Summa Logicae (Ockham)

The Summa of Logic (Latin Summa Logicae) is an important work by the English philosopher-theologian and logician William of Ockham, written some time between 1323 and 1326. Nearly a thousand pages long, it is organised in three parts according to Aristotle's three functions of the understanding, namely concepts and the terms which signify them (Part I), propositions formed by combining terms together (Part II), and argumentation (Part III). Like all scholarly works of that period, it was written in Latin. It was probably begun at the Franciscan friary at Greyfriars, London , and may have been finished while Ockham was in Avignon where he had been summoned by Pope John XXII to answer charges of heresy.

It is introduced by Ockham as a manual or textbook of logic, but he has the more ambitious purpose of promoting a philosophical programme, according to which philosophical and theological error can be resolved by a correct understanding of logic and language. This idea had a far-reaching influence in Western thought, and is regarded by some as the beginning of European empiricism, by others as an anticipation of twentieth century linguistic philosophy.

The Latin word Summa is difficult to translate, and does not mean a mere summary of its subject, but rather a comprehensive handbook, or manual or compendium, intended to cover all the salient points of the subject, written authoritatively, and from a single point of view.

Objective of the work

Ockham presents the book as a manual or textbook, and its organisation and framework is similar to other such medieval textbooks. But Ockham's objective was more than writing a textbook. His underlying purpose is to promote some radical ideas about language and logic.

He is guided by two principles. The first is that theological and philosophical difficulties are caused by ignorance of logic, by which he means Aristotelian logic, rather than mathematical logic. In his preface to the work, Ockham says the book is to help young students in theology and other faculties from being overcome by such difficulties, "falling into many errors by ignoring valid argument as though it were sophistry, and mistaking sophistry for valid argument". The second is that the root of such logico-linguistic errors is the tendency to multiply entities in accordance with the multiplicity of names, and that not everything that appears to be a name has an entity corresponding to it. This principle - nominalism in the strictest sense - has a wide range of theological and well as philosophical consequences, as Ockham suggests in his introduction. It is sometimes expressed by the maxim that we should not multiply entities beyond necessity (the so-called Ockham's Razor), but Ockham never used this formulation..

Organisation

Like all logical works of the medieval period, the Summa is organised into headings that correspond, for the most part, with the books of Aristotle's logical works known as the Organon, or their derivatives. It is in three parts, corresponding to the three Aristotelian 'operations of the understanding'. The first operation, namely the understanding of simple concepts, signified by terms, is dealt with in Part I. This covers Porphry's theory of the predicables, and the Aristotle's categories. The second operation, namely the combination of simple concepts into propositions, is handled in Part II. This covers Aristotle's book on propositions, De interpretatione. The third operation, the combination of propositions together to form arguments, is dealt with in Part III. Part III is the largest and least studied. It is divided into a further four sections. Section 1 deals with the syllogism, broadly following Aristotle's Prior Analytics, section 2 with scientific demonstration (Posterior Analytics), section 3 with the theory of consequences, a medieval development of ideas found in Aristotle's Topics, and and section 4 with fallacies (Sophistici Elenchi).

Part I. On Terms

Preliminary distinctions

Part I of the Summa presents Ockham's theory of terms. In the first 17 chapters, Ockham introduces a number of distinctions, many of which are fundamental to his whole program of nominalism.

First, he distinguishes between the semantic property of signification, which a term possesses before it forms part of a proposition, and the property of supposition, which it acquires by being combined with another term within a proposition. The first is discussed mainly in chapters 1-62, the second in the last fifteen chapters, 63-77. Ockham draws on the work of earlier logicians of the 13th century for this distinction.

Another distinction is between concrete and abstract terms (chapters 5-9). Concrete and abstract names have a similar beginning verbally, but not similar endings, such as the concrete term 'just' and its corresponding abstract term 'justice'. This allows Ockham to argue that concrete and abstract names are really synonymous. For example, both 'human' and 'humanity' can both really signify someone like Socrates. To imagine that 'humanity' really signifies some entity, different from any human but common to all of them, is to fall into the error of philosophers like Duns Scotus, who thought that human nature is a sort of common entity with 'less than numerical unity'. Ockham had already subjected Scotus' theory to intensive criticism in his earlier Ordinatio

