Notes on a Brief System of Logick
MS (LC: Madison Miscellany). One hundred and twenty-two pages of this copybook are filled with writing in JM’s youthful hand. They are preceded by four almost blank pages and followed by fourteen others devoted to the drawings described in the editorial note below. JM’s great-nephew, James Madison Cutts II, gave this manuscript to the Library of Congress in 1881. On the manuscript’s cardboard cover is written, “Mr. James A. Garlick, King William County, Virginia.” On the third of the pages in the front of the notebook is a doodle by JM consisting of a “1766” succeeded by two apparently meaningless pen marks and “6” repeated nine times. This date, if that is what it is, together with the fact that a Samuel Garlick had children in Donald Robertson’s school in 1767 when JM was a pupil there, suggests that he may have taken the notes, or at least have acquired the notebook, at about that time. Moreover, although logic was not customarily taught in a preparatory school, Robertson’s collegiate education in Scotland probably qualified him to offer instruction in the subject. Furthermore, if Robertson gave the course in 1767, Madison by then was amply prepared to employ the Latin and Greek words with which these notes are sprinkled. Finally, as will be pointed out in the editorial note, at least two of the drawings in the back of the copybook could have been based upon illustrations in volumes in Robertson’s library.
In the opinion of the editors, however, it is more probable that JM took these notes during his junior or senior year at the College of New Jersey. Its quite inflexible curriculum included a course in “Logick or Dialectick,” in all likelihood offered by the president, Reverend John Witherspoon. The intellectual level of the notes also strongly suggests what a college rather than an academy would expect of its students. Worthy of mention, although of no demonstrable significance, are the initials “h B,” twice written by JM on the third of the pages preceding the notes. Assuming that these stand for the name of one of his acquaintances, they at once call to mind Hugh Brackenridge, one of JM’s closest friends at the College of New Jersey. Judging from the account book of Donald Robertson, he had no pupil with those initials while JM attended his school. Then, too, unless John Locke’s An Essay Concerning Human Understanding is considered to be a textbook in logic, no volume on that subject seems to have been in Robertson’s school library. Although one section of the notes reflects this treatise, far more of them echo Isaac Watts’s handbook, entitled Logick: or, the Right Use of Reason in the Enquiry after Truth, first published in London in 1725, and in its twelfth London edition by 1763. This volume, apparently neither among Robertson’s books nor at Montpelier, was readily available, along with Locke’s essay, in the College of New Jersey Library (“Donald Robertson’s Account Book,” pp. 132–35, MS in Virginia Historical Society; “A Catalogue of Books belonging to His Excellency Jonathan Belcher,” p. 2, given to the College of New Jersey in 1755 by the Governor, and “Titles of Volumes once belonging to president Witherspoon, and bought by the college from president Smith,” p. 4, MSS in Princeton University Library). Furthermore, in an autobiographical sketch sent in January 1832 to James Kirke Paulding (LC: William C. Rives Papers), JM mentions the subjects he studied in Robertson’s school but does not include logic.
If JM had prepared an outline of his notes, it might have resembled the one which follows. The page numbers below are taken from the copybook. Wherever quotation marks are omitted, the headings or summaries have been supplied by the editors.
Introduction (pp. 1–2)
Definition of “Logick or Dialectick” and brief summary of its content.
|Sec. I.||“Of Ideas” (pp. 2–18)
Definition of an idea; source of ideas (perception, imagination, apprehension, remembrance); ideas vary in type according to the “Senses” which give them birth; meaning of a “sense” (internal [hunger, thirst, pain, pleasure, “the soul”] or external [seeing, hearing, smelling, tasting, and feeling]); difference between a clear and obscure idea, between a partial and adequate idea, between an abstract and concrete idea, between ideas produced by sensation and reflection, between single and complex ideas, and between ideas of entities and “non entities”; difference between spiritual and material “substances” and the “modes” (qualities) of each; difference between the essential and accidental properties of a substance; meaning of “Ideas of Relations”; meaning of “genus,” “species,” “Ens or being,” “differencia,” “proprium,” “accidens”; how abstract or general ideas arise; Aristotle’s ten categories of ideas.
|Sec. II.||“Of the Signs of Ideas” (pp. 18–31)
Definitions of natural, arbitrary, and artificial signs; types of words (noun, verb, participle; univocal and equivocal; proper and figurative); causes of disagreement between men (diversity and conflict of ideas; varying standards of value; ambiguity in the connotation of particular words, similes, metaphors); means of clearing the ground for rational discussion (preliminary definition, description, division, and explanation).
