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CHAPTER IV: Of the practical Dictates of Reason . - Richard Cumberland, A Treatise of the Laws of Nature [1672]

Edition used:

A Treatise of the Laws of Nature, translated, with Introduction and Appendix, by John Maxwell (1727), edited and with a Foreword by Jon Parkin (Indianapolis: Liberty Fund, 2005).

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Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.


CHAPTER IV

Of the practical Dictates of Reason.

All human Actions are not voluntary and, consequently, do not suppose practical Dictates of Reason. I must begin this Chapter with observing, that not all the Actions of Men are grounded upon the Dictates, or upon Notions equivalent to the Dictates, of Reason. For our first Apprehensions, and certain Motions of the Spirits, or Imagination, sometimes also muscular Motions, as the winking of the Eyes, or a sudden starting back from our Friends, seem to be effected without any Dictate of Reason;1 also, most Actions of Infants, as Comparing, Judging, &c. concerning things pleasant and hurtful, by which, nevertheless, their Treasure of Knowledge is increas’d: And, perhaps, the Desire of Good in general may be reckon’d among these.

How the practical Dictates of Reason are form’d.For the Author of Nature has so fram’d us, “That, in our Childhood, we, even unwillingly, perceive many things by our Senses, and firmly retain them in Memory, and judge by a spontaneous Comparison, whether some are greater than others, like or unlike, profitable or hurtful”; but, above all, (because we are always present to our selves, and from the particular Frame of our Mind, reflecting upon it self,) “We are necessarily conscious of the Acts of our Understanding and Will, and how much we have it in our Power, to excite, and govern, certain Motions of our Body,” which are, therefore, usually call’d voluntary; and, therefore, we necessarily know by experience, “What Actions of these Faculties bring us Harm, or Benefit and Perfection,” with which Knowledge, Desire and Pursuit, or Aversion and Avoidance, are naturally connected. Further, we easily perceive, by a Parity of Reason, (without any other Guide than Nature,) “That the like, both Advantages and Disadvantages, accrue to, and are perceiv’d by, other Beings also, as far as they resemble us, either in Mind, or Body, or both.” Hence we draw some Conclusions, concerning Actions acceptable to God, but many more, concerning such as are advantageous, and disadvantageous to Men.

When we have attain’d to a Maturity of Reason, we take into Consideration the whole of our Life, or the whole future exercise of all our Powers; and, because a greater Number of Actions, probably future, and also of good Effects, which we hope for from thence, presents itself now at once to our Mind, than formerly; and a longer Train of Events, which are to succeed in order, and mutually depend upon one another, is contemplated by the Mind, now come to a ripeness of Judgment: Therefore the Mind calls in, to the Assistance of the Memory, not single Words only, but Propositions, distinctly exhibiting the Connexion of our Actions of all Kinds, with their natural Effects. These Propositions are called Practical, nor is it necessary, that they should be pronounc’d in the Form of a Gerund, “This, or that, ought to be done,” as some Schoolmen teach; because that Fitness, which is express’d by a Gerund, wants Explanation, which is to be fetch’d, either from the necessary Connexion of the Means with the End, or from the Obligation of a Law. The Obligation of Laws is not yet to be suppos’d known by those, who are in quest of their Original. And the necessary Connexion, between the Means and the End, is sufficiently express’d, in the Connexion of them, as of Causes, with their design’d Effects.

Moreover, as we approach Manhood, it is natural for us, to compare, with one another, the Powers of several Causes, to produce the like Effects, as also the several Degrees of Perfection of those Effects, from which Comparison we form a Judgment, that this is greater, or less than, or equal to, that. Hence, for example, we conclude, “That some of those Actions, which are in our Power, can contribute more than others, or most of all, to our own Happiness, and that of others.” Such kind of practical Propositions, I call comparative Dictates of Reason.

