An Introduction to the Untaught Cultivation of the Mind: Watt's Logic

Introduction

Below are my notes of Watt's texbook on logic, used in primary schools and eventually at Harvard, Oxford, Cabridge, and Yale for over 200 years. Watts defines logic as "the art of using Reason [all the intellectual powser of man] well in our inquiries after truth, and the communication of it to others" (1). He separates and explains from four points:

  1. Perception: the "simple contemplation of things offered to our mind, without affirming or denying any thing concerning them," resulting in an idea (5).
  2. Judgment: the operation joining "two or more ideas together by one affirmation or negation," resulting in a proposition (5).
  3. Reasoning (Argumentation): inferring one proposition from two or more propositions premised, resulting in a conclusion or inference (5).
  4. Disposition: putting "ideas, propositions, and arguments... into such an order as is fittest to gain the clearest knowedge of it, to retain it longest, and to explain it to others in the best manner," resulting in a method (6).
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Perception and Ideas

Watts declares that "all... knowledge... is founded upon our conceptions and ideas" (7). Perception is the "act of mind... whereby the mind becomes conscious of any thing" (8). An idea is the "representation of a thing in the mind... the object of perception," while conception is "forming an idea of the object whether present or absent" (7-8). The theme is the "object of our idea" and being is either as possible, "an essence or nature," or as actual, which "has existence also" (9-10). Essence is "the very nature of any being" while a substance exists "in and by itself..., without dependence upon any other created being... it cannot be annihilated, or utterly destroyed and reduced to nothing..., though its present particular form, nature and properties, may be altered and destroyed by many inferior causes" (10-1).

Simple substances "have no matter or composition in them... [or] are the first principles of bodies... of which all bodies are composed" - a synonym being an element which "cannot be resolved or reduced into two or more substances of different kinds" (14). Compound substances are "made up of two or more simple substances" (14). Animal (Animated) substances have "various organical and instrumental parts, fitted by a variety of motions from place to place, and a spring of life within themselves," while inanimate substances "have no sort of life in them" (15-6).

Mode (manner of being) "subsists in and by another" and "cannot subsist in and of itself, [always] belonging to, and subsisting by, the help of some substance [its subject],... and extends to all attributes whatsoever, and includes the most essential and inward properties, as well as outward respects and relations, and reaches to actions themselves, as well as matters of action" (10 & 16). Modes are essential when the "subject can never have the same nature without it" - in a primary sense if it is the "first or chief thing aht constitues any being in its particular essence or nature" or a property (in the secondary sense) if "any other attribute of a thing, which is not a primary consideration" - or an accident when "not necessary to the being of a thing" (17-8). This is determined by the essential difference, the "one property or essential attribute, so superior to the rest, that it appears so plainly that all the rest are derived from it, and such as is sufficient to give a full distinction of that subject from all other subjects... [where] the essence of the thing consists in it" (20). Absolute mode "belongs to its subject, without respect to any other beings whatsoever," realtive mode (relation) is "derived from the regard that one being has to others" - being either real as they "arise from the nature of things" or mental because "they arise merely from the operation of the mind," from second notions (entia rationis) which "have no real being but by the operations of the mind" (20-1). Modes can be intrisic "in the subject or substance" or extrinsic, arising "from something that is not in the substance or subject itself... something that is external or foreign to the subject" (21-2). Adherent (improper) modes "arise from the joining of some accidental substace to the chief subject, which yet may be separated from it" while inherent (proper) modes "have a sort of in-being in the substance itself, and do not arise from the addition of any other substance of it" (22). Action (doing) by an agent (doer) inflicts passion (suffering) with a patient, the "subject of passion... [and] receives the operation of the agent" (22). Modes of body (qualities), "belonging... to matter or corporeal beings," are primary, belonging "to bodies considered in themselves, whether there were any man to take notice of them or no," or secondary (sensible), "ideas... we ascribe to bodies on accound of the various impressions which are made on the senses of men by them" (23). Additionally, there are modes of spirit which include "mind... knowledge, assent, dissent, doubting, reasoning, &c" and mixed (human) modes such as "sensation, imagination, passion" (23).

