Mathematics and Program Explanations

Aidan Lyon has recently argued that some mathematical explanations of empirical facts can be understood as program explanations. I present three objections to his argument.     

Blind individuals show pseudoneglect in bisecting numerical intervals

Neurologically normal individuals typically show a leftward bias--known as pseudoneglect--in bisecting physical lines as well as numerical intervals. The latter bias may reflect the spatial nature in which numbers are represented (i.e., the mental number line). In previous studies, we found that congenitally blind individuals show such leftward bias in haptic bisection. Here, we demonstrate that blind individuals also show a consistent leftward bias in numerical bisection. The leftward bias was greater when numbers were presented in descending rather than ascending order, and the magnitude of the leftward bias was comparable to that shown by a control group of blindfolded sighted participants. Our findings thus support the view that pseudoneglect operates at a mental representational level rather than being perceptually based. Moreover, the consistent leftward bias shown by blind individuals in both line and numerical bisection suggests that the right hemisphere dominance in spatial processing, resulting in an overestimation of the left side of space, develops even in the absence of any visual input.     

Effects of reduced threshold of automated speed enforcement on speed and safety

This study was designed to evaluate the effects of a reduced threshold of the fixed automated speed enforcement system on speed and safety on a two-lane rural road. The threshold was lowered from 20 km/h to 4 km/h and the public was informed about the change. Driving speeds on the experimental and control road before and after the change were compared. The main results showed that the reduced threshold decreased the mean speed by 2.5 km/h, the standard deviation of speed by 1.1 km/h and the proportion of exceeding vehicles by 11.8 percentage units. In conclusion, lowering the threshold of automated speed enforcement combined with an appropriate information campaign bring about a significant speed reduction that could contribute to substantial safety benefits.     

Logical operations and iterated infinitely deep languages

We discuss an abstract notion of a logical operation and corresponding logics. It is shown that if all the logical operations considered are implicitely definable in a logic ?*, then the same holds also for the logic obtained from these operations. As an application we show that certain iterated forms of infinitely deep languages are implicitely definable in game quantifier languages. We consider also relations between structures and show that Karttunen's characterization of elementary equivalence for the ordinary infinitely deep languages can be generalized to hold for the iterated infinitely deep languages. An early version of this work was presented in the Abstracts Section of ICM '78.     

A microcomputer system for controlling classical conditioning experiments

A microcomputer-based laboratory system for controlling stimulus presentations and data acquisition in classical conditioning experiments is described. The system comprises an Intel 386/486-based microcomputer and a commercially obtained low-cost counter/timer board with input/output lines for stimulus timing and external device control. A simple, yet versatile custom-designed structured programming language is provided for performing an unlimited number of stimulus configurations and their sequences. In electrophysiological studies, the system can be flexibly connected to computer-controlled signal conditioning systems for the amplification and filtering of multiunit and evoked field potential responses and to high-speed data acquisition systems for sampling and analyzing the responses. The costs of reserving an entire microcomputer for experiment control are well compensated for by the simplicity and efficiency of programming and transportability of the control protocols between different setups and laboratories. Furthermore, a data acquisition and analysis system most suitable for the aims of a research project can be selected.     

Burden of Proof Rules in Social Criticism

The article discusses burden of proof rules in social criticism. By social criticism I mean an argumentative situation in which an opponent publicly argues against certain social practices; the examples I consider are discrimination on the basis of species and discrimination on the basis of one's nationality. I argue that burden of proof rules assumed by those who defend discrimination are somewhat dubious. In social criticism, there are no shared values which would uncontroversially determine what is the reasonable presumption and who has the burden of proof, nor are there formal rules which would end the debate and determine the winner at a specific point.     

Living in Harmony: Nominalism and the Explanationist Argument for Realism

According to the indispensability argument, scientific realists ought to believe in the existence of mathematical entities, due to their indispensable role in theorising. Arguably the crucial sense of indispensability can be understood in terms of the contribution that mathematics sometimes makes to the super‐empirical virtues of a theory. Moreover, the way in which the scientific realist values such virtues, in general, and draws on explanatory virtues, in particular, ought to make the realist ontologically committed to abstracta. This paper shows that this version of the indispensability argument glosses over crucial detail about how the scientific realist attempts to generate justificatory commitment to unobservables. The kind of role that the Platonist attributes to mathematics in scientific reasoning is compatible with nominalism, as far as scientific realist arguments are concerned.