It is not necessary for us, who only inquire into the Formation of the Laws of Nature, to assert, that such Dictates, even after we know that they have the Force of Laws, do always determine Men to Action; it is sufficient, that they tell us, how we ought to determine. For, concerning the Power, which determines us to Action, there are different Opinions, and I care not to engage in the Dispute. All, however, I think, acknowledge, “That a practical Dictate of Reason is previously necessary to our deliberate Acts, and does, in some manner, direct the Determination of our future Actions.” Nevertheless, the essential Parts of a practical Dictate, and its Form, require, in the next place, to be more attentively consider’d; for thence its Formation, in our Mind, will more easily be apprehended.

Three Forms of practical Dictates of Reason,A practical Proposition is, sometimes, thus express’d. “This possible human Action” (universal Benevolence; for instance) “Will chiefly, beyond any other Action at the same time possible, conduce to my Happiness, and that of all others, either as an essential part thereof, or as a Cause, which will, some time or other, effect a principal essential part thereof.” It is sometimes express’d, in the Form of a Command. “Let that Action, which is in thy Power, and which will most effectually, of all those which thou can’st exert, promote the common Good in the present Circumstances, be exerted”; often also, in the Form of a Gerund; “Such an Action ought to be done.” In my Opinion, these several Forms of Speech, relating to the Law of Nature, mean the same thing, whether the Understanding judges this best to be done, or commands it, or tells me, in the Form of a Gerund, that I am bound to do it.Compar’d. For the Understanding (which in this Affair is call’d Conscience) sufficiently hints the natural Obligation, when it says, “This is best to be done, both for your self and others.” For, in omitting what is declar’d best for me, it is thence evident, that I bring mischief (which may be called Punishment) upon my self. If the Dictate be consider’d, under the Form of a Command, the same thing is inculcated, by representing every Man’s own Understanding, as a Magistrate deputed, and authorized, to make Laws: Which, because it sounds somewhat metaphorically, is, therefore, less philosophical; it is useful however, because the Comparison has a very just Foundation in Nature. The Form of a Gerund teaches the same thing; but as an inferior Judge, or Counsellor, admonishing concerning a Law already made, and requiring a Conformity of the future Action therewith. The first manner is most becoming a Philosopher, which, if we consider the Form, appears a speculative Proposition; if the Force, a Practical, as teaching the natural Foundation of Obligation. The second best becomes a Sovereign Prince; the third, a Divine. But they may all be us’d promiscously, provided we retain in Mind the Distinction, such as it is, between these Forms. The Nature of Things represents to the Mind, what is best to be done. The Mind, considering the Government of Things, does, from the Idea of God, conclude, that he wills, or commands, them to be done, and, in his Name, imposes the Command on it self, in the second Form. In the third, it reflects upon the two former, and pronounces, that an Action agreeable to that Command, will be just; the contrary, unjust.

