Supposition theory
Encyclopedia
Supposition theory was a branch of medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of reference
Reference
Reference is derived from Middle English referren, from Middle French rèférer, from Latin referre, "to carry back", formed from the prefix re- and ferre, "to bear"...

, plurality
Plural
In linguistics, plurality or [a] plural is a concept of quantity representing a value of more-than-one. Typically applied to nouns, a plural word or marker is used to distinguish a value other than the default quantity of a noun, which is typically one...

, tense
Grammatical tense
A tense is a grammatical category that locates a situation in time, to indicate when the situation takes place.Bernard Comrie, Aspect, 1976:6:...

, and modality
Linguistic modality
In linguistics, modality is what allows speakers to evaluate a proposition relative to a set of other propositions.In standard formal approaches to modality, an utterance expressing modality can always roughly be paraphrased to fit the following template:...

, from within an Aristotelian
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 context. Philosophers such as John Buridan, William of Ockham
William of Ockham
William of Ockham was an English Franciscan friar and scholastic philosopher, who is believed to have been born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of...

, William of Sherwood
William of Sherwood
William of Sherwood was a medieval English Scholastic philosopher, logician and teacher.Little is known of his life, but he is thought to have studied in Paris, as a master at Oxford in 1252, treasurer of Lincoln from 1254/8 onwards, and a rector of Aylesbury.He was the author of two books which...

, Walter Burley
Walter Burley
Walter Burley was a medieval English Scholastic philosopher and logician. He was a Master of Arts at Oxford in 1301, and a fellow of Merton College, Oxford until about 1310. He spent sixteen years at Paris until 1326, becoming a fellow of the Sorbonne by 1324. After that, he spent seventeen...

, and Peter of Spain
Peter of Spain
Peter of Spain or, in Latin, Petrus Hispanus is the Mediaeval author of Tractatus, later known as Summulae logicales magistri Petri Hispani , a standard textbook on logic...

 were its principal developers. By the 14th century it seems to have drifted into at least two fairly distinct theories, the theory of "supposition proper" which included a "ampliation" and is much like a theory of reference, and the theory of "modes of supposition" whose intended function is not clear.

Supposition proper

Supposition was a semantic relation between a term and what it is being used to talk about.
So, for example, in the suggestion Drink another cup the term cup is suppositing for the wine contained in the cup.
The logical suppositum of a term was the object the term referred to, (in grammar suppositum was used in a different way). However, supposition was a different semantic relationship than signification. Signification was a conventional relationship between utterances and objects mediated by the particularities of a language. Poculum signifies in Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

, what cup signifies in English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

. Signification is the imposition of a meaning on an utterance, but supposition is taking a meaningful term as standing in for something. According to Peter of Spain "Hence signification is prior to supposition. Neither do they belong to the same thing. For to signify belongs to an utterance, but to supposit belongs to a term already, as it were, put together out of an utterance and a signification." An easy way to see the difference is in our drink another cup example. Here cup as an utterance signifies a cup as an object, but cup as a term of the language English is being used to supposit for the wine contained in the cup.

Medieval logicians divided supposition into many different kinds, and the jargons for the different kinds, and their relations and what they all mean get complex, and differ greatly from logician to logician. Paul Spade's webpage has a series of helpful diagrams here. The most important division is probably between material, simple, personal, and improper supposition. A term supposits materially, when it is used to stand in for an utterance or inscription, rather than for what is signifies. When I say Cup is a monosyllabic word, I am using the word cup to supposit materially for the utterance cup rather than for a piece of pottery. Material supposition is a medieval way of doing the work we would do today by using quotation marks. According to Ockham (Summa of Logic I64, 8) "Simple supposition occurs when a term supposits for an intention of the soul, but is not take significatively." The idea is that simple signification happens when the term is standing in for a human concept rather than for the object itself. If I say Cups are an important type of pottery the term cups is not standing in for any particular cup, but for the idea of a cup in the human mind (according to Ockham, and many medieval logicians, but not according to John Buridan). Personal supposition in contrast is when the term supposits for what it signifies. If I say Pass me the cup the term cup is standing in for the object that is called a cup in English, so it is in personal supposition. A term is in improper supposition, if it is suppositing for an object, but a different object than it signifies, as in my example Drink another cup.

