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Introduction

In his 1981 book The Mismeasure of Man, Stephen Jay Gould mounted a long, historical argument, against scientific racism and eugenics. A key point to the book was arguing against the so-called “general factor of intelligence” (GFI). Gould argued that the GFI was a mere reification—an abstraction treated as a concrete entity. In this article, I will formalize Gould’s argument from the book (that g is a mere statistical abstraction), and that we, therefore, should reject the GFI. Gould’s argument is one of ontology—basically what g is or isn’t. I have already touched on Gould’s argument before, but this will be a more systematic approach in actually formalizing the argument and defending the premises.

Spearman’s g was falsified soon after he proposed it. Jensen’s g is an unfalsifiable tautology, a circular construct where test performance defines intelligence and intelligence explains performance. Geary’s g rests on an identity claim: that g is identical to mitochondrial functioning and can be localized to ATP, but it lacks causal clarity and direct measurability to elevate it beyond a mere correlation to a real, biologically-grounded entity.

Gould’s argument against the GFI

In Mismeasure, Gould attacked historical hereditarian figures as reifying intelligence as a unitary, measurable entity. Mainly attacking Spearman’s Burt, Gould argued that since Spearman saw positive correlations between tests that, therefore, there must be a GFI to explain test intercorrelations. Spearman’s GFI is the first principle component (PC1), which Jensen redefined to be g. (We also know that Spearman saw what he wanted to see in his data; Schlinger, 2003.) Here is Gould’s (1981: 252) argument against the GFI:

Causal reasons lie behind the positive correlations of most mental tests. But what reasons? We cannot infer the reasons from a strong first principal component any more than we can induce the cause of a single correlation coefficient from its magnitude. We cannot reify g as a “thing” unless we have convincing, independent information beyond the fact of correlation itself.

Using modus tollens, the argument is:

(P1) If g is a real, biologically-grounded entity, then it should be directly observable or measurable independently of statistical correlations in test performance.
(P2) But g is not directly observable or measurable as a distinct entity in the brain or elsewhere; it is only inferred from factor analysis of test scores.
(C) So g is not a real biologically-grounded entity—it is a reification, an abstraction mistaken for a concrete reality.

(P1) A real entity needs a clear, standalone existence—not just a shadow in data.
(P2) g lacks this standalone evidence, it’s tied to correlations.
(C) So g isn’t real; it’s reified.

Hereditarians treat g as quantifiable brainstuff. That is, they assume that it can already be measured. For g to be more than a statistical artifact, it would need to have an independent, standalone existence—like an actual physical trait—and not merely just be a statistical pattern in data. But Gould shows that no one has located where in the brain this occurs—despite even Jensen’s (1999) insistence about g being quantifiable brainstuff:

g…[is] a biological [property], a property of the brain

The ultimate arbiter among various “theories of intelligence” must be the physical properties of the brain itself. The current frontier of g research is the investigation of the anatomical and physiological features of the brain that cause g.

…psychometric g has many physical correlates…[and it] is a biological phenomenon.

Just like in Jensen’s infamous 1969 paper, he wrote that “We should not reify g as an entity…since it is only a hypothetical construct“, but then he contradicted himself 10 pages later writing that g (“intelligence”) “is a biological reality and not just a figment of social conventions.” However, here are the steps that Jensen uses to infer that g exists:

(1) If there is a general intelligence factor “g,” then it explains why people perform well on various cognitive tests.

(2) If “g” exists and explains test performance, the absence of “g” would mean that people do not perform well on these tests.

(3) We observe that people do perform well on various cognitive tests (i.e., test performance is generally positive).

(4) Therefore, since “g” would explain this positive test performance, we conclude that “g” exists.

Put another way, the argument is: If g exists then it explains test performance; we see test performance; therefore g exists. Quite obviously, it seems like logic wasn’t Jensen’s strong point.

But if g is reified as a unitary, measurable entity, then it must be a simple, indivisible capacity which uniformly underlies all cognitive abilities. So if g is a simple, indivisible capacity that uniform underlies all cognitive abilities, then it must be able to be expressed as a single, consistent property unaffected by the diversity of cognitive tasks. So if g is reified as a unitary, real entity, then it must be expressed as a single cognitive property unaffected by the diversity of cognitive tasks. But g cannot be expressed as a single, consistent property unaffected by the diversity of cognitive tasks, so g cannot be reified as a unitary, real entity. We know, a priori, that a real entity must have a nature that can be defined. Thus, if g is real then it needs to be everything (all abilities) and one thing (a conceptual impossibility). (Note that step 4 in my steps is the rectification that Gould warned about.) The fact of the matter is, the existence of g is circularly tied to the test—which is where P1 comes into play.

“Subtests within a battery of intelligence tests are included n the basis of them showing a substantial correlation with the test as a whole, and tests which do not show such correlations are excluded.” (Tyson, Jones, and Elcock, 2011: 67)

This quote shows the inherent circularity in defining intelligence from a hereditarian viewpoint. Since only subtests that correlate are chosen, there is a self-reinforcing loop, meaning that the intercorrelations merely reflect test design. Thus, the statistical analysis merely “sees” what is already built into the test which then creates a false impression of a unified general factor. So using factor analysis to show that a general factor arises is irrelevant—since it’s obviously engineered into the test. The claim that “intelligence is what IQ tests measure” (eg Van der Maas, Kan, and Borsboom, 2014) but the tests are constructed to CONFIRM a GFI. Thus, g isn’t a discovered truth, it’s a mere construct that was created due to how tests themselves are created. g emerges from IQ tests designed to produce correlated subtest scores, since we know that subtests are included on the basis of correlation. The engineering of this positive manifold creates g, not as a natural phenomenon, but as a human creation. Unlike real entities which exist independently of how we measure them, g’s existence hinges on test construction which then stripes it of its ontological autonomy.

