The Logic of the Arabians And Its Arabic Text [Al-Risala al-Shamsiyya]

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The Logic of the Arabians And Its Arabic Text [Al-Risala al-Shamsiyya] Author:
Translator: Aloys Sprenger
Publisher: www.alhassanain.org/english
Category: Islamic Philosophy

The Logic of the Arabians And Its Arabic Text [Al-Risala al-Shamsiyya]

This book is corrected and edited by Al-Hassanain (p) Institue for Islamic Heritage and Thought

Author: Najm al-Din ’Umar al-Qazwni al-Katibi
Translator: Aloys Sprenger
Publisher: www.alhassanain.org/english
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The Logic of the Arabians And Its Arabic Text [Al-Risala al-Shamsiyya]

The Logic of the Arabians And Its Arabic Text [Al-Risala al-Shamsiyya]

Author:
Publisher: www.alhassanain.org/english
English

This book is corrected and edited by Al-Hassanain (p) Institue for Islamic Heritage and Thought

The Logic of the Arabians

And Its Arabic Text

[Al-Risala al-Shamsiyya]

Author (s): Najm al-Din ’Umar al-Qazwni al-Katibi (D. 1276 A.D.)

Translator: Aloys Sprenger

Note: The Arabic Text of Al-Risala al-Shamsiyya has been corrected and edited by www.alhassanain.org/english

This book is corrected and edited by Al-Hassanain (p) Institue for Islamic Heritage and Thought

