37.Cf.pp.179ff. below.
37.Cf.pp.179ff. below.
38.The conception of probability here set forth is substantially that first developed by Mr. Venn, in hisLogic of Chance. Of course, a vague apprehension of the idea had always existed, but the problem was to make it perfectly clear, and to him belongs the credit of first doing this.
38.The conception of probability here set forth is substantially that first developed by Mr. Venn, in hisLogic of Chance. Of course, a vague apprehension of the idea had always existed, but the problem was to make it perfectly clear, and to him belongs the credit of first doing this.
39.I do not here admit an absolutely unknowable. Evidence could show us what would probably be the case after any given lapse of time; and though a subsequent time might be assigned which that evidence might not cover, yet further evidence would cover it.
39.I do not here admit an absolutely unknowable. Evidence could show us what would probably be the case after any given lapse of time; and though a subsequent time might be assigned which that evidence might not cover, yet further evidence would cover it.
40.Popular Science Monthly, April, 1878.
40.Popular Science Monthly, April, 1878.
41.Strictly we should need an infinite series of numbers each depending on the probable error of the last.
41.Strictly we should need an infinite series of numbers each depending on the probable error of the last.
42.“Perfect indecision, belief inclining neither way, an even chance.”—De Morgan, p. 182.
42.“Perfect indecision, belief inclining neither way, an even chance.”—De Morgan, p. 182.
43.Logique. The same is true, according to him, of every performance of a differentiation, but not of integration. He does not tell us whether it is the supernatural assistance which makes the former process so much the easier.
43.Logique. The same is true, according to him, of every performance of a differentiation, but not of integration. He does not tell us whether it is the supernatural assistance which makes the former process so much the easier.
44.Popular Science Monthly, June, 1878.
44.Popular Science Monthly, June, 1878.
45.[See Santayana,Reason in Religion.]
45.[See Santayana,Reason in Religion.]
46.For the present purpose, the negative of a character is to be considered as much a character as the positive, for a uniformity may either be affirmative or negative. I do not say that no distinction can be drawn between positive and negative uniformities.
46.For the present purpose, the negative of a character is to be considered as much a character as the positive, for a uniformity may either be affirmative or negative. I do not say that no distinction can be drawn between positive and negative uniformities.
47.There being 5 simple characters, with their negatives, they could be compounded in various ways so as to make 241 characters in all, without counting the charactersexistenceandnon-existence, which make up 243 or 35.
47.There being 5 simple characters, with their negatives, they could be compounded in various ways so as to make 241 characters in all, without counting the charactersexistenceandnon-existence, which make up 243 or 35.
48.This principle was, I believe, first stated by Mr. De Morgan.
48.This principle was, I believe, first stated by Mr. De Morgan.
49.Not in every idea but only in the one so formulated.
49.Not in every idea but only in the one so formulated.
50.[Note that this corollary is itself a theoretical inference and not an empirical rule.]
50.[Note that this corollary is itself a theoretical inference and not an empirical rule.]
51.Popular Science Monthly, August, 1878.
51.Popular Science Monthly, August, 1878.
52.[Later Pierce called itpresumptive inference. See Baldwin’sDictionaryart.Probable Inference.]
52.[Later Pierce called itpresumptive inference. See Baldwin’sDictionaryart.Probable Inference.]
53.This division was first made in a course of lectures by the author before the Lowell Institute, Boston, in 1866, and was printed in theProceedings of the American Academy of Arts and Sciences, for April 9, 1867.
53.This division was first made in a course of lectures by the author before the Lowell Institute, Boston, in 1866, and was printed in theProceedings of the American Academy of Arts and Sciences, for April 9, 1867.
54.The Monist, January, 1891.
54.The Monist, January, 1891.
55.The neo-Darwinian, Weismann, has shown that mortality would almost necessarily result from the action of the Darwinian principle.
55.The neo-Darwinian, Weismann, has shown that mortality would almost necessarily result from the action of the Darwinian principle.
