A FORTIORI LOGIC
Appendix 5 – A fortiori discourse in other world literature
A thorough investigation of the use of a fortiori argument would imply looking at all literature in all cultures and through the ages. This would of course be interesting to do; but it is not really necessary. The most important question is when is theearliestuse documented use of a fortiori argument in the world, and then in each culture. We may reasonably expect each culture to have its own earliest sample, and these may come at different dates. Even so, two pitfalls must obviously be avoided. (a) It would be erroneous to assume that the earliest sample we found in the world or in a specific culture is really indicative of the date when the argument first appeared in the world or in that culture. (b) It would be erroneous to assume that because the earliest sample in one culture precedes the earliest sample in another culture, it follows that the former produced the latter.
It is a reasonable hypothesis that the use of a fortiori argument, and indeed all the main forms of argument, is a general human phenomenon, which was a feature of oral culture long before it became one of written culture. For this reason, one can expect such use to appear at some time in all or most cultures, and the order of appearance is not necessarily indicative of real precedence or of antecedence. This does not mean that there may not be noticeable differences in the frequency of use in different cultures. Some cultures may exhibit little or even no use of it, while others may exhibit very frequent use. Obviously,the absence (or low score) of a fortiori discourse is as interesting as its presence (or high score).We should also note the variations in frequency of use within a given culture; a fortiori discourse may increase or decrease across time. Thus, as well as looking for the earliest use of such argument, we should try and assess how common it is in contemporary discourse.
Another problem researchers must be aware of is that of language. Looking at translations of foreign literature, we might assume the a fortiori argument to be in use when in fact it is the translator who has injected it into his translation. Often, translators use language that seems a fortiori in intent, but is only hyperbolic, the real intent being merely comparative (e.g. “all the more” sometimes means “a lot more”). Presumably this does not happen often, but it may conceivably do so. Thus, we should always qualify our findings by adding: “assuming the translation accurate.”
Needless to say, much more significant than theuseof a fortiori argument is thediscussionof such argument. This is indicative of a ‘self-consciousness’ of the thinker in the act of thinking, an awareness that his thinking has a distinct form that is worthy of study in its own right irrespective of content. Such reflection, of course, signifies an intellectual breakthrough of historical moment. And of course, beyond that initial stage we must expect increasing degrees of awareness and understanding. The highest point of development is the ability to accurately distinguish valid from invalid argument. But in the present appendix, our concern is only with use of the argument.
Some of the research work may nowadays be done by means of computer-assisted searches. In English texts, we should first look for the fifteen key phrases commonly indicative of a fortiori argument (in brackets are my proposed abbreviations), namely:a fortiori (af),all the more/less (atm, atl),how much more/less (hmm, hml),so much more/less (smm, sml), othermuch more/less (mm, ml),how much the more/less (hmtm, hmtl),so much the more/less (smtm, smtl), othermuch the more/less (mtm, mtl). To spota pariarguments, we might look foras much as (ama), as little as (ala). Additionally, to be on the safe side, we should perhaps examine cases involving the following eight less specific phrases:more/less so (ms, ls),even more/less (em, el),still more/less (sm, sl),still the more/less (stm, stl). A further possibility is to try out the truncated phrases:all the (at), how much (hm), much the (mt),in the hope of finding cases with specific adjectives or adverbs, like: (all the / how much / much the) greater or lesser, better or worse, faster or slower, and so forth (i.e. mostly words ending in –er, but not always).
As we have seen with reference to the Tanakh and Mishna, and to Plato and Aristotle, such research cannot be done mechanically, because the various search strings are not necessarily indicative of a fortiori discourse. Moreover, although useful, such computer searches do not necessarily lead to discovery of all cases of a fortiori argument, because it is often enough conveyed without use of these indicative phrases. Eventually, if we want to be thorough, we have to carefully read through each book examined and record cases we come across. Nevertheless, computer search is very helpful, giving us some tantalizing results to start with.
With these thoughts in mind, I have looked for a fortiori discourse in a number of books, both through computer search and by actual reading. Most of this research is based on my readily finding a computer searchable eBook or pdf copy of a text, although a few of the cases listed I found through actual reading or because someone pointed them out to me. Some of the findings are given above, in the main text or in previous appendices of the present volume. Some more findings are given below, without any claim to systematic effort or thoroughness. To repeat, finding no instances or a certain number of instances of a fortiori argument does not mean that there are not in fact more instances. Moreover, we are here concerned withintendeda fortiori arguments, whether these are validly or invalidly formulated.
