Peter of Spain is the author of the most famous of all medieval handbooks on logic and semantics. He composed his Tractatus, later called Summule logicales, in around 1235 (Peter of Spain 1972). Until recently, Peter was thought to be the later pope John XXI, but this is no longer accepted (Spruit 2000). His exact identity is not certain.
According to Peter, signification has an extensional and an intentional side. He defines it as the presentation of something by way of a conventional word.
The counterpart of signification is supposition and copulation. Peter defines supposition as the acceptance of a substantival term for something. In the proposition ‘‘a man runs,’’ ‘‘man’’ supposits, e. g., Socrates. Peter’s use of ‘‘acceptance’’ is remarkable. Supposition is here less a property of a term than a term as far as it is understood by someone. Supposition is equally related to existing and nonexisting things. Roger Bacon, who will be discussed below, takes a different position with respect to reference to nonexistent things or empty classes, as we shall see.
Peter makes a division of supposition. He divides it into common and discrete (i. e., when a term stands for an individual). Common supposition is subdivided into natural and accidental. Accidental supposition is further divided into simple and personal. The notions of natural, personal, and simple supposition Peter discusses also feature in the tradition, although differently defined.
Natural supposition is the natural capacity of a term to have supposition for all actual and possible individuals belonging to the universal term, e. g., ‘‘flower.’’ It owes this capacity to its signification. According to this aspect, the term is able to supposit for things, within or without a context, within or without a proposition. So natural supposition is a kind of extensional counterpart of signification. The latter is independent from any usage. The notion of natural supposition is clearly an extension of his semantics. It resembles Sherwood’s habitual supposition, which I shall explain below.
Simple supposition belongs to a general term, Peter says. An example in subject position is ‘‘man is a species’’; however, it can also occur with a term in predicate position, e. g., ‘‘man is an animal,’’ where ‘‘animal’’ has simple supposition. Another example is ‘‘of all contraries is the same discipline.’’ ‘‘Discipline’’ is in predicate position and has simple supposition. The next kind of occurrence Peter distinguishes is when a term (‘‘man’’) immediately follows an exceptive word, e. g., ‘‘every animal except man is irrational.’’ Here there is no descent to ‘‘this man.’’ It is clear that simple supposition is ambiguous: it refers to both a logical notion and to a kind of reality, for instance, animality.
Peter defines personal supposition as the acceptance of a common term for its inferiors, for instance of a man in ‘‘a man runs.’’
Peter clearly distinguishes between supposition and making a proposition true. For in ‘‘a man runs,’’ ‘‘man’’ has personal and determinate supposition, i. e., an indefinite term or a term to which a sign such as ‘‘some’’ is added (‘‘some man runs’’) supposits for every man, both running and not running. Still, the proposition is true when only a single man runs. Although the term ‘‘man’’ supposits for men both running and not running, the proposition is true for a single running man. We may conclude that Peter’s notion of supposition is wide: it includes nonexisting things.
Copulation is the acceptance of an adjectival term for something. Peter does not devote more words to it.
Ampliation is also acknowledged as a property of a term; it is discussed in Peter’s short tract IX. Together with restriction, it is taken as a further refinement of personal supposition. Ampliation is the extension of a common term from a smaller range to a wider, for instance in (Peter’s example) ‘‘a man can be the Antichrist,’’ ‘‘man’’ supposits not only for men that are, but also for men that can be. Such an ampliation occurs, Peter says, when a common noun is used in combination with a verb such as ‘‘can,’’ or with an adjectival noun like ‘‘possible,’’ as in ‘‘that a man is the Antichrist is possible,’’ or with an adverb like ‘‘ofnecessity’’ in ‘‘man ofnecessity is an animal,’’ where ‘‘man’’ is ampliated to have supposition for the present and the future (note that Peter does not mention the past, to which ampliation does not seem to be possible according to him). Specific expressions possess ampliative force, such as ‘‘can,’’ ‘‘necessity,’’ not just any noun or adverb.
Restriction is defined as the limitation of a common term from a wider to a smaller range of supposition. It occurs in virtue of an adjectival noun, for instance, in ‘‘white man,’’ where ‘‘man’’ is restricted in its supposition (note that Peter does not give a proposition with a copula). It can also occur in virtue of a verb, for instance in ‘‘man runs’’; or it occurs in virtue of a participle, for instance, ‘‘man’’ in ‘‘a running man disputes,’’ or, finally, it can occur in virtue of what he calls an ‘‘implication,’’ for instance, of ‘‘man’’ in ‘‘man who is white, runs.’’
In this tract, Peter adds the interesting comment that there is a difference between strict logic and common usage, for instance, when we say ‘‘nothing is in the box.’’ There is something in the box, viz., air. The same applies to ‘‘the queen arrives’’ said in the Netherlands. Here ‘‘queen’’ is restricted by usage to Queen Beatrix of the Netherlands.
Peter hardly devotes any attention to appellation. He defines it as the acceptance of a common term for an existing thing. He wishes to exclude terms like ‘‘Cesar,’’ ‘‘Antichrist,’’ and ‘‘chimera.’’ Appellation has been moved to the background. It is a kind of restricted supposition, in a proposition with a verb in the present tense, and it has become a secondary notion. As such it is a counterpart of supposition.
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