The distinction between terms of so-called first and second intention is intrinsic to Ockham's nominalism. It depends on a distinction made by earlier scholastic writers into written language, spoken language and 'mental' language, following remarks made by Aristotle in early parts of the linguistic work Perihermenias. Written language signifies spoken language. Spoken language signifies thoughts, or mental language. Written and spoken language signify by convention, for as Aristotle says, different languages have different words for the same external thing, but mental language is the same for all humans. A mental term in a mental sentence, such as our concept of 'dog', naturally signifies a dog, and the concept of dog is the same for English, French, German, Japanese or Chinese or Indian speakers. Ockham calls such a mental term an 'intention' – "a certain thing in the soul, which is a sign naturally signifying something for which it can stand for, or which can be part of a mental proposition". Such intentions or mental signs divide into two, namely those which are signs of ordinary external things such as men, tables, chairs etc, and signs of 'second intention', which are signs of first intentions, i.e. which are signs of signs. The concept of genus is a second intention, for when we say 'animal is a genus' we are not talking about some property of a real animal, but rather about a property of the concept or 'intention' of animal which we predicate of the concept animal itself. Ockham says that this is analogous to how one name is predicated of different names in propositions like "man is a name'" and "whiteness is a name". Ockham elaborates on this in chapters 18-25 on the predicables.

The final distinction is between connotative and absolute terms. An absolute term primarily signifies its object: "horse" primarily signifies anything which is a horse, and 'animal' signifies nothing but cattle, donkeys and men and all other animals. By contrast, a connotative name is one that signifies something primarily and something secondarily. For example, a relational term like "father" does not signify some relation of fatherhood subsisting in external reality. Rather, it primarily signifies certain singulars (fathers) and secondarily signifies other singulars (the children). This is important for Ockham's nominalistic interpretation of Aristotle's categories.

The predicables

Chapters 18-25 concern the five Aristotelian Predicables: genus, species, property, specific difference and accident. Here, he draws on the distinction between first and second 'intentions' (mental signs) outlined in chapter 12, to argue that a genus is not something outside the mind, belong to the essential attributes of a species like human, but is a mental sign, predicated of the signs of things outside the mind.

Aristotle's categories

Ockham's detailed and extensive treatment of the Aristotelian categories in chapters 40-62 is on similar lines to his treatment of the predicables. Aristotle listed the categories in order to gather every object of human conception – i.e. everything which can be either the subject or the predicate of a proposition - under one of ten headings. Ockham presents a nominalist interpretation of Aristotle's theory, based on his theory of mental language, arguing that it is a categorisation of simple meaningful terms in our mental language, to which no corresponding categorisation belongs in the world of reality.

Ockham allows only singular substances and qualities as having independent existence in external reality. He does not allow any real distinction between Aristotle's 'primary' and 'secondary' substances (such as the distinction between the individual substance Socrates, and some secondary substance 'humanity' which is common to Plato, Zeno, Aristophanes and all other humanes). Rather, this reflects a division of names, of which some are proper, others common. "Proper names are called first substances, common names are called second substances".

Thus all terms in categories apart from substance and quality are connotative names – even those belonging to the category of quantity. This explains why we should not multiply entities according to the multiplicity of terms, for there is no strict isomorphism between the basic meaningful terms (the categories) and things in external reality.

Thus in chapter 51, Ockham cites Aristotle saying "Therefore some categories signify what thing something is, others what quality it is, others its quantity, others its relation". He takes this to mean that the ten categories are things outside the mind, in external reality, or that they signify ten distinct real things. The thinking of Aristotle is not which terms signify which things, but rather he means to show how some terms are absolute, others connotative, some relative. Thus Ockham takes the teaching of Aristotle as showing that the categories "are ten terms signifying the same things in different ways".

And so, for example, many things that are customarily said about relations are improper, indeed some are "false and fantastical". When we say ‘a father is a father by paternity’, or ‘a similar thing similar by similitude’, we do not have to suppose some real external thing "by which a father is a father or a son a son or a similar thing similar". Nor do we have to multiply entities in saying "God is is good by goodness, is just by justice, is powerful by power", "a suitable thing is suitable by suitability", "a chimera is nothing by nothingness", and so on. This is to multiply entities according to the multiplicity of terms, which is erroneous "and leads far away from the truth".

And so Ockham disposes of the other eight of the ten categories, as corresponding to a linguistic distinction only.

Supposition

Ockham's treatment of 'supposition' in chapters 63-77 is a preliminary to the theory of propositions set out in Part II. When a term occurs as the subject or predicate of a proposition, it thereby acquires a new semantic property called "supposition" (suppositio). This is defined as "a sort of taking the place of another" (SL I.63 - Dicitur autem suppositio quasi pro alio positio). Supposition must be distinguished from signification because supposition is a relation between a term and objects in external reality. In general, the subject of a proposition supposits for that of which the predicate is said by the proposition to be predicated, if the suppositing term is the subject. For example, the proposition ‘A man is an animal’ says that Socrates is an animal, so that ‘This is an animal’ - pointing to Socrates - is true if the proposition is formed. And so 'man' supposits for Socrates, Plato, and all other men.