|Sec. I.||“Of Judgment” (pp. 32–34)
Definitions of judgment, error, doubt, certainty, and of a “judicious man.”
|Sec. II.||“Of Proposition” (pp. 34–49)
Definition of true, false, and “probable” propositions; logical and ethical propositions; affirmative and negative propositions; universal, particular, and singular propositions; categorical and hypothetical propositions; exclusive, reciprocal, opposite, “subalternate,” and “subcontrary” propositions; eleven types of compound propositions; metaphysical, mathematical, physical, natural, moral, collective, and distributive universalities.
|Sec. I.||Of Discourse (pp. 50–55)
Definitions and examples of discourse or argumentation, judgment, inference, and syllogism.
|Sec. II.||“Of Categorical Syllogisms” (pp. 55–84)
Analysis of a syllogism and its possible “modes”; nine “axioms”; seven “General Theorems” with example of each.
|Sec. III.||“Of the Other Forms of Syllogisms” (pp. 84–94)
Hypothetical, enthymena, disjunctive, dilemma, prosyllogism, sorites, and epichirema, with example of each.
|Sec. IV.||“Of the Invention of Middle Terms or Arguments of common places or Topicks” (pp. 95–112)
Definition of “middle term” and “topick”; twenty types of argument with an example of each; observations about the effects of argument upon the mind.
|Sec. V.||“Of False reasonings or Sophisms” (pp. 113–22)
Three types of “parallogisms” with example of each; illustrations of seven types of fallacious syllogisms arising from “impertinence, or falsehood, or ambiguity of Premises.”
One reason for presenting this outline is to make clear the traditional nature of the notes, both in their arrangement and content. Hobbes (p. 26) and Locke (p. 12) are briefly mentioned, and Part I owes more to Locke than this meager reference to him suggests. In the main, the author hews closely to a line of logic which extends back from Isaac Watts’s popular textbook through the works of Peter Ramus and the scholastics, to those of Aristotle and Plato, including Plato’s reports of what Socrates said. Isaac Watts’s Logick was levied upon for the formulation of several points of logic, for a few fairly long passages, and for a goodly number of illustrative examples. Both in their allusions and examples, the notes have a pronounced classical, biblical, and Christian flavor. In a word, they lack originality both in organization and thought. They do not even suggest the personality of their author, except that he was methodical and painstaking, something of a pedant, and a devout Christian well versed in Latin and acquainted with at least a few Greek words.*
Although the notes were written by JM, they were not the product of his mind except in the sense that he may have collated the material after extracting it from a number of books. In the judgment of the editors, however, he more probably was summarizing the lectures of a teacher, or, because of his occasional cross-references to earlier pages in the copybook, transcribing rough notes taken in class. Furthermore, the many misspellings support the conclusion that he was recording oral discourse. He would hardly have erred so often in this regard if he had taken the notes from printed texts. Whatever may have been their source, these notes owe to JM at the most their arrangement, and at the least the patience of his pen. Because they are not “Madison,” except to this very limited extent, the editors confine their publication of the notes to four extracts, one from each of the first two main parts and two from the long concluding section.
The drawings on the final fourteen pages of the copybook run sequentially as follows: (1) design of a fort whose main feature is a hexagon separated from its inclosing twelve-sided polygon by a “Fousse, Moat, Trench or Ditch”; (2) a half-circle marked to show “the Line of Chords,” “The Line of Secants,” “The Line of Signs,” and “The Line of Tangens”; (3) an elaborately annotated sundial, adjusted to latitude 38° north, approximately that of Montpelier; (4) “The Solar System from Copernicus,” consisting of the sun at the center with six concentric circles around it—one circle for each planet marked with its time of circumsolar rotation and its distance from the sun; the outermost circle, that of Saturn; the more remote planet, Uranus, not having been discovered until 1781; (5) overlapping eastern and western hemispheres, each showing the continents and main lines of latitude and longitude; (6) “The Sphere [Earth] projected on the Plane of the Meridian,” marked with the “Ecliptic or Zodiac” and degree numbers on the circumference and equator, as well as with the other lines of No. 5; (7) “The Sphere projected on the Plane of the Horizon,” marked similarly with No. 6, but with the North Pole in one hemisphere and the South Pole in the other located about halfway between the center and the circumference on the left; (8) “The Sphere projected on the plane of the Equinoctial [Equator],” similar to No. 7, except for the altered projection; (9) apparently an incomplete drawing, identical with No. 8 in its projection but designed to show the altered location of the “Ecliptic or Zodiac” when, in opposite fashion to that in No. 8, the South Pole is at the center of the hemisphere on the right rather than of the one on the left; (10) a diagram showing the sun in its effect upon the moon as the latter revolves about the earth; (11) seemingly an uncompleted tryout of No. 10; (12) merely eight squares of varying sizes—apparently an unsatisfactory start toward No. 13; (13) “A Square dra[wn] in Perspective,” with an indicated “Point of Sight” and “Point of Distance”; (14) “A Hexagon drawn in Perspective & Elevated [?],” with the two “points” of No. 13 also shown.