I foundnoinstances of the fifteen key phrases of a fortiori discourse in various ancient documents or collections, namely:the stories of Gilgamesh (Sumerian king, 2500 BCE); an anthology of ancient Egyptian literature; the Code of Hammurabi (Babylon, c. 1772 BCE) and several Roman legal documentslisted at the Avalon Project; Homer’sThe Iliad(7thor 8thcentury BCE); two collections of ancient fragments;The Analectsof Confucius (China, 551–479 BCE);the sayings of Epictetus (Greece, 55-135 CE). However, I did find a number of ancient works with one or more instances of the fifteen key phrases of a fortiori discourse. Of course, many more ancient sources could and should be similarly scanned.
InThe OdysseybyHomer(Greece, 7thor 8thcentury BCE, maybe earlier), I found one case (ml): “Fear not a losing game; Phæacian none Will reach thy measure,much lessovercast.”This is an important finding, being the earliest case I found in Greek literature.
InThe FablesbyAesop(Greece, c. 620–564 BC), I found one case (hmm): “The fox and the Leopard disputed which was the more beautiful of the two. The Leopard exhibited one by one the various spots which decorated his skin. But the Fox, interrupting him, said, ‘andhow much morebeautiful than you am I, who am decorated, not in body, but in mind.’”
InThe History of the Peloponnesian WarbyThucydides(Greece, c. 460-395 BCE), I found the seven cases (2 atm, 2 mm, 2 ml, 1 smtm), viz.:
·1:5. “It would be difficult for any system of fortifications to establish a rival city, even in time of peace,much more, surely, in an enemy’s country, with Athens just as much fortified against it as it against Athens.”
·2:6.“And if our more remote ancestors deserve praise,much moredo our own fathers, who added to their inheritance the empire which we now possess, and spared no pains to be able to leave their acquisitions to us of the present generation.”
·3:9. “Our revolt, however, has taken place prematurely and without preparation–a fact which makes itall the moreincumbent on you to receive us into alliance and to send us speedy relief, in order to show that you support your friends, and at the same time do harm to your enemies.”
·5:17. “Melians: Is that your subjects’ idea of equity, to put those who have nothing to do with you in the same category with peoples that are most of them your own colonists, and some conquered rebels? Athenians: As far as right goes they think one has as much of it as the other, and that if any maintain their independence it is because they are strong, and that if we do not molest them it is because we are afraid; so that besides extending our empire we should gain in security by your subjection; the fact that you are islanders and weaker than others rendering itall the moreimportant that you should not succeed in baffling the masters of the sea.”
·6:19. “I do not well see how they could avoid annihilation if they brought with them another city as large as Syracuse, and settled down and carried on war from our frontier;much lesscan they hope to succeed with all Sicily hostile to them.”
·6:20. “I would have him bear in mind that he will fight in my country, not more for mine than for his own, and byso much the moresafely in that he will enter on the struggle not alone, after the way has been cleared by my ruin, but with me as his ally.”
·8:24. “After its late misfortunes it could hardly be justified in voluntarily taking the offensive even with the strongest force, except in a case of absolute necessity:much lessthen without compulsion could it rush upon peril of its own seeking.”
I have elsewhere mentioned a fortiori discourse in some Indian and Chinese classics. For instances, I mention one case (hml) inTheDhammapada, which is traditionally attributed to the Buddha (c. 563-483 BCE), and four cases (hml, hmm, 2 ht) in theBhagavad-Gita(India, c. 5th-2ndcenturies BCE). Also, I mention one case (ml) in Lao Tzu’sTao Te Ching(traditionally dated 6thcentury BCE, though more probably late 4thcentury or early third century BCE), and two cases (hmm) in Sun Tzu’sThe Art of War(also traditionally dated to the 6thcentury BCE, but probably of later origin). Note that the main four moods of a fortiori argument (+s, –s, +p, –p) can be found in such ancient literature collectively.
Cicero(Rome, 106-43 BCE)uses a fortiori form at least twice (hmm, mm): in a speech to the Senate, he says: “If, twenty years ago, I declared in this house that death could never be said to have come before its time to a man who had been consul of Rome, withhow much moretruth, at my age, may I say it now;” in a letter to Paetus, he writes: “You seem to insinuate that when grandees are so moderate,much moreought a poor ex-consul like myself so to be.”
