William of Ockham in the context of "Christian apologetics"

In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are two main versions of nominalism. One denies the existence of universals—that which can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objects as such—objects that do not exist in space and time.

Most nominalists have held that only physical particulars in space and time are real, and that universals exist only post res, that is, subsequent to particular things. However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), whilst others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, and bananas). Nominalism is primarily a position on the problem of universals. It is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars, and to the hylomorphic substance theory of Aristotle, which asserts that universals are immanently real within them; however, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus.

Propositions are the meanings of declarative sentences, objects of beliefs, and bearers of truth values. They explain how different sentences, like the English "Snow is white" and the German "Schnee ist weiß", can have identical meaning by expressing the same proposition. Similarly, they ground the fact that different people can share a belief by being directed at the same content. True propositions describe the world as it is, while false ones fail to do so. Researchers distinguish types of propositions by their informational content and mode of assertion, such as the contrasts between affirmative and negative propositions, between universal and existential propositions, and between categorical and conditional propositions.

Many theories of the nature and roles of propositions have been proposed. Realists argue that propositions form part of reality, a view rejected by anti-realists. Non-reductive realists understand propositions as a unique kind of entity, whereas reductive realists analyze them in terms of other entities. One proposal sees them as sets of possible worlds, reflecting the idea that understanding a proposition involves grasping the circumstances under which it would be true. A different suggestion focuses on the individuals and concepts to which a proposition refers, defining propositions as structured entities composed of these constituents. Other accounts characterize propositions as specific kinds of properties, relations, or states of affairs. Philosophers also debate whether propositions are abstract objects outside space and time, psychological entities dependent on mental activity, or linguistic entities grounded in language. Paradoxes challenge the different theories of propositions, such as the liar's paradox. The study of propositions has its roots in ancient philosophy, with influential contributions from Aristotle and the Stoics, and later from William of Ockham, Gottlob Frege, and Bertrand Russell.

John Duns Scotus OFM (/ˈskoʊtəs/ SKOH-təs; Ecclesiastical Latin: [duns ˈskɔtus], "Duns the Scot"; c. 1265/66 – 8 November 1308) was a Scottish Catholic priest and Franciscan friar, university professor, philosopher and theologian. He is considered among the most important philosopher-theologians in Western Christendom during the last part of the medieval period, together with Thomas Aquinas, Bonaventure and William of Ockham.

Duns Scotus has had considerable influence on both Catholic and secular thought. The doctrines for which he is best known are the "univocity of being", that existence is the most abstract concept we have, applicable to everything that exists; the formal distinction, a way of distinguishing between different formalities of the same thing; and the idea of haecceity, the property supposed to be in each individual thing that makes it an individual (i.e. a certain "thisness"). Duns Scotus also developed a complex argument for the existence of God, and argued for the Immaculate Conception of Mary. The intellectual tradition derived from Scotus' work is called Scotism.

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics, and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C. I. Lewis who created the first symbolic and systematic approach to the topic, in 1912. It continued to mature as a field, reaching its modern form in 1963 with the work of Saul Kripke.

The designation "Renaissance philosophy" is used by historians of philosophy to refer to the thought of the period running in Europe roughly between 1400 and 1600. It therefore overlaps both with late medieval philosophy, which in the fourteenth and fifteenth centuries was influenced by notable figures such as Albert the Great, Thomas Aquinas, William of Ockham, and Marsilius of Padua, and early modern philosophy, which conventionally starts with René Descartes and his publication of the Discourse on Method in 1637.

The Isagoge (Greek: Εἰσαγωγή, Eisagōgḗ; /ˈaɪsəɡoʊdʒiː/) or "Introduction" to Aristotle's "Categories", written by Porphyry in Greek and translated into Latin by Boethius, was the standard textbook on logic for at least a millennium after his death. It was composed by Porphyry in Sicily during the years 268–270, and sent to Chrysaorium, according to all the ancient commentators Ammonius, Elias, and David. The work includes the highly influential hierarchical classification of genera and species from substance in general down to individuals, known as the Tree of Porphyry, and an introduction which mentions the problem of universals.

Boethius' translation of the work, in Latin, became a standard medieval textbook in European scholastic universities, setting the stage for medieval philosophical-theological developments of logic and the problem of universals. Many writers, such as Boethius himself, Averroes, Peter Abelard, Duns Scotus, wrote commentaries on the book. Other writers such as William of Ockham incorporated them into their textbooks on logic.