From what books, if any, JM derived these drawings or his ideas for them is not known. All of them, with the exception of No. 3, are similar to diagrams customarily found in eighteenth-century textbooks on geography, geometry, or astronomy. For this reason the subjects of the drawings, including the one of the sundial, are of but slight help in determining whether JM made them at Robertson’s school, at Montpelier, or at the College of New Jersey. From their elementary nature, as compared with that of “The Brief System of Logick,” they suggest exercises appropriate to Robertson’s classroom; and it is known that JM studied arithmetic, algebra, geometry, and geography there. Yet only two of the sketches could have been based upon illustrations in volumes owned by the schoolmaster—if the surviving list of them is complete.* The library at the College of New Jersey, on the other hand, could readily have supplied JM with the models needed to make these diagrams in his notebook.
Aristotle1 and after him the Scholastics have divided all Ideas into ten parts, which they call Predicaments2 or Categories. For they say every thing imaginable or concievable is either Substance, or Quality, or Quantity, or Relation, or Action, or Passion, or Place, or Time, or situation or Cloathing.3
Part 1st. Sect. 2nd.
Of the Signs of Ideas4
A Sign in general is a thing that gives notice of something different from itself. As the cause may signifie, that is, be a sign of the effect to follow: or vice versa. The effect may be the sign of the cause; as Smoak is the sign of fire: Or Concomitants may reciprocally be the signs of one another.
The signs or external marks of our internal Ideas, with which alone we are now concernd, are either Natural or Arbitrary and artificial.
The Natural signs are such as, smiling, Laughing, the indications of Joy; Dejection of countenance, weeping, wailing, the indications of Sorrow; paleness, trembling, the signs of Fear, Blushing the sign of Shame &c.
These being the Language of Nature, have been always the same with inconsiderable variation in every person, age, & Country. And by these an Acute Man may penetrate far into the most secret sentiments and affections of others: Notwithstanding Politicians and other cunning Men of Business, by great and refin’d dissimulation, have in great measure confounded and stifled the natural Indications of their inmost thoughts.
The arbitrary signs of Ideas have been invented & instituted by Men for the communication of their thoughts to one another, & discover their not being Natural but artificial by their being in various Countries and Ages, various and changeable.
The Brute creation have nothing but the Language of Nature, which is intelligible to all those of the same species; but being given only for necessary Uses, makes their conversation and correspondence very narrow and confin’d.
Men alone have contrived a more extensive communication of thoughts by inventing several Signs; which in[?] company have agreed to use & understand commonly as expressive of the same sentiments.
These signs are partly similar to the Ideas of the mind as pictures and the most ancient Hieroglyphycks, partly dismission, as words either spoken or written; which have no manner of resemblance to the Ideas which they are intended to represent.
Speech of all these Inventions, if it be an human invention, & not rather a divine Lesson, is by far the most excellent & has contributed chiefly to exalt the human species above the Brutes.
Universal Terms may denote, either a Metaphysical, a Physycal, or a Moral Universality.5
A Metaphysical or Mathematical Universality, admits of no exception. As, all Circles have a Center and circumferen[ce.]
A Physical or Natural Universality admits of some accidental and Praeternatural Exceptions. As, all men use words to express their thoughts, yet dumb Persons are excepted.
A Moral universality admits of many exceptions being a sort of Hyperbole, As all men are govern’d by affecti[ons] more than by reason. The Cretes are always Lyars.6 An universal term is sometimes taken collectively for all its particular Ideas united together; and sometimes distributively meaning each of them single and alone.
1. Collectively: as, all these Apples will fill a Busshel: all the Hours of the night are sufficient for Sleep: All the rules of Grammer overload the memory. In these Propositions it is evident, that the Predicate belongs not to the Individuals seperately, but to the whole collective Idea: for we cannot say, one Apple, or every Apple will fill a Busshel. &c. Wherefore such a Proposition is properly singular.