"All comparative and superlative degrees of any quality, are the modes of a mode" (24). Aristotle had ten predicatments, categories, or ranks of being are: substances, quantity, quality, relation, action, passion, when, where, situation, and clothing (25). Not-being, defining pure nullity ('mere nothing') as "exclusing all substance, and then all modes," negation as the "absence of that which does not naturally belong to the thing we are speaking of," and privation as the "absence of what does naturally belong to the thing we are speaking of" (26). Will conlcuding the first two chapters, Watts states that the "essence of sincerity is the conformity of our words and actions to our thoughts" (26).

In chapter three, Watts covers ideas. Sensible (corporeal) ideas are "derived... from [the] senses, and... communication which the sould has with the animal body" (28). Spiritual (intellectual) ideas, framed by abstractions, are "withdrawing some parts of an idea from other parts of it" - either in an absolute (general / universal) sense such as "entity or being, and not-being, essence, existence, act, power, substance, mode, accident, &c" or relative sense which "compare several things together, and consider merely the relations of one thing to another, entirely dropping the subject of those relations... [as with] cause, effect, likeness, unlikeness, subject, object, identity, or sameness, and contrariety, order" (30-1). A simple idea is "one uniform idea, which cannot be divided or distinguished by the mind of man into two or more ideas" while a complex idea is "made by joining two or more simple ideas together... [including] every thing that can be divided by the mind into two or more ideas" (32-3). Compound ideas are made up of "several... ideas of a different kind joined together, which are wont to be considered as distinct single beings... [and] unites a thing of a different kind" while a collective idea unites "things of the same kind" (33-4). Particular ideas "represent one thing only" while a singular idea "represents a particular idea in a determinant manner... usually limited to one singular, certain, and determined object" (34). Universal ideas "represent a common nature agreeing to several particular things... [are] formed by abstraction... withdrawling some part of an idea from other parts of it" (34-5). Ideas can be categorized by general (genus) via "one common nature agreeing to several other natures" - remote genus being where "one thing agrees with most other things" - or special (species) via "one common nature... agrees to several singular species" (35-6). Subaltern ideas are universal ideas that "may either be considered as a genus or a species," where "the highest genus [is] the most general... [and] the lowest species... the most special" (36).

Real ideas "have a just foundation in nature, and have real objects, or examplars, which did, or do, or may actually exist, according to the present state and nature of things" while imaginary (fantastical / chimerical) ideas are "made by enlarging, diminishing, uniting, dividing real ideas in the mind, in such a manner as no objects or examplars did or ever will exist, according to the present course of nature" (37-8). A clear and distinct idea "represents the object of the mind with full evidence and strength, and plainly distinguishes it from all other objects whatsoever" while an obscure and confused idea "represents the object either so faintly, so imperfectly, or so mingled with other ieads, that the object of it doth not appear plain to the mind, nor purely in its own nature, nor sufficiently distinguised from other things" (38). A vulgar idea is "the most obvious and sensible appearances that are contained in the object of them" while a learned idea "penetrates farther into the nature, properties, reasons, causes, and effects of things" (40). Adequate ideas "perfectly represent their archetypes or objects," inadequate ideas only have a "partial or incomplete representation of those archetypes to which they are referred," complete ideas represent "the perfect idea of any thing in all its parts," and comprehensive ideas represent the perfect idea of any thing "in all its properties" (42).

The comprehension of an idea "regards all the essential modes and properties of it" while the extension of a universal idea "regards all the particular kinds and single beings taht are contained under it" (36-7). The prior explanation of ideas applies to the doctrine of universals, which says that "every thing that is affirmed concerning any being must be" one of the five predicatables: genus, species, difference (primary essential mode), property (secondary essential mode), or accident (accidental essential mode) (37). True ideas are "conformable to the object or archetype of it," else they are false (43). When ending chapter three, Watts warns that "generally, where there is falsehood in ideas, there seems to be some secret or latent proposition, whereby we judge falsely of things. ... [But] since ideas are pictures of thing, it can never be very improper to pronounce them to be true or false according to their conformity or nonconformity to their examplars" (44-5).