56.A feeling may certainly be compound, but only in virtue of a perception which is not that feeling nor any feeling at all.
56.A feeling may certainly be compound, but only in virtue of a perception which is not that feeling nor any feeling at all.
57.[The reader will find further light on the following illustration in any text-book of projective geometry, e.g., Reye,Geometry of Position, I, pp. 17-24, orEncyc. Britannica, XI, p. 689.]
57.[The reader will find further light on the following illustration in any text-book of projective geometry, e.g., Reye,Geometry of Position, I, pp. 17-24, orEncyc. Britannica, XI, p. 689.]
58.[A more familiar example of this is the introduction of irrational or absurd numbers like √2. After it was proved that no ratio of two integers could possibly equal √2 the idea of number was generalized to include the latter. Fractions and the so-called imaginary numbers illustrate the same process of generalization for the sake of making certain operations (i.e. division and finding the root) continuously applicable.]
58.[A more familiar example of this is the introduction of irrational or absurd numbers like √2. After it was proved that no ratio of two integers could possibly equal √2 the idea of number was generalized to include the latter. Fractions and the so-called imaginary numbers illustrate the same process of generalization for the sake of making certain operations (i.e. division and finding the root) continuously applicable.]
59.The Monist, April, 1892.
59.The Monist, April, 1892.
60.Continuousis not exactly the right word, but I let it go to avoid a long and irrelevant discussion.
60.Continuousis not exactly the right word, but I let it go to avoid a long and irrelevant discussion.
61.The Monist, July, 1892.
61.The Monist, July, 1892.
62.This proposition is substantially the same as a theorem of Cantor, though it is enunciated in a much more general form.
62.This proposition is substantially the same as a theorem of Cantor, though it is enunciated in a much more general form.
63.The Monist, October, 1892.
63.The Monist, October, 1892.
64.I am rejoiced to find, since my last paper was printed, that a philosopher as subtle and profound as Dr. Edmund Montgomery has long been arguing for the same element in the universe. Other world-renowned thinkers, as M. Renouvier and M. Delbœuf, appear to share this opinion.
64.I am rejoiced to find, since my last paper was printed, that a philosopher as subtle and profound as Dr. Edmund Montgomery has long been arguing for the same element in the universe. Other world-renowned thinkers, as M. Renouvier and M. Delbœuf, appear to share this opinion.
65.By avera causa, in the logic of science, is meant a state of things known to exist in some cases and supposed to exist in other cases, because it would account for observed phenomena.
65.By avera causa, in the logic of science, is meant a state of things known to exist in some cases and supposed to exist in other cases, because it would account for observed phenomena.
66.Wiedemann,Annalen, 1887-1889.
66.Wiedemann,Annalen, 1887-1889.
67.See Maxwell on Spherical Harmonics, in hisElectricity and Magnetism.
67.See Maxwell on Spherical Harmonics, in hisElectricity and Magnetism.
68.The wordsystemhas three peculiar meanings in mathematics. (A.) It means an orderly exposition of the truths of astronomy, and hence a theory of the motions of the stars; as the Ptolemaicsystem, the Copernicansystem. This is much like the sense in which we speak of the Calvinisticsystemof theology, the Kantiansystemof philosophy, etc. (B.) It means the aggregate of the planets considered as all moving in somewhat the same way, as the solarsystem; and hence any aggregate of particles moving under mutual forces. (C.) It means a number of forces acting simultaneously upon a number of particles.
68.The wordsystemhas three peculiar meanings in mathematics. (A.) It means an orderly exposition of the truths of astronomy, and hence a theory of the motions of the stars; as the Ptolemaicsystem, the Copernicansystem. This is much like the sense in which we speak of the Calvinisticsystemof theology, the Kantiansystemof philosophy, etc. (B.) It means the aggregate of the planets considered as all moving in somewhat the same way, as the solarsystem; and hence any aggregate of particles moving under mutual forces. (C.) It means a number of forces acting simultaneously upon a number of particles.
