Further objections!!!

Objections range from the simplistic nature of 'g', through to the relative stability of the correlations and factor analysis to determine it. Another argument was that as it ignored group factors in test scores (corresponding to broad abilities such as spatial visualization, memory and verbal ability) that may also be found through factor analysis.

Some consider Gardner's theory of "multiple intelligences" to be a weak counter argument:
http://www.psychpage.com/learning/library/intell/iqbox.html

Stephan Jay Gould, a paleontologist, published The Mismeasure of Man (1981) that was a highly controversial book, that looked like this:

He wrote a history that analyzed the methods and reasons to take a biologically determined approach, such as that proposed by Spearman and Jensen with their g-factor theories. He argued that the fallacy of psychometric testing is that is ranks people in an ascending order, which is in stark contrast to evolutionary theory for complex variation.

According to Gould these methods suffer from "two deep fallacies." The first fallacy is of reification, that is, "our tendency to convert abstract concepts into entities." These entities include IQ (the intelligence quotient) and g (the general intelligence factor), which have been the cornerstone of much intelligence research. The second fallacy is one of ranking, or our "propensity for ordering complex variation as a gradual ascending scale."

Philip Kitcher wrote in 1985:

Many scientists are now convinced that there is no single measure of intellectual ability - no unitary intelligence. Their suspicion of the concept of general intelligence is based on the view that various intellectual capacities are not well correlated. ....it is useful to continue to expose the myth of "general intelligence".

However, views that dismiss "g" as entirely fictional or irrelevant are controversial. Most psychometricians still recognize and employ "g" as a valid and coherent evaluation of human mental ability.

Recently, researchers in the area of AI (aritificial intelligence) claim that the study of mental ability is like "computationalism" and thus of no real purpose, as cognitive ability tests only measure individual differences that are/will one day, be undertaken by computational mediums, such as personal computers and robots. As such, mental abilities have nought to do with intelligence.

Refs:

http://kryten.mm.rpi.edu/FS605BringsjordS.pdf

http://en.wikipedia.org/wiki/The_Mismeasure_of_Man