オッカム『大論理学』：Summa logicae

オッカムのウィリアム『大論理学』

Summa logicae

The Summa Logicae ("Sum of Logic") is a textbook on logic by William of Ockham. It was written around 1323. Systematically, it resembles other works of medieval logic, organised under the basic headings of the Aristotelian Predicables, Categories, terms, propositions, and syllogisms. These headings, though often given in a different order, represent the basic arrangement of scholastic works on logic. This work is important in that it contains the main account of Ockham's nominalism, a position related to the problem of universals.

Book I. On Terms	Chapters 1–17 deal with terms: what they are, and how they are divide into categorematic, abstract and concrete, absolute and connotative, first intention, and second intention. Ockham also introduces the issue of universals here.	オッカム『大論理学』註解 / オッカム [著] ; 渋谷克美訳註, 創文社　1: 第1部(第1章-第43章).
	Chapters 18–25 deal with the five predicables of Porphyry.
	Chapters 26–62 deal with the Categories of Aristotle, known to the medieval philosophers as the Praedicamenta. The first chapters of this section concern definition and description, the notions of subject and predicate, the meaning of terms like whole, being and so on. The later chapters deal with the ten Categories themselves, as follows: Substance (42–43), Quantity (44–49), Relation (50–54), Quality (55–56), Action (57), Passion (58), Time (59), Place (60), Position (61), Habit (62).	2: 第1部(第44章-第77章).
	Chapters 63–77 onwards deal with the theory of supposition.
Book II. On Propositions	On categorical propositions (1–20)	3: 第2部(第1章-第37章)
	On the conversion of propositions (21–9)
	On hypothetical propositions (30–7)
Book III. On Syllogisms	Part I. On Syllogisms	4: 第3部-1(全68章)
	On categorical syllogisms (1–19)
	On modal syllogisms (20–30)
	On mixed syllogisms (31–64)
	On syllogisms containing exponible propositions
	Part II. On Demonstration	第3部-2(全41章)
	These 41 chapters are a systematic exposition of Aristotle's Posterior Analytics.
	Part III. On Consequences	5: 第3部-3(全46章), 第3部-4(全18章)
	The first 37 chapters of Part II are a systematic exposition of Aristotle's Topics. In Part III, Ockham deals with the definition and division of consequences, and provides a treatment of Aristotle's Topical rules.[1] According to Ockham a consequence is a conditional proposition, composed of two categorical propositions by the terms 'if' and 'then'. For example, 'if a man runs, then God exists' (Si homo currit, Deus est).[2] A consequence is 'true' when the antecedent implies the consequent. Ockham distinguishes between 'material' and 'formal' consequences, which are roughly equivalent to the modern material implication and logical implication respectively. Similar accounts are given by Jean Buridan and Albert of Saxony.
	Chapters 38 to 45 deal with the Theory of obligationes.
	Chapter 46 deals with the Liar Paradox
	Part VI. On Fallacies (in 18 chapters)
	Part IV, in eighteen chapters, deals with the different species of fallacy enumerated by Aristotle in Sophistical Refutations (De sophisticis elenchis).
	Chapters 2-4 deal with the three modes of equivocation.
	Chapters 5-7 deal with the three types of amphiboly.
	Chapter 8 deals with the fallacies of composition, and division.
	Chapter 9 deals with the fallacy of accent.
	Chapter 10 deals with the fallacy of 'figure of speech'.
	Chapter 11 deals with the fallacy of accident.
	Chapter 12 deals with the fallacy of affirming the consequent.
	Chapter 13 deals with secundum quid et simpliciter.
	Chapter 14 deals with Ignoratio elenchi or irrelevant thesis.
	Chapter 15 deals with begging the question (petitio principii).
	Chapter 16 deals with false cause (non-causam ut causam)
	Chapter 17 deals with the fallacy of many questions (plures interrogationes ut unam facere)>
	Ockham ends (chapter 18) by showing how all these fallacies err against the syllogism.