Marcus Aurelius(Rome, 121-180 CE) uses the form at least three times (hmm, mm, ml) in hisMeditations:
·3:10. “Short then is the time which every man lives, and small the nook of the earth where he lives; and short too the longest posthumous fame, and even this only continued by a succession of poor human beings, who will very soon die, and who know not even themselves,much lesshim who died long ago.”
·11:18. “Considerhow much morepain is brought on us by the anger and vexation caused by such acts than by the acts themselves, at which we are angry and vexed.”
·11:29. “Neither in writing nor in reading wilt thou be able to lay down rules for others before thou shalt have first learned to obey rules thyself.Much moreis this so in life.”
From the above examples, and many other cases given earlier in the course of the present study, it is evident that a fortiori discourse has been in common use in both the West and the East for a long time. Judging by the data I have at hand, the earliest known record of such use appears to be the Torah, i.e. possibly as early as 1300 BCE, if the traditional date is accepted (and earlier still, if we consider the probable dates of the stories told within the Torah that contain an a fortiori argument). In Greek literature, the argument appears as early as the 7thor 8thcentury BCE, maybe earlier, in Homer’sThe Odyssey. In India and in China, the earliest date is probably around the 5thcentury CE. But these dates should not be considered definitive, since they are not based on thorough examination of all extant world literature.
2.More recent literature
Let us now take a look at a fortiori discourse in more recent literature. We shall here focus principally on philosophical literature. I have here again only looked for the fifteen key phrases, and not bothered to look for vaguer phrases or other indices. Moreover, I have only briefly, in an offhand manner, examined the instances found. Needless to say, to the authors mentioned below must be added the authors mentioned in the rest of the present study. In other words, the listing below is not intended by itself as an exhaustive study, but merely as a set of examples taken more or less at random.
NiccoloMachiavelli(Italy, 1469-1527), inThe Prince,uses a fortiori discourse at least 3 times (atm); for example: “And for this very reason the Prince ought the less to fear, because after a few days, when the first ardour has abated, the injury is already done and suffered, and cannot be undone; and the people will now,all the morereadily, make common cause with their Prince from his seeming to be under obligations to them, their houses having been burned and their lands wasted in his defence.”
FrancisBacon(Britain, 1561-1626), inThe Advancement of Learning, uses a fortiori discourse at least 4 times (1 hmm, 1 smm, 2 mm):
·“If the invention of the ship was thought so noble, which carrieth riches and commodities from place to place, and consociateth the most remote regions in participation of their fruits,how much moreare letters to be magnified, which as ships pass through the vast seas of time, and make ages so distant to participate of the wisdom, illuminations, and inventions, one of the other?” (1:8:6.)
·“So of degenerate and revolted spirits, the conversing with them or the employment of them is prohibited,much moreany veneration towards them.” (2:6:2.)
·“And if the government of the countenance be of such effect,much moreis that of the speech, and other carriage appertaining to conversation.” (2:23:3.)
·“As in nature, the more you remove yourself from particulars, the greater peril of error you do incur;so much morein divinity, the more you recede from the Scriptures by inferences and consequences, the more weak and dilute are your positions.” (2:25:12.) It is interesting to note that this idea is implicit in the rabbinicaldayoprinciple.
Regarding WilliamShakespeare(Britain, 1564-1616), in all of his works, I found only 13 instances of the fifteen key phrases of a fortiori discourse (3 hmm, 1 smm, 6 mm, 2 ml, 1 smtm). A bit disappointed, I exceptionally to be on the safe side tried out a couple of other phrases, and found 2 more instances of the argument (1 ama, 1 at). The following are 7 selected examples:
·The Sonnets(54). “Ohow much moredoth beauty beauteous seem, by that sweet ornament which truth doth give!”
·Macbeth(1:7). “What beast wast then that made you break this enterprise to me? When you durst do it, then you were a man, and, to be more than what you were, you would beso much morethe man.”
·Much Ado About Nothing(3:3). “I would not hang a dog by my will,much morea man who hath any honesty in him.”
·The Winter’s Tale(5:1). “To greet a man not worth her pains,much lessth’ adventure of her person?”
·King Henry the Eighth(2:3). “Alas, poor lady! She’s a stranger now again.So much the moremust pity drop upon her.”
·The Merry Wives of Windsor(1:1). “I’ faith, I’ll eat nothing; I thank youas much asthough I did.”
·As You Like It(1:2). “With his mouth full of news. Which he will put on us as pigeons feed their young. Then shall we be news-cramm’d.All thebetter; we shall be the more marketable.”
