Type Theory

Type Theory
Type Theory

Type theory, in one sense, is the view that some category of abstract entities—sets, in the simplest example, but there are analogous views of properties, relations, concepts, and functions—come in a hierarchy of levels, with an entity of one level applying to (having as members, or having as instances, or ...) entities only of a lower level.

Such a view gives an intuitively comprehensible picture of the universe of abstracta and provides a principled way of avoiding Bertrand Arthur William Russell’s Paradox and its analogues. In a second sense, the term refers to any of a wide range of formal axiomatic systems embodying some form of the view. The present entry gives a short history of the view and a brief survey of the systems.

The systems are generally formulated in many-sorted quantificational logic, with a separate alphabet of quantified variables ranging over each type of entity. Axiomatically, they incorporate the rules of propositional logic (usually though not always classical) and of quantifier logic, the latter reduplicated for each alphabet of variables.

Bas van Fraassen

Bas van Fraassen
Bas van Fraassen

Bas van Fraassen was born in Goes, in the Netherlands, on April 5. He lived in Holland until he was fifteen years old, when he moved with his family to Canada. After finishing his undergraduate studies in philosophy (with honors) at the University of Alberta in 1963, he went to the University of Pittsburgh for his Ph.D., which he completed in 1966 with a dissertation on the causal theory of time that was supervised by Adolf Grünbaum.

He taught at Yale University, the University of Toronto, and the University of Southern California before moving to Princeton University, where he has been a Professor of Philosophy since 1982.

Van Fraassen has made seminal contributions to several areas of philosophy, and his work can be roughly divided into three major “periods”:

Hans Vaihinger

Hans Vaihinger - Shanti
Hans Vaihinger

Hans Vaihinger, the German philosopher of the “as if,” was born in a devout home near Tübingen. Although he developed unorthodox religious views at an early age, he attended the Theological College of the University of Tübingen.

Vaihinger wanted to be a man of action, but his extreme nearsightedness forced him into scholarly pursuits. He regarded the contrast between his physical constitution and the way he would like to live as irrational, and his defective vision made him sensitive to other frustrating aspects of existence.

Vaihinger eventually became a professor of philosophy at Halle, but failing vision necessitated his giving up his duties in 1906.He then turned to completing his most important work, Die Philosophie des Als-Ob, which had been started in 1876. The volume went through many editions and made the philosophy of fictions well known.

Giovanni Vailati

Giovanni Vailati
Giovanni Vailati

Giovanni Vailati, the Italian analytical philosopher and historian of science, was born at Crema, Lombardy. He studied engineering and mathematics at the University of Turin, where he later became an assistant to Giuseppe Peano (1892) and Vito Volterra (1895) and lectured on the history of mechanics (1896–1899). In 1899 he resigned his university post to be free for independent work, earning his living by teaching mathematics in high schools.

By the end of his life Vailati’s ideas were internationally recognized; some of his writings had been translated into English, French, and Polish, and he was personally acquainted with many of the important scholars of his time. He was forgotten after his death, however, and only since the late 1950s has he received renewed attention.

The main feature of Vailati’s thought is his methodological and linguistic approach to philosophical problems. Rather than propounding anything resembling a doctrine, Vailati presented concrete examples of how to apply his new methods.

Value and Valuation

Value and Valuation
Value and Valuation

The terms value and valuation and their cognates and compounds are used in a confused and confusing but widespread way in our contemporary culture, not only in economics and philosophy but also and especially in other social sciences and humanities.

Their meaning was once relatively clear and their use limited. Value meant the worth of a thing, and valuation meant an estimate of its worth. The worth in question was mainly economic or quasi economic, but even when it was not, it was still worth of some sort—not beauty, truth, rightness, or even goodness.

The extension of the meaning and use of the terms began in economics, or political economy, as it was then called. Value and valuation became technical terms central to that branch of economics which was labeled the theory of value.