In the use of reasoning and judgement, it is essential to first define the words you use, understanding that words "have no natural connection with the ideas they are designed to signify, nor with the things which are represented in these ideas... [and] when single words signify complex ideas, one word can never distinctly manifest all the parts of a complex idea" (45). So, to "avoid error in our pursuit of knowledge, we must take good heed to the use of words and terms, and be acquainted with the various kinds of them" (51).

Negative terms "have a little word or syllable of denying joined to them" while positive terms "have no... negative appendices belonging to them" (51). A simple term is "one word while a complex term is "when more words are used to signify one thing" (53). Appelatives are "[c]ommon names [which] stand for universal ideas, or a whole rank of beings, whether general or special" (55-6). Terms can be abstract and "signify the mode or quality of a being, without any regard to the subject in which it is" or concrete and "express the quality, [but] also either express, or imply, or refer to some subject to which it belongs" (57). Univocal words "signify but one idea, or at least one sort of thing," equivocal words "signify two or more different ideas, or different sorts of objects," synonymous words "signify the same thing," and homonymous (ambiguous) words "signify several things" (57-8). Equivocation is the "use [of] ambiguous words, whith a design to deceive" and double entendres are "words used by wanton persons to convey lewd ideas, under the covert of expressions capable of a chaste meaning... or when persons speak falsehood with a design to deceive, under the covert of truth" (60-1). Words in their proper (literal) sense are "designed to signify those idea for which they were originally made, or to whom they are primarily and generally annexed" while words in their figurative (tropical) sense "are made to signify some things, which only bear either a reference or a resemblance to the primary ideas of them" (63). An anological word "originally signifies any particular idea or object, is attributed to several other objects, not so much by way of resemblance, but rather on the account of some evident feferene or a resemblance to the primary ideas of them" (63). Watts concludes chapter four advising:"where the design of the speaker or writer is merely to explain, to instruct, and to lead into the knowledge of naked truth, he ought, for the most part, to use plain and proper words, if the language affords them, and not to deal much in figurative speech" (64-5).

In chapter five, Watts gives some great life advice on relating ideas, calling readers to "furnish yourselves with a rich variety of ideas; acquaint yourselves with things ancient and modern; things natural, civil, and religious; things domestic and national; things of your native land, and of foreign countries; things present, past, and future; and above all, be well acquained with God and yourselves; learn animal nature, and the workings of your own spirits", pointing out, similarly to Feynman's red wine analogy, that "all sciences have a sort of mutual connection; and knowledge of all kinds fits the mind to reason and jduge better ocncerning any particular subject. ... Such a larger and general acquaintance with things will secure you from perpetual admirations and suprises, and guard you gainst that weakness of ignorant persons, who have never seen any thing beyond the confines of their own dwelling, and therefore they wonder at almost every thing they see; every thing beyond the smoke of their own chimney, and reach of their own windows, is new and strange to them. ... a universal acquaintance... will keep you grom being too positive and dogmatic, from an excess of credulity and unbelief, that is, a readiness to believe, or to deny, every thing at first hearing." The "way of attining such an etensive treasure of ideas is, with diligence to apply yourself to read the best books, converse with the most knowing and the wisest of men, and endeavor to improve by every person in whose company you are; suffer no hour to pass away in a lazy idleness, and impertinent chattering, or useless trifles; visit other cities and countries, when you ahve seen your own, under the care of one who can teach you to profit by traveling, and to make wise observations; indulge a little curiosity in seeing the wonders of art and nature; search into things yourself, as well as learn them from others; be acquainted with men as well as books; learn all things as much as you can at first hand; and let as many of your ideas as possible be the representation of things and not merely the representation of other men's ideas; thus your soul, like some noble building, shall be richly furnished with original paining, and not with mere copies" (70-1).