2. Distributively: when you may turn the word all into every: and the Predicate belongs to every Individual: which makes the Proposition truly and properly universal. As, all Men are mortal, which you may turn into every Man or any Individual Man is Mortal.
But of these Distributive Universals there are two kinds. For sometimes they include all the Individuals distributively; as, every sickness has a tendency to Death, i,e, Every individual Sickness.
Sometimes they are restricted to every Species or kind; As, every Disease was heal’d by Christ, i,e, every kind of Disease.7 The first of these is call’d by Logicians the Distribution of an universal in Singula generum, and the second in genera Singulorum.
Propositions are either Single or compound. Single Propositions are the same as categorical which have been explained already Vide. P. 37 &c.8
A compound Proposition is made up of two or more Subjects or Predicates, or both: and contains two or more single Propositions, explicit or implicit.
Of compound Propositions we shall recken up Eleven different sorts. In the first six, the composition is plain and express’d, in the others only implyed.
There9 is yet another Method of arguing remaining; call’d the Socratic from the celebrated Socrates, who employ’d it for the instruction of Scholars & company, & for the entrapping & confutation of the Sophists of his time. This manner was, when he intended to confute or convince any one, to introduce some Topick suitable to his Design, never to declare his own opinion but to ask Questions as if he desir’d instruction, having his mainpart in view, & wheeling the Stream of the Discourse Slyly to his Purpose; till at last by a sudden turn he surpriz’d his Opponent into sudden conviction or an absurdity. This is a very captitious & insiduous Method: for when you are [ac?]costed[?] in this manner, having no suspicion of an attack, or [at] least not knowing where the Push is to be made, you may expose yourself unwarily, & make such concessions as the Adversary will not fail to turn to his advantage. I own this Method may do very well between a Master & his Scholars: and so it was us’d among the Philosophers, whom their Scholars heard with reverence, and bore to be confuted without being offended. But to interrogate others in this manner is not well taken; and probably help’d to kindle & blow up that hatred against Socrates, which put a violent Period to his Life[.]
To exemplify this Method let us suppose a Dialogue between a Theist and an Atheist: imagine the Atheist to have returnd from his Travels & the Theist to accost him in the Socratic way as follows.
Theist. I would gladly know, Sir, what is [the] finest Place you have seen in your Travels.
Atheist. Why really Sir, the Place that most took up my fancy was the King of France’s Palace & Gardens at Versailles.
Athe. It far exceeded it. For till I saw it I could not imagine the greatness of the whole, the Symmetry of the Parts, the ornaments of architecture, the rich paintings, the magnificent furniture, especially the Pleasant Gardens, with their Statues, Canals & Jett-d’Eaux.
The. I suppose ingenious men of Taste find some defects & superfluities, which they themselves could supply or retrench.
Athe. It may be so. But these who laid & executed this Plan are deservedly admir’d for their ingenuity and Grand Taste.
The. No doubt they did their best: but it is possible it may be exceeded. If I should tell you of a Fabrick that for magnificence & Taste is ownd by Good Judges to be superior, what would you say?
Athe. I suppose you mean some old Roman building or St. Peters at Rome: There may be Heroes in architecture I suppose as well as in arms.
The. You Judge of the mind[,] the contrivance, the ability of the architect—by the greatness & ingenuity of his Work.
Athe. To be sure, to Judge of a man by his actions is the best way.
Athe. Aha, Sir, are you got upon the old Topic? I can make a difference between the works of art, & the necessary effects of Plastic nature.
This like every other argument, [is] easily reducible to regular Syllogisms.
There12 is no danger from plain and glaring Equivocations: But[,] however[,] the ambiguity of Words is the cause of the greatest controversies and perplexities: different People very often affixing very different Ideas to the same Words, and squabbling not about a disagreement of Sentiments but of Words. Therefore to avoid being impos’d upon or confuted by arguments of this fallacious kind, there is a necessity often to make nice distinctions, that is, to show nicely the ambiguity of Words and their various meanings: that you may discern in what Sense the Proposition is true, & in what it is false.13
These Sophisms are not so difficult to be detected either by Natural Sagacity or by the Rules of Logick, as it is hard to determine a Question in Oeconomy, Policy & other cases, where the arguments on both sides are weighty, Solid and far from being Sophistical. As it happen’d in the dispute [between] Cato the Censor, & Scipio Nasica:14 of whom the former was of opinion that Carthage should be destoy’d for the advantage and security of Rome: the latter insisted that to declare an irreconcileable War again[st] a People who had not given even a plausible pretence, was inconsistent with the Rules of Honour and Justice. In this dispute the arguments of Cato’s side were drawn ab Utili, and those of the other ab Honest[um] & it came to this issue, whether the Utile or the Honestum is to be preferr’d when they come in co[nflictio]n with one another. Wherefore if you fall into a controversy of this sort and your adversary has pr[o]ved his advice to be useful: Your business is not so much to confute his Argument, for perhaps that cannot be done, as to show the superiour [adv]antage or the Honour and Justice of your own opinion. And to be sure Honour and Justice should carry it against Utility, or a greater of Utility should carry against a lesser: for when there are Arguments in both Scales, the greater Weight must cast the Balance.
