Related papers: G\'eom\'etrie et cognition; l'exemple du continu
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them,…
The development of discursive knowledge presumes the communication of meaning as analytically different from the communication of information. Knowledge can then be considered as a meaning which makes a difference. Whereas the communication…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
The scientific study of the retina has reached a remarkable state of completion. We can now explain many aspects of early visual processing based on a relatively simple model of neural circuitry in the retina. The same model, with different…
We introduce \emph{conceptual views} as a formal framework grounded in Formal Concept Analysis for globally explaining neural networks. Experiments on twenty-four ImageNet models and Fruits-360 show that these views faithfully represent the…
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
In this essay we examine some aspects of the classical theory of definition as codified in Aristotle's \emph{Topics} and Porphyry's \emph{Eisagog\^e} in the light of the way definition is carried out in modern mathematical practice. Our…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
The continuum has been one of the most controversial topics in mathematics since the time of the Greeks. Some mathematicians, such as Euclid and Cantor, held the position that a line is composed of points, while others, like Aristotle, Weyl…
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
We revisit Smullyan's paper ``Truth and Provability'' (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan's framework discussed in that paper. Second, we clarify the…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
In this paper I want to propose an argument to support Jerry Fodor's thesis (Fodor 1983) that input systems are modular and thus informationally encapsulated. The argument starts with the suggestion that there is a "grounding problem" in…