I argue that analogue mental representations possess a canonical decomposition into privileged constituents from which they compose. I motivate this suggestion, and rebut arguments to the contrary, through reflection on the approximate number system, whose representations are widely expected to have an analogue format. I then argue that arguments for the compositionality and constituent structure of these analogue representations generalize to other analogue mental representations posited in the human mind, such as those in early vision and visual imagery.

This book argues that there is a joint in nature between seeing and thinking, perception, and cognition. Perception is constitutively iconic, nonconceptual, and nonpropositional, whereas cognition does not have these properties constitutively. The book does not appeal to “intuitions,” as is common in philosophy, but to empirical evidence, including experiments in neuroscience and psychology. The book argues that cognition affects perception, i.e., that perception is cognitively penetrable, but that this does not impugn the joint in nature. A key part of (...) the argument is that we perceive not only low-level properties like colors, shapes, and textures but also high-level properties such as faces and causation. Along the way, the book explains the difference between perception and perceptual memory, the differences between format and content, and whether perception is probabilistic despite our lack of awareness of probabilistic properties. The book argues for perceptual categories that are not concepts, that perception need not be singular, that perceptual attribution and perceptual discrimination are equally fundamental, and that basic features of the mind known as “core cognition” are not a third category in between perception and cognition. The chapter on consciousness leverages these results to argue against some of the most widely accepted theories of consciousness. Although only one chapter is about consciousness, much of the rest of the book repurposes work on consciousness to isolate the scientific basis of perception. (shrink)

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, 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 of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, 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. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations of pure (...) magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

Our conscious thought, at least at times, seems suffused with language. We may experience thinking as if we were “talking in our head”, thus using inner speech to verbalize, e.g., our premises, lemmas, and conclusions. I take inner speech to be part of a larger phenomenon I call inner semiotics, where inner semiotics involves the subjective experience of expressions in a semiotic (or symbol) system absent the overt articulation of the expressions. In this paper, I argue that inner semiotics allows (...) us to bootstrap our way into entertaining thoughts about exact numbers and quantities that we couldn't prior to our competence with a numeric code. I establish that our arithmetic thoughts literally occur as (internal ‘articulations’ of) expressions in a numeric code. However, a problem arises for my view: just as we can slip in overt speech, producing an utterance that deviates from what we mean to say, there is very good evidence that we can slip in inner speech as well. If our arithmetic thought occurs in a numeric code, it's far from clear how we determine when a covert utterance constitutes a slip. In closing, I provide an account of what makes an inner speech utterance a slip. (shrink)