In one of his meetings with members of the Vienna Circle, Wittgenstein discusses Hermann Weyl’s brief conversion to intuitionism and criticizes his arguments against applying the law of the excluded ...middle to generalizations over the natural numbers. Like Weyl, however, Wittgenstein rejects the classical model theoretic conception of generality when it comes to infinite domains. Nonetheless, he disagrees with him about the reasons for doing so. This paper provides an account of Wittgenstein’s criticism of Weyl that is based on his differing understanding of what a general statement over infinite domains consists in. This difference in their conception of generality is argued to be central to the middle Wittgenstein’s overall stance on intuitionism as well. While Weyl (and other intuitionists) reject the law of the excluded middle on grounds of constructivity, Wittgenstein argues that general statements over infinite domains do not express propositions in the first place. The origin of this position as well as its consequences for contemporary debates on generality are further assessed.
This paper presents an abstract parametrised functional interpretation of WE-HAω. It is based on families of parameters allowing for different degrees of freedom on the design of concrete ...interpretations. In this way, we are able to generalise previous work on unifying functional interpretations by including in the unification the more recent bounded and Herbrandized functional interpretations.
This paper draws upon three broad perspectives on the strategic decision-making process in order to develop a more completely specified model of strategic decision effectiveness in a different ...context, namely Egypt. The key variables in this model consist of three strategic decision-making process dimensions (rationality, intuition, and political behavior); seven moderating variables concerning decision-specific, environmental, and organizational factors; and strategic decision effectiveness as an outcome variable. A two-stage study was conducted in which the first stage provided exploratory insights and the second stage investigated hypotheses on the impact of strategic decision-making process dimensions on strategic decision effectiveness and the moderating role of broader contextual variables. The second-stage study produced three major findings: (1) both rational and political processes appear to have more influence on strategic decision effectiveness than does intuition; (2) strategic decision effectiveness is both process- and context-specific; and (3) certain results support the 'culture-free' argument, while others support the 'culture-specific' argument.
The psychological study of spiritual development continues to grow in popularity, but definitions, theories, and frameworks related to this field often focus on a narrow range of qualities associated ...with spirituality. In the present article, the importance of integrating intuitive cognition—particularly moral intuitions—into models of spiritual development is considered, the implications of such cognition for spiritual development and Christian education are examined, and various limitations are noted.
My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not ...only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. Redeveloping the constructions of natural numbers and systems sketched in an appendix to Brouwer's Cambridge lectures, I observe that the only plausible way he can make some elementary arithmetic in his separable mathematics is by allowing for the same canonical number to be determined by multiple separable entities, resulting in an overabundant mathematical ontology.
The notion that a false positive (false conviction) is worse than a false negative (false acquittal) is a deep-seated commitment in the theory of criminal law. Its most illustrious formulation, the ...so-called Blackstone’s ratio, affirms that “it is better that ten guilty persons escape than that one innocent suffer”. Are people’s evaluations of criminal statutes consitent with this tenet of the Western legal tradition? To answer this question, we conducted three experiments (total
N
= 2492) investigating how people reason about a particular class of offenses—proxy crimes—known to vary in their specificity and sensitivity in predicting actual crime. By manipulating the extent to which proxy crimes convict the innocent and acquit those guilty of a target offense, we uncovered evidence that attitudes toward proxy criminalization depend primarily on its propensity toward false positives, with false negatives exerting a substantially weaker effect. This tendency arose across multiple experimental conditions—whether we matched the rates of false positives and false negatives or their frequencies, whether information was presented visually or numerically, and whether decisions were made under time pressure or after a forced delay—and was unrelated to participants’ probability literacy or their professed views on the purpose of criminal punishment. Despite the observed inattentiveness to false negatives, when asked to justify their decisions, participants retrospectively supported their judgments by highlighting the proxy crime’s efficacy (or inefficacy) in combating crime. These results reveal a striking inconsistency: people favor criminal policies that protect the rights of the innocent, but report comparable concern for their expediency in fighting crime.
HLA Hart famously argues that legal obligation is best understood by analysing law as a species of social rule. This article engages with recent work in social psychology and norm theory to ...critically evaluate Hart's theory. We draw on the social intuitionist model of practical decision-making associated with Amos Tversky, Daniel Kahneman and Jonathan Haidt to argue that legal officials rely on holistic intuitive judgements to identify their legal obligations. We then explain the evolution and persistence of legal rules by reference to the theory of social norms offered by Cristina Bicchieri. This way of thinking about legal obligation lends support to Hart's account of law as a social practice. However, it challenges other aspects of his views, such as the idea that the only necessary factor in determining the content of law is its socially recognised sources. It also casts doubt on Hart's claim that legal obligation does not empirically extend beyond legal officials to other members of the community. Hart's account can be adapted to meet these criticisms, but not without undermining its commitment to legal positivism.
Free choice sequences play a key role in the intuitionistic theory of the continuum and especially in the theorems of intuitionistic analysis that conflict with classical analysis, leading many ...classical mathematicians to reject the concept of a free choice sequence. By treating free choice sequences as potentially infinite objects, however, they can be comfortably situated alongside classical analysis, allowing a rapprochement of these two mathematical traditions. Building on recent work on the modal analysis of potential infinity, I formulate a modal theory of the free choice sequences known as lawless sequences. Intrinsically well-motivated axioms for lawless sequences are added to a background theory of classical second-order arithmetic, leading to a theory I call
$MC_{LS}$
. This theory interprets the standard intuitionistic theory of lawless sequences and is conservative over the classical background theory.
PDF