DavidHume(Scotland, 1711-1776), inAn Enquiry Concerning Human Understandinguses a fortiori discourse at least 6 times (1 hmm, 2 mm, 3 ml), and does so very clearly:
·“When we reason a priori, and consider merely any object or cause, as it appears to the mind, independent of all observation, it never could suggest to us the notion of any distinct object, such as its effect;much less, show us the inseparable and inviolable connexion between them.” (Sect. 4, part 1, §27.)
·“Neither can they dwell with constancy on his mind, even though undisturbed by the emotions of pain or passion;much lesscan they maintain their ground when attacked by such powerful antagonists.” (Sect. 8, part 2, §79.)
·“I need not mention the difficulty of detecting a falsehood in any private or even public history, at the place, where it is said to happen;much morewhen the scene is removed to ever so small a distance.” (Sect. 10, part 2, §97.)
·“No testimony for any kind of miracle has ever amounted to a probability,much lessto a proof.” (Sect. 10, part 2, §98.)
·“So far as the traces of any attributes, at present, appear, so far may we conclude these attributes to exist. The supposition of farther attributes is mere hypothesis;much morethe supposition, that, in distant regions of space or periods of time, there has been, or will be, a more magnificent display of these attributes.” (Sect. 11, §106.)
·“Yet nothing appears more certain to reason, than that an infinite number of them composes and infinite extension.How much morean infinite number of those infinitely small parts of extension, which are still supposed infinitely divisible.” (Sect. 12, part 2, §124, fn. 32.)
Regarding ImmanuelKant(Prussia, 1724-1804): inThe Critique of Pure Reason, I found 8 instances (2 atm, 2 mm, 4 ml) of the fifteen key phrases. InThe Critique of Practical Reason, I found 3 instances (2 ml, 1 smtm). InLectures on Logic,I found 11 instances (10 atm, 1 ml). I list most cases found, out of interest in their subject-matter. Note that in none of the cases found is there any discussion of the a fortiori argument as such – these are only examples of its use.
·“For it is a necessary condition of every cognition that is to be established upon a priori grounds that it shall be held to be absolutely necessary;much moreis this the case with an attempt to determine all pure a priori cognition, and to furnish the standard—and consequently an example— of all apodeictic (philosophical) certitude.” (Pure, preface to 1sted.)
·“The early success of logic must be attributed exclusively to the narrowness of its field, in which abstraction may, or rather must, be made of all the objects of cognition with their characteristic distinctions, and in which the understanding has only to deal with itself and with its own forms. It is, obviously, amuch moredifficult task for reason to strike into the sure path of science, where it has to deal not simply with itself, but with objects external to itself.” (Pure, preface to 2nded.)
·“But of what kind is this intuition? Is it a pure a priori, or is it an empirical intuition? If the latter, then neither an universally valid,much lessan apodeictic proposition can arise from it, for experience never can give us any such proposition.” (Pure, part 1, sect. 2, sub-sect. 9, 1)
·“So that thus we should not be men, but belong to a class of beings, the possibility of whose existence,much lesstheir nature and constitution, we have no means of cognizing.” (Pure, part 2, 1stdivision, book 2, Remark on the amphiboly of the conceptions of reflection.)
·“If – as often happens – empiricism, in relation to ideas, becomes itself dogmatic and boldly denies that which is above the sphere of its phenomenal cognition, it falls itself into the error of intemperance – and error which is hereall the morereprehensible, as thereby the practical interest of reason receives an irreparable injury.” (Pure, part 2, 2nddivision, book 2, chapter 2, section 3, 2.)
·“And, how far soever we have to travel upon the path of experience to discover some fact or event, this idea requires us to believe that we have approachedall the morenearly to the completion of its use in the sphere of nature, although such completion can never be attained.” (Pure, part 2, 2nddivision, book 2, chapter 3, section 7, appendix.)
·“Negative judgements—those which are so not merely as regards their logical form, but in respect of their content—are not commonly held in especial respect. They are, on the contrary, regarded as jealous enemies of our insatiable desire for knowledge; and it almost requires an apology to induce us to tolerate,much lessto prize and to respect them.” (Pure, part 2, 2nddivision, book 2, chapter 3, section 8, 2.)
·“No power of the understanding could infer from the conceptions which we previously possessed of these substances;much lessis there any a priori law that could conduct us to such a conclusion, which experience alone can certify.” (Pure, part 2, 2nddivision, book 2, chapter 1, section 2.)
