There are two works attributed to the author known as Peter of Spain. The first one is the enormously influential Tractatus or according to the manuscripts Summule logicales magistri Petri Hispani. It is one of the most influential logic works of the Middle Ages and was standard, reading well into the seventeenth century. It was famously commented on by John Buridan in the fourteenth century.
The other work is a Syncategoremata. In almost all of the manuscripts of this work, it follows the Tractatus, and this, together with doctrinal similarities, has led to the assumption that it is by the same author as the Tractatus. Other works have traditionally been ascribed to the author of the Tractatus, for example, a treatise on the soul and also commentaries on Aristotle’s De anima, but it seems unlikely that they are by the same author.
There have been many theories as to who Peter of Spain actually was. The most known is that he was Portuguese and became Pope in 1276 under the name John XXI. Another theory is that he was Spanish and a Dominican. A third view, which has been around since the fifteenth century, is that he was Petrus Ferrandi Hispanus (d. between 1254 and 1259). There are other theories as well, but there is no way to know which one is correct and even whether any of them are correct. Both works mentioned above are from the early part of the thirteenth century, however, and the content is closely related to other logic textbooks of the same time.
The Tractatus
The Tractatus is divided into 12 treatises, they are
1. On propositions (or statements)
2. On predicables
3. On categories
4. On syllogisms
5. On topics or loci
6. On supposition
7. On fallacies
8. On relatives
9. On ampliation
10. On appellation
11. On restriction
12. On distribution
The Tractatus is a summary of logic covering both the so-called logica antiquorum and the logica modernorum.
The first treatise is an introduction dealing with the subject matter of dialectics (or logic) and the different kinds of propositions dealt with in logic. He defines dialectics in the following way:
> Dialectics is the art that holds the road to the principles of all methods, and therefore dialectics should be first in the acquisition of all the sciences (I.1,4-6).
This definition reflects the absolute fundamental aspect of logic for the scholastics. Logic is a tool or an art that, according to scholastics, is presupposed in all science. All study must start with logic.
Dialectics or argumentation presupposes discourse (sermone), and discourse presupposes utterance (vox), which in turn is sound (sono) of a special kind. A sound is either an utterance or not. If it is not an utterance, then it is not of interest to logic. An utterance is either significative or not. An utterance that is significative is a sound, which represents something, for example, ‘‘human being.’’ A non-significative utterance does not represent anything. A significative utterance is either a name (nomine) or a verb (verbo). It is a name if it signifies conventionally something without a time, while a verb signifies conventionally (ad placitum) something with a time. The difference is simply that since a verb signifies a doing of something, it requires time in which the doing takes place, but a name is atemporal; it does not require time for naming something.
An expression (oratio) is a complex significative utterance, that is, it is a sentence such as ‘‘The human being is white.’’ There are also two kinds of expressions, namely perfect or proper expressions and imperfect or improper expressions. An improper expression is, for example, ‘‘white human being.’’ It is improper since it does not contain both a name and a verb. There are, of course, different kinds of expressions according to the different grammatical modes, such as indicative, imperative, perfect, etc., but only indicative expressions are called proposition, and hence only they are important for logic.
A proposition is hence a perfect or proper expression in the indicative mode, which is either true or false. There are furthermore two kinds of propositions, namely categorical and hypothetical. The two kinds of propositions also divide into two kinds of logics; one for categorical propositions and the other for hypothetical.
A categorical proposition is a proposition that has a subject and a predicate as its principle parts. In the proposition ‘‘A human being runs’’ (‘‘homo currit’’), ‘‘human being’’ and ‘‘runs’’ are respectively the subject and the predicate. The logical form of this proposition is not ‘‘A human being runs,'' however, since there is a copula or something binding the subject and predicate (or verb) assumed in between them. The logical form is therefore ‘‘A human being is running.''
There are three kinds of hypothetical propositions, namely conditional, copulative, and disjunctive. A conditional proposition is made up of categorical propositions conjoined with the words ‘‘If... then.’’ A conjunctive proposition conjoins two categorical propositions with ‘‘and,'' and a disjunctive proposition does the same thing with ‘‘or.'' It is the also common to state the conditions under which these hypothetical propositions are true. A conditional proposition is true, if, given the truth of the antecedent, the consequent is also true. A copulative proposition is true if both conjuncts are true, and a disjunctive proposition is true, if at least one of the disjuncts is true.
After having outlined the different distinctions between various propositions, the Tractatus returns to the traditional order, which means that the next part of it deals with the predicables, that is, the topic of Porphyry’s Isagoge. The predicables are universals, which means that they are what can be predicated in the most general sense. The division is the traditional one, namely between genus, differentia, species, property (proprium), and accident.
The treatment of the theory syllogisms in the fourth treatise of the Tractatus is traditional. It does not include a discussion of modal syllogisms. There is no discussion of demonstrative syllogisms in the Tractatus.
Peter's discussion of dialectical arguments in treatise five is also traditional. The treatment of the loci (or topoi) deals with the same issues as Aristotle dealt with in the Topics, but the medieval discussions of the Topics had changed quite a lot, however, and it was Boethius that set the subject matter of this part of logic for the Middle Ages. Peter's discussion of loci is hence based on Boethius' discussion in De differentiis topicis.
