Front Page Titles (by Subject) A Compend of Logic - Logic, Metaphysics, and the Natural Sociability of Mankind
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A Compend of Logic - Francis Hutcheson, Logic, Metaphysics, and the Natural Sociability of Mankind 
Logic, Metaphysics, and the Natural Sociability of Mankind, ed. James Moore and Michael Silverthorne, texts translated from the Latin by Michael Silverthorne, introduction by James Moore (Indianapolis: Liberty Fund, 2006).
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A Compend of Logic
To which is prefixed a Dissertation On the Origin of Philosophy And Its Principal Founders and Exponents
At the University
Typeset by Robert and Andrew Foulis
Printers to the University
Dissertation on the Origin of Philosophy and Its Principal Founders and Exponents1
Philosophy is the knowledge of the true and the good which men build for themselves by the powers of their own reason. Therefore we are not concerned here with the knowledge of things which has been available to men from the earliest days and which was passed down through the generations from divine revelation.
Philosophy was either barbarian or Greek. There seems to have been a considerable amount of barbarian philosophy among the Egyptians, the Chaldeans, and the Indians, but little evidence remains.2 The study of geometry, astronomy, theology, ethics, and politics flourished among them.
The earliest authors of Greek philosophy after the poets, whose philosophy is not at all certain, were Thales of Miletus and Pythagoras, unless both of them perhaps were pupils of Pherecydes of Syros.3 They lived at least 550 years before the birth of Christ. Pythagoras founded the Sicilian sect, and Thales founded the Ionian sect about the beginning of Cyrus’s reign, before the return of the Jews from Babylon to their homeland.
I. The Italian Sect.4 Pythagoras developed geometry, arithmetic, astronomy, music, ethics, and theology. He wished to be called not wise (sophos) but a lover of wisdom (philosophos). His modesty in this has been imitated by all subsequent students of wisdom. At Croton in Italy he started a school or community. He taught that there is one supreme God, who is of a nature or substance different from matter, and he believed that men’s minds are also of this nature. By his teaching and example he commended the highest piety toward God and goodness toward men, as well as a temperance which would liberate men’s minds from the chains of the body. This school flourished for a long time among the Italians and the Greeks. Pythagoras’s successor was his son, Telauges; then Empedocles, the inventor of rhetoric; and Xenophanes; and after these, Parmenides and Leucippus. Following them came Zeno of Elea in Italy, the inventor of dialectic; Socrates was his pupil who approved the practice of arguing by questions after his example. From this school came also Democritus and Heraclitus.
II. The Ionian Sect. Thales opened a school at Miletus. Little evidence remains of him, but his successors were Anaximander, Anaximenes, Anaxagoras, and Archelaus, the last of whom is famous for his disciple Socrates.5 They particularly cultivated geometry, astronomy and the whole of physics. The rest are more unsympathetic to religion, but the excellent Anaxagoras, who was called “the Mind,” held that the whole frame and structure of the world was made by the divine mind and reason.
III. The restorer or founder of true philosophy was Socrates, born at Athens to his father Sophroniscus in the time of Darius Nothus, in the period before Philip of Macedon in human reckoning, and four centuries before the birth of Christ. This truly divine man turned his penetrating mind away from corporeal and hidden things, which contribute little to a happy life, and gave himself completely to the cultivation of true piety and the knowledge of God, and to every virtue. Particularly conversant with ethics, politics, and economics, he taught that the minds of men are immortal and that their excellence consists in being as like to God as possible, and that after death men will be happy or miserable according as they have given themselves in this life to virtue or to vice.6
IV. His disciples founded various sects.7
1. Aristippus, who was very different from his master, held that the highest good lies in the pleasure of the body. He started the Cyrenaic school in Egypt; his daughter Arete succeeded him, and she was followed by Aristippus Metrodidaktos, and then by Antipater, Theodorus the atheist, Epitemides, and some others who made many innovations, especially Hegesias.
2. Phaedo, the founder of the Elean sect, taught that virtue is the sole good. He too had a number of successors,
3. Euclides, to whom we owe the Megarian sect, which was the most contentious of all, because it was solely dedicated to dialectic, as a result of which they are called the “wranglers” and “dialecticians.”8
4. Antisthenes opened his school near the gates of the city, in a Gymnasium at Cynosarges, and it is because of this, and not because of their morals, that they are called Cynics.9 His successors were Diogenes the Cynic and Crates of Thebes; everyone knows of their harsh and boorish style of life. Zeno of Citium in Cyprus was a pupil of Crates; later in life he taught in the Stoa (“Porch”) of Pisianax, and so gave the Stoics their name.10 The Stoics developed logic in their own way; in ethics and politics they really followed Socrates, but with some change of terms. Notable Stoics include Cleanthes and Chrysippus. Epicurus flourished in the time of Zeno the Stoic, about 250 years before the birth of Christ. He started a new school; in ethics he agreed with Aristippus, though he coined new terms to avoid jealousy, while in physics he followed Democritus. His successors were Hermachus, Polystratus, and others.11
5. Most eminent among the pupils of Socrates is Plato of Athens, a man of altogether divine genius, who has no rivals in the cultivation of every elegance; he founded the Old Academy.
V. The Old, the Middle, and the New Academy. Plato and Xenophon, who were very worthy pupils of their master Socrates made outstanding advances in theology, ethics, and politics. The pupils of Plato were called Academics from the charming park of a certain Academus in which they used to hold their discussions. The successors of Plato were Speusippus, Xenocrates, Polemo, Crantor, Crates, Arcesilaus (the founder of the Middle Academy, which differed from the Old Academy only in logic, that is, over the limitations of the human understanding in discovering truth), Lasydes, Evander, Egesinus, and Carneades, the father of the New Academy, which veered more toward the Skeptics; he was succeeded by Clitomachus and others.12
VI. The Peripatetics. Outstanding among the disciples of Plato was Aristotle, who was born at Stagira, a town of Macedonia, and was given charge of the education of Alexander the Great. Because he opened his school in the Peripatos, or covered walk, of the Lyceum, his followers are called the Peripatetics. They differed very little from Plato in ethics or theology, but were rather more distinct in metaphysics and politics. Aristotle wrote famous books over virtually the whole range of philosophy, and constructed the entire system of the art of logic with supreme skill. He was succeeded by Tyrtamus, to whom he gave the name of Theophrastus because of his godlike eloquence. His successors were Strato, Lyco, Aristo, Critolaus, Diodorus,13 and others; the eleventh in succession from Aristotle was Andronicus of Rhodes, who arranged the books of the philosopher in the order in which we now have them; in his time Cicero’s son was a student of Cratippus at Athens. In the period immediately following Aristotle there flourished Pyrrho, the father of the Skeptics, an assailant of all philosophy, who taught that all things are equally unknown and uncertain.14
VII. About 140 flourished Galen, the first of the commentators. The floruit of Porphyrius is 325. In 525 Boethius was born: he was the first to translate Aristotle’s Logic into Latin. 614: John Philoponus the grammarian. 800: John of Damascus. 1000: Eustathius and Eustratius. 1100: Michael of Ephesus and Michael Psellus. 1200: George Pachymerus. In these same times the Arabs Alfarabius, Avicenna, and Averroes won a great reputation. Then followed the age of the Scholastics, whose thorny and uncouth philosophy retained its influence until 1453, when after the capture of Constantinople by the Turks, the literary heritage of the Greeks was brought over to the West.15
VIII. The Eclectics.16 Although the best of the ancients, Pythagoras, Socrates, Plato, Aristotle, etc., are rightly included among the Eclectics because they were not enslaved to any master but adopted the views that seemed to them to be closest to the truth, the term “eclectic” was especially given to those who, after the formation of the different schools, refused to join any one of them. We note Potamon of Egypt, who flourished about the time of Augustus and was imitated by the philosophers of Alexandria, though they leaned more toward the views of Plato; some of them were pagan, others Christian. [They include] from the third and fourth centuries, Ammonius, Plotinus, Clement of Alexandria, Origen, Porphyry, Iamblichus, Syrianus, and Olympiodorus. With the revival of humane letters in the West, philosophy too was improved, especially through the strenuous efforts of those who have earned the gratitude of the human race by editing and interpreting the books of the ancients. With great acclaim, however, [moderns] have pointed out or entered upon a new road: in physics, Bacon, Descartes, Kepler, Galileo, and Newton; in ethics Grotius, Cumberland, and Pufendorf (for it was the Old Academy that was revived by Mirandula, Ficino, and the Earl of Shaftesbury); and Locke in logic and metaphysics.
Prolegomena The Definitions and Divisions of Logic
A faculty (habitus) is a more or less efficacious ability (facultas) to act, formed by repeated actions. Faculties are either intellectual or moral: the former strengthen and perfect the powers of the intellect, the latter the powers of the will.
