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Name given by medieval logicians to a categorical syllogism whose standard form has the mood and figure designated as OAO-3.

Example: Some local jails are not maximum-security prisons, but since all local jails are correctional institutions, it follows that some correctional institutions are not maximum-security prisons.

This is one of the fifteen forms of valid syllogism.

Boethius, Anicius Manlius Severinus (480-524)

Roman logician who maintained an active public life until imprisoned and executed by Theodoric. Although the stated aim of his intense study of Greek philosophy was to translate all of the works pf Plato and Aristotle into Latin, he concentrated mainly on Aristotelean logic. His Commentary on the Isagoge of Porphyry (itself a discussion of Aristotle's Categories) carefully distinguished Aristotelean essences from Platonic Forms, setting the basic terms to be employed in subsequent medieval discussion of the problem of universals. De consolatione philosophiae (The Consolation of Philosophy), written during his final imprisonment, considers the possibility of achieving human happiness despite the inescapable presence of evil, extols the benefits of reason even in the face of misfortune and bad advice, and proposes a compatibilist account of human freedom in the face of divine foreknowledge.

Recommended Reading: Five Texts on the Mediaeval Problem of Universals, ed. by Paul Vincent Spade (Hackett, 1994).

Also see CE, SEP, R. J. Kilcullen, EB, ELC, James E. Kiefer, and MMT.

Boetius of Dacia (1230-1285)

Swedish Dominican philosopher. Doubts about personal immortality and the espousal of a fideistic account of the relation between faith and reason during his service in Romania resulted in the condemnation of his teachings, along with those of Siger of Brabant and the other radical Aristoteleans.

Recommended Reading: Boethius of Dacia: On the Supreme Good, on the Eternity of the World, on Dreams, tr. by John F. Wippel (Pontifical Inst., 1987)

Bohr, Niels Henrik David (1885-1962)

Danish physicist. Although best known for his contributions to atomic theory and quantum mechanics, Bohr also reflected on epistemological issues, defending a sophisticated variety of cultural relativism. Bohr won the Nobel Prize in Physics in 1922.

Recommended Reading: Dugald Murdoch, Niels Bohr's Philosophy of Physics (Cambridge, 1989); Abraham Pais, Niels Bohr's Times: In Physics, Philosophy, and Polity (Oxford, 1993); and Andrew Whitaker, Einstein, Bohr and the Quantum Dilemma (Cambridge, 1996).

Also see EB on Bohr and the Bohr model, SEP, ELC, WSB, and MMT.

Bolzano, Bernard (1781-1848)

Austrian mathematician, theologian, and philosopher. In opposition to the idealism of Kant and Hegel, Bolzano maintained that numbers, ideas, and truths all exist independently of the human beings who think about them. His Wissenschaftslehre (1837) and Grössenlehre (1850) offer a philosophical foundation for mathematics, employing a modern theory of classes to define the real numbers. Bolzano's work was a significant influence on that of Husserl, Frege, Lukasiewicz, and Tarski.

Recommended Reading: Jan Sebestik, Logique et mathématique chez Bernard Bolzano (Paris, 1992).

Also see SEP on Bolzano and his logic, EB, ELC, WSB, Helena Lorenzová, and MMT.

Bonaventure (Giovanni di Fidanza) (1221-1274)

Franciscan philosopher and theologian. Following Augustine, Bonaventure held that reason is valuable only in support of faith. Bonaventure's philosophy was predominantly neoplatonic; he accepted Aristotle's philosophical principles only when they could be used in service of his Christian aims, but argued against the eternal reality of the universe. In Itinerarium mentis in deum (The Journey of the Mind to God) (1259) he argued that human beings, as emanations of the deity, embody a footprint {Lat. vestiguum} of the divine nature.

Recommended Reading: Etienne Gilson, The Philosophy of St. Bonaventure (Franciscan, 1965).

Also see R. J. Kilcullen, CE, SEP, EB, and ELC.

Boole, George (1815-1864)

British logician whose The Mathematical Analysis of Logic (1847) proposed the "Boolean algebra" of propositional connectives representing negation and conjunction. An Investigation into the Laws of Thought (1859) further develops a symbolic system for the expression and evaluation of categorical syllogisms, understood as elements in the logic of classes.

Recommended Reading: A Boole Anthology: Recent and Classical Studies in the Logic of George Boole, ed. by James Gasser (Kluwer, 2000).

Also see SEP on Boole and Boolean algebra, MMT, EB on Boole and Boolean algebra, DPM, ELC, and WSB.

Bordo, Susan (1947- )

American philosopher. In The Flight to Objectivity: Essays on Cartesianism and Culture (1987) she explores the masculinization of thought in Cartesian modernism. Bordo's Unbearable Weight: Feminism, Western Culture, and the Body (1993) is a cultural exploration of the significance of social constructions of the human body. Similar themes are explored in Bordo's Twilight Zones: The Hidden Life of Cultural Images from Plato to O.J. (1997) and The Male Body: A New Look at Men in Public and in Private (1999).

Also see FTW and Janet C. Wesselius.

Bosanquet, Bernard (1848-1923)

British philosopher who defended a modified version of Hegel's absolute idealism in Logic, or the Morphology of Knowledge (1888), The Principle of Individuality and Value (1912), and The Value and Destiny of the Individual (1914). According to Bosanquet, all contradictions are merely apparent and are wholly harmonized as part of the Absolute, a process said to account for the possibility of judgments about beauty in his History of Aesthetics (1892). Bosanquet further argued in The Philosophical Theory of the State (1899) that individual human beings are properly understood only in terms of their social and cultural efforts at transcendence.

Recommended Reading: The Collected Works of Bernard Bosanquet, ed. by William Sweet (Thoemmes, 1999)

Also see Will Sweet, SEP, EB, and ELC.

Boundless, the {Gk. απειρων [apeirôn]}

The eternal, infinite, undifferentiated stuff from which Anaximander believed the material world to be formed.

Boyle, Robert (1627-1692)

English scientist who discovered the relationship between the temperature, pressure, and volume of a gas and founded The Royal Society. In The Skeptical Chymist (1661) and The Origins of Forms and Qualities (1666), Boyle helped to establish the discipline of chemistry and drew a careful distinction between primary and secondary qualities, later used by his friend Locke. A principled corpuscularian, Boyle defended the reliability of mechanistic philosophy in The Excellency and Grounds of the Corpuscular or Mechanical Philosophy (1674) and in extended controversies with Spinoza and Henry More. Boyle employed the teleological argument for god's existence and defended a traditional theology in The Excellence of Theology (1674) and The Christian Virtuoso (1690).

Recommended Reading: Selected Philosophical Papers of Robert Boyle (Hackett, 1991); Robert Boyle on Natural Philosophy, ed. by Marie Boas Hall (Greenwood, 1980); Peter Alexander, Ideas, Qualities and Corpuscles: Locke and Boyle on the External World; Elizabeth Potter, Gender and Boyle's Law of Gasses (Indiana, 2001); Peter R. Anstey, The Philosophy of Robert Boyle (Routledge, 2000); Rose-Mary Sargent, The Diffident Naturalist: Robert Boyle and the Philosophy of Experiment (Chicago, 1995); and Thomas Duddy, A History of Irish Thought (Routledge, 2002).

Also see SEP, WSB, EB on Boyle and Boyle's Law, MMT, and ELC.


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