Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Military doctrine, command philosophy and the generation of fighting power: genesis and theory

Military doctrine is one of the conceptual components of war. Its raison d’être is that of a force multiplier. It enables a smaller force to take on and defeat a larger force in battle. This article’s departure point is the aphorism of Sir Julian Corbett, who described doctrine as ‘the soul of warfare’. The second dimension to creating a force multiplier effect is forging doctrine with an appropriate command philosophy. The challenge for commanders is how, in unique circumstances, to formulate, disseminate and apply an appropriate doctrine and combine it with a relevant command philosophy. This can only be achieved by policy-makers and senior commanders successfully answering the Clausewitzian question: what kind of conflict are they involved in? Once an answer has been provided, a synthesis of these two factors can be developed and applied. Doctrine has implications for all three levels of war. Tactically, doctrine does two things: first, it helps to create a tempo of operations; second, it develops a transitory quality that will produce operational effect, and ultimately facilitate the pursuit of strategic objectives. Its function is to provide both training and instruction. At the operational level instruction and understanding are critical functions. Third, at the strategic level it provides understanding and direction. Using John Gooch’s six components of doctrine, it will be argued that there is a lacunae in the theory of doctrine as these components can manifest themselves in very different ways at the three levels of war. They can in turn affect the transitory quality of tactical operations. Doctrine is pivotal to success in war. Without doctrine and the appropriate command philosophy military operations cannot be successfully concluded against an active and determined foe.

Experimenting on contextualism

In this article we refine the design of context shifting experiments, which play a central role in contextualist debates, and we subject a large number of scenarios involving different types of expressions of interest to contextualists, including ‘know’ and color adjectives like ‘green’, to experimental investigation. Our experiment (i) reveals an effect of changing contexts on the evaluation of uses of the sentences that we examine, thereby overturning the absence of results reported in previous experimental studies (so-called null results), (ii) uncovers evidence for a ‘truth bias' in favor of positive over negative sentences, and (iii) reveals previously unnoticed distinctions between the strength of the contextual effects displayed by scenarios involving knowledge ascriptions and scenarios concerning color and other miscellaneous scenarios.

On collective intentions: collective action in economics and philosophy

Philosophers and economists write about collective action from distinct but related points of view. This paper aims to bridge these perspectives. Economists have been concerned with rationality in a strategic context. There, problems posed by “coordination games” seem to point to a form of rational action, “team thinking,” which is not individualistic. Philosophers’ analyses of collective intention, however, sometimes reduce collective action to a set of individually instrumental actions. They do not, therefore, capture the first person plural perspective characteristic of team thinking. Other analyses, problematically, depict intentions ranging over others’ actions. I offer an analysis of collective intention which avoids these problems. A collective intention aims only at causing an individual action, but its propositional content stipulates its mirroring in other minds.

Linguistic experiments and ordinary language philosophy

J.L. Austin is regarded as having an especially acute ear for fine distinctions of meaning overlooked by other philosophers. Austin employs an informal experimental approach to gathering evidence in support of these fine distinctions in meaning, an approach that has become a standard technique for investigating meaning in both philosophy and linguistics. In this paper, we subject Austin's methods to formal experimental investigation. His methods produce mixed results: We find support for his most famous distinction, drawn on the basis of his `donkey stories', that `mistake' and `accident' apply to different cases, but not for some of his other attempts to distinguish the meaning of philosophically significant terms (such as `intentionally' and `deliberately'). We critically examine the methodology of informal experiments employed in ordinary language philosophy and much of contemporary philosophy of language and linguistics, and discuss the role that experimenter bias can play in influencing judgments about informal and formal linguistic experiments.

A slugfest of intuitions: contextualism and experimental design

This paper considers ways that experimental design can affect judgments about informally presented context shifting experiments. Reasons are given to think that judgments about informal context shifting experiments are affected by an exclusive reliance on binary truth value judgments and by experimenter bias. Exclusive reliance on binary truth value judgments may produce experimental artifacts by obscuring important differences of degree between the phenomena being investigated. Experimenter bias is an effect generated when, for example, experimenters disclose (even unconsciously) their own beliefs about the outcome of an experiment. Eliminating experimenter bias from context shifting experiments makes it far less obvious what the “intuitive” responses to those experiments are. After it is shown how those different kinds of bias can affect judgments about informal context shifting experiments, those experiments are revised to control for those forms of bias. The upshot of these investigations is that participants in the contextualist debate who employ informal experiments should pay just as much attention to the design of their experiments as those who employ more formal experimental techniques if they want to avoid obscuring the phenomena they aim to uncover

Applied philosophy of language

This chapter explores the extent to which philosophy of language can be considered an applied discipline. I consider, first, ways in which sub-sections of philosophy of language may be considered as applied in terms of their subject matter and/or the kinds of questions being addressed (e.g. philosophy of language which deals with derogatory or inflammatory uses of language, or the role of philosophy of language within feminist philosophy). Then, in the second part of the chapter, I turn to consider a more general (and perhaps more controversial) conception of philosophy of language as applied, which arises from the methodology adopted and the relationship of the discipline to empirical data.