There are five distinct names (they are not distinct kinds) given to our intellectual faculties: intelligence, wisdom, prudence, science, and skill, which in Greek are: nous, sophia, phronesis, episteme, techne.1 Intelligence is the faculty of first principles. Wisdom is knowledge of the most excellent things. Prudence is the faculty of acting with right reason. Science is the faculty of demonstration. Skill is the faculty of producing things with right reason. Philosophy is the whole bundle of these liberal arts, and is commonly defined as “acquisition of the knowledge (cognitio) of human and divine things, which we pursue by the sole power of human reason.” Philosophy is frequently divided into rational philosophy (or logic), natural philosophy, and moral philosophy.2 Logic is the art which directs the mind in its acquisition of knowledge of things, and may also be called science (scientia).3 Others define it as “the art of investigating and expressing truth.”4 The material object of any skill or science is the material which it treats. The formal object is the reason or purpose of treating it. The material object of logic is the intellectual operations. The formal object is to be directed to the discovery of truth. There are two natural faculties of the mind, the understanding and the will. The understanding is the faculty (facultas) which is concerned with getting to know the truth. The will is the faculty (facultas) which seeks good and avoids evil.5
There are three classes of operations in the intellect: (1) apprehension, (2) judgment, and (3) discourse; a twofold division into apprehension and judgment is also possible. Judgments are subdivided into noetic and dianoetic judgments. Hence logic is divided into three parts, defined by the kind of operation each is dealing with.6
On the Divisions of Apprehension
Apprehension is also called perception, concept, notion, intention,1 and idea; the word which signifies it is called a term.
Apprehension is a bare representation of a thing without any opinion (sententia) of the mind, and is either noncomplex, for instance pen, or complex, for instance, pen in the hand.
Judgment is an act of the mind by which it forms an opinion about two ideas. The sign [of a judgment] is a proposition or expression, which is an utterance that affirms or denies something of something; it is also called predication.
Discourse is an act of the mind by which from two or more judgments a third is inferred.
1. Ideas are divided into sensations, imaginations, and pure intellections.2
Sensation is twofold, external and internal. External sensation is “the perception of a corporeal thing impacting the organs of the body.”
Imagination is “the idea of a corporeal thing which is not impacting the body.”
A pure intellection is “any idea which is not reached or grasped by any of the bodily senses.” By intellection we not only discern things which are different from body as well as their modes, but we also attain more accurate ideas of numbers and of shapes which have several parts than those which the senses provide.3
The powers of bodies to excite ideas of “colors, sounds, smells, tastes, heat and cold” are called secondary qualities, or qualities which are sensible in the proper sense that we perceive each of them only by a single sense. Things which are perceived by more than one sense, by both sight and touch, for example, such as extension, figure, position, motion and rest, are primary and true qualities of bodies; hence they have the power to excite ideas of secondary qualities to which there is nothing corresponding in the bodies themselves. There are also two ideas which can be perceived both by internal and by external sense, and these are duration and number.
2. Imagination calls up a rather weak idea of a thing that had been formerly perceived by sense. And the mind can form only images whose elements have all been perceived by sense.
3. There is also an internal sense which above all furnishes pure intellections; this is called consciousness (conscientia) or the power of reflection. This sense affects all the actions, passions, and modes of the mind: namely, judgment, discourse, certainty, doubt, joy, sorrow, desires, aversions, love and hatred, virtues, vices. The more precise and abstract ideas of primary qualities are also attributed to pure intellections. But in truth all ideas arise from reflection or from [an] external sense.4
1. Ideas are either clear or obscure: a clear idea is one which “vividly affects the mind”; an obscure idea is one which affects the mind faintly.
2. Ideas may be proper [ideas] and truly depict the thing put before it or at least represent the appearance (speciem) which nature commonly intended; or they may be analogical [ideas] and exhibit a kind of general and imperfect impression of a thing, not as it is in itself or as it is represented in the common order of nature, but by a kind of analogy with other, very different things which are known by proper ideas. Those who have the use of sight have a proper idea of sight; a blind man has an analogous idea, but he does still have some kind of useful notion of this faculty.
3. Ideas are either simple or complex; a simple idea is a kind of uniform representation not made up of parts that are different from each other.
A complex idea is one “which is made up of dissimilar parts into which it can also be resolved.”
The idea of being is the simplest [idea]; ideas of secondary qualities are also mostly simple, as well as abstract ideas of certain modes of thinking.
4. In respect of their names, ideas are either distinct or confused. A distinct idea is one “which is easily told apart from others.” A confused idea is one “which is not easily told apart from others from which it is thought to be different.”
But perhaps more correctly the name itself or the term which denotes the idea is said to be distinct “when a known and certain complex of ideas is bound together by a name which cannot be altered without our being aware of it”; it is confused when “that complex is not sufficiently certain, so that something may at some point be added or removed [from it] without our noticing.”
5. In respect of their objects, ideas are either of substances or of modes, or of substances together with their modes. A substance is “a being subsisting in itself.” A mode is “a being which inheres in another [being].”
6. Ideas likewise may be real (or true), or they may be fictitious. Real ideas are “ideas which have corresponding objects,” or [ideas] which arise from natural causes following the order of nature. Fictitious [ideas] are “arbitrary conjunctions of ideas not drawn from true things.”
7. Ideas are either adequate or inadequate. Adequate ideas are those “which represent the whole nature of an object,” or at least all of it that we want to conceive in our minds. Such are the complex or combined ideas of modes which the mind assembles in an arbitrary fashion without referring them to an external model; also ideas of modes of thinking or of states of mind. Our ideas of substances are all inadequate.
Abstraction is “the act of the mind by which it directs itself to one or some of the ideas which are contained in a complex [idea] and ignores the rest.” Abstract ideas are ideas which are denoted by names or symbols that signify several things that are similar to each other but which also have some evident differences.6
After the mind has observed a variety of things that give rise to various complex ideas, and has seen that they are alike in certain qualities and unlike in others, it forms a universal idea by abstracting itself from the points in which they differ, while retaining the ideas of the points in which they are alike, and by denoting them with a specific name. This is how the eighth distinction between ideas arises, that some are universal and others singular.
A singular idea is an idea “which is intended to represent one thing alone” and is denoted either by a proper noun, like Alexander the Great, or by a common noun applied to one man, for example, this man or that man.
A universal idea is an idea “which is suitable for representing several things individually” whose sign (which is a common noun) can be predicated distributively of individuals, as man [can be predicated] of Peter, Paul, etc.
Nouns which denote a collection [of things], or one thing which is an aggregate of several things, are not properly predicated of individuals and often denote singular complex ideas. Examples are the city of Rome, Alexander’s army, the human race, the world.
Complex ideas are said to have comprehension, which “is a collection of all the simpler ideas which are combined in the complex,” for example, in animal [are contained the ideas of] body, living, and sentient.
Universal ideas are said to have extension, or quantity, which is “a collection of objects which an idea can represent, or [objects] the word for which is predicable individually.”
From what has been said about abstraction, it will be clear that the greater the extension, the less the comprehension, and vice versa.
A universal idea or predicable word has five species: genus, species, differentia, property, and accident.8 They are defined with regard either to ideas or to terms as follows:
With respect to ideas
1. A genus is a universal idea representing an object as a thing, which extends to other universal ideas.
2. A species is “a universal idea representing a thing, which is subordinate to a more general idea,” or [an idea] which applies only to individual things.
With respect to terms
1. A genus is a [word] predicable of several things which differ in kind (specie) in some respect (in quid) “or as a material part of the essence, as animal of man and brute.”
2. A species is “a [word] predicable of several things which are numerically different in some respect (in quid ),” or as the total essence, as man [is predicable] of Peter and Paul.
The highest genus is [the genus] “which does not have a more general genus above it,” for example, being. A subaltern is one “which can be a species with respect to a more general [genus].”
The lowest species is [the species] “which covers individuals alone”; a subaltern species can be a genus.
3. A differentia is “a universal idea which represents a thing modified by an essential primary attribute,” i.e., [an idea] which divides a genus into species, and combines with a genus to constitute a species.
4. A property is the “universal idea of a thing modified by an essential secondary attribute,” that is, [an attribute] which is contained in the idea of the thing not formally but as a consequence; for instance, being subject to law is a property of man.
5. An accident is “the universal idea of a thing modified by a true/true mode,” that is, [a mode] which may be either present or absent.
3. A differentia is “a [word] predicable of several things that differ in species or number, in respect of some quality (in Quale Quid )” or as a formal part of the essence; for when it is added to a genus it completes the essence of a species and its definition.
4. A property is “a [word] predicable of several things in respect of a quality necessarily” (in Quale necessario), that is, [an attribute] which belongs to this species, and only this species, and the whole of this species, at all times, or as bound up with its essence.
5. An accident is “a [word] predicable of several things in respect of a quality contingently” (in Quale contingenter).
A genus is said to be a logical whole or universal with respect to its species which are logical parts in the division of it. On the other hand a species is said to be a metaphysical whole, with respect to its genus and its differentia, which are metaphysical parts of its essence, but is said to be a physical whole with respect to its integrating parts. For example, (1) animal is the logical whole with respect to man and the brutes; (2) man is the metaphysical whole, or formal [whole], with respect to that which is animal and rational; (3) man is the physical or integral whole with respect to body and soul. The human body is also the integral whole with respect to head, chest, abdomen, limbs, etc., which are the integrating parts.9
N.B. Abstract, absolute, or denominating names of true modes, as well as abstract ideas themselves, may be either genera or species when they represent objects as things, without any distinct or direct idea of the subject, for instance, justice, virtue, and their opposites; true substances regarded as appendices of other things, and their concrete and connotative names, may be differentiae, properties, or accidents, for example, golden, silvery, clothed, shod.
A logical whole, or the extension of an idea, is expressed by a division, which is “the enumeration of the several things contained in the extension of a common idea or name.” These are its rules:
1. “The parts should be so distinct that no single one contains within its own [extension] the extension or part of the extension of another [part].”