·“These, on account of the uniformity of conduct, exhibit a natural connection, which however does not make the vicious quality of the will necessary, but on the contrary, is the consequence of the evil principles voluntarily adopted and unchangeable, which only make itso much the moreculpable and deserving of punishment.” (Practical, book 1, chapter 3.)
·“A scholar who has not come so far as to guide himself,much lessto guide others.” (Practical, book 2, chapter 1.)
·“In all cases where the want is founded on inclination, which cannot necessarily postulate the existence of its object even for the man that is affected by it,much lesscan it contain a demand valid for everyone.” (Practical, book 2, chapter 2.)
·“Through an excess of learnedness people often becomeall the moreabsurd and completely unfit for judgingin concreto. The healthy understanding, which is small but correct, involvessimplicity. Itremains on the ground of experience and does not love chimerical ideals. This very simplicity makes the understandingall the morecorrect, certain, and reliable than science.” (Logic, p. 10).
·“Many prejudices are such and of the kind that if one dared to attack them, to extinguish them, to try to clear them away, they would nonetheless make [the] mind of manall the moreembittered, indeed, would deafen man to listening and attending to true doctrines and importantdogmata,which have great consequences for them.” (Logic, p. 134-5).
·“There are cases where precision cannot appropriately be sought, and where it causes indistinctness, although it providesall the moredistinctness for a capable mind.” (Logic, p. 302).
·“In the case of unity, I infer that because many consequences fit with one ground, it isall the moreprobable that [this] ground is true and is the right one.” (Logic, p. 335).
·“He who hates science but loves wisdomall the moreis called amisologist.Misology arises commonly out of an emptiness of scientific cognitions and a certain vanity bound up with that.” (Logic, p. 539).
HendrikLorentz(Holland, 1853-1928), inThe Einstein Theory of Relativity, has one a fortiori argument (atm): “It is not necessary to give up entirely even the ether. Many natural philosophers find satisfaction in the idea of a material intermediate substance in which the vibrations of light take place, and they will very probably beall the moreinclined to imagine such a medium when they learn that, according to the Einstein theory, gravitation itself does not spread instantly, but with a velocity that at the first estimate may be compared with that of light.”
KaitenNukariya(Japan, c. 1913), inThe Religion of the Samurai: A Study of Zen Philosophy and Discipline in China and Japan, uses the argument at least 4 times (2 atm, 2 hmm): For example: “Similarly, it is the case with religion and morality. If we admit extreme idealism as true, there can be nothing objectively real. God is little more than a mental image. He must be a creature of mind instead of a Creator. He has no objective reality. He is when we think He is. He is not when we think He is not. He is at the mercy of our thought.How much moreunreal the world must be, which is supposed to have been created by an unreal God! Providence, salvation, and divine grace–what are they? A bare dream dreamed in a dream!” Also: “The believer of Buddha is thankful even for death itself, the which is the sole means of conquering death. If he be thankful even for death,how much morefor the rest of things!”
Moreover, I found instances of a fortiori discourse using the fifteen key phrases in the following books. (I give no examples in these cases, but the reader may readily find them.)
·J.-J. Rousseau (Geneva-France, 1712-1778), in theConfessions, three cases (1 hml, 2 ml).
·Adam Smith (Scotland, 1723-1790), inThe Wealth of Nations, four cases (2 hml, 1 smtg, 1 smtl).
·Thomas Paine (England-America,1737-1809), inCommon Sense, two cases (1 mm, 1 ml).
·InThe Federalist Papers(USA, 1787-8), written by Alexander Hamilton, James Madison, and John Jay, under the pseudonym of Publius, one case (hmm).
·Arthur Schopenhauer (Germany, 1788-1860), in a collection of his essays, two cases (hmm).
·John Stuart Mill (Britain, 1806-1873), inA System of Logic, seventeen cases (4 af, 1 atm, 1 hmm, 3 mm, 8 ml); inOn Liberty, four cases (1 af, 3 atm).
·W. Stanley Jevons (Britain, 1835-1882), inThe Principles of Science, one case (atm).
·Friedrich Nietzsche (Germany, 1844-1900), inBeyond Good And Evil, four cases (2 atm, 2 ml); inThus Spake Zarathustra, two cases (ml).
·Wilhelm Windelband (Germany, 1848-1915), inHistory of Philosophy, forty-six cases (45 atm, 1 ml); inAn Introduction To Philosophy, five cases (all atm).