www.alhassanain.org/english

Table of Contents

(Preface of Wilfrid Hodges)5

The Logic of the Arabians6

INTRODUCTION 7

First Inquiry: On what Logic is and its utility 7

Second Inquiry: On the Subject of Logic7

FIRST BOOK 9

First Section: On Words9

Second Section: On Simple Meanings (Predicables)10

Third Section: Five Inquiries on Universals and Particulars 12

First Inquiry 12

Second Inquiry 12

Third Inquiry 12

Fourth Inquiry 13

Fifth Inquiry 14

Fourth Section: On Definitions (i.e. the ways of defining)15

SECOND BOOK: On propositions and rules regarding them16

INTRODUCTION 16

Definition of proposition and its primary division 16

First Section: On the categorical (proposition)16

First Inquiry: Its parts and kinds16

Second Inquiry: On the four fenced Propositions 17

Third Section: On Privatives and Attributes17

Fourth Inquiry: On Modal Propositions18

Second Section: On the different kinds of hypothetical Propositions20

Third Section: Rules concerning propositions22

First Inquiry: On Contradiction 22

Second Inquiry: On even Conversion (Conversio simplex)23

Third Inquiry: On Conversion by Contradiction 24

Fourth Inquiry: On the Cohesion of Hypotheticals24

THIRD BOOK: On Syllogism 26

First Chapter: Definition and division of Syllogism 26

Third Section: Conjugate Syllogism containing hypothetical premisses29

Fourth Section: On the Interpellative Syllogism 31

Fifth Section: Pendents of the Syllogism 31

CONCLUSION 33

First Inquiry: On the matter of Syllogisms33

Second Inquiry: On the parts of which Sciences consist35

The Arabic Text of Al-Risala al-Shamsiyya36

متن الرسالة الشمسيّة36

أما المقدمة ففيها بحثان37

البحث] الأوّل في ماهية المنطق وبيان الحاجة إليه]37

البحث الثاني] في موضوع المنطق]37

المقالة الأولى] في المفردات]38

الفصل الأول] في الألفاظ]38

الفصل الثاني] في المعاني المفردة]39

الفصل الثالث] في مباحث الكلّيّ والجزئيّ]40

الفصل الرابع] في التعريفات]42

المقالة الثانية] في القضايا وأحكامها]43

أما [المقدّمة] ففي تعريف القضية وأقسامها الأوليّ 43

الفصل الأوّل] في الحمليّة]43

البحث الأوّل] في أجزائها وأقسامها]43

البحث الثاني] في تحقيق المحصورات الأربع]44

البحث الثالث] في العدول والتحصيل]44

البحث الرابع] في القضايا الموجّهة]45

الفصل الثاني] في أقسام الشرطية]47

الفصل الثالث] في أحكام القضايا]49

البحث الأول] في التناقض]49

البحث الثاني] في العكس المستوي]50

البحث الثالث] في عكس النقيض]52

المبحث الرابع] في تلازم الشّرطيّات]53

المقالة الثالثة] في القياس ]54

الفصل الأوّل] في تعريف القياس وأقسامه]54

أما الشكل الأوّل 54

أما الشكل الثاني 55

وأمّا الشكل الثالث 55

وأما الشكل الرابع 56

الفصل الثاني[في المختلطات]57

الفصل الثالث] في الاقترانيات الكائنة من الشرطيّات]57

الفصل الرابع] في القياس الاستثنائي]59

الفصل الخامس] في لواحق القياس]59

وأما [الخاتمة] ففيها بحثان60

البحث الأوّل] في مواد الأقيسة]60

البحث الثاني] في أجزاء العلوم]62

(Preface of Wilfrid Hodges)

This file contains a transcription of the translation by Aloys Sprenger of Al-Ris¯ala al-Shamsiyya, a logic textbook by Najm al-D¯ın ’Umar al-Qazw¯ın¯ı al-K¯atib¯ı, who died in 1276.

Sprenger’s translation was published in his First Appendix to the Dictionary of Technical Terms used in the Sciences of the Mussalmans, containing the Logic of the Arabians, Bengal Military Orphan Press, Calcutta 1854. I have left out Sprenger’s footnotes. Sprenger himself leaves out some sections on modal logic; Nicholas Rescher published a translation of this missing part as an appendix to his Temporal Modalities in Arabic Logic, Reidel, Dordrecht 1967, pp. 39–45.

Sprenger’s numbering of the sections is slightly different from the numbering of the Arabic text, which is in the same book as his translation. (which is removed in this edition by the www.alhassanain.org/english)

There is some discussion of this text in Tony Street, ‘Logic’, in The Cambridge Companion to Arabic Philosophy, ed. Peter Adamson and Richard C. Taylor, Cambridge University Press, Cambridge 2005, pp. 247–265.

Wilfrid Hodges, December 2007

The Logic of the Arabians

§1. Praise be to God, who has created the system of the universe, who has produced the essences of things in conformitywith their existence,who has made by His omnipotence the different species of mental substances (i.e. logoi or demiurgs), and who, in His bounty, has given motion to the heavenly bodies.

Blessings be upon those noble and holy essences (inspired persons) who are pure from human defilement, more particularly upon Mohammad, the doer of signs and miracles, and upon his family and his companions who followed him [and thereby became] his argument and demonstration.

§2. Whereas, agreeably to the opinion of all men ofmind and liberal education, the sciences, more particularly the positive sciences, are the highest pursuits in life, and whereas the professors thereof are the most noble among human beings, their minds being sooner prepared to be absorbed into the angelic minds (that is to say, the demiurgs or logoi), and farther, whereas it is impossible to comprehend the subtilties of sciences and to preserve the acme of their verities except by the assistance of the science which is called Logic, and which teaches us howto discern betweenwhat is correct and erroneous, Shams aldyn Mohammad, a son of the Wazyr Bah´a aldyn Mohammad, has desired me to write a book, which shall comprise the principles of Logic, and contain its fundamental doctrines and rules. Ready to follow his directions, I began to write a book on Logic, making it a rule not to omit any thing that belongs to it. I made some beautiful original additions and acute observations, avoided mere compilation and followed plain truths, which will never be controverted. I gave it the name of Ris´alah Shamsyyah on the Principles of Logic, and divided it into an Introduction, three Books and a Conclusion. My reliance is in God.