Paul Valéry

Paul Valéry
Paul Valéry

As a law student in Montpellier, Valéry published poems and befriended such influential authors as André Gide and Stéphane Mallarmé. As a result of a personal crisis in 1892, he resolved to abandon literature and devote himself to his autodidactical pursuit of knowledge.

While serving in the Ministry of War, and then as private secretary to a powerful businessman, Valéry found time to read and write. In 1894 he began the first of some 261 notebooks in which he developed his matinal reflections for over fifty years.

At Gide’s instigation Valéry began to prepare a volume of poems, and ended up writing La jeune parque (The young fate) (1917), a hermetic allegory of consciousness that established him as an eminent French poet.

Giambattista Vico

Giambattista Vico
Giambattista Vico

Born in Naples, Italy, in 1668, Giambattista Vico is best known for his critique of the Cartesian method and his philosophy of history. Beyond these areas, he is also known for contributions to linguistic theory, legal history, and cultural anthropology. Many have construed Vico as an eighteenth-century thinker who expressed the germ of ideas more fully developed in the nineteenth century.

Thus, for example, Karl Löwith understands Vico’s master work The New Science to anticipate “not only fundamental ideas of Herder and Hegel, Dilthey and Spengler, but also the more particular discoveries of Roman history by Niebuhr and Mommsen, the theory of Homer by Wolf, the interpretation of mythology by Bachofen, the reconstruction of ancient life through etymology by Grimm, the historical understanding of laws by Savigny, of the ancient city and of feudalism by Fustel de Coulanges, and of the class struggles by Marx and Sorel”.

The familiar picture of Vico as the “great anticipator” contains some truth.More recent scholarship, in contrast, has tried to understand Vico as a thinker in his own right. The result has been a proliferation of different and often incompatible interpretations.

Virtue and Vice

Virtue and Vice
Virtue and Vice

Assuming that human agents possess settled dispositions or character traits, some of which are especially deemed worthy of praise while others deserve blame or reproach, moral philosophers have long treated the first sort under the category “virtue” and their opposites under the general term “vice.”

The fin-de-siecle revival of the virtue tradition in normative ethics as a third force, alongside Kantianism and consequentialism, has resulted in focused attention by theorists of all persuasions on the nature and proper role of virtues and vices in any comprehensive treatment of morality. Thus, two consequentialists have produced full-length treatments of the virtues, and there has been a growing appreciation of the key role of virtue in Immanuel Kant’s ethics.

While the attention to virtue among Kantians and neo-Kantians is not too surprising, since much of Kant’s later work was devoted to working out the important role that virtue and character play in morality (the weighty concluding section of the 1797 Metaphysics of Morals is rightly titled “The Doctrine of Virtue”), the consequentialist turn to virtue is, perhaps, more surprising. Jeremy Bentham, for example, gave a rather rude treatment of virtue in his Deontology.

Violence

Violence
Violence

“Violence” is derived from the Latin violentia, “vehemence,” which itself comes from vis (force) + latus (to carry) and means, literally, intense force. Violence shares its etymology with violate, “injure.” Violence is used to refer to swift, extreme force (e.g., a violent storm) and to forceful injurious violation (e.g., rape, terrorism, war).

Violence has received some philosophical consideration since ancient times, but only since the twentieth century has the concept of violence itself been of particular concern to philosophers.

Perhaps this is due to the exponential growth in the efficiency of and access to the means of violence in the modern era, to the unprecedented carnage the twentieth century saw, or to the emergence of champions of nonviolence such as Mohandas Gandhi and Martin Luther King Jr. Beyond clarifying the concept of violence, philosophical argument has turned to the moral and cultural justifiability of violence to achieve personal, social, or political ends.

Volition

Volition - Natsuna Amakawa
Volition

The action of opening a door by pushing on it is composed of the agent’s action of voluntarily exerting force with his or her arm and hand plus that action’s causing the door to open. Is the voluntary exertion of arm and hand similarly composed of an action producing a result? There is a clear candidate here for the role of result—namely, the limb’s exerting force.

