Cognitive access to numbers: the philosophical significance of empirical findings about basic number abilities

Muscimol-induced inactivation of the ventral prefrontal cortex impairs counting performance in rhesus monkeys

Numbers are one of the three basic concepts of human abstract thinking. When human beings count, they often point to things, one by one, and read numbers in a positive integer column. The prefrontal cortex plays a wide range of roles in executive functions, including active maintenance and achievement of goals, adaptive coding and exertion of general intelligence, and completion of time complexity events. Nonhuman animals do not use number names, such as "one, two, three," or numerals, such as "1, 2, 3" to "count" in the same way as humans do. Our previous study established an animal model of counting in monkeys. Here, we used this model to determine whether the prefrontal cortex participates in counting in monkeys. Two 5-year-old female rhesus monkeys (macaques), weighing 5.0 kg and 5.5 kg, were selected to train in a counting task, counting from 1 to 5. When their counting task performance stabilized, we performed surgery on the prefrontal cortex to implant drug delivery tubes. After allowing the monkeys' physical condition and counting performance to recover, we injected either muscimol or normal saline into their dorsal and ventral prefrontal cortex. Thereafter, we observed their counting task performance and analyzed the error types and reaction time during the counting task. The monkeys' performance in the counting task decreased significantly after muscimol injection into the ventral prefrontal cortex; however, it was not affected after saline injection into the ventral prefrontal cortex, or after muscimol or saline injection into the dorsal prefrontal cortex. The ventral prefrontal cortex of the monkey is necessary for counting performance.

Spontaneous quantity discrimination in a family-living lizard

While foraging or during social interactions, animals may benefit from judging relative quantity. Individuals may select larger prey or a patch with more food and, likewise, it may pay to track the number and type of individuals and social interactions. We tested for spontaneous quantity discrimination in the gidgee skink (Egernia stokesii), a family-living lizard. Lizards were presented with food quantities differing in number or size and were able to select the larger quantity of food items when they differed in number but not when items differed in size. We show, for the first time, superior spontaneous discrimination of items differing in number over size in a lizard species, which contrasts with previous findings. Our simple method, however, did not include controls for the use of continuous quantities, and further tests are required to determine the role of such information during quantity discrimination. Our results provide support for the use of the parallel individuation system for the discrimination of small quantities (four or fewer items). Lizards might, however, still use the approximate number system if items in larger quantities (more than four) are presented. Overall, we uncovered evidence that species might possess specific cognitive abilities potentially adapted to their niche with respect to quantity information (discrete and/or continuous) and the processing system used when judging quantities. Importantly, our results highlight the need for testing multiple species using similar testing procedures to gain a better understanding of the underlying causes leading to differences across species.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

Absence perception and the philosophy of zero

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.