A fourth Form,§II. There is also another manner of expressing the Laws of Nature, as thus, “This, or that, possible Action is most agreeable to human Nature.” But the Sense is doubtful; for, (1.) Human Nature, either signifies the particular nature of the Agent, and then it is not expressive enough of what ought to be consider’d before Action: For, not the Happiness of one particular Person only, but the greatest common Good, ought to be regarded. Or, (2.) Human Nature respects all Men, and so God is not taken into Consideration. But, if, in either of these Notions, the publick Good is, by consequence, implied, this Form of speaking is coincident with the first, which is therefore to be preferr’d, because it is free from this Ambiguity.Coincident with the first, which is less ambiguous, Again, it is doubtful, to what the Expression [is agreeable] relates: For, (1.) An Action may be said to be agreeable to any Nature, when it is agreeable to the Principles of acting, such are Faculties, Habits, and Objects, either treasur’d up in the Memory, or solliciting to Action from without; and to these Heads may be reduced the practical Dictates of Reason, (that is, Propositions, which are the Rules of Action,) whose Terms, having taken their Rise from Objects, are retain’d in the Memory, and are, by the Mind, form’d into Propositions, where by they determine our Actions, and constitute Habits. (2.) An Action may be said to be agreeable to human Nature, when its Effects preserve, or improve, the Nature of one or more Men. This latter Sense coincides with the Form 1 first propos’d, which is free from Ambiguity: And the first Sense of the Agreeableness of Actions, may, for the most part, be reduced thereto. For practical Propositions, which are among the internal Principles of Action, relate all to the Desire of an End, the chief principally, and to the Use of the Means. Those Propositions, which relate to the Desire of the ultimate End, pronounce only to this Purpose, “This is, in its own Nature, Good, or a part of human Happiness, and that the greatest possible in the present Circumstances.” Those, which determine concerning the Means, inculcate only thus, “This conduces to the obtaining such Good, and that the most effectually in the Case propos’d.” And these Forms of speaking coincide with the first. The first Form is to be preferr’d, because this manner of resolving a Proposition, concerning the Agreeableness of an Action, is not, for the most part, obvious to the Understanding; and, beside, what I aim at, is, “To explain the manner of forming these first Dictates of Reason, with which Actions ought to agree”; wherefore it is not sufficient to our purpose, to say, “That an Action is agreeable to Dictates already form’d, such as, alone, are the immediate Principles of human Actions.” It may not, however, be useless, to remark, that we may truly affirm, “That all good Actions, or Virtues, do perfectly and essentially agree with the Notion or Idea of a rational Agent, whose Reason has ripen’d into Prudence, whither it naturally tends.” For Prudence necessarily includes, both the Desire of the best and greatest End, which is within the reach of any one’s Faculties, and the Prosecution of the same, by the most effectual means. The greatest End is the common Good of all rational Agents, and the Consent of all, to give mutual Assistance toward obtaining that End, is the most effectual means of promoting it. In Actions pursuant to such Consent, consists all Religion and Virtue. And it may be presum’d, even before Compacts are enter’d into, that all will agree, that this is the greatest End, and this the only Means plainly necessary, because no Cause can be assign’d to human Actions, of mutual Assistance, beside the Consent of the Will.2 Therefore, if we reckon such Dictates of Reason, (which, whilst they are stored up in the Memory, determine us to Action,) among the inward Principles of human Actions, (which we may very justly do, since they contain in them selves the whole Essence and Force of Habits,) then it may, truly and agreeably to what we have said, be affirm’d, “That every thing is Just, which agrees with these Principles, and the Laws of a rational Nature.”

Whether the Law of Nature be sufficiently promulg’d.§III. We are next to consider, especially with respect to the first, which is Nature’s principal Form of proposing its Laws, “Whether that Law, or practical Proposition, be taught, or promulg’d, with sufficient clearness, when its Terms, (and consequently their Connexion, or the Truth of the Proposition,) are obvious, and as it were expos’d to the View of those Men, who are willing to attend to the Consequences of their own Actions?” Or, “Whether we are to think, that Nature has not with sufficient Plainness declar’d such a Truth, so as to oblige those, who, thro Wickedness,3 or other Cares with which they distract their Mind, do not compare these Terms with one another, nor form such practical Propositions, for the future Direction of their Actions”? The former Opinion seems to me the more probable, because whoever shews me a Triangle, shews me with sufficient evidence, that the two sides of a Triangle are longer than the third, altho he does not form the Proposition for me. It is, however, incumbent upon me, in this Treatise,4 to prove, (1.) “That the Terms of the Laws of Nature are, as things are fram’d, in the same manner clearly enough laid before the Minds of Men.” (2.) “That the Minds of Men are in like manner excited, by their own Nature, or by their Union with the Body and the rest of the System of the World, to consider, abstract, and compare, those Terms among themselves, and thence to form Propositions for the Conduct of their Actions; and that, therefore, all Persons, in their Senses, retain such Propositions in their Mind, tho sometimes blended with what is impertinent or false, and thereby obscur’d.”

