147.[54]Cf.Principia Mathematica, § 20, and Introduction, chapter iii.[55]In the above remarks I am making use of unpublished work by my friend Ludwig Wittgenstein.[56]Thus we are not using “thing” here in the sense of a class of correlated “aspects,” as we did inLecture III. Each “aspect” will count separately in stating causal laws.[57]The above remarks, for purposes of illustration, adopt one of several possible opinions on each of several disputed points.

[1]Delivered as Lowell Lectures in Boston, in March and April 1914.

[2]London and New York, 1912 (“Home University Library”).

[3]The first volume was published at Cambridge in 1910, the second in 1912, and the third in 1913.

[4]Appearance and Reality, pp. 32–33.

[5]Creative Evolution, English translation, p. 41.

[6]Cf.Burnet,Early Greek Philosophy, pp. 85 ff.

[7]Introduction to Metaphysics, p. 1.

[8]Logic, book iii., chapter iii., § 2.

[9]Book iii., chapter xxi., § 3.

[10]Or rather a propositional function.

[11]The subject of causality and induction will be discussed again inLecture VIII.

[12]See the translation by H. S. Macran,Hegel's Doctrine of Formal Logic, Oxford, 1912. Hegel's argument in this portion of his “Logic” depends throughout upon confusing the “is” of predication, as in “Socrates is mortal,” with the “is” of identity, as in “Socrates is the philosopher who drank the hemlock.” Owing to this confusion, he thinks that “Socrates” and “mortal” must be identical. Seeing that they are different, he does not infer, as others would, that there is a mistake somewhere, but that they exhibit “identity in difference.” Again, Socrates is particular, “mortal” is universal. Therefore, he says, since Socrates is mortal, it follows that the particular is the universal—taking the “is” to be throughout expressive of identity. But to say “the particular is the universal” is self-contradictory. Again Hegel does not suspect a mistake but proceeds to synthesise particular and universal in the individual, or concrete universal. This is an example of how, for want of care at the start, vast and imposing systems of philosophy are built upon stupid and trivial confusions, which, but for the almost incredible fact that they are unintentional, one would be tempted to characterise as puns.

[13]Cf.Couturat,La Logique de Leibniz, pp. 361, 386.

[14]It was often recognised that there wassomedifference between them, but it was not recognised that the difference is fundamental, and of very great importance.

[15]Encyclopædia of the Philosophical Sciences, vol. i. p. 97.

[16]This perhaps requires modification in order to include such facts as beliefs and wishes, since such facts apparently contain propositions as components. Such facts, though not strictly atomic, must be supposed included if the statement in the text is to be true.

[17]The assumptions made concerning time-relations in the above are as follows:—I. In order to secure that instants form a series, we assume:(a) No event wholly precedes itself. (An “event” is defined as whatever is simultaneous with something or other.)(b) If one event wholly precedes another, and the other wholly precedes a third, then the first wholly precedes the third.(c) If one event wholly precedes another, it is not simultaneous with it.(d) Of two events which are not simultaneous, one must wholly precede the other.II. In order to secure that the initial contemporaries of a given event should form an instant, we assume:(e) An event wholly after some contemporary of a given event is wholly after someinitialcontemporary of the given event.III. In order to secure that the series of instants shall be compact, we assume:(f) If one event wholly precedes another, there is an event wholly after the one and simultaneous with something wholly before the other.This assumption entails the consequence that if one event covers the whole of a stretch of time immediately preceding another event, then it must have at least one instant in common with the other event;i.e.it is impossible for one event to cease just before another begins. I do not know whether this should be regarded as inadmissible. For a mathematico-logical treatment of the above topics,cf.N. Wilner, “A Contribution to the Theory of Relative Position,”Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449.

[17]The assumptions made concerning time-relations in the above are as follows:—

I. In order to secure that instants form a series, we assume:

(a) No event wholly precedes itself. (An “event” is defined as whatever is simultaneous with something or other.)

(b) If one event wholly precedes another, and the other wholly precedes a third, then the first wholly precedes the third.

(d) Of two events which are not simultaneous, one must wholly precede the other.

II. In order to secure that the initial contemporaries of a given event should form an instant, we assume:

(e) An event wholly after some contemporary of a given event is wholly after someinitialcontemporary of the given event.

III. In order to secure that the series of instants shall be compact, we assume:

(f) If one event wholly precedes another, there is an event wholly after the one and simultaneous with something wholly before the other.