Use "the proper methods to retain that treasure of ideas which you have acquired; [especially those] most directly suited, either to your eternal welfare as a Christian, or to your particular stations and professions in life" by (71-4):

Most importantly, "learn to acquire a government over your ideas and your thoughts, that they may come when they are called and depart when they are bidden," acknowledging "we must be resolute and laborious, and sometimes conflict with ourselves, if we would be wise and learned," understanding "a student shall do more in one hour, when all things concur to invite him to his special study, tahn in four hours, at a dull and improper season" (75-6). Watts offers a reccomendation for those with ADHD tendencie: "If the natural genius and temper be too volatile, fickle, and wandering, such persons ought in a more especial manner to apply themselves to mathematical learning, and to begin their studies with arithmetic and geometry; wherein new truths, continually arising to the mind out of the plainest and easiest principles, will allure the thoughts with incredible pleasure in the pursuit: this will give the student such a delightful taste of reasoning, as will fix his attention to the single subject which he pursues, and by degrees will cure the habitual levity of this spirit." (76-7).

In chapter six, Watts commends us to concieve of things "clearly and distinclty in their own natures,... all of their parts,... comprehensively in all their properties and relations,... extensively in all their kinds,... [and] orderly,... in their proper method" (77-8).

  1. First, "get exact definitions of the words we make us of [and] determine precisely the sense of our words... never rest satisfied... with mere words which have not ideas belonging to them, nor at least in subtle and determinate ideas" (80-2).
  2. Second, one must distinguish "well between knowables and unknowables... [to] unclothe them of all these relations and mixtures, that we may contemplate them naked, and in their own natures, and ditinguish the subject that we have in view from all other subjects whatsoever" (79).
  3. Third, "in conversation or reading be diligent to find out the true sense, or distinct idea, which the speaker or writer affixes to his words; and especially to those words which are the chief subject of his discourse," which will aid in avoiding logomachies - "strifes and quarrels about names and words, and vain janglings" (90-1).
  4. Fourth, "When we communicate our notions to others, merely with a design to inform and improve their knowledge, let us, in the beginning of our discourse, take care to adjust the definition of names wheresoever there is need of it... determine plainly what we mean by the chief words wich are the subject of our discourse; and be sure always to keep the same ideas, whensoever we use the same words, unless we give due notice to the change. ...avoid ambiguous and equovocal terms as much as possible. ... Where your chief business is to inform the judgment, and to explain a matter, rather than to persuade or affect, be not fond of expressing yourselves, in figurative language, when there are any proper words that signify the same ideas in their literal sense. ... In communicating your notions, use every word as near as possible in the same sense in which mankind commonly uses it... when any word has been used to signify an idea, that old idea will recur to the mind, when the word is heard or read, rather than any new ideas which we may fasten to it[, so] the received definition of names should be changed as little as possible" (91-4).
    • In some cases, it may be "much easier to lead the word into truth by indulging their fondness for a phrase, and by assigning and applying new ideas and notions to their favorite word; and this is much safer aso than to awaken all their passions by rejection both of their old words, and prases, and notions, and introducing all new at once" (95-6).

Definition = genius + difference, the general and similar metaphorical plus what it makes special (99). Good definitions are (102-4):

  1. "universal [and] must agree to all the particular species or individuals that are included under the same idea"
  2. "proper and particular to the thing define and agree to that alone"
  3. "clear and plain"
  4. "short [with] no tautology [or superfluity"
  5. not circular - "neither the thing defined, nor a synonymous name, should make any part of the definition"
When looking for a definition, if "we cannot find out the essence or essential difference of any species or kinds of being that we would define, we must contend ourselves with a collection of such chief parts or properties of it, as may best explain it so far as it is known, and best distinguish it from other things" (108). A nominal essence (definition) is "[defined] by a collection of those properties, which according to our observations, distinguishes them from all other things" while an imperfect definition (description) is "made up of a mere collection of the most remakrable parts or properties" - a perfect description is "composed of the essential differenced added to the general nature or genus" (109).