2. “The division should be made into the species immediately below.”
3. “The parts should exhaust the thing divided”; or the division should be adequate.
A metaphysical whole, or the comprehension of a complex idea, is expressed by a definition, which is “a statement which explicates the simpler ideas that are combined in a complex [idea].” There are other definitions which are improper, for instance, nominal [definition], which explicates a word, as coelum (“sky”), which is from [Greek] koilon (“hollow”). There is also accidental definition, which explicates modes, causes [and] effects. For example, man is an animal which is featherless, biped, erect, etc.; this constitutes a description. [And] there is physical definition, which explicates natural parts; for instance, man is an animal consisting of an organic body and a soul endowed with reason.
The rules [of definition] are:
1. “Definitions should be short.”
2. “They should be clear.”
3. “They should be adequate,” so that they may be reciprocating, i.e., so that the definition and the thing defined may be mutually predicated of each other distributively.
4. “Avoid metaphors.”
5. “They should consist of the nearest genus and the proper differentia.”10
Categories or predicaments are “a series of ideas or terms arranged by degrees (gradatim) under the same highest genus.” Different authorities give different categories. For Aristotle there are ten: substance, quantity, quality, relation, action, passion, place, time, position, and state.11 He means that every predication or affirmation may be reduced to one of these. If we explain one, the rest will be understood.
These are the substances:12
Hence also that of which something is affirmed or denied in any category should be called a subject.
A term is “a name which signifies an idea or a thing, and which can be the subject or predicate of a proposition”; hence it is called a predicable (categorema).
Other components of terms are jointly predicable (syncategoremata), such as all, no. Some are mixed, such as always, i.e., in all time; no one, i.e., no man; [he] runs, [he] is running.13
An intention of signifying, or the understanding (acceptio) of a word, is called a suppositio. When it stands for an idea or a thing, it is called a formal suppositio; when it stands for the uttered word itself, it is called a material suppositio.
An example of the former is saying, Man is an animal; an example of the latter is, Man is a monosyllable. In a formal suppositio, the name is sometimes of the first intention, or of personal supposition, that is, in a normal act of understanding (acceptio): as in the phrase, Man is an animal. Otherwise it is of the second intention, or of simple suppositio for the idea or the term, that is, when a term of art (aliquid artificiale) is used of the same thing, for example, Man is a species.14
The divisions of terms into universal and singular, abstract and concrete, are evident from the divisions of ideas.
A transcendent term is one which belongs to every real thing, such as being, thing, one, something. A supertranscendent term is one which also belongs to fictions, such as imaginable, possible. All other terms are non-transcendental.
Every term where “not” is absent is finite; where the particle “not” is present, it is infinite, as in not-man, not-learned. “Not” is said to be infinitans. Finite and infinite [terms] together comprehend every being disjunctively: every being is either learned or not-learned, and so on; they exaust the whole range of being.
A univocal term is “predicable of several things individually according to the same idea,” as animal [is predicable] of man and of beast.
An equivocal term is “predicable of several things individually according to different ideas,” like Gallus. “Where there is some underlying reason for it or affinity of meaning,” a term is said to be analogous or deliberately equivocal, as [when] healthy [is predicated] of animal and of food, or Alexander of a man and of a picture. When there is no reason, it is said to be equivocal by chance, like Gallus or (in English) canon.15
Compatible terms may be predicated of one and the same thing at the same time, like strong and pious; they are often disparate.
Conflicting or opposed terms [are those] which “cannot be predicated of each other, nor of the same thing, in the same respect, and at the same time.” This opposition of terms is noncomplex; the opposition of propositions, on the other hand, is said to be complex.16
There are four species of noncomplex opposition: contrary, contradictory, relatively opposed, and privatively opposed. Disparates do not conflict ( pugnant), for they are “terms denoting ideas in which there is very little or nothing in common, beyond the vague idea of being or of mode,” as in brave and tall or sweet and white.
Contraries are “true opposed qualities,” such as pain and pleasure.
Contradictories are “a word and its negation,” such as learned and not-learned or man and not-man.
Relatively opposed are relative terms, such as father and son.
Privatively opposed are “a quality and its absence in a subject which has the capacity for it,” as in sighted and blind in the case of an animal.
Negatively opposed are “a quality and its absence in any kind of subject,” as in sighted and nonsighted, which are also contradictories.
On the Noetic Judgment and the Proposition
A judgment is “an action of the mind by which it gives a verdict on two ideas in comparison with each other.” That is, a verdict is given that either the ideas represent the same object, or a certain relation or connection exists between their objects.1
A noetic judgment is “when a verdict is given about ideas which are being directly compared with each other.”
A dianoetic judgment is “a verdict of the mind about two ideas, by means of comparison of both with a third.”2
A proposition is “a statement which expresses a noetic judgment.” There are three parts to it: subject, predicate, and copula.
The subject is “that about which something is affirmed or denied.” The predicate is “that which is affirmed or denied.” The copula is the logical verb (verbum), is or is-not.
N.B. Subjects and predicates are distinguished not by their position but by the sequence of speech. These three parts are always present, either explicitly or suppressed and implied: for example, curro [“I-run”] = ego sum currens [“I am running”].
In respect of their internal form or quality, propositions, like judgments, are either affimative or negative.3
In respect of their content, propositions are either true or false. Every [proposition] is either true or false; no [proposition] is both true and false; and there are no [propositions] which change from true to false, if we look at the judgment itself and not at the words. Those which seem to be both true and false are double or denote two judgments. Those which seem to change are likewise double; this is obvious from the nature of the word, which is “a word which implies time.” Hence, when the same words are uttered at different times, they sometimes give rise to quite different propositions.
Logical truth is “the agreement (convenientia) of the signs with the things signified.” Moral truth is “the agreement of the signs with the sense of the mind”; it belongs to the ethical forum.
With regard to quantity, propositions are universal, particular, singular, or indefinite.
1. A universal proposition is “when the subject is a universal term in its whole extension,” or is distributed.
2. A particular proposition is one “whose common subject is restricted to a part of its extension,” or is not distributed.
The marks of distribution or universality are all, no, each, etc. Notes of particularity are someone, a certain, not every, etc.
3. A singular proposition is one “whose subject is singular or individual,” i.e., [a subject] which, not having a divisible extension, is understood of the whole; the same rules apply to singulars as to universals.
4. An indefinite proposition is “when a common subject is not modified by any mark of quantity.” In the sense of the speaker, however, it is always either universal or particular. For example, men are animals is universal; men are learned is particular; it depends whether the content is necessary or contingent.
We need only look at two of these kinds, namely universal and particular, because the others come under the same rules.
From the different combinations of quality and quantity, four classes of propositions arise, which are indicated by well-known symbols.
In respect of substance, propositions are either categorical or hypothetical. A categorical [proposition] “indicates something absolutely.” A hypothetical proposition “indicates something subject to a condition.”
The [following] divisions show the responses to the most frequent questions about propositions.
What [proposition]? Categorical or hypothetical. What sort of [proposition]? Negative or affirmative. What quantity of [proposition]? Universal, particular, indefinite, singular.
Axioms about the quantity of terms:
1. “In every affirmative proposition the predicate is taken particularly,” and it is not also required that it be true.
2. “In a negative proposition the predicate is taken universally” or is distributed, for a negation is understood to be false if any part of the predicate may be truly affirmed of the subject.
3. The quantity of subjects is understood from the signs prefixed [to them]. Hence in A, the subject is universal, and the predicate is particular. In E, both are universal. In I, both are particular. In O, the subject is particular, and the predicate is universal.
Only those propositions are said to be universal in which the subject is distributed, and a predicate is affirmed or denied of the individual things which are covered by the common word. This is not the case when the predicate is [made up] of several [things] collectively: thus, All men are mortal is universal, but not the following: All men form one state; all the apostles were twelve.
Propositions about kinds of individuals are in a certain sense universal; e.g., Every animal was in Noah’s ark, or, the Gospel has been preached to men of all nations.
Here it is said that certain individuals of each kind were in the ark or have heard the Gospel, but these things are not predicated separately of every individual or of each individual in the kinds.
These are the axioms about universals:
1. “Whatever is affirmed of a distributed subject (that is, [of a subject] universally taken) may be affirmed of all the inferiors which are contained in its extension.”
2. “Whatever is denied of a distributed subject can equally be denied of all its inferiors.” These two in combination are the dictum de omni et nullo; on this depend both subalternation and the force of the syllogism, which we shall discuss later.5
Some propositions are simple, others complex; simple [propositions] “denote one single judgment”; complex [propositions] “denote more than one judgment.”
Among complex propositions, the modal propositions are preeminent [which are] “when something is both predicated and the mode of its connection with the subject is made clear.” There are four modes: the necessary, the impossible, the possible, and the contingent.6 But generally modal [propositions] are simple [propositions], or signify a single judgment of a speaker. For they are ambiguous. Sometimes they merely affirm or deny the statement itself more emphatically, as in saying, “God most certainly exists” or “Certainly no man is immortal.” Sometimes the proposition itself, which is called the statement, is the subject, and the mode is predicated of it, as in saying, “the Divine existence is necessary,” or “God is, is a necessary proposition”; and similarly with the other modals.
In the same way it is shown that the four kinds [of modal propositions], which might appear from their names to be complex, are simple, namely: (1) conditional [propositions]; (2) disjunctive [propositions]; (3) negative copulative [propositions]; and (4) relative [propositions].