It could have exerted exactly the same force, by means of just the same muscle contractions, without the agent’s voluntarily exerting the force with it. So the exerting of force by the limb is only a part of the whole action.

But does the remainder consist of this part’s being caused by action of the agent? Philosophers disagree on the answer to this question. Section I below offers one way of spelling out an affirmative answer (which is developed more fully in Ginet). Section II briefly sketches some alternative views.

Vitalism

Vitalism
Vitalism

“Vitalism” is primarily a metaphysical doctrine concerning the nature of living organisms, although it has been generalized, by Henri Bergson for example, into a comprehensive metaphysics applicable to all phenomena. We shall examine vitalism only as a theory of life.

There have been three general answers to the question “What distinguishes living from nonliving things?” The first, and currently most fashionable, answer is “A complex pattern of organization in which each element of the pattern is itself a nonliving entity.”

In this view, a living organism, and each of its living parts, is exhaustively composed of inanimate parts; and these parts have no relations except those that are also exhibited in inanimate systems. The second answer is “The presence in living systems of emergent properties, contingent upon the organization of inanimate parts but not reducible to them.”

Juan Luis Vives

Juan Luis Vives
Juan Luis Vives

 Juan Luis Vives, the Spanish humanist, was born in Valencia and died in Bruges. Considerably younger than such scholars as Desiderius Erasmus, Guillaume Budé, and John Colet, Vives deserves an honorable place among them for his moral seriousness, sincerity of religious belief, promotion of education, and social concern, as manifested in projects for the promotion of peace and the relief of the poor.

In many of these respects Vives is approached only by his nearer contemporary, Thomas More; his character emerges very favorably from any comparison with the earlier group. His efforts to secure patronage from the nobility did not blind him to the plight of those more needy than he, nor did he engage in the acrimonious personal quarrels that marred the character of some humanists.

Vives was a fine scholar and an excellent writer. After initial schooling in Spain he went to Paris to attend the university. Here he found still active a school of terminist logicians and physicists whose influence extended, so Vives tells us, to all the higher faculties.

Alfred Russel Wallace

Alfred Russel Wallace
Alfred Russel Wallace

Alfred Russel Wallace, the English naturalist and coformulator with Charles Darwin of the theory of natural selection, was born at Usk, Monmouthshire. He was largely self-educated, having left school at fourteen to serve as a surveyor’s assistant with his brother. Like many of his contemporaries he acquired an early taste for the study of nature.

But he also read widely and was influenced by the works of Alexander von Humboldt, Thomas Malthus, and Charles Lyell, as Darwin was. In 1844, while teaching school at Leicester, he met the naturalist H. W. Bates (1825–1892), who introduced him to scientific entomology. The two men later embarked on a collecting trip to the Amazon, where Wallace remained for four years examining the tropical flora and fauna.

In 1854, after a brief visit to England,Wallace set out by himself for the Malay Archipelago. He subsequently wrote an account of this trip, The Malay Archipelago (London, 1869),which is a fascinating narrative. When he returned in 1862, he had become a convinced evolutionist and was known in scientific circles for his formulation of the theory of natural selection.

Richard Wahle

Richard Wahle - Sakie Ejima
Richard Wahle

Richard Wahle, the Austrian philosopher and psychologist, was born in Vienna. He was appointed Privatdozent in philosophy at the University of Vienna in 1885. A decade later he was called to a professorship in philosophy at the University of Czernowitz, where he taught until 1917.

From 1919 to 1933 he again lectured at the University of Vienna. Possessed of originality and an unusually lively style, he published a number of books in the fields of psychology, general philosophy, and ethics.

Wahle is known especially for his relentlessly sharp critique of traditional philosophy, particularly of metaphysics, which he regarded as “one of the most dangerous breeding-places of empty phrases.” An absolute, true knowledge, of the sort to which metaphysics aspires, cannot exist.