Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills) consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations) also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a) perceived differences between numbers, b) the extent to which proportional differences are weighed in decisions, and, ultimately, c) the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.

Interval estimates are commonly used to descriptively communicate the degree of uncertainty in numerical values. Conventionally, low alpha levels (e.g., .05) ensure a high probability of capturing the target value between interval endpoints. Here, we test whether alpha levels and individual differences in numeracy influence distributional inferences. In the reported experiment, participants received prediction intervals for fictitious towns’ annual rainfall totals (assuming approximately normal distributions). Then, participants estimated probabilities that future totals would be captured within varying margins about the mean, indicating the approximate shapes of their inferred probability distributions. Results showed that low alpha levels (vs. moderate levels; e.g., .25) more frequently led to inferences of over-dispersed approximately normal distributions or approximately uniform distributions, reducing estimate accuracy. Highly numerate participants made more accurate estimates overall, but were more prone to inferring approximately uniform distributions. These findings have important implications for presenting interval estimates to various audiences.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g., 7), but also non-natural rational numbers (e.g., 3.5). It does not represent irrational numbers (e.g., √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

In this review, we are pitting two theories against each other: the more accepted theory, the number sense theory, suggesting that a sense of number is innate and non-symbolic numerosity is being processed independently of continuous magnitudes (e.g., size, area, and density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities and (2) a sense of number might not be innate. In the first part of this review, we discuss the number sense theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore, the results of behavioral and imaging studies with infants, adults, and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the sense of magnitude theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test and consider whether such an assumption is even testable in the light of the correlation of numerosity and continuous magnitudes.

The role of numeric language in basic numerical cognition is explored via the consideration of results obtained in two recent independent studies, one with Nicaraguan homesigners and one with speakers of Pirahã. Attention is drawn to remarkable parallels between the relevant findings, parallels that provide compelling evidence that adults without access to numeric language face difficulties when simply attempting to differentiate quantities greater than three.