The phrase "intelligence is task-specific" suggests that while 'general intelligence' can indeed be assessed, all that that would really amount to is a sum total of a given individual's competencies minus any perceived in competencies.
Most experts accept the concept of a single dominant factor of intelligence, general mental ability or g, while others argue that intelligence consists of a set of relatively independent abilities. The evidence for g comes from factor analysis of tests of cognitive abilities. The methods of factor analysis do not guarantee a single dominant factor will be discovered. Other psychological tests which do not measure cognitive ability, such as personality tests, generate multiple factors.
Proponents of multiple-intelligence theories often claim that g is, at best, a measure of academic ability. Other types of intelligence, they claim, might be just as important outside of a school setting.
Yale psychologist Robert J. Sternberg has proposed a Triarchic Theory of Intelligence. Harvard psychologist Howard Gardner's theory of multiple intelligence's breaks intelligence down into at least eight different components: logical, linguistic, spatial, musical, kinesthetic, naturalist, intra-personal and inter-personal intelligence's Daniel Goleman and several other researchers have developed the concept of emotional intelligence and claim it is at least as important as more traditional sorts of intelligence. These theories grew from observations of human development and of brain injury victims who demonstrate an acute loss of a particular cognitive function -- e.g. the ability to think numerically, or the ability to understand written language -- without showing any loss in other cognitive areas.
In response, g theorists have pointed out that g's predictive validity has been repeatedly demonstrated, for example in predicting important non-academic outcomes such as job performance (see IQ), while no multiple-intelligence's theory has shown comparable validity. Meanwhile, they argue, the relevance, and even the existence, of multiple intelligence's have not been borne out when actually tested. Furthermore, g theorists contend that proponents of multiple intelligence's have not disproved the existence of a general factor of intelligence. The fundamental argument for a general factor is that test scores on a wide range of seemingly unrelated cognitive ability tests (such as sentence completion, arithmetic, and memorization) are positively correlated: people who score highly on one test tend to score highly on all of them, and g thus emerges in a factor analysis. This suggests that the tests are not unrelated, but that they all tap a common factor.