203.1-2 Metaphysical philosophy . . . the child of geometry.] See also W5:292-93 (1886), where Peirce showed how "metaphysics is an imitation of geometry."

203.2 Ionic] Thales of Miletus is said to have been the first to introduce geometry to Greece, and that he used it to determine the distance of ships at sea. Anaximander, in turn, is said to have introduced the gnomon and made known an outline of geometry. See also Peirce's extensive discussion of Thales's geometry in his 1892-93 "History of Science Lectures" (R 1277:17-34).

203.3-4 Eleatics] Early school of thought originating with Parmenides of Elea and including Zeno of Elea and Melissus of Samos. Of special interest for Peirce was Zeno, who wrote a treatise consisting of forty arguments, including the famous ones about motion, which rely on geometric concepts and were advanced to defend Parmenides's views.

203.5-6 Aristotle . . . potent conceptions.] Geometry, as the study of space, plays a central part in Aristotle's work. In Posterior Analytics, geometry provides a model for predication in the sciences; in Physics, the distinction of physics and mathematics leads Aristotle to further distinguish matter from form and to describe the four causes; in Metaphysics, geometry and mathematics provide the models for investigating being, distinguishing potentiality and actuality, etc.

203.9-11 the conviction . . . a similar science.] This is one of the convictions that Kant criticized in his Critique: see the preface to the second edition, especially Bx-xxii, and also A712/B740-A738/B766.

203.12-13 The unconditional surrender . . . of geometry] See also W4:544-46 (December 1883-January 1884), and W5:292-93 (1886).

203.14 Gauss,] Carl Friedrich Gauss (1777-1855), see ann. 64.21-22.

203.15-16 "there is no reason . . . two right angles."] An exact match for this quotation has not been found. Peirce implies that this was Gauss's stand on the issue of the Euclidean or non-Euclidean nature of physical space. However, Gauss is not known to have taken such a definite position on this question. Gauss was, nevertheless, well acquainted with mathematical instances of non-Euclidean triangles. An example is in his 8 November 1824 letter to F. A. Taurinus (Werke, vol. 8, 186-87), where he wrote that "the assumption that the sum of the three angles is smaller than 180 degrees leads to a peculiar geometry, quite distinct from the Euclidean, and which is quite consistent."

203.19-21 but experience . . . considerations.] In an earlier version Peirce added at this point: "Induction is utterly incompetent to establish any proposition at all as absolutely exact; and therefore if we are to rest on induction we cannot think that any general proposition is absolutely exact" (R 1600:10).

204.2-4 The first to go . . . inviolable law.] The criticism of determinism, or as it is also called necessitarianism, plays a prominent role in Peirce's 1892-93 Monist papers. See especially "The Doctrine of Necessity Examined" (EP1:298-311, April 1892) and "Reply to the Necessitarians: Rejoinder to Dr. Carus" (CP 6.588-618, July 1893). Although the argument does not return in the printed version of either, it does appear in one of the drafts of the rejoinder to Dr. Carus, where Peirce connects it with the doctrine of infallibilism (R 958:61, 1893).

204.11-12 Phoenix, . . . on Astronomy,"] John Phoenix was the pseudonym of George Horatio Derby (1823-1862), American humorist. The story is given in the first chapter of his humorous "Lectures on Astronomy" (1854), reprinted in his Phoenixiana; or, Sketches and Burlesques (New York: Appleton & Co., 1856), 57. The story of Joshua alludes to Jos. 10:12-13. See also CP 1.156 (1892).

204.27-28 Aristotle often lays . . . by chance.] Physics, 195b31-198a13.

204.28-31 Lucretius . . . reason at all.] Titus Lucretius Carus (c. 99-55 B.C.), Roman philosophical poet, disciple of Epicurus (and thereby of Democritus of Abdera), author of De rerum natura, in which he sought to abolish in an Epicurean vein the fear of gods and of death by demonstrating that the soul is mortal and the world not governed by gods but by mechanical laws. Lucretius expounded the doctrine of the "swerve" of atoms (clinamen), with which Epicurus sought to undermine the determinism of the earlier atomists, in De rerum natura II, 216-93. Compare with what Peirce wrote in 1898:

But there is another class of objectors for whom I have more respect. They are shocked at the atheism of Lucretius and his great master. They do not perceive that that which offends them is not the Firstness in the swerving atoms, because they themselves are just as much advocates of Firstness as the ancient Atomists were. But what they cannot accept is the attribution of this firstness to things perfectly dead and material. Now I am quite with them there. I think too that whatever is First is ipso facto sentient. If I make atoms swerve,--as I do,--I make them swerve but very very little, because I conceive they are not absolutely dead (CP 6.201, RLT 260-61).

204.37 Whewell's views . . . truer than Mill's;] William Whewell (1794-1866), English philosopher and mathematician. John Stuart Mill (1806-1873), English philosopher and economist. For Peirce's earlier views, see his 1865 "Lecture on the Theories of Whewell, Mill, and Comte" (W1:205-23), where he draws on Whewell's Novum Organon Renovatum (1858) and Mill's A System of Logic. See also Peirce's 1869 lecture on Whewell's logic of science (W2:337-45).

205.17 haecceities] In CD 2677 Peirce gives the following definition: "That element of existence which confers individuality upon a nature . . . so that it is in a particular place at a particular time; hereness and nowness." The term is introduced by Scotus in Ordinatio, bk. II, dist. 3, part 1, qu. 6 (Opera omnia studio et cura Commissionis Scotisticae ad fidem codicum edita, Vatican City: Typis Polyglottis Vaticanis, 1950-). English transl.: P. V. Spade, Five Texts on the Medieval Problem of Universals (Indianapolis: Hackett, 1994), 96-113.