INTRODUCTION

It contains two inquiries:

First Inquiry: On what Logic is and its utility

§3. Knowledge is either apprehension, and nothing further or apprehension together with judgment. Apprehension is the perception of the image of a thing in the mind. Judgment means referring (literally leaning) one thing to another affirmatively or negatively. The whole [apprehension and a judgment combined] is called declaration.

§4. Neither is the whole of either of these two things entirely intuitive, else there would be nothing we do not know; nor entirely deductive, else our reasoning would be a circle, or an [interminable] chain.

§5. Part of each is intuitive, and part is deductive, and the result of reasoning, i.e. of such an arrangement of known things [in the mind] that they lead to [the knowledge of] unknown things. But this arrangement is not always correct, for some thinkers contradict others as regards the results of their reasonings, nay the same person contradicts himself at different times; therefore a canon (a code of rules) is required, acquainting uswith theways of deriving deductive knowledge from self-evident [knowledge], and marking the boundaries between sound and bad reasoning. This canon is Logic. It is described as the canonic organon, (i.e. an instrument consisting of rules), the observance of which guards our intellect from error in reasoning.

Logic is neither entirely intuitive, else there would be no need for learning it, not is it entirely deductive, else it would be a circle or [interminable] chain, but some [of its doctrines] are intuitive and others are deductive, and founded upon the intuitive ones.

Second Inquiry: On the Subject of Logic

§6. The subjects of a Science are those of its accidents which are inquired into, whether they belong to it immediately, that is to say, belong to its essence, or whether they belong to its parts or whether they belong to it [mediately, but are] co-extensive. The subjects of Logic are apprehensional and declarative notions, for the Logician inquires into them so far as they lead to unknown apprehensional or declarative [notions], and in so far as there rests upon them that which leads to apprehension; he inquires, for instance, whether [such apprehensions as lead to other apprehensions]

are universals, particulars, essentials, accidents, genera, species, or differences - and in so far as there rests upon them that which leads to declaration (assertion) whether it rests upon them proximately - they (the declarations which lead to other declarations) being, for instance, propositions or conversions of propositions, or contradictories of propositions; or remotely - they being, for instance, subjects and predicates.

§7. It is usual to call that which leads to apprehension oratio explicans [or mo’arrif “definiens”]; and that which leads to declaration, argument. It behoves us to premit the former to the latter in our system, because apprehension precedes declaration in nature, inasmuch as every declaration must contain [firstly] the apprehension of the subject itself, or of an assertion regarding it; and [secondly either the apprehension itself of the thing] whereby the judgment is formed, (predicate), or an assertion regarding it; and [thirdly] the judgment, for judgment is impossible if one of these (three) things [subject or predicate or judgment] is unknown.

FIRST BOOK

It contains three Sections:

First Section: On Words

§8. That a word is the indication of a meaning (idea), by reason of [its]

appointment for it (so as to represent that idea), is [called] coincidence, as, for instance, that “homo” is the indication of (is used to express the idea of) “rational animal.” [That a word is the indication of an idea] by reason of its appointment for that in which it (the idea) is included is [called] implication, as for instance, that “homo” is an indication of an animal. [That a word is the indication of an idea] by reason of its appointment for that to which it (the idea) is external is [called] nexus; for instance, that “homo” is an indication of “capable of instruction” and of “acquiring the art of writing”.

§9. It is necessary in the indication per nexum that the external thing be in such a condition that the apprehension thereof adhere in the intellect to the apprehension of the thing named, if this be not the case the word will not convey the meaning thereof. But it is not necessary that it be in such a condition that its actual existence be connected with the actual existence of the thing named. For instance the word “blind” is (per nexum) the indication of sight, yet these two things are not connected in their actual existence.

§10. Coincidence does not (always) comprize implication, as, for instance, in indivisibles (i.e. things the quiddity of which is not composed of parts see notes 18, 19 and 27) and it may or may not comprize nexus; this is uncertain, for it is not known whether there exists an adherens (inseparable property) of every essence, the apprehension of which is connected with the apprehension of that essence. [The opinion of Im´am R´azy] that the apprehension of every essence comprizes [per nexum at least if nothing else,] the apprehension that it is [that essence and] no other, is not admissible.