"If the particular essences of natural bodies are unknown to us, we may yet be good philosophers, good artists, good neighbors, good subjects, and good Christians, without that knoweldge; and we have just reason to be content" but we should still "concieve of things completely in all their parts [where all] parts have a reference to some whole (111-3). Watts defines four wholes:

"Since our minds are narrow in their capacities, and cannot survey the several parts of any complex being with one single view,... we must as it were take it to pieces, and consider the parts taken separately, taht we may have a more complete conception of the whole" (115). The division of an idea is "en explication of the [integral] whole into several parts," the partition the "property [which] comes under this part of the doctrine of integral division," and the subdivision when "any of the parts of an idea are yet farther divided, in order to a clear explication of the whole" (115-6). The rules of good division are (116-9):

  1. "Each part singly taken must contin less than the whole, but all parts taken collectivly... must contain neither more nor less than the whole... [and thus] it is necessary to examine the whole idea with diligence."
  2. "First consider the larger and more immediate parts of the subject, and not divide it at once into the more minute and remote parts."
  3. "The several parts of a division ought to be opposite [where] one part [does] not contain another."
  4. Don't have uncessary divisions.
  5. "Let the parts of your division be... distinguised in nature. Do not divide asuner those parts of the idea which are intimately united in nature, nor unite those things in one part which nature has evidently disjoined."

Again, "our minds are narrow and scanty in their capacities; and as they are not able to consider all the parts of a complex idea at once, so neither can they at once contemplate all the different attributes and circumstances of it: we must therefore consider things successivly and gradually in their various parts" (120). To gain a comprehnesive view of an idea: "first consider whether the object of it has an existence as well as an essence;... [if it is] simple or complex... a substance or mode: if it be a substance... [find] the essentail modes of it... [and] properties or accidents of it... its internal and absolute modes... its powers and capacities... [and] trace it up to its various causes, whether supreme or subordinate. ... If [it] be a mere mode, we must inquire whetehr it belongs to spirits or bodies... physical or moral mode: if moral... consider its realtion to God, ourselves, to our neighbors.... If virtue, [seek] the principles... the rules of it. ... If historical... whether the action was done at all... in such a manner or by such a person as is reported" (121-2). Use abstraction to "consider each single relation or property of the subject alone, and thus... withdraw and separate it in our minds both from the subject itself, as well as from other properties and relations, in order to make a fuller observation of it," either in a precisive manner "consider[ing] those things apart which cannot really exist apart" or negatively "consider[ing] one thing separate from another, which may also exist without it" (123). After concieving "of things in all of their extension," concieve of them in all their distribution - "several kinds of species [of a universal whole]" (124).

For definition, "concieve of it in completion, or survey the several parts that compose it... consider it comprehensively in its various properties... take cognizance of the various kinds of it [having] an extensive conception of it" (131-2). "The design of logic is not to furnish us with teh perceiving faculty, but only to direct and assist us in the use of it: it doth not give us the objects of our ideas, but only casts such a light on those objects which nature furnishes us with, that they may be the more clearly and distinctly known: it doth noth add anew parts or properties to things, but it discovers the various parts, properties, relations, and dependences of one thing upon another; and by ranking all things under general and special heads, it renders the nature, or any of the properties, powers, and uses of a thing, more ready to be found out, when we seek in what rank of being it lies, and wherein it agrees with, and wherein it differs from others" (133).

Judgment and Proposition

An idea is the "result of ourconcpetions or apprehension" and judgment is the act of mind which works "to compare... ideas together, and to join them by affirmation, or disjoin them by negation, according as we find them to agree or disagree... when mere ideas are joined in the mind without words" (137-9). A proposition is the "effect of judgement... a sentence wherein two or more ideas or terms are joined or disjoined by one affirmation or negation... where mree ideas are joined to the mind... clothed with words" (138-9). The subject (of proposition) is "that concerning which any thing is affirmed or denied" while the predicate is "that which is affirmed or denied of the subject" (139). The matter (of a proposition) is "the subject and predicate... taken together" while the copula is "the form of a proposition [which] represents the act of the mind affirming or denying, and it is expressed by [the words] am, art, is, are, &c or am not, art not, is not, are not, &c" (139).