In a conditional or hypothetical [proposition] there are two parts, the antecedent and the consequent: for example, if God exists, the world is governed by providence. Neither of these is asserted; it is merely asserted that they are connected. Hence this [proposition] also is equally true: If there were no God, there would be no providence.
In disjunctive [propositions] the whole subject is said to be included in two connected predicates; for example, it is either day or night means the same as all time is included in daytime and nighttime.7
In negative copulative [propositions] it is denied that both the predicates are compatible with the subject at the same time: it is not both day and night; i.e., no time is both daytime and nighttime.
In relative [propositions] the terms may be complex, but the judgment is single, namely, that the reasons (rationes) are equal or unequal.
The true complex propositions therefore are (1) copulative, (2) causal, (3) adversative, (4) exclusive, (5) inceptive, and (6) desitive;8 and they are easy to learn.
Some propositions or judgments are abstract, “in which from the comparison of ideas itself, there is seen or shown to be a relationship apart from any consideration of time”; hence they are said to be eternal and unalterable truths.
Other propositions are absolute; they assert that a thing is, was or will be at a certain time, or ascribe a common accident to it as existing at a certain time.
Abstract affirmative propositions, in which ideas are not only viewed in themselves but are related to objects, are all hypothetical and merely predicate attributes on the hypothesis that the thing exists. An absolute conclusion can only be deduced from absolute premisses, and abstract conclusions from abstract [premisses].
Other propositions are [self-]evident; here, by a power natural to the mind, “a certain relation or connection is perceived among the terms in themselves.” Nor is there any other criterion of truth.9 Other [propositions] are probable, when connection of that kind is not certain. And others are manifestly false.
The relative states (affectiones) of propositions are subalternation, conversion, and opposition.
1. Subalternation is “the deduction of a particular proposition from a universal [proposition]”; the former is called the subalternating [proposition], the latter the subalternated; for example, Every man is an animal, therefore, Some man is an animal. This is clear from the dictum de omni. “But from a particular to a universal [proposition] there is no inference.”
2. Conversion is “the transposition of the subject into the place of the predicate.” The given proposition is called the convertend, and the derived proposition the converse. And since every relation, likeness, or equality is mutual, the consequence will be valid provided that the same terms are used in the converse with the same extension and with the same temporal relation (ratio).
Conversion is threefold. It is either (i) simpliciter, “when the same quantity of propositions is kept”: no A is B and no B is A; or (ii) it is per accidens, “when the convertend is universal and the converse is particular”: as in, all A is B, some B is A; or (iii) by contraposition, “when the negations [of the terms] are put in the place of the terms and are transposed”: as in, Every man is an animal, therefore, that which is not-animal is not-man.10
Universal negative and particular affirmative [propositions] are converted simpliciter. Universal affirmative [propositions], as well as [universal] negative [propositions], may be converted per accidens; and it is only in this way that [universal] affirmative [propositions] can [be converted], because their predicates are particular.
Universal affirmative [propositions] and particular negative [propositions] [can be converted] by contraposition: Some man is not European, therefore, some not-European is not a not-man, i.e., is a man.
The value of these [conversions] lies in proving the validity of syllogisms, and in perfecting them.
3. Opposition of propositions is said to be complex. Opposed propositions are “two propositions which affirm and deny the same predicate about the same subject, in accordance with the same thing, in the same manner, at the same time.”
There are three kinds of opposed [propositions], namely, contradictory, contrary, and subcontrary. Subaltern [propositions] do not conflict.
Contradictory [propositions] are those “of which one is universal, the other particular, one is affirmative, the other negative”; or which are opposed in quantity and quality, as, A and O, E and I.
Contrary [propositions] are “two universal [propositions], one affirmative, the other negative,” which conflict in quality, not in quantity, like A and E.
Subcontrary [propositions] are “two particular [propositions], one affirmative, the other negative”; they too are in conflict by quality alone, like I and O. Since they are often both true at the same time, namely when they have contingent content, they are not truly opposed.
The rules of opposition are: (1) “of contradictories, one is always true, the other false”; this is the major opposition. (2) “Contraries are never at the same time true, but are sometimes both false at the same time,” i.e., with contingent content. (3) “Subcontrary [propositions] are never false at the same time.” If it is false that some man is learned, it will not be false that some man is not learned, since the contradictory of the former is true.12
When the relation or connection of two ideas or terms cannot be directly perceived, the relation between them will often be able to be seen by a comparison of both of them with some third or middle [idea or term] or with several middle [ideas or terms] which are clearly connected with each other. This mental process is dianoetic judgment or discourse.
When there is only one middle, we are said to have a syllogism; when there are several middles connected with each other, by which the comparison of the terms is made, it is a sorites, or complex form of reasoning.1 First, therefore, we must deal with the simple and categorical syllogism, for the other more complex forms may be reduced to syllogisms.
A syllogism is “discourse in which a third proposition is inferred from two propositions rightly arranged.”
Before a proof is given by means of a syllogism, there is a question or problem of showing the relationship between two terms. These terms are called the Extremes; they are the Major term and the Minor term. The Major term is “the predicate of the question” or of the conclusion, and the Minor term is “the subject of the question.” The Middle Term is that which is compared with both of the extreme terms in the premissed propositions.
Irrespective of the content of the syllogism, there are these three terms: the Major, the Minor, and the Middle Terms. Taking account of the content, there are three propositions: the Major Proposition, the Minor Proposition (these are also called the Premisses), and the Conclusion. They are distinguished not by their order but by their nature.
1. The major proposition “is that in which the major term is compared with the middle term” and is called the proposition par excellence.
2. The minor proposition is that “in which the minor term is compared with the middle term” and is called the assumption or subsumption.
3. The conclusion is that “in which the extremes are compared with each other,” and the middle term never appears here.
The whole force of the syllogism may be explained from the following axioms.2
Axiom 1. “Those things which agree with a single third thing agree with each other.”
2. “Those of which one agrees and the other does not agree with one and the same third thing, do not agree with each other.”
3. “Those which agree in no third thing, do not agree with each other.”
4. “Those which do not disagree with any third thing, do not disagree with each other.” From these [axioms] the general rules of syllogisms are deduced. The first three are about the quality of propositions.
Rule 1. If one of the premisses is negative, the conclusion will be negative (by axiom 2).
Rule 2. If both the premisses are affirmative, the conclusion will be affirmative (axiom 1).
Rule 3. From two negative [premisses] nothing follows because those which agree with each other and those which disagree with each other may both be different from a third.
Two [rules] on the Quantity of Terms:
Rule 4. The middle must be distributed once, or taken universally; for a common term often contains two or more species which are mutually opposed to each other, and from which predication may be made according to different parts of its own extension; therefore terms do not truly agree with a third term, unless one at least agrees with the whole of the middle.
Rule 5. No term may be taken more universally in the conclusion than it was in the premisses, because an inference from particular to universal is not valid.
On the Quantity of Propositions:
Rule 6. “If one of the premisses is particular, the conclusion will be particular.” For (i) suppose the conclusion is affirmative: therefore (by rule 1) both premisses are affirmative; but no term is distributed in a particular [premiss]; therefore (by rule 4) the middle term has to be distributed in the other one; it is therefore the subject of a universal affirmative; therefore the other extreme is also taken particularly, since it is the predicate of an affirmative, ergo, the conclusion will be particular (by rule 5). (ii): Suppose the conclusion is negative: therefore, its predicate is distributed; hence (by rules 5 and 4) both the major term and the middle term have to be distributed in the premisses, but (rule 3) when one premiss is negative, the other is affirmative. If one [premiss] is particular, only these two terms can be distributed; when one premiss is affirmative, the other should be particular. Therefore the minor extreme, the subject of the conclusion, is not distributed in the premisses; therefore (by rule 5) it is not distributed in the conclusion.
Rule 7. “From two particulars nothing follows,” at least in our normal way of speaking, according to which the predicate of a negative is taken to be distributed. For (i) if the conclusion is affirmative and both premisses are affirmative, no term in the premisses is distributed (contrary to rule 4). (ii) Suppose the conclusion is negative; therefore some predicate is distributed, but the predicate is distributed only in particular premisses; it will therefore be invalid (contrary to rule 4 or 5).
Rules 1 and 7 are thus reduced to one rule. The conclusion follows the weaker side, i.e., the negative or particular. All the rules are contained in these verses:3
In a curious and unusual manner of speaking, a certain negative conclusion may be reached, with the predicate undistributed, as in this example:
A figure of a syllogism is “the proper arrangement of the middle in the premisses”; there are only four figures.
1. That in which the middle is the subject of the major and the predicate of the minor.
2. That in which the middle is the predicate of both.
3. That in which the middle is the subject of both.
4. That in which the middle is the predicate of the major and the subject of the minor.
In the first [the middle is] sub[ject and] pre[dicate]; in the second [it is] twice a pre[dicate]; in the third [it is] twice a sub[ject]; and in the fourth [it is] pre[dicate and] sub[ject].
The mood of the syllogism is “the correct determination of the propositions according to quantity and quality.”
Sixty-four arrangements are possible of the four letters A, E, I, O; of these, fifty-two are excluded by the general rules. There remain, therefore, twelve concluding modes of which not all lead to a conclusion in every figure because of the nature of the figure; and some are not useful at all.
The special rules of the figures are as follows.