206.5-8 But every fact . . . inexplicable.] Peirce began an earlier version of this chapter with a call for a natural history of the laws of nature (R 909:60):

We need a Natural History of the laws of nature. For physical speculation is now in this condition; the mathematical development and physical testing of any hypothesis as to the ultimate or molecular constitution of matter, beyond what is now substantially demonstrated, will take at least fifty years, and the antecedent probability of any given hypothesis being correct, since the possible false hypotheses are indefinitely numerous, while there is but one true one, is practically infinitesimal. How long, at that rate, will it take to make any valuable advance in our knowledge. We made a great leap in dynamics, as soon as it began to be studied scientifically, because we were guided by our inborn instincts concerning force, which only needed to be corrected in the light of experiment, to yield the truth. In other words, we had sufficient innate tendency to believe that which was true, that if not the first, then the second or third idea which came into our heads, was the right one. So with astronomy, it so happened that the conic sections, nearly the easiest of curves for us to think about, were those in which the heavenly bodies really moved. But this guide of natural instinct seems to fail us in regard to the molecular constitution of matter; and we are embarrassed to know what sort of behaviour to expect from a molecule. Let us then treat the laws of nature as objects of natural history, and study them as we do animals and plants, comparing them, classing them, arranging them, in regard to their different characteristics. In this way, we may perhaps get, not to hope for a positive criterion, yet a hint or clue, to aid our guesses about the nature of atoms. The hypothesis which I am about to propose in this chapter is designed to form a nucleus for such a natural //history/study// of physical laws.

206.8-9 This is what Kant calls a regulative principle,] See for instance Critique of the Pure Reason, A179-80/B222-23, A509/B537.

206.9-10 The sole immediate purpose . . . things intelligible;] Compare with what Peirce wrote in the following incomplete fragment (R 1600:8-9).

The chief philosophies of the universe that are now current trace things back to certain laws which are supported to be ultimate and inexplicable, such as the conservation of force. But I maintain that every philosophy is illogical that posits an ultimate and inexplicable fact. This is a variety of the absolutely incognizeable; and we can have no right to suppose that any thing whatever is absolutely unknowable. The only function of thought is to make things intelligible and it is a stultification of thought to think things to be unintelligible; and whatever is inexplicable and ultimate is unintelligible. It is true, that it may be that some things are unintelligible; perhaps it is not unlikely. But to lay your finger on any one and say I believe this to be an ultimate and inexplicable fact, is as unwarrantable as it would be,--because we hold no doubt to many erroneous opinions,--to pick out one and say this is my opinion but I think it is erroneous. A given problem may be insoluble, but if we are to think about it at all, since the only use of reason is to solve problems, the only consistent course is to hope it will be found soluble, and to proceed upon that hope; and not to think about it, which thinking really consists in an attempt to understand it, and yet think that the right mode of understanding it is to be to understand it as not understandable. Abstain by all means from inquiring how it happens that energy is always conserved, if you do not find any interest in the problem; but do not ask the question and seek to put yourself off with the ridiculous answer that the question is irresolvable. Your mind was given you to resolve questions; and in point of fact you cannot use it otherwise. To say that a fact is ultimate and inexplicable is an attempt to give an account of it, but it is an absurd and self-stultifying attempt. It is as though a man having arms in his hand to resist an enemy, should become frightened and use his arms to commit suicide to prevent being killed by the enemy.

If the reader goes with me so far, and will allow that we are to admit that any given question, whose answer can make any conceivable practical or sensible difference, must always be assumed to be answerable if we had sufficient time to investigate it, then I think that he must also go a step further.

Peirce repeats this in nearly the same words in a second draft (R 909:60, R 1600:11, 10), where he added:

Does the reader admit the truth of this principle of hope? If not, I fear we must part company here; but if he does, then he will allow that we must seek for a philosophy of the universe according to which it shall always be possible to find an explanation for every phenomenon for which an explanation can be asked. Every regular phenomenon is of this kind; and we are entitled to ask for an explanation for Law itself.

206.28-29 Law or regularity itself.] In CD 3375 Peirce defines law in terms of regularity, catering to both his own view and the one he here opposes:

A proposition which expresses the constant or regular order of certain phenomena, or the constant mode of action of a force; a general formula or rule to which all things, or all things or phenomena within the limits of a certain class or group, conform, precisely and without exception; a rule to which events really tend to conform.

206n.1 Eckius] Johann Eck, original name Johann Maier (1486-1543), German theologian and Martin Luther's principal Roman Catholic opponent. The work referred to is his In summulas Petri Hispani extemporaria et succincta explanatio; sed succosa explanatio (1516).

207.13-14 But we pay . . . us.] In an earlier version (R 1600:11) Peirce wrote:

The only kind of phenomenon which does not required to be explained is mere irregularity. For example, when in the kinetical theory of gases we are told that the reason why gases press their enveloping vessels equally in all directions is that the molecules move irregularly, it is unreasonable to ask why they should move irregularly. In like manner, our explanations of the universe cannot stop or pause, until we get some notion of how regularity can emerge from irregularity.

Later, in 1898, he wrote: "fortuitous distribution, that is, utter irregularity, is the only thing which it is legitimate to explain by the absence of any reason to the contrary" (CP 7.521, RLT 211).

209.14 Our conceptions of the first stages of the development,] Compare with Peirce's later cosmological accounts, such as CP 6.215-19 (Dec. 1897) and CP 6.200 (RLT 260), 1898.