An identical proposition is a "subject is taken according to th whole of its extension... [ex:] no man is amightly" while a particular proposition is a "subject... not taken according to its whole extension... when the term is limited and restrained to some one or more of those species or individuals whose general nature it expresses, but reaches not to all... [ex:] few men are truly wise" (142). In a singular proposition, "the subject is a singular or individual term or idea... [ex:] Descartes was an ingenious philosopher... The subject here must be taken according to the whole extension, because being an individual it can extend only to one, and it must therefore be regulated by the laws of universal propositions" (142). For an indefinite proposition, "no note, either of universality or particularity, is prefixed to a subject which is in its own nature general... [ex:] angels are noble creatures" (143).

Watts divides universality similarly to how he divides wholes (143-5):

  1. Metaphysical (mathematical): "when all the particulars contained under any general idea have the same predicate belonging to them, without any exception whatsoever; or when the predicate is so essential to the universal subject, that it destroys the very nature of the subject to be without it... [ex:] all circles ahve a center and circumference."
  2. Physical (natural): "when, according to the order and common course of nature, a predicate agrees to all the subjects of that kind... [ex:] all men use words to express their thoughts, yet dumb persons are excepted, for they cannot speak."
  3. Moral: "when the predicate agrees to the greatest part of the particulars which are contained under the universal subject... [ex:] the Crtes are always liars."
  4. Collective: "the predicate belongs not to the individuals separately, but to the whole collective idea... [with] all its particular ideas united together... [ex:] all these apples will fill a bushel."
  5. Distributive: "will allow the word all to be changed into every, or into one... sometimes it includes all the individuals contained in its inferior speices [and] sometimes it concludes no more than merely each species or kind."

In an affirmative proposition, "the idea of the predicate is supposed to agree to the idea of the subject, and is joined to it by the word is or are, which are copula... [again, where] we assert one thing to elong to another,... unit[ing] them in thought and word," while a negative proposition separates "one thing from another, and [denies] their agreement" (150). Note: a "proposition, according to its quantity, is... universal or particular;... [and] according to its quality,... affirmative or negative. Propositions are opposite when "that which is deined in one is affimred in the other, either in whole or in part," contradictory when they "differ both in quantity and quality," contraries when "two universals differ in quality," and subcontraries when "two particular propositions differ in quality" (153). Subaltern are "particular and universal propositions, which agree in quality but not in quantity" (153). This is sometimes represented in logical notation by 'AEIO,' representing universal affirmative (A) and negative (E) as well as particular affirmative (I) and negative (O) (152). Propositions can be convertedwhen the "subject and predicate is a nominal or real definition of the subject, or the difference of it, or a property of the fourth kind, or a superlative degree of any property or quality whatsoever, or... wheresoever the predicate and the subject have exactly the same extension or the same comprehension... [which] are properly convertible" (154-5). Pure propositions "merely expresses that the predicate is connected with the subject" while a modal proposition "includes also the way and manner wherein the predicate is connected with the subject" - via necessity, contingency, possibility, and impossibility (155-6).

Watts advises to "gain a just and precise idea of every universal, particular, and indefinite expression [and] not only consider the particular idiom of the language, but the time, the place, the occasion, the circumstances of the matter spoken of, and thus penetrate as far as possible into the design of the speaker or writer" (150). Addtionally, "attend the entire comprehension of our ideas, and to the universal extension of them, as far as we have proper capacity for it before we grow too confident in our affirming or denying any thing, which may have the least darkness, doubt, or difficulty attending it: it is the want of that attention that betrays us into many mistakes" (152).

Reason and Syllogism

Disposition and Method

Finishing key takeaway from the book