オッカムさんのこと：”William of Ockham was born in Ockham, Surrey in 1287.[citation needed] He received his elementary education in the London House of the Greyfriars.[13] It is believed that he then studied theology at the University of Oxford[2][3] from 1309 to 1321,[14] but while he completed all the requirements for a master's degree in theology, he was never made a regent master.[15] Because of this, he acquired the honorific title Venerabilis Inceptor, or "Venerable Beginner" (an inceptor was a student formally admitted to the ranks of teachers by the university authorities).[16] During the Middle Ages, theologian Peter Lombard's Sentences (1150) had become a standard work of theology, and many ambitious theological scholars wrote commentaries on it.[17] William of Ockham was among these scholarly commentators. However, William's commentary was not well received by his colleagues, or by the Church authorities.[18] In 1324, his commentary was condemned as unorthodox by a synod of bishops,[citation needed] and he was ordered to Avignon, France, to defend himself before a papal court.[17] An alternative understanding, recently proposed by George Knysh, suggests that he was initially appointed in Avignon as a professor of philosophy in the Franciscan school, and that his disciplinary difficulties did not begin until 1327.[19] It is generally believed that these charges were levied by Oxford chancellor John Lutterell.[20][21] The Franciscan Minister General, Michael of Cesena, had been summoned to Avignon, to answer charges of heresy. A theological commission had been asked to review his Commentary on the Sentences, and it was during this that William of Ockham found himself involved in a different debate. Michael of Cesena had asked William to review arguments surrounding Apostolic poverty. The Franciscans believed that Jesus and his apostles owned no property either individually or in common, and the Rule of Saint Francis commanded members of the order to follow this practice.[22] This brought them into conflict with Pope John XXII. Because of the pope's attack on the Rule of Saint Francis, William of Ockham, Michael of Cesena and other leading Franciscans fled Avignon on 26 May 1328, and eventually took refuge in the court of the Holy Roman Emperor Louis IV of Bavaria, who was also engaged in dispute with the papacy, and became William's patron.[17] After studying the works of John XXII and previous papal statements, William agreed with the Minister General. In return for protection and patronage William wrote treatises that argued for emperor Louis to have supreme control over church and state in the Holy Roman Empire.[17] "On June 6, 1328, William was officially excommunicated for leaving Avignon without permission,"[15] and William argued that John XXII was a heretic for attacking the doctrine of Apostolic poverty and the Rule of Saint Francis, which had been endorsed by previous popes.[15] William of Ockham's philosophy was never officially condemned as heretical.[15] He spent much of the remainder of his life writing about political issues, including the relative authority and rights of the spiritual and temporal powers. After Michael of Cesena's death in 1342, William became the leader of the small band of Franciscan dissidents living in exile with Louis IV. William of Ockham died (prior to the outbreak of the plague) on 9 April 1347.[23]”