On the other hand, using the fifteen key phrases I looked for a fortiori discourse in the following books, and foundnoinstances in them:The Book of Five Ringsby Miyamoto Musashi (Japan,c. 1584-1645);Discourse on Methodby Rene Descartes (France,1596-1650);Candideby Voltaire (France,1694-1778);The Age of Reasonby Thomas Paine (England-America,1737-1809);The U.S. Constitutionby James Madison (USA,1751-1836);The Origin of Speciesby Charles Darwin (Britain, 1809-1882);Dream Psychologyby Sigmund Freud (Austria-England,1856-1939);The Book of Teaby Kakuzo Okakura (Japan, 1863-1913);The Problems of PhilosophyandMysticism and Logic and Other Essaysby Bertrand Russell (Britain,1872-1970).
Summarizing the above information somewhat, we obtain the following results regarding the language used and its frequency: in the 16th– 17thcent., 4 atm, 4 hmm, 2 smm, 7 mm, 2 ml, 1 smtm; in the 18thcent., 2 atm, 2 hmm, 5 mm, 3 hml, 12 ml, 2 smtm, 1 smtl; in the 19thcent., 5 af, 5 atm, 3 hmm, 3 mm, 12 ml; in the 20thcent., 48 atm, 2 hmm, 1 ml. We cannot, of course, draw any definite conclusions from such scattered data. But we can say that the verbal expression of a fortiori discourse has remained widely used and pretty uniform in modern times.
These are given online atetcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=c.1.8.1*#.
Ancient Egyptian Literature: An Anthology. Tr. John L. Foster. Austin, Tx.: U. of Texas, 2001.
Namely: The Twelve Tables (450 BCE), The Acilian Law on the Right to Recovery of Property Officially Extorted (122 BCE), The Agrarian Law (111 BCE), The Edicts of Augustus and Decree of the Senate on the Judicial Process in Cyrene (64 BCE), The Julian Law on Agrarian Matters (c. 58 BCE), The Law of Caesar on Municipalities (44 BCE), and The Charter of Urso (44 BCE).
The Yale Law School Avalon Projectavalon.law.yale.edu/subject_menus/ancient.asp. I tested all Roman law documents shown there, but notThe Athenian Constitution, because it is included in the works of Aristotle (dealt with in Appendix 4).
Ancient Fragments, Containing What Remains Of The Writings Of Sanchoniatho, Berossus, Abydenus, Megasthenes, And Manetho(Isaac P. Cory, undated – Forgotten Books, 2010); andAncilla To The Pre-Socratic Philosophers(Kathleen Freeman, 1948 – Forgotten Books, 2010).
Wiseman, in a footnote on p. 131, claims an example of a fortiori argument is to be found in “Homer 386;” maybe it is the same case.
Tr. by George F. Townsend. Kindle, undated.
Tr. by Richard Crawley. Kindle, 2008-9. The references here given are the book and chapter numbers (although the book numbers are continuous).
See chapter 12.2-3.
Cicero. Ancient Classics for English Readers.Ed. by W. Lucas Collins. Kindle, 2004.
Thoughts of Marcus Aurelius. Kindle, 2004.
Kindle, 2004 (based on Cassel, 1893 ed.).
The Complete Works of William Shakespeare. Kindle, 1994.
The 8 other cases found are in:The Sonnets(2), hmm.King Henry the Eighth(5:3), hmm.King Henry the Fourth, Second Part(1:3), mm.The Life ofKing Henry the Fifth(5, prologue), 2 mm.Measure for Measure(5:1), mm.The History of Troilus and Cressida(5:6), mm.The Tempest(3:1), ml.
Kindle, 2006 (based on a 1902 ed. based on 1777 ed.), fn 32.
Tr. Michael Young. Cambridge: UP, 1992.
The cases not listed are inLogic, p. 146 (3 atm), p. 318 (atm), p. 366 (atm), p. 474 (ml). Note that the systems of reference in the twoCritiquesare very confusing, at least in the editions I have used; I do the best I can but without full certainty that the references I give are accurate.
The Essays of Arthur Schopenhauer; Religion, a Dialogue, Etc.Kindle, 2004.
A System of Logic, Ratiocinative and Inductive. Kindle, 2009.
The Principles of Science: A Treatise on Logic and Scientific Method. London: MacMillan, 1913.
Tr. James H. Tufts. 2nded. London: MacMillan, 1914.
Tr. Joseph McCabe. London: Fisher-Unwin, 1914.