1. i. In figure 1 the minor [premiss] must be affirmative; if it were negative, the conclusion would be negative (by rule 1), and its predicate would be distributed. But the major would be affirmative (by rule 3), and its predicate would not be distributed; hence there would be a fallacy (contrary to rule 5).
ii. The major [premiss] must be universal. For the minor is affirmative (from the former rule), and therefore its predicate is particular, namely the middle term. It must therefore (by rule 4) be distributed in the major of which it is the subject. These things will be more easily made clear by the schema below, where the letters denote distributed terms.5
Here are examples of fallacies.
N.B. Capital letters denote distributed terms; lowercase letters particular terms.
2. Rules of the second figure:
i. One of the premisses must be negative. For since the middle term is predicated of both, it would be distributed in neither if both were affirmative (contrary to rule 4).
ii. The major must be universal. For the conclusion is negative, and its predicate is distributed. It must therefore (by rule 5) be distributed in the major of which it is the subject.
3. Rules of the third figure:
i. The minor must be affirmative, for the same reason as in the previous figure.
ii. The conclusion must be particular. For since the minor is affirmative, its predicate, the minor term, is not distributed; therefore (by rule 5) it is not distributed in the conclusion of which it is the subject.
Examples of fallacies:
4. Rules of the fourth figure:
i. “If the major is affirmative, the minor must be universal”; otherwise it will contravene rule 4.
ii. If the conclusion is negative, the major must be universal; otherwise it will contravene 5.
iii. If the minor is affirmative, the conclusion must be particular, for the same reason as in the third figure.8
The concluding modes in the four figures are six.
1. AAA, EAE, AII, EIO, *AAI, *EAO.
2. EAE, AEE, EIO, AOO, *EAO, *AEO.
3. AAI, EAO, IAI, AII, OAO, EIO.
4. AAI, AEE, IAI, EAO, EIO, *AEO.9
Thus there are two [modes] in the first [figure], two likewise in the second, and one in the fourth, which are useless and have no names, because they make a particular inference where the valid conclusion would be universal.
The named modes are contained in these verses:
Here are examples of the modes according to the vowels which are contained in the words [of the mnemonic], A, E, I, O.
From axioms 1 and 2 (p. 32) the force of the inference in all of these modes will be clear, since both of the extremes are compared with the middle, and one of them with the distributed middle; and either both agree with it, or one only does not agree.
The Aristotelians neatly demonstrate the force of the inference, and perfect the syllogisms, by means of reduction, since the validity of all [the syllogisms] in figure 1 is evident from the dictum de omni et nullo (see p. 26); they also give, in their technical language, the rules of conversion and opposition, by means of which all the other modes can be reduced to the four modes of the first figure, which Aristotle calls the perfect [modes].10
There are two kinds of reduction, ostensive and ad absurdum. The initial letters in each of the modes (B, C, D, and F) indicate the modes of the first figure to which the modes of the other [figures] are to be reduced, i.e., those of which the initial letter is the same.11 S and P following a vowel show that that proposition is to be converted, S simpliciter, P per accidens. M shows that the propositions are to be transposed, K that the reduction is made per impossibile, of which more later. When this is done, the conclusion reached will be either the same as in reducing Cesare, Festino, etc., or [a conclusion] which implies the same conclusion, or the contradictory to the conceded premiss. The validity of an ostensive reduction is known from the rules of conversion and subalternation.
Reduction to the impossible is as follows. If it is denied that a given conclusion follows from true premisses, let the contradictory of the conclusion be substituted for the premiss whose symbol includes a K, like the major in Bokardo and the minor in Baroko; these premisses will then show in Barbara the truth of the contradictory of the premiss which was claimed to be true. If therefore the given premisses had been true, the conclusion would also have been true; for if it was not, its contradictory would have been true, and if that had been true, it will show (in Barbara) that the other premiss is false, contrary to the hypothesis.
For these rules of syllogisms to hold, we have to look carefully for the true subjects and predicates of the propositions, which are sometimes not at all obvious to beginners; and then we have to determine whether they are really affirmative or negative as they are used in the argument. For in complex [propositions], sometimes one part is negative, the other is affirmative, and occasionally it is the negative part (the less obvious part) which is chiefly in point. For example,
Everything different from God may err, }
Every council is different from God. }
All Holy Scripture is worthy of belief, }
Mathematical proof is not Holy Scripture. }
And the dictum de omni et nullo is so useful in proving a true argument and detecting a false one, that by its help any intelligent person may be able to see both true syllogistic force and its fallacious semblance, according to whether one of the premisses contains the conclusion or not, even before applying the special rules of syllogisms.
With regard to the remaining forms of argument, it is evident that they are imperfect syllogisms or may be reduced to imperfect syllogisms.
1. The enthymeme12 or rhetorical syllogism is “when one of the premisses is unspoken because it is quite obvious”; it is for this reason that an enthymematic judgment has full syllogistic force.
2. Induction is “an inference from various examples,” of which the chief use is in physics, in politics, and in household matters. It does not generate the highest credit or exclude all fears of the contrary, unless it is clear that there are absolutely no contrary examples.
3. An epicheirema13 is “a complex syllogism in which a confirmation is attached to one or both of the premisses.”
4. Sorites is “discourse which contains several syllogisms which are connected with each other,” or where there are several middle terms which are connected with each other or with the extremes in several propositions of which if even one is negative, the conclusion will be negative, and if two are negative or any middle term is not distributed at least once, there will be no inference.
5. A dilemma is “a kind of epicheirema, where in making a division, that which is shown about the individual parts in the premisses is concluded of the whole.”
6. A hypothetical syllogism is “one in which one of the premisses is hypothetical”; when the minor is hypothetical, so also is the conclusion; these also serve to prove the inference in an enthymeme. More frequent are those in which the major is hypothetical, for example:
But since a more general predicate follows from any of the corresponding kinds (for example, If it is a man, if it is a horse, etc., it will also be an animal), but from a general predicate, no one particular species will follow (for from the fact that it is an animal, it does not follow that it will be a horse or an ass), it is evident that hypothetical syllogisms rightly proceed (1) from the positing of an antecedent to the positing of a consequent, or (2) from the removal of a consequent to the removal of an antecedent.
It is a fallacious inference from the removal of an antecedent, or the positing of a consequent:
The positing of a negative will be a negation, and the removal of it an affirmation.
Hypothetical [syllogisms] are reduced to categorical [syllogisms] by this general method: “every case which posits that Titius is a man, posits that he is an animal; but every case, or some case, posits that he is a man; therefore, etc.” But often it may be more easily and briefly done when there is either the same subject or the same predicate to the antecedent and the consequent; for example:
7. Disjunctive syllogisms are “those in which the major is disjunctive, [whether] affirmative or negative.” Either it is day, or it is night; but it is not day, therefore it is night. Or, it is not both night and day, but it is day; therefore it is not night. The force of the inference is obvious enough, when by positing an affirmative disjunctive major, an affirmative conclusion is drawn from a negative minor; or from a copulative negative major and an affirmative minor, the conclusion is negative. For in the former case the syllogism will be reduced to Barbara.
There is no inference from an affirmative minor, in the former, or from a negative [minor] in the latter.
As far as content is concerned, syllogisms are either certain or probable depending on their premisses.
A demonstration is “an argument duly reaching a conclusion from certain premisses,” and it is either ostensive, or leading to absurdity; the latter is the case when the contradictory of a proposition is shown to be false, from which it will be clear that it is itself true. The former is either a priori, or of a cause,14 “when an effect is shown from a known cause.” But there are causes of being and causes of knowing. The former are prior by nature and per se; the latter [are prior] in being known and in relation to us. Demonstrations drawn from both kinds of causes are called a priori, but especially those which are drawn from things prior by nature.15
“The discipline which relies on demonstrations” is science. The general rules of science are
1. “All terms must be accurately defined,” nor is their meaning ever to be altered.
2. “Certain and evident axioms are to be posited.”
3. “One must proceed from the better known to the less known by demonstrations step by step,” and premisses which go beyond axioms and propositions previously demonstrated are not to be admitted.
Demonstrations only deal with abstract propositions, especially in geometry and arithmetic.
There is no single principle of human knowledge which you may rightly say is prior to the rest. There are many evident principles apart from the most general axioms. Nor will any syllogism carry full credence unless both terms of the conclusion are found connected with the middle term in evident propositions. In demonstration, therefore, through several syllogisms which are connected in a continuous series, the number of evident propositions will exceed the number of middle terms by one.
In absolute propositions, and in those which are chiefly useful in life, there is another way of knowing which has its own proper evidence, albeit different from demonstrative [evidence]. Absolute propositions asserting that things exist are known (1) by consciousness, (2) by sense, (3) by reasoning, or by an observed link with existing things, or (4) by testimony. Other experiential truths about the powers and qualities of things are chiefly learned by experience, and by a varied acquaintance with life, and by induction; and whenever any example is similar, it should, other things being equal, be included with the larger rather than the smaller number. For rarely can men see any connection among the actual powers and qualities of things.
There are innumerable degrees of likelihood, from the slightest probability to full and stable assent; from the judicious appreciation [of their degrees] grave men are more likely to earn a reputation for prudence and wisdom than from cleverness in the sciences.
“Assent given to arguments which are probable but do not achieve the highest likelihood” is called opinion. Where either of the premisses is uncertain, there is only a probable conclusion; hence in a long chain of arguments, the result will be a very weak assent.
