Anthony Kenny

Human Abilities and Dynamic Modalities

In his pioneering Essay in Modal Logic, G. H. von Wright, after system- atising the uses of various modal words, said in a concluding note An important use of [the modal words] is connected with the notions of an ability and of a disposition and with the verb ‘can’. For example : Jones can speak German (=it is possible for Jones to make himself understood in German) ; Jones cannot speak German (=it is impossible for Jones to make himself understood in German). We shall call the modal concepts which refer to abilities and dispositions dynamic modalities (I am indebted for the term to Mr. Geach)… The question whether the dynamic modalities, i.e. the logic of abilities and dispositions, is subject to exactly the same formal rules as the alethic modalities will have to be investigated separately. (An Essay in Modal Logic, Amsterdam, 1951, p. 54.)

The psychiatric expert in court

The law about expert evidence is unsatisfactory: it gives scope for the expert to usurp the role of judge, jury and parliament; it brings the professions of the experts into disrepute; and it sets juries the impossible task of sorting pseudo sciences from genuine ones. The law should be reformed by changing statutes which force expert witnesses to testify beyond their science, by taking the provision of expert evidence out of the adversarial context, and by removing from the courts the decision whether a nascent discipline is or is not a science.

Duress Per Minas as a Defence to Crime: II

I am honoured to be invited to reply to Lord Kilbrandon’s paper on duress. The paper contains proposals of the highest interest for reform of the law. It is particularly interesting to hear these proposals from a noble and learned judge who has himself played an important part in the legal debate of the law of England on this topic. The present condition of that law, as he ably illustrates, is a very difficult one to justify. As Lord Kilbrandon modestly refuses to dwell on the judgements in which he took part, and as he assumed perhaps a greater familiarity with the cases in question than can be expected of the philosophers among his audience, I would like to spend some time on the present state of the law before considering the pros and cons of each of the proposals for reform.

Wittgenstein on Mind and Metaphysics

Wittgenstein is often regarded as being both positivist and behaviorist: positivist in rejecting all metaphysics, and behaviorist in denying inner human life. So far as concerns philosophy of mind, this view is based on a misunderstanding of Wittgenstein’s work. He did indeed attack one particular metaphysical theory of mind: the Cartesian theory. Cartesianism is metaphysical in the sense of isolating statements about mental life from any possibility of verification or falsification in the public world. But much of Wittgenstein’s work in philosophy of mind is devoted to showing the importance of distinctions between different kinds of potentiality and actuality. These distinctions were one of the major concerns of the work of Aristotle which was the first book to bear the name Metaphysics, and were a main target of classical anti-metaphysicians. In this sense Wittgenstein himself had a metaphysics of mind; and the metaphysical sensitivity which he shared with Aristotle was what enabled him to reject Cartesianism without falling into behaviorism. In this paper I will try to illustrate different forms of metaphysics, and sketch Wittgenstein’s attitude to each.

Testing for Significance

This chapter discusses the general strategy of significance testing. In literary contexts, significance testing can be useful in connection with authorship attribution. The first step in significance testing is to formulate a hypothesis. The hypothesis in a significance test is about the value of a population parameter. A specific hypothesis about the relation between two parameters is called the null hypothesis, and it plays a special part in significance testing. If one is testing two texts in the course of trying to decide whether they are by the same author, there are various differences between word frequencies, word and sentence length, and the like. One sets up the null hypothesis that there is no difference between these parameters in the populations from which the passages are drawn and that the variations that are observed are because of sampling error. If the chance probability of the observed divergences is less than the level of probability fixed in advance, the null hypothesis is rejected.

Measures of Central Tendency

This chapter reviews measures of central tendency. The two most important things to know about a frequency polygon are where it is centered and how it is spread out. Statisticians have devised measures that give this information in compact numerical form. Measures that indicate the central location of a distribution are called measures of central tendency. Measures that indicate the way in which a distribution is spread out are called measures of variability or measures of dispersion. The everyday word for a measure of central tendency is “average”. The mode is the simplest and crudest index of central tendency: it is simply the peak, or highest point, of the frequency polygon. The mode, though the most easily calculated, is the least useful of the measures of central tendency. It cannot be made the basis of any further statistical calculation, and it may give a misleading impression of where the majority of data in a distribution lie.

Theoretical Distributions and the Theory of Sampling

This chapter reviews theoretical distributions and the theory of sampling. The typical phenomena studied by the literary statistician are discrete phenomena—the occurrence of words, the number of letters in a word, the length of a verse in syllables. Distributions of such features as sentence length are highly skew and far from symmetrical, bearing little resemblance to the bell-shaped curve of the normal distribution. Nonetheless, the normal distribution is almost as important in the statistical study of literature as it is in the natural and social sciences. One of the most important results of the mathematical theory of statistics is a theorem called the central limit theorem. This states that when samples are repeatedly drawn from a population, the means of the samples will be normally distributed around the population mean. Distributions may be actual or theoretical. The sampling distribution that interests statisticians is the theoretical distribution of all possible values of a test statistic. The larger the number of items in the sample, the closer is the approximation between the binomial and the normal distribution.

The Practice of Literary Sampling

This chapter reviews the selection, preparation, and presentation of textual material in stylometric studies of literature. The statistical theory on which significance testing is based concerns the relationship between random samples and the populations from which they are drawn. If a fragment of text is to be chosen, it must be chosen in a very different way. Once the population is defined, the sample must be chosen. It is not difficult to choose a random sample from a text. The samples on which statistical studies of literature are based are rarely completely random samples. The use of statistics to study the distribution of successive or concomitant events does not presuppose that these events are causally independent of each other. If determinism is true, then no two events are causally independent, but the use of statistical methods does not presuppose disbelief in determinism.

4 – Measures of Variability

This chapter provides an overview of measures of variability. Any distribution can be concisely described by assigning it a measure of central tendency and a measure of variability. There are three commonly used measures of variability: the range, the standard deviation, and the interquartile range. The range is the easiest measure of variability to calculate. The range is the crudest and least informative measure of dispersion. The standard deviation is the measure of variability that corresponds to the mean as a measure of central tendency. The standard deviation is the square root of the average squared deviation from the mean. It is calculated in four stages: (1) the deviation of each item in the distribution from the mean is noted, (2) each of these deviation scores is squared, (3) the mean of these squared deviations is calculated, and (4) the square root of this mean is then calculated; this is the standard deviation of the distribution. The mean squared deviation, the penultimate stage in working out the standard deviation, is called the variance of the distribution.

The Analysis of Variance

This chapter presents the analysis of variance. A method of testing for significance differences between means and proportions where more than two samples are involved is given by the analysis of variance. It permits the testing of the statistical significance between the means and proportions derived from several samples. The analysis of variance proceeds by separating or partitioning the total variance in the data into two parts: (1) the variance between the samples and (2) the variance within the individual samples. Two estimates of the population variance are then calculated: (1) one based on the variance between one sample and another, and (2) the other based on the variation of the values between each sample. When the analysis of variation is completed, the two estimates are compared with each other, and the ratio between them is evaluated for statistical significance.