This assumption entails the consequence that if one event covers the whole of a stretch of time immediately preceding another event, then it must have at least one instant in common with the other event;i.e.it is impossible for one event to cease just before another begins. I do not know whether this should be regarded as inadmissible. For a mathematico-logical treatment of the above topics,cf.N. Wilner, “A Contribution to the Theory of Relative Position,”Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449.

[18]The above paradox is essentially the same as Zeno's argument of the stadium which will be considered in ournext lecture.

[19]Seenext lecture.

[20]Monist, July 1912, pp. 337–341.

[21]“Le continu mathématique,”Revue de Métaphysique et de Morale, vol. i. p. 29.

[22]In what concerns the early Greek philosophers, my knowledge is largely derived from Burnet's valuable work,Early Greek Philosophy(2nd ed., London, 1908). I have also been greatly assisted by Mr D. S. Robertson of Trinity College, who has supplied the deficiencies of my knowledge of Greek, and brought important references to my notice.

[23]Cf.Aristotle,Metaphysics, M. 6, 1080b, 18sqq., and 1083b, 8sqq.

[24]There is some reason to think that the Pythagoreans distinguished between discrete and continuous quantity. G. J. Allman, in hisGreek Geometry from Thales to Euclid, says (p. 23): “The Pythagoreans made a fourfold division of mathematical science, attributing one of its parts to the how many,τὸ πόσον, and the other to the how much,τὸ πηλίκον; and they assigned to each of these parts a twofold division. For they said that discrete quantity, or thehow many, either subsists by itself or must be considered with relation to some other; but that continued quantity, or thehow much, is either stable or in motion. Hence they affirmed that arithmetic contemplates that discrete quantity which subsists by itself, but music that which is related to another; and that geometry considers continued quantity so far as it is immovable; but astronomy (τὴν σφαιρικήν) contemplates continued quantity so far as it is of a self-motive nature. (Proclus, ed. Friedlein, p. 35. As to the distinction betweenτὸ πηλίκον, continuous, andτὸ πόσον, discrete quantity, see Iambl.,in Nicomachi Geraseni Arithmeticam introductionem, ed. Tennulius, p. 148.)”Cf.p. 48.

[25]Referred to by Burnet,op. cit., p. 120.

[26]iv., 6. 213b, 22; H. Ritter and L. Preller,Historia Philosophiæ Græcæ, 8th ed., Gotha, 1898, p. 75 (this work will be referred to in future as “R. P.”).

[27]The Pythagorean proof is roughly as follows. If possible, let the ratio of the diagonal to the side of a square bem/n, wheremandnare whole numbers having no common factor. Then we must havem2= 2n2. Now the square of an odd number is odd, butm2, being equal to 2n2, is even. Hencemmust be even. But the square of an even number divides by 4, thereforen2, which is half ofm2, must be even. Thereforenmust be even. But, sincemis even, andmandnhave no common factor,nmust be odd. Thusnmust be both odd and even, which is impossible; and therefore the diagonal and the side cannot have a rational ratio.

[28]In regard to Zeno and the Pythagoreans, I have derived much valuable information and criticism from Mr P. E. B. Jourdain.

[29]So Plato makes Zeno say in theParmenides, apropos of his philosophy as a whole; and all internal and external evidence supports this view.

[30]“With Parmenides,” Hegel says, “philosophising proper began.”Werke(edition of 1840), vol. xiii. p. 274.

[31]Parmenides, 128A–D.

[32]This interpretation is combated by Milhaud,Les philosophes-géomètres de la Grèce, p. 140 n., but his reasons do not seem to me convincing. All the interpretations in what follows are open to question, but all have the support of reputable authorities.

[33]Physics, vi. 9. 2396 (R.P. 136–139).

[34]Cf.Gaston Milhaud,Les philosophes-géomètres de la Grèce, p. 140 n.; Paul Tannery,Pour l'histoire de la science hellène, p. 249; Burnet,op. cit., p. 362.

[35]Cf.R. K. Gaye, “On Aristotle,Physics, Z ix.”Journal of Philology, vol. xxxi., esp. p. 111. Also Moritz Cantor,Vorlesungen über Geschichte der Mathematik, 1st ed., vol. i., 1880, p. 168, who, however, subsequently adopted Paul Tannery's opinion,Vorlesungen, 3rd ed. (vol. i. p. 200).

[36]“Le mouvement et les partisans des indivisibles,”Revue de Métaphysique et de Morale, vol. i. pp. 382–395.

[37]“Le mouvement et les arguments de Zénon d'Élée,”Revue de Métaphysique et de Morale, vol. i. pp. 107–125.

[38]Cf.M. Brochard, “Les prétendus sophismes de Zénon d'Élée,”Revue de Métaphysique et de Morale, vol. i. pp. 209–215.

