intuitionism School of mathematical thought introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881-1966). In contrast with mathematical Platonism, which holds that mathematical concepts exist independent of any human realization of them, intuitionism holds that only those mathematical concepts that can be demonstrated, or con¬ structed, following a finite number of steps are legitimate. Few mathema¬ ticians have been willing to abandon the vast realms of mathematics built with nonconstructive proofs.
intuitionism In metaethics, a form of cognitivism that holds that moral statements can be known to be true or false immediately through a kind of rational intuition. In the 17th and 18th centuries, intuitionism was defended by Ralph Cudworth, Henry More (1614-87), Samuel Clarke (1675-1729), and Richard Price (1723-91); in the 20th century its sup¬ porters included H.A Prichard (1871-1947), G.E. Moore, and David Ross. Intuitionists have differed over the kinds of moral truths that are ame¬ nable to direct apprehension. For example, whereas Moore thought that it is self-evident that certain things are morally valuable, Ross thought that we know immediately that it is our duty to do acts of a certain type.
Inuit See Eskimo
Invar Trademark name for an alloy of iron (64% iron, 36% nickel) that expands very little when heated. Invar was formerly used for absolute standards of length measurement and is now used for surveying tapes and in watches and various other temperature-sensitive devices. The name expresses the invariability of its dimensions. It was developed by Charles- Edouard Guillaume (1861-1938), winner of the 1920 Nobel Prize for Physics.
inventory In business, any item of property held in stock by a firm, including finished goods held for sale, goods in the process of production, raw materials, and items that will be consumed in the process of produc¬ ing salable goods. Inventories appear on a company’s balance sheet as assets. Inventory turnover, which indicates the rate at which goods are converted into cash, is a key factor in appraising a firm’s financial con¬ dition. For financial statements, inventories may be priced either at cost or at market value.
Inverness \,in-v9r-'nes\ Royal burgh (pop., 2001: 44,084), Highland council area, in the historic county of Inverness-shire, northwestern Scot¬ land. Located on the River Ness and the Caledonian Canal, it has long been the centre of the Scottish Highlands. In the 6th century it was the capital of the Pictish king Brude. By the 12th century it had become a burgh near the castle of Malcolm III Canmore. Inverness is now an edu¬
cational and tourist centre. Its manufacturing has expanded in conjunc¬ tion with the growth of offshore oil production.
inverse function Mathematical function that undoes the effect of another function. For example, the inverse function of the formula that converts Celsius temperature to Fahrenheit temperature is the formula that converts Fahrenheit to Celsius. Applying one formula and then the other yields the original temperature. Inverse procedures are essential to solv¬ ing equations because they allow mathematical operations to be reversed (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations). Whenever a mathematical procedure is intro¬ duced, one of the most important questions is how to invert it. Thus, for example, the trigonometric functions gave rise to the inverse trigonomet¬ ric functions.
invertebrate Any animal that lacks a vertebral column, or backbone. They include the protozoans, annelids, cnidarians, echinoderms, flatworms, nematodes, mollusks, and arthropods. More than 90% of living animals are invertebrates. Worldwide in distribution, they range in size from minute protozoans to giant squids. Apart from the absence of a vertebral column, invertebrates have little in common. They are generally soft-bodied and have an external skeleton for muscle attachment and protection. See also VERTEBRATE.
Investiture Controversy Struggle between the papacy and the secu¬ lar rulers of Europe over the latter’s presentation of the symbols of office to churchmen. Pope Gregory VII condemned lay investiture in 1078 as an unjustified assertion of secular authority over the church; the issue was pivotal in his dispute with King Henry IV and in the larger struggle over Henry’s refusal to obey papal commands. Henry successfully drove Gre¬ gory from Rome and installed an antipope, but it would be Gregory’s rejection of lay investiture that would ultimately prevail. Henry I of England renounced lay investiture (1106) in return for the guarantee that homage would be paid to the king before consecration, and the Concor¬ dat of Worms (1122) forged a similar compromise between Henry V and Calixtus II.
investment Process of exchanging income for an asset that is expected to produce earnings at a later time. An investor refrains from consumption in the present in hopes of a greater return in the future. Investment may be influenced by rates of interest, with the rate of investment rising as interest rates fall, but other factors more difficult to measure may also be important—for example, the business community’s expectations about future demand and profit, technical changes in production methods, and expected relative costs of labour and capital. Investment cannot occur without saving, which provides funding. Because investment increases an economy’s capacity to produce, it is a factor contributing to economic growth.
investment bank Firm that originates, underwrites, and distributes new security issues of corporations and government agencies. The Banking
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954 I investment casting ► Ionian
Act of 1933 required the separation of investment banking and commercial BANKing functions. Investment banks operate by purchasing all the new securities issued by a corporation at one price and selling fractions of the new issue to the investing public at prices high enough to yield a profit. The investment bank is responsible for setting the public offering price, which it bases on probable demand and assessments of the economic climate. A syndicate of investment banking firms underwrites and distributes most security issues in order to divide the risk of the new issue. An initial public offering (IPO) refers to the issuance of the first public shares of a formerly nonpublic company. See also bank; central bank; savings bank; security.
investment casting Precision casting for forming metal shapes with minutely precise details. Casting bronze or precious metals typically involves several steps, including forming a mold around the sculptured form; detaching the mold (in two or more sections); coating its inside with wax; forming a second mold, of heat-resisting clay, around the wax shell, and filling the interior with a clay core; baking the assembly (hardening the clay and melting the wax, which escapes through openings in the outer mold); pouring molten bronze into the space vacated by the wax; and breaking the mold to expose the cast form. In modern foundries, plastics, or occasionally frozen mercury, are used instead of wax. See also lost- wax CASTING, DIE CASTING.
investment credit or investment tax credit Tax incentive that permits companies or individuals to deduct a specified percentage of cer¬ tain investment costs from their tax liability in addition to the normal allowances for depreciation. Investment credits are similar to investment allowances, which permit investors or businesses to deduct a specified percentage of certain capital costs from taxable income. Both investment credits and investment allowances differ from accelerated depreciation by offering a percentage deduction at the time an asset is purchased. In effect, the credits are subsidies for investment. Investment credits and investment allowances were adopted by the U.S. in 1962 in order to protect domes¬ tic business from foreign competition but have since been applied toward the support of energy conservation, pollution control, or various forms of desirable economic development.