This chapter examines early scholastic discussions of the ontology of grace and how grace is related to the theological virtues and other spiritual gifts conferred on the soul.

This chapter discusses the early scholastic debates on predestination and merit, which were influenced by Augustine as well as Peter Lombard. In particular, scholastics sought to explain the compatibility of contingent temporal actions and eternal predestination.

This chapter illustrates how Greek and Arabic sources influenced the thinking of early scholastic theologians working on the topic of human nature in four main areas. These are debates about the powers of the soul, the composition of the soul, the relationship between the body and the soul, and the theory of knowledge.

In this introduction, we first describe the contents of the Summa Logicae in some detail, situating the work in the larger context of medieval logical texts of the thirteen and fourteenth centuries and explaining why it occupies pride of place in Ockham’s philosophical project. Second, we argue that the Summa Logicae was most likely composed in Avignon between 1324 and 1328 contrary to the accepted view that Ockham wrote it in London over the summer of 1323. Third, we trace the legacy of the Summa Logicae from its first reception in Oxford and Paris in the 1330s, into the Parisian controversies of the 1330s and 1340s, and its dissemination further into Europe over the course of the next century or so. We end this history by noting the 1974 publication of the modern critical edition of the Summa Logicae, which was an enormously significant landmark in Ockham studies.

Inspired by the later medieval development in logic, especially theories on the properties of terms, Ockham’s modal logic is an innovative expansion of Aristotelian modal logic. Ockham’s treatment of modal logic is evolved systematically on the ground of the medieval distinction between two readings of modal propositions, that is, the reading in the divided and in the composite sense, which can be compared to the de re and de dicto reading in modern modal logic. The result is a comprehensive theory of propositional modal logic and syllogistics. In addition to Aristotle’s modal term logic, Ockham works out syntactic rules for inferences of modal sentences in the composite sense and offers a framework for propositional modal logic. In this chapter, I outline Ockham’s modal logic by describing the related texts, semantics for modalities, the linguistic and logical structure of modal sentences, their truth conditions, propositional modal logic, and modal syllogistics in Ockham.

Ockham’s Summa Logicae treats what modern philosophers would consider philosophy of language and metaphysics, including semantics, Aristotle’s ten categories, and mental language. It is also deeply polemical, especially in Part I (the section covering the notion of a term); hence it is no surprise that his theory of terms supports and defends his parsimonious metaphysics against opponents. Ockham’s view of relational terms in SL is a great example of such a logical theory arising at the crossroads of such issues. Central for Ockham were (1) the ontological implications of relational terms, (2) the question of how they refer, (3) the proper interpretation of Aristotle on relations, and (4) the question of how propositions carrying relational terms should be evaluated by logicians and theologians. After explaining the background ontological controversies mentioned earlier, this chapter exposits Ockham’s main conclusions and most important arguments supporting his favored view of relations.

This chapter provides an overview of William of Ockham’s theory of obligationes, a type of logical disputation developed in the twelfth century, popularized in the thirteenth century and persisting into the Renaissance, as it is found in Part III-3, chapters 39–45, of the Summa Logicae. Ockham discusses six types of obligationes: positio, depositio, dubitatio, impositio, petitio, and sit verum, with a focus on positio. In this chapter I show how Ockham’s theory fits into the history of the development of obligationes, and then discuss, in depth, each of the six types. I highlight some of the distinctive, and in some cases puzzling, aspects of Ockham’s theory.

The idea of figurative discourse plays a salient role in Ockham’s nominalism. He frequently reinterprets certain authoritative statements as mere figurative ways of speaking and this allows him to neutralize the apparent ontological commitments of these authoritative statements when they conflict with the parsimonious ontology that he favors. Section 13.1 of this chapter shows how the method works in practice by providing examples of such figurative interpretations. Sections 13.2 and 13.3 review the theoretical elements that are proposed in the Summa Logicae with respect to figurative speech. It discusses in particular Ockham’s approach to metaphor and his unexpected insistence on hypallage. Section 13.4, finally, examines Ockham’s distinction between the sense a sentence has in virtue of the language and the sense in which it is intended by the speaker. Ockham’s implicit conditions for figurative meaning as opposed to literal meaning are thus brought out.

This chapter discusses Ockham’s views of the formation and character of syncategorematic terms and the roles these views play in his metaphysics and philosophy of language. Ockham claims that thoughts are sentences composed of categorematic and syncategorematic terms and spoken and written descriptions are subordinated to them. He maintains that everything in his ontology can be signified by a categorematic term while syncategorematic terms do not signify. For Ockham, categorematic terms can be thought of as effects of causal contacts made with things and some contemporary scholars, and some of Ockham’s contemporaries, extend this picture to syncategorematic terms as well. This chapter argues that Ockham rejects this extension, denies that distinct true sentences are made true by distinct beings, and embraces the conclusion that there are more truths than truth-makers with profound consequences for his metaphysics.

