‘When a child learns this ....’ ‘What is “learning a rule”?— This.’ Anyone familiar with Wittgenstein’s later philosophy recognizes these phrases as wholly typical of that philosophy. The appeals to the way in which a child learns, to learning in general, and to the italicized use of the indexical – all are familiar themes. In the Philosophical Investigations Wittgenstein develops his position on three crucial philosophical issues by beginning with the way in which a child learns. First, his critique of referential theories of meaning: ‘An important part of the training will consist in the teacher’s pointing to the objects, directing the child’s attention to them, and at the same time uttering a word’ (PI §6). Second, his attack on essentialist theories of understanding: ‘How does [the pupil] get to understand this notation? – First of all the series of numbers will be written down for him and he will be required to copy them .... And here there is a normal and an abnormal learner’s reaction’ (PI §143). And finally, his attack on the Cartesian model of consciousness: ‘A child has hurt himself and he cries; and then adults talk to him and teach him exclamations and, later, sentences’ (PI §244). These three critiques are the cornerstones for his later philosophy, and at the beginning of each he appeals to how children learn. Moreover, Wittgen-stein’s subsequent writings show an increase in the explicit appeal to learning and to a child’s learning. In On Certainty, Wittgenstein’s final work, virtually every page involves appeal to learning. In spite of this, most commentators treat the appeal as incidental.

In this paper I offer a probabilistic analysis of the notion of an event’s having an overall positive causal impact on a later event; that is, of overall positive causal impact. The analysis will be based on the notion of objective chance-like probability presented elsewhere. This paper deals only with token causal relations, i.e., those between particular actual event-tokens. (The corresponding generic relation will not be discussed here The key concept in the analysis of overall positive causal impact, I argue, is that of a clincher, roughly, an event which ‘seals’ (makes unreversed) a probability increase or a probability decrease condition. In the first part of the paper, I bring an example to illustrate the thesis that the presence of only an increaser-clincher yields overall positive causal impact (and correspondingly for a decreaser-clincher and overall negative causal impact). The more complex case in which both an increaser-clincher and a decreaser-clincher are present is then discussed, and a condition assessing their relative weight is proposed for determining whether a given case is one of overall positive causal impact or overall negative causal impact. Finally, the condition is modified to capture relative causal weight as opposed to the mere relative probabilistic weight of the two clinchers.

I want to discuss a certain class of paradoxes, which I will call ‘pragmatic paradoxes.’ The term reflects the role of indexical elements in some familiar instances of the class, such as the statements ‘I am not here,’ or ‘I am not now speaking,’ and serves to distinguish the paradoxes in which I’m interested, from the semantic paradoxes, like the Liar.

An analysis of the Surprise Exam paradox affords a natural approach. Here is one version of the paradox. On Friday the teacher informs the class that one day next week (Monday- Friday) an exam will take place, and that it will be unexpected until announced, on the day it is to take place. The students reason that it can’t take place on Friday, since, were it not to occur by Thursday, they would be expecting it Friday, contrary to the teacher’s specification. If it can’t take place Friday, then it can’t take place Thursday either, for similar reasons. And so forth. The students conclude that no such exam can take place. But of course it can. So, what went wrong?

If all politics is local, then any sensible political theory must be sensitive to the fine-grained features of the political landscape. No one thinks that one form of government is best for every situation, and a theory that fails to accommodate ‘local knowledge’ runs the risk of irrelevance. Yet we also think that political philosophy must rise above the particularities of context and transcend the muck-a-muck of daily politics.

Most theories, however, leave only a secondary role for context. They see it either as the basis for an excuse or merely as the data that must be plugged into a predetermined agenda. On the first view, contexts are only relevant when they prevent a society from achieving whatever the view regards as the best government for humans. If a society lacks the conceptual, technological, or economic resources to attain the best form of government, then its context absolves it from charges of illegitimacy. We find this view reflected in the attitudes of, say, those Americans who think every country should be a liberal democracy, but admit that some places are not yet developed enough to realize such a society.

In its earliest stages the macroscopic properties of a human embryo are merely those of a few-celled organism, not so very different from (say) a fly embryo. If all goes well, however, it will eventually develop into a human infant. Expectation of such future development leads to the absolutist view that from the moment of conception the zygote has the same moral status as an infant. When the absolutist view is based on this expectation, I shall say it is based on a potentialist intuition that sees fetal development as the unfolding of a pre-established essence. This intuition was expressed by a Tennessee judge dealing with a custody case concerning frozen embryos, who claimed that ‘the entire constitution of the man is clearly, unequivocally spelled-out, including arms, legs, nervous system and the like ....’ Singer and Dawson put the potentialist picture (with which they disagree) in these terms: ‘The development of the embryo inside the female body can be seen as a mere unfolding of a potential that is inherent in it.’

Philosophy is a difficult mode of expression, and anyone who uses the word ‘potentiality’ invites misunderstanding. It is no surprise, then, that John Fisher ascribes to me a doomed position I do not hold. According to him I argue:

1. X is a creature of a certain sort.

2. Creatures of this sort have right R.

3. Therefore, X has a right R.