People and Society

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 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, 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, 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

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

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

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.