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.

A method to weight three categories of adaptive thermal comfort

The adaptive thermal comfort theory considers people as active rather than passive recipients in response to ambient physical thermal stimuli, in contrast with conventional, heat-balance-based, thermal comfort theory. Occupants actively interact with the environments they occupy by means of utilizing adaptations in terms of physiological, behavioural and psychological dimensions to achieve ‘real world’ thermal comfort. This paper introduces a method of quantifying the physiological, behavioural and psychological portions of the adaptation process by using the analytic hierarchy process (AHP) based on the case studies conducted in the UK and China. Apart from three categories of adaptations which are viewed as criteria, six possible alternatives are considered: physiological indices/health status, the indoor environment, the outdoor environment, personal physical factors, environmental control and thermal expectation. With the AHP technique, all the above-mentioned criteria, factors and corresponding elements are arranged in a hierarchy tree and quantified by using a series of pair-wise judgements. A sensitivity analysis is carried out to improve the quality of these results. The proposed quantitative weighting method provides researchers with opportunities to better understand the adaptive mechanisms and reveal the significance of each category for the achievement of adaptive thermal comfort.

Processing empty categories in a second language: When naturalistic exposure fills the (intermediate) gap

An ongoing debate on second language (L2) processing revolves around whether or not L2 learners process syntactic information similarly to monolinguals (L1), and what factors lead to a native-like processing. According to the Shallow Structure Hypothesis (Clahsen & Felser, 2006a), L2 learners’ processing does not include abstract syntactic features, such as intermediate gaps of wh-movement, but relies more on lexical/semantic information. Other researchers have suggested that naturalistic L2 exposure can lead to native-like processing (Dussias, 2003). This study investigates the effect of naturalistic exposure in processing wh-dependencies. Twenty-six advanced Greek learners of L2 English with an average nine years of naturalistic exposure, 30 with classroom exposure, and 30 native speakers of English completed a self-paced reading task with sentences involving intermediate gaps. L2 learners with naturalistic exposure showed evidence of native-like processing of the intermediate gaps, suggesting that linguistic immersion can lead to native-like abstract syntactic processing in the L2.

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.

Interaction between grammatical categories and cognition in bilinguals: The role of proficiency, cultural immersion, and language of instruction

Previous studies have demonstrated that there is a tight link between grammatical concepts and cognitive preferences in monolingual speakers (Lucy 1992, Lucy & Gaskins 2003, Imai & Gentner 1997, Imai & Mazuka 2003). Recent research has also shown that bilinguals with languages that differ in their concepts may shift their cognitive preferences as a function of their proficiency (Athanasopoulos, 2006) or cultural immersion (Cook, Bassetti, Kasai, Sasaki, & Takahashi, 2006). The current short paper assesses the relative impact of each of these variables, and furthermore asks whether bilinguals alternate between two distinct cognitive representations of language-specific concepts depending on the language used in the experiment. Results from an object classification task showed that Japanese–English bilinguals shifted their behaviour towards the second language (L2) pattern primarily as a function of their L2 proficiency, while cultural immersion and language of instruction played a minimal role. These findings suggest that acquisition of novel grammatical categories leads to cognitive restructuring in the bilingual mind and have implications for the relationship between language and cognitive processing.