One, certainly novel, view on the biology supposedly underlying g is Geary’s (2018, 2019, 2020, 2021) argument that mitochondrial functioning—specifically the role of mitochondrial functioning in producing ATP through oxidative phosphorylation—is the biological basis for g. Thus, since mitochondria fuel cellular processes including neuronal activity, Geary links that efficiency to cognitive performance across diverse tasks which then explains the positive manifold. But Geary relies on correlations between mitochondrial health and cognitive outcomes without causal evidence tying it to g. Furthermore, environmental factors like pollutants affect mitochondrial functioning which means that external influences—and not an intrinsic g—could drive the observed patterns. Moreover, Schubert and Hagemann (2020)  showed that Geary’s hypothesis doesn’t hold under scrutiny. Again, g is inferred from correlational outcomes, and not observed independently. Since Geary identifies g with mitochondrial functioning, he assumes that the positive manifold reflects a single entity, namely ATP efficiency. Thus, without proving the identity, Geary reifies a correlation into a thing, which is what Gould warned about not doing. Geary also assumes that the positive manifold demands a biological cause, making it circular (much like Jensen’s g). My rejection of Geary’s hypothesis hinges on causality and identity—mitochondrial functioning just isn’t identical with the mythical g.

The ultimate claim I’m making here is that if psychometricians are actually measuring something, then it must be physical (going back to what Jensen argued about g having a biological basis and being a brain property). So if g is what psychometricians are measuring, then g must be a physical entity. But if g lacks a physical basis or the mental defies physical reduction, then psychometrics isn’t measuring anything real. This is indeed why psychometrics isn’t measurement and, therefore, why a science of the mind is impossible.

For something to exist as a real, biological entity, it must exhibit real verifiable properties, like hemoglobin and dopamine, and it must exhibit specific, verifiable properties: a well-defined structure or mechanism; a clear function; and causal powers that can be directly observed and measured independently of the tools used to detect it. Clearly, these hallmarks distinguish real entities from mere abstractions/statistical artifacts. As we have seen, g doesn’t meet the above criteria, so the claim that g is a biologically-grounded entity is philosophically untenable. Real biological entities have specific, delimited roles, like the role of hemoglobin in the transportation of oxygen. But g is proposed as a single, unified factor that explains ALL cognitive abilities. So the g concept is vague and lacks the specificity expected of real biological entities.

Hemoglobin can be measured in a blood sample but g can’t be directly observed or quantified outside of the statistical framework of IQ test correlations. Factor analysis derives g from patters of test performance, not from an independent biological substrate. Further, intelligence encompasses distinct abilities, as I have argued. g cannot coherently unify the multiplicity of what makes up intelligence, without sacrificing ontological precision. As I argued above, real entities maintain stable, specific identities—g’s elasticity, which is stretched to explain all cognition—undermines it’s claims to be a singular, real thing.

Now I can unpack the argument like this:

(P1) A concept is valid if, and only if, it corresponds to an independently verifiable reality.
(P2) If g corresponds to an independently verifiable reality, then it must be directly measurable or observable beyond the correlations of IQ test scores.
(P3) But g is not directly observable beyond the correlations of IQ test scores; it is constructed through the deliberate selection of subtests that correlate with the overall test.
(C1) Thus g does not correspond to an independently verifiable reality.
(C2) Thus, g is not a valid concept.

Conclusion

The so-called evidence that hereditarians have brought to the table to infer the existence of g for almost 100 years since Spearman clearly fails. Even after Spearman formulated it, it was quickly falsified (Heene, 2008). Even then, for the neuroreductionist who would try to argue that MRI or fMRI would show a biological basis to the GFI, they would run right into the empirical/logical arguments from Uttal’s anti-neuroreduction arguments.

g is not a real, measurable entity in the brain or biology but a reified abstraction shaped by methodological biases and statistical convenience. g lacks the ontological coherence and empirical support of real biological entities. Now, if g doesn’t exist—especially as an explanation for IQ test performance—then we need an explanation, and it can be found in social class.

(P1) If g doesn’t exist then psychometricians are showing other sources of variation.
(P2) The items on the test are class-dependent.
(P3) If psychometricians are showing other sources of variation and the items on the tests are class-dependent, then IQ score differences are mere surrogates for social class.
(C) Thus, if g doesn’t exist then IQ score differences are mere surrogates for social class.

We don’t need a mysterious factor to explain the intercorrelations. What does explain it is class—exposure to the item content of the test. We need to dispense with a GFI, since it’s conceptual incoherence and biological implausibility undermine it’s validity as a scientific construct. Thus, g will remain a myth. This is another thing that Gould got right in his book, along with his attack on Morton.

Gould was obviously right about the reification of g.