Related papers: Is mathematics like a game?
Metaphysics is traditionally conceived as aiming at the truth -- indeed, the most fundamental truths about the most general features of reality. Philosophical naturalists, urging that philosophical claims be grounded on science, have often…
Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…
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…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
As the etymology of the word shows, logic is intimately related to language, as exemplified by the work of philosophers from Antiquity and from the Middle-Age. At the beginning of the XX century, the crisis of the foundations of mathematics…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…