The philosolphy of strict finitism is a research programme containing developmental theory and mathematics as its main branches. The first branch is concerned with the ontogenetic and historicaldevelopment of various concepts of infinity. The frame work is Jean Piaget’s genetic epistemology. Based upon these develop mental studies, the mathematical branch introduces a new concept of infinity into mathematics. Cantor propagated the actual infinite, Brouwer and the constructivists the potential infinite. Still more radical is strict finitism, favoring the natural infinite, i.e. the phenomena of the unsurveyable, unfeasible, unreachable. There exist by this time strict finitistic reconstructions for arithmetic, geometry, calculus, and even for infinitistic set theory.

The aim of this paper is to analyze Leibniz and Newton’s conception of space, and to point out where their agreements and disagreements lie with respect to its mode of existence. I shall offer a definite characterization of Leibniz and Newton’s conceptions of space. I will show that, according to their own concepts of substance, both Newtonian and Leibnizian spaces are not substantiva!. The reason of that consists in the fact that space is not capable of action. Moreover, there is a sense in which space is relational, because their parts are individuated only by means of their mutual relations.

In his criticism of Armstrong’s argument against nominalism, Parsons (1999) makes a crucial use of a notion of truthmaking in terms of weak supervenience which assumedly: (i) does not entail truthmaker essentialism, (ii) is neutral as to the issue of nominalism, and (iii) is useful in Armstrong’s argument against Ryle. I will try to show that Parsons’ notion is defective because it does not preserve the explanatory character of truthmakers. Besides, I argue that the natural reformulation of the notion in terms of strong supervenience fails in two respects: (i) it is not neutral as to the issue of nominalism and (ii) it does not preserve the explanatory character of truthmakers if it succeeds in avoiding truthmaker essentialism. As a corollary, Armstrong’s truthmaker argument against nominalism is vindicated.

Two versions of minimal intuitionism are defined restricting Contraction. Both are defined by means of a falsity constant F. The first one follows the historical trend, the second is the result of imposing specialconstraints on F. RelationaI ternary semantics are provided.

Language is a spontaneously evolved emergent adaptation, not a formal computational system. Its structure does not derive from either innate or social instruction but rather self-organization and selection. Its quasi-universal features emerge from the interactions among semiotic constraints, neural processing limitations, and social transmission dynamics. The neurological processing of sentence structure is more analogous to embryonic differentiation than to algorithmic computation. The biological basis of this unprecedented adaptation is not located in some unique neurologieal structure nor the result of any single mutation, but is vested in the synergistic interaction of numerous coevolved neurological biases and social dynamics.

This paper presents the Functional/Emotional approach to language development, which explains the process leading up to the core capacities necessary for language (e.g., pattern-recognition, joint attention); shows how this process leads to the formation of internal symbols; and how it shapes and is shaped by the child’s development of language. The heart of this approach is that, through a series of affective transformations, a child develops these core capacities and the capacity to form meaningful symbols. Far from being a sudden jump, the transition from pre-symbolic communication to language is enabled by the advances taking place in the child’s affective gesturing.