Abstract

Counting objects, especially moving ones, is an important capacity that has been intensively explored in experimental psychology and related disciplines. The common approach is to trace the three counting principles (estimating, subitizing, serial counting) back to functional constructs like the Approximate Number System and the Object Tracking System. While usually attempts are made to explain these competing models by computational processes at the neural level, their first-person dimensions have been hardly investigated so far. However, explanatory gaps in both psychological and philosophical terms may suggest a methodologically complementary approach that systematically incorporates introspective data. For example, the mental-action debate raises the question of whether mental activity plays only a marginal role in otherwise automatic cognitive processes or if it can be developed in such a way that it can count as genuine mental action. To address this question not only theoretically, we conducted an exploratory study with a moving-dots task and analyze the self-report data qualitatively and quantitatively on different levels. Building on this, a multi-layered, consciousness-immanent model of counting is presented, which integrates the various counting principles and concretizes mental agency as developing from pre-reflective to increasingly conscious mental activity.

Highlights

  • Counting of moving objects is an elementary activity that relates to the structuring of our immediate perceptual environment but is relevant for an abstract and operational understanding of various processes in society, science and technology

  • It became clear that the test persons approached the task from sometimes quite different perspectives; in the end they worked with the same quantification principles, but with individual weightings and combinations

  • This shall be illustrated with some exemplary formulations: “I counted very fast in the second round and was able to distinguish the counted from the uncounted points for a moment, despite the movement” (Part. 8)

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Summary

Introduction

Counting of moving objects is an elementary activity that relates to the structuring of our immediate perceptual environment but is relevant for an abstract and operational understanding of various processes in society, science and technology. The OTS, in contrast, is based on discrete representation of perceptual items to be counted by parallel as well as serial processes and serves for explaining both subitizing and one-byone counting (Trick and Pylyshyn 1993, 1994). This first exploration does not yet answer the question of what kind of activity counting essentially is. For it is speculative to conclude from the mastery of a technology to an ultimate understanding of the processes modeled by it Why, in this respect, should the computational paradigm have a different fate from other anthropomorphizing models derived from ancient technologies (combustion, hydraulics, mechanics, steam engine) which have been established over the centuries and thrown over again in scientific revolutions (Kuhn 1970)? The identification of brains or their parts with digital circuits would imply a mind-like user of this machinery in a dualistic way or attribute emerging mental powers to the biological “hardware.” These contradictory options directly lead to the hard problem of consciousness (the mind–body problem), which cannot be regarded as solved by third-person or materialistic approaches either (Chalmers 1995; Bennett and Hacker 2003; Wagemann 2011a; Majorek 2012)

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