オッカムさんの哲学："In scholasticism, William of Ockham advocated reform in both method and content, the aim of which was simplification. William incorporated much of the work of some previous theologians, especially Duns Scotus. From Duns Scotus, William of Ockham derived his view of divine omnipotence, his view of grace and justification, much of his epistemology[citation needed] and ethical convictions.[24] However, he also reacted to and against Scotus in the areas of predestination, penance, his understanding of universals, his formal distinction ex parte rei (that is, "as applied to created things"), and his view of parsimony which became known as Occam's Razor. Faith and reason William of Ockham espoused fideism, stating that "only faith gives us access to theological truths. The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic or rationality can uncover."[25] He believed that science was a matter of discovery and saw God as the only ontological necessity.[15] His importance is as a theologian with a strongly developed interest in logical method, and whose approach was critical rather than system building.[26] Nominalism William of Ockham was a pioneer of nominalism, and some consider him the father of modern epistemology, because of his strongly argued position that only individuals exist, rather than supra-individual universals, essences, or forms, and that universals are the products of abstraction from individuals by the human mind and have no extra-mental existence.[27] He denied the real existence of metaphysical universals and advocated the reduction of ontology. William of Ockham is sometimes considered an advocate of conceptualism rather than nominalism, for whereas nominalists held that universals were merely names, i.e. words rather than extant realities, conceptualists held that they were mental concepts, i.e. the names were names of concepts, which do exist, although only in the mind. Therefore, the universal concept has for its object, not a reality existing in the world outside us, but an internal representation which is a product of the understanding itself and which "supposes" in the mind the things to which the mind attributes it; that is, it holds, for the time being, the place of the things which it represents. It is the term of the reflective act of the mind. Hence the universal is not a mere word, as Roscelin taught, nor a sermo, as Peter Abelard held, namely the word as used in the sentence, but the mental substitute for real things, and the term of the reflective process. For this reason William has sometimes also been called a "terminist", to distinguish him from a nominalist or a conceptualist.[28] William of Ockham was a theological voluntarist who believed that if God had wanted to, he could have become incarnate as a donkey or an ox, or even as both a donkey and a man at the same time. He was criticized for this belief by his fellow theologians and philosophers.[29] Efficient reasoning One important contribution that he made to modern science and modern intellectual culture was efficient reasoning with the principle of parsimony in explanation and theory building that came to be known as Occam's Razor. This maxim, as interpreted by Bertrand Russell,[30] states that if one can explain a phenomenon without assuming this or that hypothetical entity, there is no ground for assuming it, i.e. that one should always opt for an explanation in terms of the fewest possible causes, factors, or variables. He turned this into a concern for ontological parsimony; the principle says that one should not multiply entities beyond necessity – Entia non sunt multiplicanda sine necessitate – although this well-known formulation of the principle is not to be found in any of William's extant writings.[31] He formulates it as: "For nothing ought to be posited without a reason given, unless it is self-evident (literally, known through itself) or known by experience or proved by the authority of Sacred Scripture."[32] For William of Ockham, the only truly necessary entity is God; everything else is contingent. He thus does not accept the principle of sufficient reason, rejects the distinction between essence and existence, and opposes the Thomistic doctrine of active and passive intellect. His scepticism to which his ontological parsimony request leads appears in his doctrine that human reason can prove neither the immortality of the soul; nor the existence, unity, and infinity of God. These truths, he teaches, are known to us by revelation alone.[28] Natural philosophy William wrote a great deal on natural philosophy, including a long commentary on Aristotle's Physics.[33] According to the principle of ontological parsimony, he holds that we do not need to allow entities in all ten of Aristotle's categories; we thus do not need the category of quantity, as the mathematical entities are not "real". Mathematics must be applied to other categories, such as the categories of substance or qualities, thus anticipating modern scientific renaissance while violating Aristotelian prohibition of metabasis. Theory of knowledge In the theory of knowledge, William rejected the scholastic theory of species, as unnecessary and not supported by experience, in favour of a theory of abstraction. This was an important development in late medieval epistemology. He also distinguished between intuitive and abstract cognition; intuitive cognition depends on the existence or non-existence of the object, whereas abstractive cognition "abstracts" the object from the existence predicate. Interpreters are, as yet, undecided about the roles of these two types of cognitive activities.[34] Political theory William of Ockham is also increasingly being recognized as an important contributor to the development of Western constitutional ideas, especially those of government with limited responsibility.[35] He was one of the first medieval authors to advocate a form of church/state separation,[35] and was important for the early development of the notion of property rights. His political ideas are regarded as "natural" or "secular", holding for a secular absolutism.[35] The views on monarchical accountability espoused in his Dialogus (written between 1332 and 1347)[36] greatly influenced the Conciliar movement and assisted in the emergence of liberal democratic ideologies.[citation needed] William argued for complete separation of spiritual rule and earthly rule.[37] He thought that the pope and churchmen have no right or grounds at all for secular rule like having property, citing 2 Tim. 2:4. That belongs solely to earthly rulers, who may also accuse the pope of crimes, if need be.[38] After the Fall God had given men, including non-Christians, two powers: private ownership and the right to set their rulers, who should serve the interest of the people, not some special interests. Thus he preceded Thomas Hobbes in formulating social contract theory along with earlier scholars.[38] William of Ockham said that the Franciscans avoided both private and common ownership by using commodities, including food and clothes, without any rights, with mere usus facti, the ownership still belonging to the donor of the item or to the pope. Their opponents such as Pope John XXII wrote that use without any ownership cannot be justified: "It is impossible that an external deed could be just if the person has no right to do it."[38] Thus the disputes on the heresy of Franciscans led William of Ockham and others to formulate some fundamentals of economic theory and the theory of ownership.[38] Logic In logic, William of Ockham wrote down in words the formulae that would later be called De Morgan's Laws,[39] and he pondered ternary logic, that is, a logical system with three truth values; a concept that would be taken up again in the mathematical logic of the 19th and 20th centuries. His contributions to semantics, especially to the maturing theory of supposition, are still studied by logicians.[40][41] William of Ockham was probably the first logician to treat empty terms in Aristotelian syllogistic effectively; he devised an empty term semantics that exactly fit the syllogistic. Specifically, an argument is valid according to William's semantics if and only if it is valid according to Prior Analytics.[42]"

