Bartosz Brożek

Professional mathematicians differ from controls in their spatial-numerical associations

While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.

The troublesome ‘person’

In this paper I argue that the concept of person as utilized in legal and ethical discourse has no stable meaning, which often leads to premature conclusions and confusion. I identify three different ways of philosophical understanding of ‘person’ – the classical, the psychological and the ethical. I further observe that in the law the term is used as a technical device, which has little to do with the philosophical conceptions of the person. Finally, I claim that ‘person’ is also a part of the conceptual repertoire of folk psychology, and hence cannot be simply dispensed with. Rather, its use in legal and ethical debates should be accompanied by methodological awareness and caution.

On the legal responsibility of autonomous machines

AbstractThe paper concerns the problem of the legal responsibility of autonomous machines. In our opinion it boils down to the question of whether such machines can be seen as real agents through the prism of folk-psychology. We argue that autonomous machines cannot be granted the status of legal agents. Although this is quite possible from purely technical point of view, since the law is a conventional tool of regulating social interactions and as such can accommodate various legislative constructs, including legal responsibility of autonomous artificial agents, we believe that it would remain a mere ‘law in books’, never materializing as ‘law in action’. It is not impossible to imagine that the evolution of our conceptual apparatus will reach a stage, when autonomous robots become full-blooded moral and legal agents. However, today at least, we seem to be far from this point.

Law, Normativity, and Supervenience

In this chapter I argue that the relation of supervenience is insufficient to account for the normative dimension of the law. I begin by analyzing in some detail the traditional ways of relating normative (especially legal) and non-normative (natural) facts or properties: separation and reduction. Having identified their flaws, I consider the possibility of rendering the relationship in question with the use of the concept of supervenience. It transpires, however, that the claim that legal facts (properties) supervene on natural facts (properties) has limitations of its own. In particular, it cannot explain the normative character of legal rules, but rather presupposes it. Therefore, supervenience turns out to be insufficient when it comes to providing a full account of the normativity of law.

Introduction to the special issue on machine law

We are surrounded by machines. From simple ones—AC motors and transformers—through radio receivers, TV sets, smartphones and personal computers, to sophisticated AI systems, such as self-driving cars, autonomous weapons and IBM’s Watson. The advances in technology have reshaped the world we inhabit, including our social environment. When iPhone is the girl’s best friend, our communication and decision-making is aided by complex algorithms, and various tasks so far reserved for human beings are carried out by robots, the contemporary societies are not what they used to be. Moreover, the technology is advancing at such a rapid pace that many ideas, such as companion and sex robots, which used to be a fodder for science fiction are fast becoming a reality. This is a profound challenge for any legal system. The law is there to regulate the actions of individuals so that they contribute to the functioning of large societies. It means that legal institutions should be designed in such a way as to embrace any changes and developments that reshape our communal practices. For this reason, technological progress has been a focus of lawyers’ debates since the first industrial revolution. The great discoveries of the nineteenth and twentieth centuries—car, airplane, radio, TV, computer, the Internet—have not only influenced the existing legal institutions, but have also led to the establishment of entirely new branches of law. Arguably, however, they did not revamp the very foundations of their contemporary legal systems, but served as a means for regulating interactions between human beings. Technology has been considered only as a tool used by

Language as a Tool. An Insight From Cognitive Science

Abstract In this paper it has been argued that the theory of conceptual maps developed recently by Paul M. Churchland provides support for Wittgenstein’s claim that language is a tool for acting in the world. The role of language is to coordinate and shape the conceptual maps of the members of the given language community, reducing the cross-individual cognitive idiosyncrasies and paving the way for joint cognitive enterprises. Moreover, Churchland’s theory also explains our tendency to speak of language as consisting of concepts which correspond to things we encounter in the world. The puzzle of common sense reference is no longer a puzzle: while at the fundamental level language remains a tool for orchestrating conceptual maps, the fact that the maps encode some communally shared categorization of experience fuels our talk of concepts capturing the essences of things, natural kinds, prototypes, etc.