Arguments which create belief are either artificial and involve the use of reasoning, or inartificial, from testimony. “In recent [writers]16 assent resting on testimony is belief (par excellence).” Belief is either divine or human, depending on whether the assent rests on the testimony of God or of men.
Divine belief will be a fully firm assent when it is clearly established that God has revealed something, since a superior nature cannot deceive or be deceived.
Human belief too, although often hazardous, may sometimes attain full certainty, when it is clear that the witnesses could not have been deceived, and could not have intended to deceive others, so that neither their knowledge nor their reliability nor their truthfulness is in doubt.
Sometimes the knowledge of witnesses will be evident from the nature of the matter in hand; and their reliability will be established if they have not been induced to give testimony about the question in hand by any reward or other inducements; even more so when they testify to their own peril or loss, and could not expect to persuade others, if they themselves knew that the thing was otherwise.
If testimony is not liable to any suspicion of fraud or ignorance, belief may be given (1) to facts which cannot be known in any other way; (2) also to things totally different from what we have previously observed, if indeed there are no internal arguments that prevent belief; (3) and third, even to things that are strange and contrary to all our experience or observation, provided the testimony deals with material and circumstances that are different and remote from our own affairs.
Appendix on Topics, Fallacies, and Method
The doctrine of topics, which should not perhaps be ignored by orators, who often have to marshal a large array of arguments to create or confirm belief, is not so useful for logicians, whose art aims chiefly at developing or teaching sciences in which nothing further needs to be added to any valid argument.1 In any case, topics are “certain general heads of arguments, or the names of the genera in which they are found.” Each science or art has its own topics, together with the actual [art] of teaching them. Only the broadest genera need to be treated by the logician.
I. The topics of grammar are drawn either from the meanings of words or from etymological connections; critics have further [topics], which are the rules of interpretation.
II. The topics of logic are:
1. From definition: what the definition agrees with, that also the thing defined agrees with, and vice versa. What the definition does not agree with, neither does the thing defined [agree with], and vice versa.
2. From division (which are also the topics from the genus): (i) A logical part being posited, i.e., a species, the whole too is posited, i.e., the genus, but not the other way about: He is a man, therefore also an animal. (ii) Another topic is the dictum de omni et nullo. (iii) What may be predicated of individual parts, is true of the whole, if something is not collectively negatived; or negation of parts affects the totality or whole number.2
3. From genus and species: (i) when the species is posited, the genus is posited, and (ii) when the genus is removed, the species is removed; but neither will hold vice versa.
4. From differentia and property: (i) With whatever either one of these agrees under the same nearest genus, the species also agrees, and vice versa. (ii) Anything of which either one is denied, the species is also denied of it.
5. From accident: when an accident is posited, a substance is posited, but not vice versa.
6. From things which are opposed, whether complexly or incomplexly. The rules given above are so many topics.
III. Metaphysical topics:
1. From the whole and the part: when a physical whole is posited, all the combined parts [of it] are posited, and when these are posited and combined, the whole is posited.
2. The part is less than the whole both in quantity and dignity. Topics here may include those from definition, genus and species, depending upon different understandings (acceptio) of the whole. Metaphysical topics also include all the axioms about efficient causes.
IV. Ethical topics are nearly all ends, especially ultimate ends, but there are also the different species of the fitting and the good; and when we learn these from the topics, we also learn the virtues, duties, natural laws, and different degrees of goodness and badness. Arguments are also drawn from men’s appetites and from natural desires to demonstrate laws and to dissect questions of fact, since all plans of action derive from these. The axioms are as follows:
(1) The more that dispositions, intentions, and habits of mind contribute to human advantage, the better they are. And (2) the more they facilitate the assaults of evil, so much the worse they are. (3) Things which are commended by men’s higher desires, which are more proper to man, and which exercise the faculties which are proper to man, are better than those which we share with the beasts. (4) All things gentler and kindlier are, other things being equal, more worthy of a good man, all contrary things are unworthy, and so on.
In questions of fact we should chiefly look at the Cassian query: “Who benefits?”3 These are the axioms: (1) No one is gratuitously either bad or deceitful. (2) No one deliberately acts against the obvious advantage of himself and his own, except in hope of a greater advantage or from a specially strong sense of duty. (3) No sane man, however evil, attempts to deceive, when he has no reason to expect that his deceit will succeed. (4) No sane man is mistaken in things which are exposed to a long and full scrutiny by his senses.
V. The topics of physics are also “from ends,” for the perfect work whether of nature or of art which is that which is most suited to the ends it sets itself. We make best progress in the knowledge of things by combining experiments and geometrical reasoning.
On Fallacies and Sophisms
I. The causes of errors lie either in the will or in the understanding, though the understanding is also to some extent influenced by defects of the will.
[Errors] of the [will] are haste or rashness, bad passions and emotions. For where there is no sincere zeal to know the truth and a love of goodness, a man will soon tire of careful and painstaking inquiry; he will turn his mind to other pursuits or pleasures, content with an immediate appearance of truth, however deceptive. Where there is party zeal or pride or indolence, men will remain stuck in their childhood prejudices or in the opinions favored by the sect to which they have attached themselves, and assail with senseless passion all those who hold contrary opinions, however innocent those opinions may be and truer than their own. When a man anticipates honor or riches from a vigorous defense of his sect, oil is poured on the flames; and the arrogance of a proud person is deeply wounded if anyone who disagrees with him assumes he has deeper insight, and appears to be accusing him of ignorance or low intelligence.
Men are also too quick to take up beliefs which contribute to their own advantage or pleasure; arguments in the other direction are either ignored or weighed on an unequal balance.
II. The causes of the errors which afflict the understanding are slowness of mind (which however can be quite well remedied by hard work) and the deceptive appearances of things. Deceptive appearances are either axioms or principles, rashly picked up and not always true, or terms which are confused, or of indeterminate meaning, and frequently altered without our knowledge. These are the sources of fallacious arguments or sophisms.
Paralogisms openly err in the form itself. Sophisms seem to retain legitimate form, but contain either false or ambiguous propositions or conceal a fault of form under a misleading veil of words.
III. The Aristotelians count thirteen classes of sophisms, six in diction and seven outside of diction.4 Of sophisms in language, the first and second are equivocations in words, or ambiguities in expression or speech. Casual equivocations do not even deceive children, but confused terms may deceive even the learned: this is the great value of definitions.
The third and fourth [linguistic sophisms] proceed from a divided sense to a compound sense, or from a compound sense to a divided [sense]. Thus it would be wrong to infer that the wicked are approved by God, or that God delights in them while their wickedness persists, [simply] because they please him when their character changes, or that the blind can see or the deaf hear, because they can do so when cured.
The fifth and sixth are sophisms of nuance, or figurative expression, which will not deceive anyone unless he is very careless.
IV. The seven fallacies outside of diction are these:
1. From the accident to the thing itself. Thus the Epicureans badly argued that God has a form because neither virtue nor reason is seen without form; it is also incorrect to condemn all use of wine and all civil power because serious evils arise from their abuse.
2. From the qualified statement to the simple statement. Thus it would be wrong to infer that reasoning, discourse, and restraint of emotions should be ascribed to God because they are perfections and virtues; or to argue that because these things cannot be ascribed to God, therefore there is not in God every virtue and perfection. Riches do harm to the wicked; therefore they are simply bad in their kind.
3.Ignoratio elenchi occurs when one believes that a dispute can be resolved by proving something about which both sides agree. Thus, they will say that all the pagans will perish for ever, because no one can be saved except through Christ, when what needed to be proved was that no one could be saved through Christ who did not know him. Thus some men attempt to show that taking up arms against tyrants is always wicked, because it is illicit to resist a legitimate ruler.
4. Not causes for cause: for example, nature everywhere abhors a vacuum; therefore water in pumps will rise to any height you please. Seditions and factions are more frequent in free states; therefore liberty must be proscribed. Greed and many other evils arise from private property; therefore it is desirable to have community of property. Any free man will make mistakes in using his own judgment; therefore it is not to be permitted.
5. The fallacy of the consequent. Examples of this even include mistakes by quite learned people: bodies projected directly upward fall straight back to the place from which they were projected; therefore the earth does not move: and a thousand others.
6.Petitio principii, when what has to be proved is assumed as given. For example, the following “proof ” of the Ptolemaic system: the center of the universe is the point to which all things are borne by their own weight; but all things that we see are borne toward the earth; therefore, etc.
7. The fallacy of more than one question, of which examples are afforded by questions about exclusive, inceptive, and desitive5 propositions.
On Method and Logical Practice
I.6 One method is the way of discovery, which is also called the analytic [method]; the other is the way of teaching, and is the synthetic [method]. Both may be either professional and academic, or public and popular.
The analytic [method], beginning from consideration of singular or more complex [things], or from effects or from a proposed end, proceeds to general, simple [things], to causes, means, and origins. The synthetic [method] proceeds in the opposite order, from the latter to the former.
Principles of knowledge are included among causes, as well as what are properly called causes of being.
The synthetic [method] first proposes definitions, then postulates and axioms, and simpler and easier propositions; and when these have been proved, it proceeds by way of them to more complex and difficult [propositions], following the rules of demonstration given above. Writers of geometry afford examples of both methods.
II. Logical practice consists in the treatment of themes.7
A theme is anything that can be put forward for the understanding to grasp. It is either simple, or a term of some kind; or it is complex, that is, a proposition or statement which has to be confirmed or explained.