The chapter on insolubles in Ockham’s Summa Logicae is a short appendix inserted toward the end of Part III-3 in chapter 46, alongside a section on obligations, after the treatment of the Topics and before the transition to the material on the Sophistical Refutations. By Ockham’s own admission, the purpose of the section is not to leave “so great a part of logic completely untouched.” Despite the concise character of the exposition, however, Ockham’s analysis of insoluble propositions is notable for his usual clarity of style and purpose, and by the adoption of a standard medieval solution to semantic paradoxes based on a principle of restriction on self-referential expressions containing the predicates ‘true’ or ‘false.’ The present chapter discusses Ockham’s solution and examples in detail, presenting them in the broader context of coeval discussions of semantic paradoxes from the first quarter of the fourteenth century and against the backdrop of Ockham’s own semantic theory.

Many scholars argue that Ockham is ontologically committed to non-present temporalia. Often, that claim is defended by an appeal to Ockham’s account of the truth conditions for tensed propositions, which these scholars argue entails that a true tensed proposition presupposes non-present temporalia. I argue, however, that the truth conditions that Ockham provides for tensed propositions entail no such thing. For, according to the account that Ockham provides, a tensed proposition is true just in case some equivalent present-tense proposition was (will be) true. A present-tense proposition is ontologically committing only when it is true, however, and, at those times at which it is true, the things it presupposes are presently existing things, not non-present temporalia. Consequently, the claim that Ockham is committed to non-present temporalia cannot be defended by appeal to his account of the truth conditions for tensed propositions.

This chapter examines William of Ockham’s theory of mental speech, focusing on aspects that have been claimed to give rise to the possibility of pernicious ambiguity. Against these claims, which center on the varieties of reference allowed by supposition theory, we argue that Ockham’s theory remains coherent despite marginal instances of ambiguity. We review two types of suppositional ambiguity: Type 1, in which referring terms can be interpreted as suppositing personally, materially, or simply; and Type 2, in which supposition is personal but can vary in tense or modality. Type 1 ambiguity is ruled out, except in extreme cases, by the fact that “changing” the supposition of a term requires a conscious, reflexive act of the speaker; Type 2 ambiguity, while more of a live possibility, is generally either absent or harmless. In neither case does ambiguity seriously compromise the function of mental speech as a vehicle of human cognition.

This chapter presents Ockham’s theory of demonstration in Summa Logicae III-2, the syllogism that produces scientific knowledge. He relies on Aristotle’s Posterior Analytics and Grosseteste’s commentary it. Grosseteste, however, founded the necessity of demonstration on necessary relations in the world. For Ockham, the main challenge is to elaborate a theory of science that addresses the singular beings in a contingent world. His theory is characterized by a conception of purely logical necessity, a semiotic conception of cause, and the requirement that subject terms must have reference in order for affirmative propositions to be true. Many propositions about the natural world are not susceptible to demonstration in the strict sense, but Ockham distinguishes different kinds of demonstration. He is not so much trying to limit the field of demonstrable natural knowledge as to relax the meaning of demonstrability so that it includes many dubitable propositions that can be made evident.

This chapter gives a critical exposition of Ockham’s innovations in the theory of the assertoric syllogism: his extensions of the class of syllogistic propositions to include singular propositions, propositions with a quantified predicate, tensed propositions and propositions in grammatical cases other than the nominative; his rules for the conversion of these propositions and for syllogisms containing them; his un-Aristotelian style of reducing syllogisms to the first figure by inference-to-inference transformations; and above all his use of supposition theory as a semantic base for this expanded syllogistic theory. His broadening of the scope of syllogistic theory resulted in abandoning several Aristotelian rules of the syllogism; it also resulted in a toleration of inferences containing redundant premises. The chapter provides proof-theoretic justifications for certain inferences that Ockham merely declared to be valid. It also argues that the originality of certain aspects of Ockham’s logic results from his philosophical nominalism.

At several points in the Summa Logicae, Ockham appeals to or relies on grammatical doctrines and terminology. One prominent example of this is his use of modes of signifying (modi significandi), which played a central role in a specific brand of speculative grammar whose proponents were known as “modists” (“modistae”). A central tenet of modism is that there is a correspondence between language and the world, mediated by thought, so that for every mode of signifying there is a corresponding mode of being. Ockham appeals to modes of signifying explicitly in at least three parts of his logic – fallacies, connotation, and synonymy – but his proclivity for ontological parsimony suggests that he would have had no fondness for the metaphysical commitments of modism. I argue that Ockham might be considered a “moderate modist” who denies the ontological excesses of modism but nonetheless utilizes much of its theoretical apparatus in his logic.