Of this Nature [was] the Question proposed by Rehoboan to his old & his Young Counsellers [whet]her he should answer the tumultuous People mildly or imperiously. The old Men recommended mildness & complyance, till the King having got into the Saddle might establish his full authority: The young men advis’d the contrary: because commonly Inferiours seeing their Govirnours timorous, are ready to encroach mo[re] and more. The Arguments are both good: but the circumstance of the occasion, & especially the event determin’d in favour of the Old Men.15
1. Extract from Part I, pp. 18–21 of “A Brief System of Logick.”
2. Madison probably should have written “predicates.” This word, in one form or another, recurs frequently in Aristotle’s “Categoriae” and “De Interpretatione,” upon which much in these notes was based. Thus, an English translation of lb, lines 10–16 of “Categoriae” runs: “When one thing is predicated of another, all that which is predicable of the predicate will be predicable also of the subject. Thus, ‘man’ is predicated of the individual man; but ‘animal’ is predicated of ‘man’; it will, therefore, be predicable of the individual man also: for the individual man is both ‘man’ and ‘animal’” (E. M. Edghill, ed., “Categoriae and De Interpretatione,” passim, in Vol. I of William D. Ross, general ed., The Works of Aristotle Translated into English [12 vols.; Oxford and London, 1908–52]).
3. This could have been taken from Watts, Logick, p. 25.
4. This excerpt shows clearly the influence of John Locke’s An Essay Concerning Human Understanding, first published at London in 1690. See Book II, chaps. x and xi, of this essay.
5. Extract from Part II, pp. 42–44 of “A Brief System of Logick.” Virtually this whole excerpt, except its last two paragraphs, is taken either verbatim or almost verbatim from Watts, Logick, pp. 149–53, 165–70.
6. Titus 1:12 (“The Cretans are always liars, evil beasts, slow bellies”). St. Paul, however, merely repeated a common opinion about the Cretans, found in Greek literature as far back, so it has been said, as Epimenides, ca. 600 b.c. See also The Histories of Polybius, VI, 472.
7. Matthew 4:23.
8. The excerpt here given is from “Sect. 2,” entitled “Of Proposition,” of “Part 2d,” of JM’s notes, headed “Of Judgment and Proposition.” On p. 37, and continuing on until the notes make junction with this excerpt, they discuss “categorical,” “hypothetical,” “singular,” and “universal” propositions.
9. Extract from Part III, pp. 95–98, of “A Brief System of Logick.”
10. Although in its brevity, quality, and conclusion, this dialogue hardly bears comparison with the dialogues led by Socrates, as reported by Plato, there is a faint echo of Socrates in “Phaedo,” stating, “I can not help thinking, if there be anything beautiful other than absolute beauty, should there be such, that it can be beautiful only in so far as it partakes of absolute beauty” (Irwin Edman, ed., Works of Plato [Modern Library Edition, 1928], p. 166). See also ibid., pp. 217–26, 290–94, 378–79, 434–35, 472–74.
11. Probably the instructor followed up this word by quoting one or both of two biblical passages, or Madison added this word to remind himself of them (“When I consider thy heavens,” etc. [Psalms 8:3–4], and “Consider the lilies of the field,” etc. [Matthew 6:28–29]).
12. Extract from Part III, pp. 121–22 of “A Brief System of Logick.”
13. It is possible rather than probable that the thought in this paragraph was derived from Locke, An Essay Concerning Human Understanding, Book III, chap. xi.
14. This dispute in about 150 b.c. between Marcus Cato and Publius Cornelius Scipio Nasica Corculum is mentioned by Plutarch in his “Marcus Cato” (A[rthur] H. Clough, ed., Dryden’s Translation of Plutarch’s Lives [4 vols.; New York, undated], II, 276).
15. I Kings 12:6–21. The “event” was the desertion of King Rehoboam by all the tribes of Israel, except Judah and Benjamin, because he heeded the advice of the “young men” to be a harsher ruler than had been his father, King Solomon.