In treating a simple theme, (1) we must first explain the origin of a complex word or term and its different meanings and particularly the sense which we want, then (2) its essential attributes, whether primary or secondary, and its more prominent accidents. (3) We must also discuss their origin and end and their causes, if the subject allows it, and (4) the relations existing between it and other things. (5) It is to be divided into its parts, either logical or physical, if there are any.
III. The treatment of a complex theme is either solo or social.8 The solo treatment consists either of exegesis or of analysis. There is exegesis of the proposition or illustration of its effect, and there is confirmation. There is analysis of the exegesis or the resolution into its parts of a longer piece which someone else has written, and its explication.
There are three chief parts of exegesis: (1) paraskeue or preparation, which explains the terms of the question, settles its status, and puts forward the major opinions of the learned. (2) There is kataskeue, or confirmation, which chooses the true view and confirms it by the best arguments, rebuts counterarguments, and cites the testimonies of learned men. (3) And finally there is anaskeue, which dissolves objections and either claims for the speaker’s side, or modestly refutes, the testimonies of famous men which seem to oppose it. Sometimes we should preface it all with a proparaskeue about the importance and occasion of the question; and sometimes there is an episkeue attached, which gives a summing-up, together with useful corollaries. But above all the rules, we should listen to the poet’s [advice]:
Take material, you who write, equal to your powers; and ponder for a long time what your shoulders can bear and what they refuse to bear: if a man has chosen his subject effectively, eloquence will not desert him nor lucid order fail him.9
It is the function of an analysis to demonstrate in a given piece all these parts of exegesis and to explain them, or at least to reveal the true sense of the writer. One must therefore look at: (1) Who is speaking? (2) what about? (3) with what purpose and intention? (4) to whom? And (5) on what occasion? Finally, accounts should be given of the antecedents and consequents.
In treating a complex theme with a companion, or in disputation, the rules to be observed are easy and well known, and swiftly learned by practice.10
[1 ]The primary source in the ancient world for the origin of philosophy and the lives of the philosophers was written in the third century by Diogenes Laertius, Lives of Eminent Philosophers. This work provided material for the more comprehensive histories of ancient philosophy composed by Thomas Stanley, The History of Philosophy: Containing the Lives, Opinions, Actions and Discourses of the Philosophers of Every Sect, and Johann Jakob Brucker, Historia Critica Philosophiae. (Brucker’s work was recast in English by William Enfield as The History of Philosophy from the Earliest Times to the Beginning of the Present Century: Drawn up from Brucker’s Historia Critica Philosophiae; page references are from the 1819 edition.) Hutcheson’s brief account of the origin of philosophy appears to be digested mainly from these three sources, supplemented by the preface to Henry Aldrich, Artis Logicae Compendium: see below, note 9 and especially note 15.
[2 ]Brucker’s Historia, vol. 1, bk. 1 (Enfield, pp. 43-95) was devoted to the philosophy of the Chaldeans, Indians, Egyptians, and others.
[3 ]Diogenes Laertius, Lives, I, pp. 23-47, 121-29.
[4 ]Diogenes Laertius, Lives, II, pp. 321-463. Stanley, History, narrates the lives and opinions of Pythagoras and other members of “the Italick Sect,” pp. 346-469. Hutcheson’s unusual account of Pythagoras’s religious beliefs is also found in Ephraim Chambers, Cyclopedia, s.v. “Pythagoras.”
[5 ]Diogenes Laertius, Lives, I, pp. 131-49, for this succession of philosophers; also Stanley, History, pp. 60-73.
[6 ]Stanley, History, pp. 77-78, drawing upon texts of Plato, Plutarch, and Xenophon, underlines the piety of Socrates and his belief in the immortality of the soul.
[7 ]Diogenes Laertius, Lives, I, pp. 195-233, provides a narrative of the lives and opinions of Aristippus, Theodorus, and Hegesias. Stanley rehearsed this account under the headings of the Cyrenaic, Megaric, and Eleatic sects in History, pp. 132-53.
[8 ]“Eristici” and “elenctici.”
[9 ]Stanley, History, p. 277 ff.; Aldrich, Artis Logicae Compendium, preface, sec. 6, explains the origin of the term “cynic” in the same manner as Hutcheson.
[10 ]Stanley, History, p. 293 ff., and Brucker, Historia, II, p. 531 ff. (Enfield, I, p. 296) treat the Stoics as successors to the Cynics. It is remarkable that no reference is made by Hutcheson to the Stoic philosophers whom he most admired: Epictetus (in the gloss by Simplicius) and Marcus Aurelius.
[11 ]Diogenes Laertius, Lives, II, p. 528 ff., and Stanley, History, pp. 533-633.
[12 ]Stanley, History, pp. 154-55, identified the same members of the Old, the Middle, and the New Academy. This succession of names derives from Diogenes Laertius, Lives, I, pp. 375-444.
[13 ]See Stanley, History, pp. 269-76.
[14 ]Hutcheson’s perfunctory dismissal of Pyrrho and the Skeptics stands in marked contrast with the extensive discussion of Skeptical modes of argument, in Stanley, History, pp. 475-532.
[15 ]This paragraph and its curious chronology derive from Aldrich, Artis Logicae Compendium, preface, secs. 9, 10, and 12.
[16 ]There is no discussion of the Eclectics in Stanley’s History. But Brucker wrote at length on “the Eclectic Sect” in Historia, II, pp. 189-462 (Enfield, II, pp. 59-101) and included among the Eclectics those modern philosophers to whom Hutcheson alludes in his final sentence. Eclecticism in modern philosophy meant for Brucker concentration on the facts of nature rather than on the authority of philosophical sects: Historia, V, pp. 4-6.
[1 ]These were the names given by Aristotle to the intellectual or rational part of the soul in Nichomachean Ethics, bk. 6, chaps. 3-7.
[2 ]This division of philosophy was reflected in the curriculum and in the distribution of professorships in the University of Glasgow and in other Scottish universities. See Coutts, History of the University of Glasgow, pp. 207-8. Hutcheson considered it “the accepted division” in antiquity; see A Synopsis of Metaphysics, Part I, chap. 1, p. 65.
[3 ]Burgersdijk, Monitio Logica, p. 1; Aldrich, Artis Logicae Compendium, p. 3.
[4 ]Le Clerc, Logica, p. 1; Watts, “Logick,” p. 5.
[5 ]On Hutcheson’s insistence on the scholastic distinction between understanding and will, see A Synopsis of Metaphysics, Part II, chap. 1, p. 112 and n. 4.
[6 ]The tripartite division of logic into apprehension, judgment, and discourse is characteristic of the logics of the seventeenth-century English Aristotelians (Robert Sanderson, Henry Aldrich), who also make it clear that these divisions of logic refer to terms, propositions, and syllogisms. The same division of the subject was employed in logics based on ideas (by Arnauld, Le Clerc, and Watts). But all of the latter also attached importance to a fourth part of logic, which they called method. Hutcheson’s logic drew upon both traditions: initially upon the logic of ideas, and later, and more substantially, on the logic of the Aristotelians. His discussion of method was located, with topics and fallacies, in an appendix: see p. 54.
[1 ]Hutcheson followed John Loudon, “Logica,” closely in this chapter. Loudon had written (dictated) under “Apprehension” that “first, the operations of the mind are said to be ideas or notions, perceptions, intentions.” Loudon was responding (like Antoine Arnauld in The Art of Thinking and Nicholas Malebranche in The Search After Truth) to the skeptical and Epicurean logic of Pierre Gassendi, Institutio Logicae, for whom the first operation of the mind was “simple imagination” or “conception, apprehension, intellection, notion”: p. 3 (Latin), p. 83 (English).
[2 ]Loudon, “Logica,” p. 2: “On the division of ideas into sensations, imaginations, and pure intellections.”
[3 ]In opposition to the arguments of Gassendi (and Hobbes), who derived all ideas from the senses and the imagination, Arnauld, in The Art of Thinking, pt. 1, chap. 1, p. 32 ff., maintained that “as soon as we reflect on what occurs in the mind we recognize the difference between imagination and pure intellection.” And Malebranche argued that sensation and imagination are only modifications of thought or pure intellect (The Search After Truth, bk. 3). John Loudon, in “Logica,” included among ideas of pure intellect all ideas of spiritual things, of affirmation and negation, of truth and virtue.
[4 ]Hutcheson’s theory that ideas of pure intellect are generated by internal sensation and therefore include ideas of beauty and virtue, and other concomitant ideas, as described in his Inquiry (1725) and Essay (1728), constitutes the principal point of connection between his logic and his writings on aesthetics and morals. For his proposal that ideas of internal sensation should be considered ideas of reflection, as Locke understood them: see A Synopsis of Metaphysics, Part II, chap. 1, p. 115, n. 9.
[5 ]The types of ideas distinguished in this chapter derive primarily from Locke, Essay, bk. 2, chaps. 29, 30, 31, and 32. See also Le Clerc, Logica, pt. 1, chaps. 9 and 10, pp. 36-43; and Loudon, “Logica,” p. 27 ff.
[6 ]On abstraction, and on the application of knowledge by abstraction to universal ideas, see Arnauld, The Art of Thinking, pt. 1, chaps. 5 and 6; Locke, Essay, bk. 2, chap. 12, pp. 163-66; Le Clerc, Logica, pt. 1, chaps. 6 and 7, pp. 25-36; and Loudon, “Logica,” pp. 9-11.