[39]Simplicius,Phys., 140, 28D(R.P. 133); Burnet,op. cit., pp. 364–365.

[40]Op. cit., p. 367.

[41]Aristotle's words are: “The first is the one on the non-existence of motion on the ground that what is moved must always attain the middle point sooner than the end-point, on which we gave our opinion in the earlier part of our discourse.”Phys., vi. 9. 939B(R.P. 136). Aristotle seems to refer toPhys., vi. 2. 223AB[R.P. 136A]: “All space is continuous, for time and space are divided into the same and equal divisions…. Wherefore also Zeno's argument is fallacious, that it is impossible to go through an infinite collection or to touch an infinite collection one by one in a finite time. For there are two senses in which the term ‘infinite’ is applied both to length and to time, and in fact to all continuous things, either in regard to divisibility, or in regard to the ends. Now it is not possible to touch things infinite in regard to number in a finite time, but it is possible to touch things infinite in regard to divisibility: for time itself also is infinite in this sense. So that in fact we go through an infinite, [space] in an infinite [time] and not in a finite [time], and we touch infinite things with infinite things, not with finite things.” Philoponus, a sixth-century commentator (R.P. 136A,Exc. Paris Philop. in Arist. Phys., 803, 2. Vit.), gives the following illustration: “For if a thing were moved the space of a cubit in one hour, since in every space there are an infinite number of points, the thing moved must needs touch all the points of the space: it will then go through an infinite collection in a finite time, which is impossible.”

[42]Cf.Mr C. D. Broad, “Note on Achilles and the Tortoise,”Mind, N.S., vol. xxii. pp. 318–9.

[43]Op. cit.

[44]Aristotle's words are: “The second is the so-called Achilles. It consists in this, that the slower will never be overtaken in its course by the quickest, for the pursuer must always come first to the point from which the pursued has just departed, so that the slower must necessarily be always still more or less in advance.”Phys., vi. 9. 239B(R.P. 137).

[45]Phys., vi. 9. 239B(R.P. 138).

[46]Phys., vi. 9. 239B(R.P. 139).

[47]Loc. cit.

[48]Loc. cit., p. 105.

[49]Phil. Werke, Gerhardt's edition, vol. i. p. 338.

[50]Mathematical Discourses concerning two new sciences relating to mechanics and local motion, in four dialogues.By Galileo Galilei, Chief Philosopher and Mathematician to the Grand Duke of Tuscany. Done into English from the Italian, by Tho. Weston, late Master, and now published by John Weston, present Master, of the Academy at Greenwich. See pp. 46 ff.

[51]In hisGrundlagen einer allgemeinen Mannichfaltigkeitslehreand in articles inActa Mathematica, vol. ii.

[52]The definition of number contained in this book, and elaborated in theGrundgesetze der Arithmetik(vol. i., 1893; vol. ii., 1903), was rediscovered by me in ignorance of Frege's work. I wish to state as emphatically as possible—what seems still often ignored—that his discovery antedated mine by eighteen years.

[53]Giles,The Civilisation of China(Home University Library), p. 147.

[54]Cf.Principia Mathematica, § 20, and Introduction, chapter iii.

[55]In the above remarks I am making use of unpublished work by my friend Ludwig Wittgenstein.

[56]Thus we are not using “thing” here in the sense of a class of correlated “aspects,” as we did inLecture III. Each “aspect” will count separately in stating causal laws.

[57]The above remarks, for purposes of illustration, adopt one of several possible opinions on each of several disputed points.

Transcriber's Note:The following is a list of corrections made to the original. The first passage is the original passage, the second the corrected one.Advertisement:SecondImpressionCr. 8vo, 6s. net.SecondImpression.Cr. 8vo, 6s. net.Page 8:impossibility of alternatives which seemedprimafacieimpossibility of alternatives which seemedprimâfaciePage 119:with it. We will call these the “initialcontemporarieswith it. We will call these the “initialcontemporaries”Page 197:of infinitenumber. Many of the mostof infinitenumbers. Many of the mostPage 200:pscyhicalprocesses as the North Sea…. The botanistpsychicalprocesses as the North Sea…. The botanistPage 215:something which existed a quarter ofahour ago, thesomething which existed a quarter ofanhour ago, thePage 244:Intelligence, how displayed by friends,93Intelligence, how displayed by friends,93.Page 244:Number, cardinal,131186 ff.Number, cardinal,131,186 ff.

Transcriber's Note:

The following is a list of corrections made to the original. The first passage is the original passage, the second the corrected one.

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