From this it is clear that implication does not comprize nexus, they, in fact, are (only) found along with coincidence, for the sequens cannot possibly exist as sequens without something of which it is the sequens.

§11. If any part of the (term which is) indicans by coincidence, is intended to indicate a part of the total meaning, it (the term) is [called] complex, as a thrower of stones, else it is [called] simple. If the simple word is not by itself fit to be a predicable, it is [called] a tool (syncategorematic), as “in” and “not,” and if it is fit to be a predicable, and indicates by its form one of the three times, it is a verb, else it is a noun.

§12. A noun has either one meaning or more than one. In the first case if it individuates that meaning it is called a proper-name, else (there are two cases possible: firstly), if its conceivable (literally intellective) and real individua are [all] equally represented by it, it is called univocal (literally agreeing, consentient,) as “homo,” “sun;” [secondly,] if it applies to some of the individua] more forcibly, and in preference to others, it is called doubtful as existence in reference to the being which exists of necessity (God), and the beings of contingent existence (the creation.) In the second case, [if a noun has many meanings] it may be, by appointment, equally applicable to those several meanings, like spring [the spring of a clock, a spring of water], - in this case it is called equivocal: or it may have been appointed for one meaning and then have been transferred to a second. If the original meaning has become obsolete the noun is called a transferred word, it depends whether it has been transferred by common usage [as the word “omnibus”] or as a law term, or as a term of science; in the first case it is called “a conventionally transferred (word),” in the second “a juristically transferred (word),” and in the third “a technically transferred (word).” If a word has not quitted its original subject (lost its original meaning), it is called, in relation to it, proper, and in relation (to the signification) to which it has been transferred, trop. Example, lion, in reference to the animal of that name and in reference to a brave man.

§13. A word is in reference to another word synonymous (literally riding on the same camel, one behind the other,) with it if they agree in meaning, and heteronymous (literally distinct) if they differ in meaning.

§14. A compound (oratio) is either complete, that is to say, it has a sense by itself (literally, silence after it is admissible) or incomplete. If a complete compound predicates something true or false, it is called information or proposition, and if it does not predicate any thing it is called interjection. If an interjection has by appointment the meaning of a request that a thing be done, and if (it be uttered) with an authoritative voice, it is an order (or an imperative) as, beat thou! if (it be uttered) in a humble voice it is a question or prayer, and if in a middling voice, a request. If it has not the meaning of a request that a thing be done, it is a warning (exclamation) expressive of whining, or weeping, or wondering, or exclaiming, or swearing. If a compound is not complete, it is either a limitation as “rational animal,” or it is not a limitation, as if it consist of a noun and a tool, or of a verb and a tool (adverb).

Second Section: On Simple Meanings (Predicables)

§15. A notion is particular (singular) if the apprehension thereof of itself excludes the taking place of association, and it is universal (common), if it does not exclude association. The terms indicating these two things are called particular and universal respectively.

§16. An universal [notion] is either the whole of the quiddity of the particulars under it, or is included in it (i.e. is part of it), or is external, [but joined] to it. The first is called species, whether it contains many individua [or only one, in the former case] it is said in answer to [the question], “what is it?” in regard both to association and peculiarity as homo, [in the latter case] if it does not contain several individua it is said in answer to [the question] “what is it,” in regard to its peculiarity only, as “sun.” Species is therefore an universal, which is said of one or several things which agree in their verities in answer to [the question] “what is it.”

§17. In the second case [if the universal is part of the quiddity it must be one of two things, either a genus of the quiddity or its difference], it is called a genus if the universal is the totality of that part [of the quiddity] which is common to the quiddity and to another species. It is said in answer to [the question] “what is it?” in regard to association only. Genus is described as a universal, which is said of many things differing in their verities, in answer to [the question] “what is it.”