Book III. On Syllogisms, Chapter 15 deals with begging the question (petitio principii).

ラテン語	英語	日本語
CAP. 15. DE FALLACIA PETITIONIS PRINCIPII.
Post fallacias penes quas peccant argumenta peccantia in forma dicendum est de fallaciis penes quas non peccant argumenta sophistica, sed penes quas peccat opponens in arguendo contra respondentem. Quarum prima est petitio principii, quae tunc accidit quando opponens, quamvis inferat conclusionem quam intendit, tamen non potest convincere respondentem, eo quod accipit quod deberet probare.	After the fallacies where the arguments are erroneous in form, we must speak of fallacies where the sophistical arguments are not erroneous, but where the opponent is in error against the respondent. Of which the first is ‘begging the question’, which happens when the opponent, although he infers the conclusion which he intends, nevertheless cannot refute the respondent, because he accepts what ought to be proved.	論証の形式が誤っている場合の誤謬の次に、詭弁が誤っているのではなく、相手が回答者に対して誤りを犯している場合の誤謬について述べなければならない。このうち、第一の誤りは「論点先取（begging the question）」である。これは、相手が自分の意図する結論を推論しているにもかかわらず、証明されるべきことを受け入れているために、回答者に反論できない場合である。
Et dicitur `petitio principii' non quia accipit illud idem quod deberet inferre, tunc enim nulla esset apparentia, sed dicitur opponens petere principium quando accipit aeque ignotum vel ignotius illo quod deberet inferre.	And it is called ‘begging the question’ not because he accepts that same thing which ought to be inferred, for then nothing would be apparent, but rather the opponent is said to beg the question when he accepts what is equally unknown, or more unknown than that which ought to be inferred.	そして、このようなことが「論点」と呼ばれるのは、彼が推論されるべき同じものを受け入れているからではなく、それでは何も明らかでなくなるからであるが、むしろ、相手が、推論されるべきものと同等かそれ以上に未知のものを受け入れるとき、質問をはぐらかすと言われるのだ。
Et propter hoc semper potest respondens petere probationem assumpti quousque accipiat aliquid notius.	And because of this the respondent can always seek a proof of what is assumed until he accepts something more known.	このため、回答者は、より既知のものを受け入れるまで、常に想定されることの証明を求めることができる。
Fit autem ista fallacia multis modis. Uno modo fit quando arguitur a nomine synonymo ad synonymum; sicut sic arguendo `Marcus currit, igitur Tullius currit'.	This fallacy can happen in many ways. It happens in one way when it is argued from a synonymous name to a synonym, for example in arguing ‘Mark runs therefore Tully runs’.	この誤謬はいろいろな形で起こりうる。例えば、「マークが走るからタリーが走る」と主張するように、同義語の名前から同義語へ論証する場合に起こる。
Statim enim accipitur aliquid aeque ignotum cum conclusione inferenda.	For immediately there is accepted something as equally unknown as the conclusion to be inferred.	なぜなら、推論される結論と同じくらい未知のものが即座に受け入れられるからである。