The Terms of those practical Propositions, which are called the Laws of Nature, are such human Actions, as are capable of being guided by Counsel or Reason; and which, after they are exerted, do jointly contribute to the greatest Happiness of all rational Agents, and to our own in particular. Such Actions are commonly divided, justly enough, into,(1.) The Elicit (that is, the proper and immediate) Acts of the Understanding and Will, and, consequently, of the Affections, (at least so far as the stronger Affections have place in the Mind itself;) and, (2.) The Imperate, which are exerted, in the Body, by the Power of the Mind.

The Nature of the practical Dictates of Reason illustrated by a Comparison of them with mathematical Practice.§IV. But, before we consider these Laws more particularly, it will be worth while, to insist somewhat longer, on treating of the nature of practical Propositions, and first to shew their great Affinity, or Agreement in meaning, whether they be Absolute or Conditional, with speculative Propositions. 2dly, That, in them all, the Effect is look’d upon as the End; Actions in our Power, as the Means.

In order to which we are first to observe, that those are properly called practical Propositions, which declare the Origin of an Effect from human Actions, which Definition I think proper to illustrate by Examples.Practical Propositions, Such is this in Arithmetick, “The Addition of Numbers forms the Sum,” or, “The Subtraction of one Number from another, leaves their Difference.” So in Geometry, “The Practice, prescrib’d in the first Proposition of Euclid ’s Elements, will effect an Equilateral Triangle, ” is, a practical Proposition, pronouncing concerning the Effect of a certain Series of human Actions.

which are near of kin to Theorems,Moreover, the Mind certainly understands the Truth of such a practical Proposition, in the same manner it does that of any Theorem, which is, by considering its Terms, of which one includes the other. So the Truth of this Proposition, “The Construction of a whole Equilateral Triangle is made, by constructing and uniting all its Parts,” is known after the same manner with this Theorem, “A whole Equilateral Triangle is the same, with all its Parts united among themselves.”

consider the Effect as the End, Actions as Means.It comes to the same thing, if the Construction of this Whole be consider’d as the End, and the several Motions, by which the three sides of that Triangle are form’d and fitted to one another, are consider’d as the Means necessary to that End. The same Proposition, as to Sense, may be otherwise thus express’d. “It is necessary to the Construction of a whole Equilateral Triangle, that all its sides be form’d, and mutually join’d, after the manner prescrib’d by Euclid, or some equivalent Method.” For, truly, the End is the Effect intended, and all the Causes, effecting a proper Union of all the Parts, include at once all the Means. What we have already said about the Construction, may be very easily accommodated to these other Operations,5 the Preservation or Perfection, of any Whole, which needs such Operations. Seeing the Preservation of any thing, is only the continuing those Actions, by which it was first form’d. Hence this practical Proposition, “It is necessary, in order to procure the Preservation of the whole System of rational Agents, as far as in us lies, that we should preserve, as much as possible, all its Parts, and their Union among them-selves, (such as the Perfection of such a System requires.)” This, I say, has a like Evidence with that Theorem, which affirms, “That the Whole is the same with all its Parts united.” And in that Proposition, rightly understood, I will prove are contain’d the Foundations of all natural Laws. What I have offer’d, concerning the Conversion of Euclid’s first Problem into a Theorem, I would have, by a Parity of Reason, understood universally. For nothing hinders, but that “The Solution of all those things may be perfectly propos’d in Theorems, which are usually sought after in the Form of Problems.” Therefore Archimedes, in his second Book of the Sphere, plainly professes, “That, of Problems, whose Solution consists of Propositions directing Practice, he form’d Theorems.” And Ramus, in Imitation of him, in his Geometry, converts all Euclid’s Problems into Theorems.6 And in specious Arithmetick, (the happiest art of solving Problems,) at the end of the Operation is always produc’d a Theorem, pointing out the Solution of the Problem.

Nor is it to be doubted, but, as Des-Cartes, Vieta, Wallis, and others, have successfully taught an expeditious Method of solving Problems in pure Mathematicks, (Arithmetick and Geometry,) by Theorems algebraically invented and exhibited: so also Problems might be solv’d, in the same manner, in mixt Mathematicks; not in Astronomy only, (which Ward has excellently perform’d,) but also in Mechanicks, Staticks, &c. and in great part of natural Philosophy.7

Yet farther; the science of Morality and Politicks, both can, and ought to, imitate the Analytick Art, (in which I comprehend, not only the Extraction of Roots, but also the whole doctrine of specious Arithmetick or Algebra,) as the noblest Pattern of Science.