§18. The genus is called near, if the answer [to the question] regarding a [given] quiddity and regarding certain [other species] which are associated with it under that genus is the immediate answer regarding that quiddity, and regarding all [the species] which are associated with the said quiddity, under the same genus, as animal in reference to man.

The genus is called remote, if the answer [to the question] regarding the quiddity and regarding certain [other species] which are associated with it under that genus, is different from the answer regarding the quiddity, and those other [species mentioned above as coming under the near genus]. If the genus is remote by one degree, two answers can be given, as living being in reference to man; and if it is remote by two degrees, three answers can be given, as body in reference to man; and if it is remote by three degrees, four answers can be given, as substance in reference to man, etc.

§19. If it (the universal notion) is not (or does not comprehend) the totality of that part [of the quiddity], which is common to it (the quiddity) and to another species [i.e. if it is not a genus, one of two things must be the case]; either it cannot be common [to both] at all [being peculiar to the quiddity as rational is according to the Arabs to man] or it [is only] a portion of the part which is common to both; although co-extensive therewith. Else (if it were more extensive it would follow that) it must be common to the quiddity and to some other species [not included in the genus] but, agreeably to the above supposition, it must, in reference to such other species, not comprehend the whole part which may be common [to the quiddity and that species], but only a portion of it [and so by assuming that the notion is part of the quiddity of another species we should only rise to a higher branch on the tree of Porphyry]. (This reasoning) does not lead to an [interminable] chain, but to something which is co-extensive with the totality of the part which is common (or genus). This [universal] consequently divides the genus, and whether it distinguish the quiddity from what is associated with it under a genus or under “existence,” [which may be considered the summum genus] it is [called] difference (literally division).

§20. Difference is described as a universal predicated of a thing to the question “what thing is it in its substance?” It follows that if a verity is composed of two - or several - co-extensive things, each of these two things is its difference, for it distinguishes it from those things which are associated with it in “existence”.

§21. The difference which distinguishes a species from what is associated with it in the genus, is called near (specific), provided it distinguishes it in the near genus e.g. “rational” is the difference of “man” [in the subaltern genus “animal,” distinguishing it from other animals]. And it is called remote (generic) if it distinguishes a species from what is associated with it in the remote genus, e.g. “sensitive” is the difference of “man” [in the remote genus “living being”].

§22. The third [universal is external to the quiddity but joined to it.]

If it is inseparable from the essence it is called adherent (property), else it is called separable accident. The adherent adheres to the existence [of a thing], as blackness to the negro, or it adheres to the quiddity, like being even to four. The adherent is [called] evident, if the apprehension of the adherent together with the apprehension of the thing to which it adheres, is sufficient to convince the intellect of the cohesion between the two, as the divisibility of four into two equal parts; and it is [called] not-evident, if a medium is required to convince the intellect of their cohesion, as the equality of the three angles of a triangle to two right angles. Some say that an adherent is evident, if the apprehension thereof adheres to the apprehension of the thing of which it is the adherent. The first [definition] is more general. The separable accident may either pass quickly, as the blushing of shame and flushing of anger, or slowly, like greyness of hair, [under the use of certain medicines which are supposed to have this effect], or youth.

§23. Both the adherent and separable [accident], if they are peculiar to singulars of the same verity, are called peculiar, as risible, else they are called general accident, as locomotion. The “peculiar” is described as a universal said, as a accident, only of things of the same verity. Common accident is described as a universal, said as an accident, of singulars of the same verity and of other things also in the way of accidentality. The universals therefore are five: species, genus, difference, peculiar (accident) and common accident.

Third Section: Five Inquiries on Universals and Particulars.

First Inquiry

§24. [There are] universals, whose existence is impossible in reality, but not the conception thereof of itself, as “an equal to God.” [There are universals] whose existence may be possible but they do not really exist, as “a griffon.” [Under some universals] there is only one [individual], and it is impossible that there should be another, as God; or it is possible that there be others, as the sun; or there are many but they are limited in number, as the seven planets; or they are unlimited in number, as the rational souls.