The properties of terms are part of the so-called logica modermorum and are dealt with by Peter in treatises VI, IX, X, XI, and XII, which contain discussion about signification, supposition, copulation, appellation, ampliation, restriction, and distribution. To draw the distinction between signification and supposition, Peter notes that some things are said with construction, such as ‘‘A human being runs'' or ‘‘a white human being,'' and things said without construction, such as ‘‘animal.'' Unconstructed terms have signification, and they signify something in one of the ten categories.
Supposition is defined by Peter as the acceptance of a substantive term for something. Signification is prior to supposition in the sense that signification is what a term has all by itself, while supposition is what a term has in a composition. The division of supposition differs a little bit between the textbook authors, but it is foremost only a difference in terminology.
Supposition is either common or discrete, according to Peter. Common supposition is what common terms such as ‘‘human being'' have, while discrete supposition is what discrete terms such as ‘‘Socrates'' and ‘‘this human being'' have. Common supposition is divided into natural and accidental supposition. The natural supposition of ‘‘human being’’ includes all that is naturally apt to stand for, that is, all humans that have been, are, and will be. Accidental supposition is the supposition of a term such as ‘‘human being’’ has in conjunction with something else such as ‘‘a human being exists.’’ In that case, ‘‘human being’’ stands for presently existing humans.
Accidental supposition is divided into simple and personal supposition. A common term has simple supposition when it stands for a universal, like in ‘‘human being is a species.’’ Personal supposition is the acceptance of a common term for its inferiors. It is divided into determinate and confused supposition. A common term has determinate supposition if it is taken indefinitely or with a particular sign; for example, in ‘‘a human being runs’’ or ‘‘Some human being is running.’’ Confused supposition is the acceptance of a common term for several things by means of a universal sign. In ‘‘Every human being is running,’’ ‘‘human being’’ has confused supposition.
Peter makes a further division of confused supposition. There is confused supposition by the necessity of the mode or sign (necessitate signi vel modi) and confused supposition by the necessity of the thing (necessitate rei). In ‘‘Every human being is an animal,’’ ‘‘human being’’ is by the necessity of the mode taken confusedly and distributively for all its supposita. Given that all humans have their own essence, the copula ‘‘is’’ is taken by the necessity of the thing for all essences that ‘‘human being’’ supposits for, and therefore, ‘‘animal’’ is taken by the necessity of the thing for all animality in each human being. By this reasoning, ‘‘human being’’ is said to supposit confusedly, mobilely, and distributively. It supposits confusedly and distributively because it holds for all humans, and it supposits mobilely because descent can be made from it to any of its supposita. ‘‘Animal’’ is said to supposit confusedly and immobilely, since descent is not allowed.
In relation to supposition Peter also discussed notions such as ampliation, appellation, restriction, and distribution. Ampliation and restriction is a division of personal supposition. Restriction is the narrowing of a common term from a larger to a smaller supposition. In ‘‘A white human being is running,’’ ‘‘white’’ has a narrowing effect on the supposition of ‘‘human being.’’ Ampliation is the opposite, that is, the broadening of the supposition of a common term. In the proposition ‘‘A human being can be the Antichrist,’’ the term ‘‘can’’ extends the supposition of ‘‘human being’’ to future things. Tensed or modal proposition tend to have ampliated supposition.
Appellation is related to these two notions. Appellation is the acceptance of a term for an existing thing. It is distinct from signification and supposition, since it only concerns existing things while signification and supposition is wider than that and includes also nonexistence. The appellata of a term are the existing things it stands for. Distribution, which has already been mentioned, is the multiplication of a common term by a universal sign. In ‘‘Every human being,’’ ‘‘human being’’ is distributed for all humans.
The discussion of fallacies is by far the largest part of the Tractatus. His discussion begins by a treatment of disputations. A disputation is an activity of one person ‘‘syllogizing’’ with another to reach a conclusion. Peter explains that five things are needed for a disputation: the originator or the opponent, a respondent, a disputed proposition, the act of disputing, and the instruments of the disputation.
There are four kinds of disputations, namely didactic (doctrinal), dialectical, probative (temptative), and sophistical. The didactic disputation comes to its conclusions from premises peculiar to each discipline and not from what seems true to the respondent. The instruments of such a disputation are demonstrative syllogisms. A dialectical disputation draws contradictions from probable premises. Its instruments are the dialectical syllogisms. Probative disputations argue from what seems true to the respondent. Sophistical disputations argue from what seems probable but is not. The difference between the last two is that the first disputation from what seems true or probable to what is true, but the latter from what seems true or probable but is not.
There are five kinds of sophistical disputations, which derive from the five goals of such disputations, namely refutation (redargutio), falsity (falsum), paradox (inopinabile), babbling (nugatio), and solecism
(soloecismus). Refutation is the denying of what was previously granted or granting what was previously denied. Falsity occurs in the case when a proposition does not conform to reality. A paradoxical disputation is when the conclusion is contrary to the opinion of the many or the wise. Babbling is simply the repetition of the same thing, and finally, solecism is a disputation developing a discourse contrary to grammar.
The presentation of logic in the Tractatus became standard and all discussions started on the foundation presented there. Buridan chose to base his own view on Peter’s not because he thought it was the best of clearest presentation, but because it was most influential.
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