(1.) By delivering the Rules of its Practice, and the whole Substance of its Art, in a few universal Theorems. Where I think proper to observe, “That its certainty is no more weaken’d, or usefulness lessen’d, because we cannot exactly determine what is fit to be done, in our external Actions, with relation to a Subject involv’d in a vast Variety of Circumstances; than the Truth or Usefulness of Geometrical Principles, about measuring Lines, Surfaces or Solids, is overthrown, because neither our Senses, nor Instruments, will enable us, to form without us a Line exactly strait, or a Surface perfectly plane or spherical, or a Body, in all respects, regular.” It is sufficient, that we approach so near to Exactness, that what we want of it, is of no consequence in Practice. We may attain a like Degree of Exactness, in Morality, by the help of its Principles. I confess, however, “That those things which, in Morality, are granted, or assumed as known, such as GOD and Man, their Actions and mutual Relations, are not soexactly known, as those things, which in Mathematicks are assum’d, in a fix’d determinate Proportion or Quantity; and that, therefore, the Conclusions thence drawn must labour under the same want of Exactness.” Yet the Method, the Rules of Operation, and the Manner of drawing Consequences, is the same. Nor is Exactness necessary for the Uses of Life; as neither is it requir’d, in the Practice of measuring Planes and Solids.

(2.) As Algebra, by beginning with, and supposing, the most compounded and involv’d Aequations, where the known Quantities are mingled with the unknown, then diligently comparing among themselves the several Terms, does at length discover some simple uncompounded thing, of which the compounded parts may be compos’d, and which, consequently, leads us to the Knowledge and Explanation of the unknown Quantities, by the known. So, likewise, moral Philosophy begins with contemplating an End very intricate, and Means variously involv’d. For the End is a Collection of all those good things within our Power, which are capable of adorning the Kingdom of God, the whole System of intelligent Agents, and its several Parts. The Means, by which this End is to be obtain’d, are all our possible free Actions, about what Object soever. And, from an Equality suppos’d between these two Ideas, as between the Powers of the Cause, and their adequate Effect, are to be drawn all moral Rules, and all virtuous Actions enjoin’d by them. It is evident, that these Things are equal, because the End is the intire Effect to be produc’d, and all our possible Actions make up the intire efficient Cause. But in this consists the Art of Life, “To consider every publick Good in our Power, and all our particular Actions, and their Order, (by which some may prepare Matter for, or add Force to, others,) with such Attention and Care, that having, at length, trac’d out the most easy Actions, which may serve to promote to that End, by their Help we may proceed to the more difficult, and, at last, reach those utmost and most intricate bounds of our Faculties.” And this Practice perfectly corresponds to that of Algebra.

(3.) As Algebra supposes the Quantity unknown, and yet sought after, in some sort already known, by a certain Anticipation of the Mind, and expresses it by a proper Character, and is thus enabled to exhibit its given Relation to the known Quantities, by means whereof it-self at last becomes known: So Ethicks, also, forms some kind of Idea of the End or Effect propos’d; by the help of those Relations, which it bears to our Operations in some measure known, (at least in general,) it distinguishes it by the name of the chief Good, or of Happiness, from other Objects, altho’ it knows, “That it does not yet exist,” and altho’ it does not distinctly know, “What shall at last be the Effect of our Operations, and of the Concurrence of Things without us”; whence it may justly be called Unknown: But, by the help of those Actions and Faculties, to which it is related, as the Effect to its Causes, and on which, consequently, it most certainly intirely depends, it at last gradually becomes known. Hither also is to be referr’d, that, whereas the End propos’d by every one, is that intire and greatest Good, which he can procure to the Universe, and to himself in his station, it follows, “That the End is to be conceiv’d as the greatest Aggregate, or Sum, of good Effects, most acceptable to God and Men, which can be effected, by the greatest Industry of all our future Actions.” It often happens, (and we ought to endeavour that it should happen as often as may be,) “That the good Effects of our Power increase in a Geometrical Progression”; (as in increase arising from Interest upon Interest, or in Husbandry, or Merchandizing, when every year the increase of the former is added to the main Stock;) whence arises a vast increase, both of publick and private Happiness, beyond what can be distinctly foreseen.