Second Inquiry

§25. Ifwe say of “animal” for instance, that it is a universal, three things are to be observed. Animal is to be considered in itself, and as a universal, and as the compound of these two things. The first is called a physical universal, the second a logical universal, and the third amental (metaphysical) universal. The physical universal is existing in reality, for it (animality) is a part of every animal which exists, and a part of what exists has [of course] existence. In regard to the other two universals, opinions are divided as to their existence in reality. The inquiry on this subject does not belong to logic.

Third Inquiry

§26. Universals are co-extensive, if one is true of just as much (i.e. of as many individuals) as the other, as “homo” and “rational.” There is absolute generality and peculiarity between them (i.e. one ismore extensive than the other and contains it wholly), if one of the two, is true of all of which the other is true, but not vice versa; as “animal” and “man.” There is generality and peculiarity between them in some respect if either is true only of a part of that of which the other is true; as man and white. And they are heterogeneous if neither of the two is true of any thing of which the other is true; as man and horse.

§27. The contradictories of two co-extensive [terms] are co-extensive; for else one of them (contradictories) would be true of that about which the other is false, and it would follow that one of the two co-extensive [terms] is true of that about which the other is false - this is impossible. [E.g. every non-man is an irrational being and every irrational being is a non-man.]

The contradictory of an absolutely more general [term] is more peculiar than the contradictory of an absolutely more peculiar [term,] for the contradictory of the more peculiar [term] is true of every thing of what the contradictory of the more general term is true, but not vice versa, [non-man contains more than non-animal]. Were the first [of these two assertions] not founded, the peculiar [term] itself [i.e. not its contradictory; man e.g.,] would be true of some things of which the contradictory of the more general [term e.g. non-animal] is true, and hence it would follow that the more peculiar is true [of certain things] and that the more general is not true [of the same things] - this is impossible. As to the second [assertion viz., that the contradictory of a more general term contains less than the contradictory of a more peculiar term], were it unfounded the contradictory of the more general [term] would be true of every thing of which the contradictory of themore peculiar [term] is true, and hence it would follow that the more peculiar [term] is true of every thing of which the more general is true - this is impossible. There is no generality whatever between the contradictories of terms one of which is more general in ‘some respect,’

because it is certain that such a generality exists between the absolutely more general [term] itself [e.g. animal] and the contradictory of the more peculiar [term, as for instance non-man;] whilst there is universal heterogeneousness between the contradictory of the absolutely more general and the more peculiar [term] itself. The contradictories of two heterogeneous [terms] are heterogeneous, and their heterogeneousness is [called] particular heterogeneousness, for if [two terms] are in no case true simultaneously [of the same thing], as non-existence and non-nihilum (non-existence and existence), it is [called] universal heterogeneousness; and if they are true simultaneously, as non-man and non-horse, it is called particular heterogeneousness, because one of the two heterogeneous terms is necessarily true [of certain objects] of which the contradictory of the other heterogeneous term is true. Particular heterogeneousness is, therefore, surely an adherent [of the contradictories of two heterogeneous terms.]

Fourth Inquiry

§28. [The term] “particular” is not only used in the abovementioned sense [see §15] - in which it is called “veritable particular” - but also to de-note any more peculiar [term] which is under a more general one, and in this case it is called “relative particular.” The latter term is more general than the former, for every veritable particular is a relative particular, but not vice versa. The former is the case (i.e. every veritable particular is a relative particular), because every individuumcomes under its quiddity,which denudes [the individua under it] of their individuality, (i.e. which abstracts from the individuality of the individua); and the second is the case (i.e. the reverse is not true), because the relative particular may be a universal, but the veritable particular cannot be a universal.