69.But, in fact, an inspection of these curves is sufficient to show that they are of a higher degree than the third. For they have the lineV= O, or some lineVa constant for an asymptote, while for small values ofP, the values ofd2p/(dV)2are positive.
69.But, in fact, an inspection of these curves is sufficient to show that they are of a higher degree than the third. For they have the lineV= O, or some lineVa constant for an asymptote, while for small values ofP, the values ofd2p/(dV)2are positive.
70.Anticipated by Clausius as long ago as 1857; and by Williamson in 1851.
70.Anticipated by Clausius as long ago as 1857; and by Williamson in 1851.
71.“Physiologically, ... accommodation means the breaking up of a habit.... Psychologically, it means reviving consciousness.” Baldwin,Psychology, Part III, ch. i., § 5.
71.“Physiologically, ... accommodation means the breaking up of a habit.... Psychologically, it means reviving consciousness.” Baldwin,Psychology, Part III, ch. i., § 5.
72.The Monist, January, 1893.
72.The Monist, January, 1893.
73.How can a writer have any respect for science, as such, who is capable of confounding with the scientific propositions of political economy, which have nothing to say concerning what is “beneficent,” such brummagem generalisations as this?
73.How can a writer have any respect for science, as such, who is capable of confounding with the scientific propositions of political economy, which have nothing to say concerning what is “beneficent,” such brummagem generalisations as this?
74.I am happy to find that Dr. Carus, too, ranks Weismann among the opponents of Darwin, notwithstanding his flying that flag.
74.I am happy to find that Dr. Carus, too, ranks Weismann among the opponents of Darwin, notwithstanding his flying that flag.
75.SeeDraper’s History of Intellectual Development, chap. x.
75.SeeDraper’s History of Intellectual Development, chap. x.
76.Thomson, himself, in his articleHeatin theEncyclopedia Britannica, never once mentions the name of Clausius.
76.Thomson, himself, in his articleHeatin theEncyclopedia Britannica, never once mentions the name of Clausius.
77.See article on “Pragmatism,” inBaldwin’s Dictionary, Vol. 2., p. 322, and theMonist, Vol. 15, p. 162.
77.See article on “Pragmatism,” inBaldwin’s Dictionary, Vol. 2., p. 322, and theMonist, Vol. 15, p. 162.
78.Kant discriminates the laws of morality, which area priori, from rules of skill, having to do with technique or art, and counsels of prudence, having to do with welfare. The latter he calls pragmatic; thea priorilaws practical. SeeMetaphysics of Morals, Abbott’s trans., pp. 33 and 34.
78.Kant discriminates the laws of morality, which area priori, from rules of skill, having to do with technique or art, and counsels of prudence, having to do with welfare. The latter he calls pragmatic; thea priorilaws practical. SeeMetaphysics of Morals, Abbott’s trans., pp. 33 and 34.
79.See the article in theMonistalready mentioned, and another one in the same volume, p. 481, “The Issues of Pragmaticism.”
79.See the article in theMonistalready mentioned, and another one in the same volume, p. 481, “The Issues of Pragmaticism.”
80.It is probably fair to see here an empirical rendering of the Kantian generality of moral action, while the distinction and connection of “rational purport” and “sensible particular” have also obvious Kantian associations.
80.It is probably fair to see here an empirical rendering of the Kantian generality of moral action, while the distinction and connection of “rational purport” and “sensible particular” have also obvious Kantian associations.
81.P. 26.
81.P. 26.
82.P. 56-57.
82.P. 56-57.
83.P. 105.
83.P. 105.
84.P. 45.
84.P. 45.
85.P. 43.
85.P. 43.
86.P. 151.
86.P. 151.
87.P. 53.
87.P. 53.
88.The following classification is arbitrary, as some of Peirce’s most significant reflections occur in papers under headings II. and III. It may, however, be useful.
88.The following classification is arbitrary, as some of Peirce’s most significant reflections occur in papers under headings II. and III. It may, however, be useful.
Transcriber’s Notes:Footnotes have been collected at the end of the text, and are linked for ease of reference.