(4.) Since it is manifest, “That Man, without the Concurrence of God, can contribute nothing, without that of other Men, almost nothing, toward the common Good (the Glory of God, and Happiness of Men;)” but on the contrary, “That by any Action entering into, or preserving, Society with God and Men, any one may contribute much (comparatively speaking) to the publick Good”: The Judgment of Reason must, therefore, necessarily determine Man to such Actions, as tend to the forming or preserving such Society. But little, or nothing, is transacted in Society among Men, which does not depend upon the Knowledge of Numbers and Measure; and, therefore, if all Questions, concerning Practice, were handled accurately, they might be reduced to mathematical Evidence and Certainty; such are the determining the Value, both of Things and human Labour or Actions, either by comparing them among themselves, or with a third Thing, Money, of which also there are various Species; to reduce the Values of which to the most known and convenient Denomination, there is need of Arithmetick, either Natural or Artificial. To this Head are to be reduced, the Calculation of Prices in all Commerce, the Computation of Time, the investigating the Proportion of every Man’s Profit, or Loss, in Partnership. It would be endless, to attempt enumerating the Uses of Mathematicks in Tacticks, in Navigation, in the Contrivance and Application of all Kinds of Engines, in Surveying, and in Building, whether Houses, Ships, or Fortifications. It is sufficient, in few Words, to affirm, “That in all Affairs, whether private or publick, Mathematicks is the principal Instrument of Certainty and Justice in Action, where soever Exactness is requisite.” Which I do not advance, with a view to commend Mathematicks, (which is needless,) but to demonstrate the Certainty of the Rules of Life and Morality, upon this Account, that Natural Prudence almost always makes Use of the Assistance of a Science that is certain, or of self-evident Principles. To this Head also, I think, may be referr’d, “That, whereas we know not what shall hereafter happen, we may, nevertheless, know what is possible: And things possible may be compar’d among themselves; and it may be certainly known, not only, which of two possible Things will be of greater or less Value, when they do happen; but, also, which of them may be produc’d by more, which by fewer, Causes, that do now, or shall soon, exist. But that is more probable, which may happen more ways, and its Chance or Expectation is of greater Value.” Now it is of great Consequence, in the Management of Affairs, “To know certainly the Probability, and Value, of the Hope of the several Things, or Effects, we have occasion to consider.” For such is the condition of human Life, that we must lay out almost our whole Labour, our Expence often, nay expose Life it-self to Danger, for the Hope of such Things, as conduce to the Preservation or Happiness of our-selves, or of others, altho’ that Hope be probable only, not certain; even in Affairs of Peace, such as Agriculture, Merchandize, &c. much more in the Chance of War. That skill of investigation by Analysis, which all Men exercise naturally, teaches how to weigh these things very well; how the Value may be farther ascertain’d by Analysis, improv’d by Art, the famous Huygens hath finely shewn in his Calculations of the Chances of the Dice, which you may find at the End of Schooten’s Miscellaneous Mathematical Exercitations.8