Fifth Inquiry

§29. The species which is of the description mentioned above [§16] is called the veritable species; but the term is also used of any quiddity, if to the question “what is it” regarding the said quiddity [e.g. what is “man?”] and some other quiddity [e.g. what is “horse”], the genus [e.g. “animal”] is primarily said in answer. This is called the relative species.

§30. Species has four degrees, for either it is the most general of all species, and in this case it is called the high species (summa species), as “body;” or it is themost peculiar, and in this case it is called the low species, as “man,” this is also called the species specierum; or it is more general than the low species and more peculiar than the high, this is called the intermediate species, as “animal” and “living body;” or it is detached from all other species, this is called the singular (or solitary) species, as logos, if we say that substance is the genus of logos.

§31. Genus has the same four degrees, but the high genus (summum genus), e.g. “substance,” and not the low genus, e.g. “animal,” is called the genus generum in the gradation of the genera. Examples of the intermediate genus, are “living being” and “body,” and an example of the singular genus is “logos,” supposing that “substance” is not the genus of “logos.”

§32. The relative species is to be found without the veritable species, as in the intermediate species. Again the veritable species is to be found without the relative one, e.g. in indivisible verities. These two kinds of species do not stand to each other in the relation of absolute generality and peculiarity, but either of the two is in some respects more general than the other, because they are both true of the low species.

§33. If [only] a part of what ought to be said in answer to the question “what is it” is said, and if that be [a] coincident [term,] it is called jacens in via [questionis], quid est, e.g. if we ask regarding man, “what is it,” and receive the answer “animal” or “rational,” in reference to (or instead of) “rational animal.” If [only] a part is said in answer to the same question, and if, what is said, be a term for it by implication, it is called inclusum in responsione (i.e. pars responsionis) [ad questionem] quid est, as “living being,” “sensitive,” “endowed with voluntary motion,” animal being indicated by these terms by implication.

§34. The summum genusmay have a difference which establishes it (or is an essential part of it), for it may be composed of two or more co-extensivle things; but it must necessarily have a difference which divides it (separates its significates). The low species must necessarily have a difference which establishes it, but it can have no difference which divides it. The intermediate [genera] must have differentiae which establish them and differentiae which divide them. Every difference which establishes the summum genus establishes also the low genus, but not vice versa; again every difference which divides a lower genus divides also the summum genus but not vice versa.

Fourth Section: On Definitions (i.e. the ways of defining)

§35. The definiens (definition) of a thing is [an expression] the apprehension of whcih involves the apprehension of the thing defined, or its distinction from every thing else. The definiens must not be the essence itself [i.e. homo is not a definition for man], for the definiens is known prior to the definitum, and a thing is not known prior to itself. It further must not be more general (more extensive) than the definitum else it does not answer the purpose of definition (or limiting), nor must it be more peculiar (more limited), else it conceals (or excludes some of the individua). The definiens must be co-extensive in generality and peculiarity.

§36. The definiens is called a limes perfectus (perfect boundary) if it consists of the near genus and near difference, [as rational animal for man]; and limes imperfectus (imperfect boundary) if it consists of the near difference only, [as rationalis for homo], or of the near difference and the distant genus, [as a rational body for man]. And it is called complete description (literally sketch,) if it consists of the near genus and a property, [as the risible animal for man], and imperfect description, if it consists of the property alone, or of the property and the distant genus, [as risible body for man.]

§37. Care must be taken not to define a thing by what is equally known or unknown, as if we were to define “motion” by “absence of rest,” or “couple” by “what is not single.” Nor must a thing be defined by another thing, which is known only through the former. It is equally objectionable whether it be immediately known through it, e.g., ifwewere to say “report” means an “account” and “account” means “report;” ormediately, e.g., if we were to say the number two is the first pair; pair is what can be divided into two equal parts, two parts are called equal if neither exceed the other and the parts are two.

Care must also be taken not to use barbarous unusual words, whose indication (meaning) is not intelligible to the hearer, for in this case the purpose is lost sight of.