Modes of supposition

Personal Supposition was further divided in types such as discrete, determinate, merely confused, and confused and distributive. In 1966 T.K. Scott proposed giving a separate name for Medieval discussions of the subvarieties of personal supposition, because he thought it was a fairly distinct issue from the other varieties of supposition. He proposed calling the subvarieties of personal supposition a theory of "modes of supposition."

The Medieval logicians give elaborate sets of syntactical rules for determining when a term supposits discretely, determinately, confusedly, or confusedly and distributively. So for example the subject of a negative claim, or indefinite one supposits determinately, but the subject of a singular claim supposits discretely, while the subject of an affirmative claim supposits confusedly and determinately. Albert of Saxony
Albert of Saxony (philosopher)
Albert of Saxony was a German philosopher known for his contributions to logic and physics...

gives 15 rules for determining which type of personal supposition a term is using. Further the medieval logicians did not seem to dispute about the details of the syntactic rules for determining type of personal supposition. These rules seem to be important because they were linked to theories of descent to particulars and ascent from particulars.

When I say I want to buy a cup I've made an indefinite affirmative claim, with cup as the predicate term. Further cup is a common term, including many particular cups within it. So if I "descend to particulars" I can re-phrase my claim as I want to buy this cup or I want to buy that cup, or I want to buy that other cup - and so on for all cups. If I had an infinite disjunction of all particular cups, it could stand in for the term cup, in its simple supposition in I want to buy a cup. This is called determinate supposition. That is when I say I want to buy a cup I mean some determinate cup, but I don't necessarily know which one yet. Likewise if I say Some cup isn't a table, I could substitute This cup isn't a table, or that cup isn't a table or ...

On the other hand if I say No cup is a table, I don't mean This cup isn't a table or that one isn't a table or ... I mean This cup isn't a table, AND that cup isn't a table, AND that other cup isn't a table, AND .... Here I am referring not to a determinate particular cup, but to all cups "fused" together, that is all cups "confusedly." This is called confused and distributive supposition.

If I say This cup is made of gold I cannot descend to a disjunction of particulars, or to a conjunction of particulars, but only because this cup is already a particular. This kind of personal supposition is called discrete supposition.

However, the predicate of a universal affirmative claim won't really fit any of these models. All coffee cups are cups does not imply All coffee cups are this cup, or all coffee cups are that cup, or ..., but still less does it imply All coffee cups are this cup, and all coffee cups are that cup, and .... On the other hand, if it happened to be the case that there was only one coffee cup left in the world, it would be true that All coffee cups are that cup, so I can validly infer from All coffee cups are that cup, to All coffee cups are cups. Here descent to disjunction fails, and descent to conjunction fails, but "ascent from particulars" is valid. This is called "merely confused supposition."

That is basically how the theory works, a much thornier problem is exactly what the theory is for. Some commentators, like Michael Loux, have suggested that the theory of ascent and descent to particulars is intended to provide truth conditions for the quantifiers. T. K. Scott has suggested that the theory of supposition proper was designed to answer the question What kind of thing are you talking about? but the theory of personal supposition was aimed at answering the question How many of them are you talking about? Paul Spade has suggested that by the 14th century the theory of modes of personal supposition wasn't aimed at anything at all anymore.

Ampliation

When I say No cups are made of lead, cups supposits for all the cups that exist. But if I say Some cups were made of lead in Roman times, cups cannot just be suppositing for all the cups that exist, but for cups in the past as well. Here I am expanding the normal supposition of the terms I use. Peter of Spain says "Ampliation is the extension of a common term from a lesser supposition to a greater one." In practice, if I speak of the past, or the future, or make a modal claim, the terms I use get ampliated to supposit for past things, future things, or possible things, rather than their usual supposition for present actual things. Thus, ampliation becomes the medieval theory for explaining modal and tense logics within the theory of supposition.

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