Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...) show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

This paper explores a unified approach to linguistic reference and the nature of objects, addressing both abstract and concrete entities. We propose a method of redefining ultra-thin objects through a modified abstraction principle, which involves two distinct computations: subsemantic computation processes direct physical input, while semantic computation derives the semantic values of a sentence from the meanings of its constituents. These computations take different inputs—one physical and one semantic—but yield identical outputs. Among these, the subsemantic computation is more accessible. This (...) approach facilitates a consistent treatment across various types of objects, including mathematical, concrete, social, and mental entities, thereby eliminating the need for domain-specific justifications. We advocate for this innovative perspective and address potential objections related to idealism and the utility of introducing objects. Our proposal advances the discourse of the nature of objects and linguistic reference, providing a comprehensive framework for understanding the existence and reference of objects across diverse discourse domains. (shrink)