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      Absence perception and the philosophy of zero

      Springer Netherlands
      Number cognition, Zero, Absence perception, Ontogeny

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          Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating (1) an account of numbers as properties of collections, (2) work on the philosophy of absences, and (3) recent work in numerical cognition and ontogenetic studies.

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          A mode control model of counting and timing processes.

          The similarity of animal counting and timing processes was demonstrated in four experiments that used a psychophysical choice procedure. In Experiment 1, rats initially learned a discrimination between a two-cycle auditory signal of 2-sec duration and an eight-cycle auditory signal of 8-sec duration. For the number discrimination test, the number of cycles was varied, and the signal duration was held constant at an intermediate value. For the duration discrimination test, the signal duration was varied, and the number of cycles was held constant at an intermediate value. Rats were equally sensitive to a 4:1 ratio of counts (with duration controlled) and a 4:1 ratio of times (with number controlled). The point of subjective equality for the psychophysical functions that related response classification to signal value was near the geometric mean of the extreme values for both number and duration discriminations. Experiment 2 demonstrated that 1.5 mg/kg of methamphetamine administered intraperitoneally shifted the psychophysical functions for both number and duration leftward by approximately 10%. Experiment 3 demonstrated that the magnitude of cross-modal transfer from auditory signals to cutaneous signals was similar for number and duration. In Experiment 4 the mapping of number onto duration demonstrated that a count was approximately equal to 200 msec. The psychophysical functions for number and duration were fit with a scalar expectancy model with the same parameter values for each attribute. The conclusion was that the same internal mechanism is used for counting and timing. This mechanism can be used in several modes: the "event" mode for counting or the "run" and the "stop" modes for timing.
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            Psychological foundations of number: numerical competence in human infants.

            An enduring question in philosophy and psychology is that of how we come to possess knowledge of number. Here I review research suggesting that the capacity to represent and reason about number is part of the inherent structure of the human mind. In the first few months of life, human infants can enumerate sets of entities and perform numerical computations. One proposal is that these abilities arise from general cognitive capacities not specific to number. I argue that the body of data supports a very different proposal: humans possess a specialized mental mechanism for number, one which we share with other species and which has evolved through natural selection. This mechanism is inherently restricted in the kinds of numerical knowledge it can support, leading to some striking limitations to early competence.
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              Mathematical Truth


                Author and article information

                Springer Netherlands (Dordrecht )
                6 May 2019
                6 May 2019
                : 197
                : 9
                : 3823-3850
                Kurt Gödel Research Center for Mathematical Logic (KGRC), Währinger Straße, 25, 1090 Vienna, Austria
                © The Author(s) 2019

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                : 15 March 2018
                : 19 April 2019
                Funded by: FundRef http://dx.doi.org/10.13039/501100002428, Austrian Science Fund;
                Award ID: P 28420
                S.I.: MathCogEncul
                Custom metadata
                © Springer Nature B.V. 2020

                number cognition,zero,absence perception,ontogeny
                number cognition, zero, absence perception, ontogeny


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