[7 ]This is where chapter 4 began in Hutcheson’s “Logica,” p. 7. There was no chapter 4 in the published version of Hutcheson’s Logicae Compendium.
[8 ]These were the five predicables distinguished by Porphyry in his Isagoge or introduction to the logic of Aristotle. See Aristotle, The Organon, or Logical Treatises of Aristotle with the Introduction of Porphyry, vol. 2, pp. 609-33. Hutcheson’s table, which describes the parallels between the predicables considered as ideas and as terms, appears to have drawn upon Arnauld, The Art of Thinking, pt. 1, chap. 7, pp. 52-59 (for the predicables as ideas) and Henry Aldrich, Artis Logicae Compendium, bk. 1, chap. 1, sec. 5, p. 5 (for the predicables considered as terms).
[9 ]In the logic of the Aristotelian scholastics, where every whole was explained by the manner in which parts participate in the whole, the tripartite division followed by Hutcheson was sometimes expressed by the terms universal (logical), essential (metaphysical), and integral (physical). See Robert Sanderson, Logicae Artis Compendium, I, 8, pp. 62-64; Franco Burgersdijk, Monitio Logica (an abstract in translation of Institutiones Logicae), I, 14, pp. 43-48; and Aldrich, Artis Logicae Compendium, I, 1, 5, p. 5.
[10 ]See Sanderson, Logicae Artis Compendium, I, 17, pp. 59-60.
[11 ]See Aristotle, Organon, II, pp. 636-39, and A Synopsis of Metaphysics, Part I, chap. 5, pp. 101-10, for an extended discussion of Aristotle’s categories.
[12 ]This illustration of the various forms of substance is “the tree of Porphyry” (Arbor Porphyriana): see Aldrich, Artis Logicae Compendium, II, 1, 2, p. 36.
[13 ]See Aldrich, Artis Logicae Compendium, I, 1, 3, pp. 3-4.
[14 ]See Sanderson, Logicae Artis Compendium, II, 2, pp. 75-82.
[15 ]See Sanderson, Logicae Artis Compendium, I, 8, pp. 26-27, and Aldrich, Artis Logicae Compendium, I, 1, 3, p. 4.
[16 ]See Sanderson, Logicae Artis Compendium, I, 15, pp. 51-54.
[1 ]Compare Carmichael, “A Short Introduction to Logic,” in Natural Rights, p. 298, who had employed the same language in his definition of judgment.
[2 ]The distinction between noetic and dianoetic judgments was made by Loudon, “Compendium Logicae,” p. 51. Carmichael, “Short Introduction,” p. 304, made a similar distinction between immediate judgment, in which two ideas are compared, and mediate judgment, which requires the intervention of a third idea.
[3 ]In this chapter, Hutcheson followed Loudon’s classification of noetic judgments or propositions, set out in “Compendium Logicae.” He did not reiterate Loudon’s illustrations, which were designed to reinforce Presbyterian orthodoxy: for instance, as an example of an affirmative proposition, “a sincerely pious life leads to beatitude”; of a negative proposition, “a disgraceful life does not lead to beatitude” (pp. 18-19).
[4 ]The symbols (A, E, I, O) employed to denote the four classes of propositions are described by James Clow, “A System of Logic,” as “a Distich invented by the School-men,” p. 140. See also W. and M. Kneale, The Development of Logic, p. 56: “the vowels by which the four types have been distinguished since the Middle Ages [formed] no part of Aristotle’s work.” These symbols were widely used by logicians in the early modern period to illustrate the four figures of the syllogism. See Part III, chap. 5, p. 37.
[5 ]The dictum de omni et nullo (the saying concerning all and none) derives via scholastic logicians from Aristotle, “The Prior Analytics,” I, 1, 7, analyzed in Organon, II, p. 649. It was used by Hutcheson to explain subalternation, II, 7, p. 29, and the reduction of syllogisms, III, 6, p. 41.
[6 ]See Sanderson, Logicae Artis Compendium, II, 8, p. 103 ff.
[7 ]See Sanderson, Logicae Artis Compendium, II, 10, pp. 112-16; Arnauld, The Art of Thinking, II, 9, pp. 128-34.
[8 ]These terms are explained in Arnauld, The Art of Thinking, II, 10, pp. 134-42: “Sentences stating that something commences are inceptives; those stating that something ceases are desistives.”
[9 ]Carmichael, “A Short Introduction to Logic,” chap. 2, sec. 7, in Natural Rights, pp. 302-3, provides a more ample discussion of abstract, absolute hypothetical, and intuitive propositions.
[10 ]On subalternation and conversion of propositions, see Sanderson, Logicae Artis Compendium, II, 7, pp. 100-103, and Aldrich, Artis Logicae Compendium, I, 2, pp. 10-12.
[11 ]The Latin is a mnemonic in two hexameter verses: “FEc1 simpliciter convertitur, Ev A per accid./Ast O per contra; sic fit conversio tota.” See Aldrich, Artis Logicae Compendium, I, 2, 5, p. 12, for a slightly modified form of these verses.
[12 ]On contradictory, contrary, and subcontrary propositions, see Sanderson, Logicae Artis Compendium, I, 15, pp. 51-54, and Arnauld, The Art of Thinking, II, 4, pp. 113-14.
[1 ]See Part III, chap. 7, p. 43.
[2 ]See Aldrich, Artis Logicae Compendium, III, 2, p. 4.
[3 ]Aldrich, Artis Logicae Compendium, cites this mnemonic in the same form at III, 3, p. 16.
[4 ]This paragraph was a footnote in Hutcheson’s text.
[5 ]The letters used in this chapter to denote distributed terms are not found in the mss. of Hutcheson’s “Logica,” nor were they employed by Aldrich. James Clow, in his lectures on Hutcheson’s logic, “A System of Logic,” p. 179, offered the following clarification of the symbols used by Hutcheson:
[8 ]Clow also identified in his lectures the modes of the four figures which are excluded by an application of the rules and those modes which remain valid: “A System of Logic,” pp. 179-83. Those modes of the four figures which remain valid or useful are summarized by Hutcheson in the first paragraph of chap. 5.
[9 ]Hutcheson considered the five modes marked by asterisks to be redundant. They are represented as subaltern modes in the figures that follow.
[10 ]See Sanderson, Logicae Artis Compendium, III, 5, pp. 132-37, and Aldrich, Artis Logicae Compendium, I, 3, pp. 20-21. The reader may find it helpful to compare Hutcheson’s presentation with the more elaborate commentary on Aldrich’s logic provided in John Huyshe, A Treatise on Logic, on the Basis of Aldrich, with Illustrative Notes.
[11 ]Thus C in Cesare indicates that it may be reduced to Celarent, Ferison to Ferio, and so on.
[12 ]Literally, something retained in the mind: where the syllogism is reduced from three propositions to two, an antecedent and consequent, the implicit premise must be made explicit for the argument to be tested by the figures and modes outlined above.
[13 ]Literally, to move one’s hand to a thing and thereby confirm it or to make an inference from common experience.
[14 ]Hutcheson writes this in Greek (tou dioti ); the terminology goes back to Aristotle, “Analytica Posteriora,” I, 13, 3: Organon, vol. 2, p. 669.
[15 ]See Sanderson, Logicae Artis Compendium, III, 5, p. 132, and Aldrich, Artis Logicae Compendium, I, 5, p. 32.
[16 ]For example, Locke, Essay, IV, XV, and XVI, pp. 654-68.
[1 ]Hutcheson’s examination of “topics” (treated at length by Aristotle: see Organon, II, pp. 357-540) appears rather to have been an abridgment of the treatment of this subject in Arnauld, The Art of Thinking, pt. 3, chap. 18, pp. 240-46, where topics taken from grammar, logic, and metaphysics were summarized. Hutcheson’s presentation added a fourth and a fifth set of topics, taken from ethics and physics.
[2 ]The numbers assigned topics 3, 4, 5, and 6 follow “Logica,” pp. 45-46. In the 1756 edition, these topics were numbered 4, 5, 6, 7; there was no number 3.
[3 ]Cui bono? “For whose good?” “Who benefits?” This is the question which L. Cassius Longinus (consul, 127 ) used to ask when sitting as a judge. The main source is Cicero, Pro Sexto Roscio Amerino 30 (84), in vol. 6, The Speeches.
[4 ]Aristotle, “The Sophistical Elenchi,” in Organon, II, pp. 540-608; Sanderson, Logicae Artis Compendium, III, 28, pp. 206-10, and III, 29, pp. 210-16.
[5 ]See Part II, chap. 5, p. 28, n. 8.
[6 ]The divisions of this chapter (I, II, III) derive from “Logica,” pp. 54-58. In the published text (1756) only Section II was marked.
[7 ]Hutcheson’s treatment of themes and of the rules for considering a simple theme rehearse the observations made on this subject by Gershom Carmichael, “A Short Introduction to Logic,” chap. 4, sec. 2, in Natural Rights, pp. 309-11.
[8 ]Hutcheson’s remarks on the solo treatment of a complex theme again reflect Carmichael’s observations in “A Short Introduction to Logic,” chap. 4, sec. 3, Natural Rights, pp. 311-12.
[9 ]From Horace, Ars Poetica, ll. 38-41, in Satires, Epistles, and Ars Poetica, p. 452.
[10 ]See Carmichael, “A Short Introduction to Logic,” chap. 4, sec. 4, in Natural Rights, pp. 312-15.