It is an Observation pertinent to this Head, “That, as in Matters of Prudence we must sometimes try several Ways, before we can know certainly, whether the Affair shall succeed, according to our Wish, in this or that manner? Or whether we can at all obtain what we hop’d for? So, also, in Algebraick Investigations, sometimes various Comparisons, sometimes various Divisions, and other Kinds of Reduction, are to be tried, before we can solve the Problem propos’d.” It would not be impertinent here, to proceed farther, in tracing the resemblance between these Arts, in shewing, how the Method of Operation in both, does sometimes discover the Supposition built upon, to be false or impossible, not much less usefully, than it discovers another Supposition to be true or possible: And, moreover, by shewing, how negative Signs resemble Motions contrary to the Motion design’d, and how the Labours of different Men, conspiring to the same Effect, are correspondent to a compounding of Motions, concurring to form one and the same Line. But, since such matters are not very obvious, and the Resemblance is seldom carried on throughout, I thought it properer to stop here, whither those, who are but superficially conversant in Mathematicks, or who have a genius happily form’d by Nature for Science, may go along with me; than, by Comparisons with Things little known, to obscure, instead of reflecting light upon, Morality.

General Remarks on Chapter IV

Tho’ the Nature of future Contingencies will not admit of a Demonstration, “That any particular virtuous Action will be more for the Advantage of the Agent upon the whole in this Life”: Yet a Man of an enlarged Understanding may, in most moral Actions, have an intuitive Knowledge, that it is highly probable, “The Action will be for his Advantage,” altho’ he has not a precise Knowledge of the Degree of the Probability, or Value of the Chance. And perhaps it is not impossible to the human Capacity, to determine even the exact Degree of Probability in most moral Cases of Action, tho’ this wou’d be a Work of very great Difficulty, most Cases being exceedingly complicated. An exact Enumeration and Comparison of our Ideas of Pleasure, would be a great Step towards this Work. Tho’ this would be of great Use in Morality, yet we may with Pleasure observe the Benevolence of the Deity, “in giving us so great a Knowledge of the Consequences of Action, without any great Pains or Labour, as that, in most Cases, we may have a certain Knowledge of the Probability, That the Action will be for the Advantage of the Agent upon the whole, tho’ we have not an accurate Knowledge of the Degree of the Probability.” And this is sufficient to influence Action. For any Probability of Advantage, whatever the Degree of it be, if it be sufficient to overcome our natural Indolence and Inactivity, is sufficient to determine us to Action, upon a calm and thorough Deliberation.

[1. ]Barbeyrac (Traité Philosophique, p. 194, n. 1) suggests that Cumberland’s classical source for this discussion is Seneca’s De Ira, II.iv.1–2.

[2. ]Barbeyrac (Traité Philosophique, p. 198, n. 1) suggests that this sentence lacks the reference to rational ideas required by the subsequent sentences and suggests that Cumberland’s sentence should have read, “Nulla praeter consensum INTELLECTUS ET voluntatis esse potest causa.” It could be argued that Cumberland presupposes that the consenting will is rational and that Barbeyrac’s correction here is possibly superfluous. Neither Cumberland nor Bentley amended this passage in the corrected copy.

[3. ]Barbeyrac (Traité Philosophique p. 198, n. 1) indicates that Maxwell, in translating injuriam, has translated a printer’s error. The word should be incuriam (negligence), and this does sit more naturally with the rest of the sentence.

[4. ][Maxwell] “The Author considers these two Points in the following Chapter.”

[5. ]The original Latin text here is “ad operations conservantium,” which Maxwell has translated as “to these other operations, the Preservation.” Bentley and Barbeyrac felt that the operations under consideration in the passage were linked to preservation and perfection, and sought different solutions to make the parts of the sentence agree. Bentley’s solution is the neatest. He amends the text to “operation is conservantionem.” See Barbeyrac, Traité Philosophique, p. 200, n. 1.

[6. ]Euclid, Elementa Geometriae; Archimedes, De Sphaera et Cylindro, II; Ramus, Arithmeticae (1555).

[7. ]Cumberland refers to Descartes, La Géométrie (1637); Vieta, Canon-Mathematicus (1571) and In Artem Analyticum Isagoge (1591); Wallis, Arithmetica Infinitorum (1656) and De sectionibus conicis tratatus (1655); Ward, Astronomia Geometrica (1656).

[8. ]Huygens, Tractatus de ratiociniis in aleae ludo in van Schooten, Exercitationum Mathematicarum libri quinque (1657), vol. V.