Mario Graziano

The System 2

We think that the numbers are accurate, that tells us the truth, and that are not exposed to any interpretation. Consequently, the numbers are merely numbers, regardless of the context in which they occur, regardless of the culture of single population. However, in recent years there have been some studies that go against this conception of common sense. This chapter considers the role of language, focusing in particular on studies of Munduruku and Chinese numerical cognition.

The System 1

This chapter is devoted to the discovery of the core abilities underlying human numerical cognition. Neuroscientists hypothesises that human beings are born with a “number sense” that they share with other animals and that this instinct is the expression of the functioning of a “mental organ”, a set of brain circuits that exist also in other species. According to neuroscientist Stanislas Dehaene, this “mental organ” works as an accumulator, namely a kind of approximate counting device that allows us to perceive, store, and compare numerical quantities.

Dual Process Theories for Calculus

The dual process theories are popular in many domains of psychology, such as reasoning, decision making, social cognition, cognitive development, clinical psychology, and cognitive neuroscience. In the last chapter, this theoretical approach is applied, for the first time, to the studies on numerical cognition with the aim of review the results brought about by psychological and neuroscientific studies conducted on numerical cognition and laying the foundations of a new potential philosophical explanation on mathematical knowledge.

Dissociations Between System 1 and System 2

Calculation ability represents an extremely complex cognitive process. It has been understood to represent a multifactor skill, including verbal, spatial, memory, and executive function abilities. In this chapter, we will deal with it by calculation disturbances are analyzed. Specifically, evidence from brain-damaged patients indicates that deficits in mathematics can follow injury to either cerebral hemisphere, but that the nature of the impairment will differ depending upon the locus of the cerebral insult.

Numerical cognition and philosophy of mathematics. Dehaene's (neuro)intuitionism and the relevance of language

Can investigations carried out in the field of cognitive science about numerical cognition shed light on the issues traditionally raised by philosophers of mathematics? What kind of relation exists between the current neuroscientific research and the philosophical reflection on mathematics? This paper critically explores the answers to these questions provided by the French neuroscientist Stanislas Dehaene, identifying the framework of a possible future collaboration between these disciplines

Individual and Social Preferences Defending the Agent’s Perspective Rather than the Theoretician’s

Standard economic theory usually analyzes the decisions made by individuals as a rational process in which each individual has sound and consistent preferences and makes decisions according to the principle of subjective expected utility maximization. Starting from the pioneering work of Herbert Simon and the research of cognitive psychologists Kahneman and Tversky, the contributions provided by cognitive-behavioral theory have repeatedly shown that real agents make choices in a way that differs systematically from standard theory, hence highlighting its limits. Rather than considering standard normative theory as false or unable to explain the data obtained by behavioral economists, several economists decided to develop new formal models that could include the results of different experiments and empirical observations that captured all dimensions of the choice made by an individual. In this sense, they proposed new models that were not intended to challenge standard theory but rather designed to provide a kind of psychological expansion to it. This article has the aim of describing and analyzing the advantages and limitations of these new models, which unfortunately are not always suited to describe the individual behavior, the individuals’ actions, or the equilibria due to the combination of the actions of several players. To overcome the limits of these models, we decided to take into consideration the unfortunately unfinished work of Michael Bacharach, who strived to understand the individual and collective forms of rationality without applying only analytical devices or a theoretical vision of the world but bringing rationality back to the perception level of the agents.

Genetics and Philosophy by Paul Griffiths and Karola Stotz

In this book, Paul Griffiths and Karola Stotz deal with the classic issues addressed by the philosophy of biology: from the topic of reductionism to the metaphysical assumptions implied by the laws of nature or the issues regarding the use of certain biological organisms as models, from the analysis of the theories of reference to the field of developmental biology. The book specifically addresses the particular type of information reductionism employed in some fields of genetics and molecular biology. The book is undoubtedly aimed at exploring the philosophy of science, despite the fact that many of the issues relating to the philosophy of physics and mathematics— main reference points in the current philosophical debate—are explicitly split off from the biological issues and are often consciously overlooked, as in the case of the genetics of populations. The arguments and the structure of the book’s nine chapters rely on the idea that, in the current philosophy of biology, there is a remarkable tension between a reductionist point of view and an approach that could be defined as ‘pluralist’. According to the reductionist approach, the activities of genes play a primary role at both an ontological and an explanatory level: not only are genes seen as the fundamental units for selection and reproduction; they represent also the key factors in explaining the form and development of living creatures. On the other hand, the pluralist approach emphasizes the equal influence played on an explanatory and ontological level by factors other than genes, such as other organisms and the surrounding environment. The two authors provide a thorough and comprehensive review of the concept of the gene, showing how over the years this concept has been linked to a series of causing conditions and—with the development of molecular biology—to a series of specific structures. The book discusses these topics in an exemplary and comprehensive way, especially when the authors address theories particularly close to their hearts, such as the anti-reductionist, pluralist, and structuralist theories (cf. chapter 3, ‘The material gene’). Going beyond the book’s core issue, the authors provide a good number of in-depth analyses on a wide range of topics, presenting them in a way that requires no specialist philosophical or biological knowledge. For this reason, the book is suited also for people without specialist knowledge, even if sometimes a reader might usefully refer to a biology or chemistry dictionary in order to understand the full meaning of some technical vocabulary. Finally, the book’s long list of bibliographic references allows readers to further deepen the information provided in every single chapter.

Rationality and Experimental Economics

The theory of rational choice (TRC) is a model of explanation used by social science theorists to interpret behavior. Initially, the theory was the dominant paradigm of economics. A fundamental postulate of neoclassical economics was that economic phenomena primarily resulted from the action of agents who were fully rational, equal and therefore indistinguishable from each other and all agents pursuing their own personal and individual gain.

Evolutionary Economics and Biological Complexity

According to some theorists, economic phenomena that determine wealth are prioritized in research. This “substantial” definition is often contrasted with the “formal” definition by Lionel Robbins (1935), stating that economic science owes its unity and specificity to the fact that it studies contradictory choices. The agent has limited resources to distribute between different objectives, and he must choose to sacrifice some objectives for the benefit of others. This definition, by intrinsically linking economics to the theory of choice, has led economics, as a science, to focus on human behavior as a relationship between ends and means. In other words, economics is the science of choosing the most advantageous option among several alternatives, depending on one’s context and needs. The aim is therefore to make the most favorable long-term choice. However, in everyday life, many possibilities arise when we make an important decision; thus, the consequences of our choices are not clearly predictable or known a priori. In this complex and uncertain environment, our choices have consequences that become more or less attractive over time. Experience allows an agent to accumulate knowledge about the consequences of different choices and to develop preferences for some. If an agent understands the consequences associated with each choice, uncertainty decreases, and decisions are driven by the agent’s preference or by risk aversion.