Mathematics and Statistics in the Social Sciences

Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit also concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth

The three worlds of AGI. Popper’s theory of the three worlds applied to artificial general intelligence

This Capstone applies Popper’s Three-worlds paradigm to the academic discourse on Artificial General Intelligence (AGI). It intends to assess how this paradigm can be used to frame the opinions of scientists and philosophers on Artificial General Intelligence (AGI) and what it reveals about the way the topic of AGI is approached from the fields of the Sciences and the Humanities. This has been achieved by means of a Literature Review reporting the opinions of main philosophers and scientists and by analysing two main projects – project CYC and project SOAR- advanced as possible ways to achieve AGI. As a result, most academics from the field of Science seem to better fit views on AGI interpreted through the lens of Popper’s World 2, the world of the mind. On the contrary, most philosophers seem to better fit views on AGI interpreted through the lens of Popper’s world 3, the world of the products of the human mind such as theories, knowledge and ideas. As a suggestion, this Thesis advocates the promotion of interdisciplinarity and discussion among the different academic fields

Destructive realism: Metaphysics as the foundation of natural science

This thesis has two philosophical positions as its targets. The first is 'scientific realism' of the form defended by Boyd, (the early) Putnam, and most recently Psillos. The second is empiricism in the vein of Mill, Mach, Ayer, Carnap, and Van Fraassen. My objections to both have a rather Popperian flavour. For I argue that 'confirmation' is a misnomer, that so-called 'ampliative inferences' are heuristics at best, and that naturalism and subjectivism are regressive doctrines. At the heart of genuine realism, I argue, is a stance on the issues of perception and conception. In particular, I hold that to be a realist is to reject the notion that there are representations which have some sort of epistemic priority. And along related lines, I maintain that the closely aligned doctrine of physicalism cannot simply be presupposed. What this amounts to is that the search for some sort of 'solid foundation' for knowledge' is a futile enterprise. Such a foundation would be unimportant, even if there were to be one, and we ought to be free to critically examine any claim we like. So rather than sapere aude, I would have 'dare to err', and place an intersubjective emphasis on inquiry. And this goes for metaphysics, logic, and mathematics, as well as for natural science. Yet I also advocate the view that we ought to be optimistic about our ability to find the truth, ceteris paribus. And to this end, I argue that we should accept that our faculty of conception is sufficient to allow us to connect with the possibilities of being, whereas our faculty of sense is sufficient to allow us to connect with that which is actual; this, given considerable critical struggle on our parts, both individually and collectively. I urge that it is methodologically advisable to behave as if this is so, if we are not to асһieve only the self-paralysis of the Pyrrhonist. In a nutshell, destructive realism says that natural science progresses by ruling out possibilities, in particular by ruling out possible worlds as candidates for the actual world, but that this is a two-stage process, involving both an a priori (metaphysical) and an a posteriori (observational) component. The aim of natural science is to eliminate false theories. Its aspiration is truth

Scientific Progress on the Semantic View : An Account of Scientific Progress as Objective Logical and Empirical Strength Increments

The aim of this master thesis is to make a convincing argument that scientific progress can be spoken of in objective terms. In order to make this argument I will propose a philosophical theory of scientific progress. Two concepts will be constructed with this aim in mind, both which are types of strength measures on scientific theories. The first concept, that of logical strength, pertains to the way a theory may exclude, or permit less, model classes compared to another theory. The second concept, that of empirical strength, pertains to an objective measure of the informational content of data models, defined in terms of Kolmogorov complexity. This latter idea stems from communication and computational theory. Scientific progress is then defined as the interaction, or the stepwise increases, of these two strength measures. Central for the conception of a scientific theory is the philosophical framework known as The Semantic View of Scientific Theories. This view can briefly be characterized as an empirical extension of Tarskian model-theory. Another central notion for this theory of scientific progress is the philosophical or metaphysical thesis called structural realism. Both will accordingly be explained and argued for. Finally, as a test on this proposed theory of scientific progress, it will be applied to two examples of theory transition from the history of physical theory. I conclude that the proposed theory handles these two cases well

The Nature of Theory in Information Systems

The aim of this research essay is to examine the structural nature of theory in Information Systems. Despite the importance of theory, questions relating to its form and structure are neglected in comparison with questions relating to epistemology. The essay addresses issues of causality, explanation, prediction, and generalization that underlie an understanding of theory. A taxonomy is proposed that classifies information systems theories with respect to the manner in which four central goals are addressed: analysis, explanation, prediction, and prescription. Five interrelated types of theory are distinguished: (1) theory for analyzing, (2) theory for explaining, (3) theory for predicting, (4) theory for explaining and predicting, and (5) theory for design and action. Examples illustrate the nature of each theory type. The applicability of the taxonomy is demonstrated by classifying a sample of journal articles. The paper contributes by showing that multiple views of theory exist and by exposing the assumptions underlying different viewpoints. In addition, it is suggested that the type of theory under development can influence the choice of an epistemological approach. Support is given for the legitimacy and value of each theory type. The building of integrated bodies of theory that encompass all theory types is advocated