Alius modus est quando arguitur a definitione exprimente quid nominis ad definitum vel e converso. Et hoc quia in omni disputatione debent praesupponi significata vocabulorum. Unde patet quod hic est petitio principii `ignis est productivus caloris, igitur ignis est calefactivus'. Alius modus est quando arguitur ab una convertibili propositione ad aliam, quarum neutra est prior vel notior alia; sicut hic `nullus musicus est grammaticus, igitur nullus grammaticus est musicus'. Unde universaliter quando assumitur aeque ignotum vel ignotius ipsi respondenti quam sit conclusio inferenda, est petitio principii. Sciendum est tamen quod quamvis respondens non possit convinci per rationem dum accipitur aeque ignotum vel ignotius, potest tamen convinci per auctoritatem, si velit auctoritatem recipere. Sicut si respondens nolens negare auctoritatem aliquam, neget istam `Marcus currit', quamvis opponens sic arguat `Tullius currit, igitur Marcus currit' non convincet eum; si tamen ostendit istam `Tullius currit' in auctore quem non vult negare, convincet eum sufficienter.	Another way is when it is argued from a nominal definition to what is defined, or conversely. And this is because in every disputation the significates of the words (vocabulorum) ought to be presupposed. Hence it is clear that 'fire is productive of heat, therefore fire is calefactive' is begging the question.[1] Another way is when it is argued from one convertible proposition to another, of which neither is prior or better known than the other, for example 'no musical thing is skilled in grammar, therefore nothing skilled in grammar is a musical thing'. Hence universally when it is assumed what is equally unknown, or more unknown to that respondent than the conclusion to be inferred, there is begging of the question. It should be known that although the respondent could not be refuted by reasoning while he accepts what is equally unknown or more unknown, yet he may be refuted by authority, if he wishes to receive the authority. For example, if the respondent, not wishing to deny some authority, denies 'Mark runs', although the opponent argues 'Tully runs, therefore Mark runs', the opponent does not refute him. But if if he shows 'Tully runs' in some author which he does not wish to deny, he refutes him sufficiently.	もう一つの方法は、名目的な定義から定義されたものへと論じる場合、あるいはその逆の場合である。なぜなら、あらゆる論争において、言葉の意味（vocabulorum）は前提されるべきものだからである。したがって、「火は熱を生産する、したがって火は熱量がある」というのは明らかに論点先取である[1]。もう一つの方法は、例えば「音楽的なものは文法に熟達していない、したがって文法に熟達しているものは音楽的ではない」というように、どちらも他よりも先行したりよく知られていない、ある変換可能な命題から別の命題へ論じる場合である。したがって、普遍的に、その回答者にとって推論される結論と同等かそれ以上に未知であるものを仮定する場合、そこには論点先取（begging of the question）が存在するのである。回答者が同様に未知のもの、あるいはより未知のものを受け入れている間は、推論によって反論することはできないが、権威を受けようと思えば、権威によって反論することができる、ということは知っておくべきだろう。例えば、ある権威を否定したくない回答者が「マークは走る」を否定した場合、相手が「タリーは走る、だからマークは走る」と主張しても、相手は反論しない。しかし、否定したくない何らかの著者の中で『タリーが走る』を示せば、十分に反論することができる。
Et ita est de aliis.	And so it is in other [cases].	そして、それは他の［ケース］でも同様であう。
http://www.logicmuseum.com/wiki/Authors/Ockham/Summa_Logicae/Book_III-4/Chapter_15	[1] i.e. because 'productive of heat' and 'calefactive' are synonyms	[1]たとえば、「熱が生み出すもの」と「熱い状態」は同義だからである。

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