Following earlier writers, Ockham divides supposition into simple, material, and personal. Simple supposition is when a term supposits for an intention of the soul, i.e. a mental sign like the concept man, as in "man is a species". Material supposition is when a term supposits for an utterance or for writing, as in ‘Man is a name’. Personal supposition, generally, is when a term supposits for its proper significate, whether the significate is a thing outside the mind, or an utterance, or a concept. For example, in saying ‘every man is an animal’, the word ‘man’ supposits for all men because ‘man’ is imposed only to signify these men.

Supposition plays an important role in the theory of propositions that Ockham develops in Part II.

Part II

Simple non-modal propositions

A significant portion (chapters 2-29) of Part II deals with simple propositions, namely those consisting of a subject, the verb 'is' in one of its tenses, and a predicate, where the subject and predicate are singular or general terms having a 'supposition'. The last eight chapters (30-57) deal with more complex ones such as conditional, conjunctive, disjunctive, causal, and temporal).

In chapters 2-8 Ockham provides the truth conditions of non-modal elementary propositions, using the theory of supposition developed in the last fifteen chapters of Part I. A singular affirmative proposition such as "Socrates is a man" does not say that the subject and predicate terms are identical, nor that the predicate 'man' refers to some universal or secondary substance or common nature that inheres in Socrates, for this would require endorsing the Realist theory of common natures or universals that Ockham's nominalism rejects. Rather, the truth-conditions should be expressed in terms of a relation between the supposition of the subject-term and that of the predicate-term. Rather, he says "it is sufficient and requisite that the subject and predicate supposit for the same thing". That is, when the name "Socrates" supposits for Socrates, the proposition 'Socrates is a man' is true when Socrates is one of the individuals that 'man' supposits for in that proposition.

For the truth of 'particular' propositions such as 'some man is running', it is sufficient that the subject and predicate supposit for at least one thing that is the same. Thus if Socrates is running (and if Socrates is a man), it is true. The corresponding negative proposition 'some man is not running' is true when the subject and predicate do not supposit for all the same things, i.e. either that the subject supposits for nothing or that it supposits for something for which the predicate does not supposit. Ockham explains the truth conditions of universal propositions (chapter 4), of propositions where the subject only supposits for two things (chapter 5), and other varieties of proposition including tensed propositions.

Thus the truth-values of such propositions depends on the supposition of their terms (which will depend on how things are in reality – Ockham is not arguing for a form of Linguistic idealism here).

Simple modal propositions

Chapters 9 and 10 deal with the more complicated case of truth-conditions of modal propositions (including belief ascriptions of the form "it is believed by S that p"), a subject to which he returns in the first section of Part III.

Complex propositions

Chapters 11-20 deal with special cases such as hypothetical propositions, propositions using terms like 'begin' or 'stop', so-called exceptive propositions like 'everyone apart from Socrates is running' and other such cases.

Part III

Part III of the Summa the longest, and remains the least studied. Only section 2, on scientific demonstration, has been completely translated.

The first section in 68 chapters, is based on Aristotle's Prior Analytics, containing Ockham's theory of the syllogism. The second, in 41 chapters, is a commentary on the Posterior Analytics, which develops Ockham's theory of scientific demonstration. It deals with questions such as how our concepts of natural things are formed from sensory experience, the relation between everyday notions and more 'scientific' conceptions, how causal principles are based in the real natures of things, and the nature and function of scientific knowledge.

The third section (46 chapters) is partly based on Aristotle's Topics but also partly on medieval developments in the so-called theory of "consequences," or non-syllogistic inferences. The fourth one (18 chapters) is a conspectus of the various sorts of fallacies identified by Aristotle in his treatise On Sophistical Refutations.

References

• Brown, S., "Sign conceptions of logic in the Latin Middle Ages", in Robering and Sebeok,eds., Semiotikein Handbuch zu den zeichentheoretischen Grundlagen von Natur and Kultur, vol. I (pp. 1035-46), Berlin and New York 1997.
• Courtenay, William, "Ockham, Chatton, and the London Studium: Observations on Recent Changes in Ockham's Biography", in Die Gegenwart Ockhams, W. Vossenkuhl and R. Schoeberger, eds., Weinheim 1990, pp. 327-37.

See also

• Summa Logicae in Latin with partial English translation, at the Logic Museum.

Links

• Wikipedia article, which is awful.