Related papers: Tension between Intuitive Infinitesimals and Forma…
The last decades saw dramatic progress in brain research. These advances were often buttressed by probing single variables to make circumscribed discoveries, typically through null hypothesis significance testing. New ways for generating…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
The role of continua has been clear since antiquity in the mathematical approaches to physics, while discrete manifolds were brought to the limelight mostly by Quantum and Information Theories, in the XX century. We first recall how…
With the growing interest in social applications of Natural Language Processing and Computational Argumentation, a natural question is how controversial a given concept is. Prior works relied on Wikipedia's metadata and on content analysis…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
In this letter, we point to three widely accepted challenges that the quantum theory, quantum information, and quantum foundations communities are currently facing: indeterminism, the semantics of conditional probabilities, and the spooky…
Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be together formalized and studied logically. We consider several logics in the setting of causal multiteam…
Machine learning models have had discernible achievements in a myriad of applications. However, most of these models are black-boxes, and it is obscure how the decisions are made by them. This makes the models unreliable and untrustworthy.…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
There are many philosophies and theories on what creativity is and how it works, but one popular idea is that of variations on a theme and intersection of concepts. This literature review explores philosophical proposals of how creativity…
We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy and other giants of infinitesimal…
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
Quantum theory, originally proposed as a physical theory to describe the motions of microscopic particles, has been applied to various non-physics domains involving human cognition and decision-making that are inherently uncertain and…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…