‘Metamathematics’ in Transition

In this paper, we trace the conceptual history of the term ‘metamathematics’ in the nineteenth century. It is well known that Hilbert introduced the term for his proof-theoretic enterprise in about 1922. But he was verifiably inspired by an earlier usage of the phrase in the 1870s. After outlining Hilbert's understanding of the term, we will explore the lines of inducement and elucidate the different meanings of ‘metamathematics’ in the final decades of the nineteenth century. Finally, we will investigate the earlier occurrences and come to the conclusion that the conceptual prehistory of the Hilbertian notion of metamathematics dates back to 1870, whereas the history of the word starts in 1799 at the latest.

What is this: metamathematics? It is something amazing everybody, […] since it makes the mind dizzy and withdraws thinking its sole fulcrum.1 ¹ Brunner 1898, p. 832: ‘Was ist das: Metamathematik? Es ist etwas, was einen Jeden in das äusserste Staunen versetzt, […] was das Gehirn schwindlig macht und dem Denken seinen einzigen Stütz- und Angelpunkt zu entziehen droht’.      

THE YOUNG AND THE RESTLESS. GENDER, ‘YOUTH’, AND THE DELHI GANG RAPE CASE OF 2012

Following the Delhi gang rape and murder of Jyoti Singh Pandhey in New Delhi and the unprecedented levels of protest that followed, high numbers of young people in the subcontinent and specifically urban India were blamed for sexual violence, while also heralded as a progressive vanguard.¹1 The Justice Verma Commission report that followed the Delhi gang rape described a ‘…?mass of young, prospectless men’ who were blamed for violent assaults of women in urban India. The report further concluded that ‘?…?large scale disempowerment of urban man is lending intensity to a pre-existing culture of sexual violence’. Paradoxically, Justice Verma also praised the young for their political activism following the Delhi gang rape and murder case. Justice Verma specifically praised the Youth Movement, stating that:Much to Learn from the youth, not possible to name everyone who contributed. Even when there was provocation, they did not react and continued to maintain calm. It was the young men who were conscious that this gender inequality has to be done away with.One can see how discourses concerning young urban Indians are fraught with contradictions that gesture to how political leaders want to cease on the energies of young people to support national interests, while also blaming them for their insecurity within a neoliberal economy. In this piece, I discuss the paradoxical discourses that surround the Delhi gang rape and the unprecedented levels of protest that followed in relation to global austerity and anxieties concerning youth. While ‘idle young men’ are blamed for sexual violence and ‘young’ women are subject to paternalistic protectionism, I suggest that gendered violence in urban India must be thought of in relation to a wider moment of global recession and austerity. I use the Delhi gang rape case and discursive constructions of ‘youth’ as both deviant and politically progressive to discuss the gendered effects that increased forms of global precarity supports.     

A Critical Examination of the Historical Origins of Connexive Logic

It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of its consequent is incompatible with its antecedent’, a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to ‘normal’ conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle’s and Boethius’ theses to such self-consistent antecedents, however, turn out to be theorems of ordinary modal logic and thus don’t give rise to any non-classical system of genuinely connexive logic.     

Fleeting encounter

Abstract

This short paper describes a recent visit to an exhibition of modern art. It examines my impressions in the light of contemporary psychodynamic theory. The exhibition was called ‘Some Went Mad, Some Ran Away…’ It included the work of fifteen modern artists, mainly created between 1992 and 1994, and selected by the British artist Damien Hirst. The exhibition leaflet said that the artists had used ‘real objects, body-casts, natural and man-made forms, sculpture, painting and photography, to set up a number of provocative juxtapositions’.     

Aristotle's Prior Analytics and Boole's Laws of Thought

Prior Analytics by the Greek philosopher Aristotle (384?–?322 BCE) and Laws of Thought by the English mathematician George Boole (1815?–?1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.

… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.     

Memory: Between traumatic shock and psychic historicization

‘I want to erase him from my memory,’ she said, ‘his eyes, his eyes staring at me … they are there every night, his hand … every night it hits me again and again …’. On the basis of these few words taken from the therapeutic work with Keltoum, the author reflects theoretically and clinically on the place of memory in a traumatism: a fixed memory, a ‘frozen image’, the signs of a traumatic compulsion to repeat, are the expressions of a process of psychic disorganization but also of a ‘symbolized and symbolizing’ memory anticipating a possible historicization of this memory, of a path, therefore, towards a resolution of the trauma resulting from a process of psychic integration and reorganization.     

Multi‐Peer Disagreement and the Preface Paradox

The problem of multi‐peer disagreement concerns the reasonable response to a situation in which you believe P₁ … P_n and disagree with a group of ‘epistemic peers’ of yours, who believe ～P₁ … ～P_n, respectively. However, the problem of multi‐peer disagreement is a variant on the preface paradox; because of this the problem poses no challenge to the so‐called ‘steadfast view’ in the epistemology of disagreement, on which it is sometimes reasonable to believe P in the face of peer disagreement about P. After some terminology is defined (§1), Peter van Inwagen's challenge to the steadfast view will be presented (§2). The preface paradox will then be presented and diagnosed (§3), and it will be argued that van Inwagen's challenge relies on the same principle that generates the preface paradox (§4). The reasonable response to multi‐peer disagreement will be discussed (§5), and an objection addressed (§6).     

Examining direct and indirect pathways to health behaviour: The influence of cognitive and affective probability beliefs

This study aimed to extricate the influence of rational (e.g. ‘I think …’) and intuitive (e.g. ‘I feel …’) probability beliefs in the behavioural decision-making process regarding skin cancer prevention practices. Structural equation modelling was used in two longitudinal surveys (sun protection during winter sports [N?=?491]; sun protection during summer [N?=?277]) to examine direct and indirect behavioural effects of affective and cognitive likelihood (i.e. unmediated or mediated by intention), controlled for attitude, social influence and self-efficacy. Affective likelihood was directly related to sun protection in both studies, whereas no direct effects were found for cognitive likelihood. After accounting for past sun protective behaviour, affective likelihood was only directly related to sun protection in Study 1. No support was found for the indirect effects of affective and cognitive likelihood through intention. The findings underscore the importance of feelings of (cancer) risk in the decision-making process and should be acknowledged by health behaviour theories and risk communication practices. Suggestions for future research are discussed.     

The effects of counterfactual defences on social judgements

Research on counterfactuals (‘If only…’) has seldom considered the effects of counterfactual communication, especially in a defensive context. In three studies, we investigated the effects of counterfactual defences employed by politicians. We assumed that self‐focused upward counterfactuals (‘If only I…, the outcome would have been better’) are a form of concession, other‐focused upward counterfactuals (‘If only they…, the outcome would have been better’) are a form of excuse, and self‐focused downward counterfactuals (‘If only I…, the outcome would have been worse’) are a form of justification. In Study 1, a counterfactual defence led to a more positive evaluation of the politician than a corresponding factual defence. Of the two types of defence, the counterfactual defence reduced the extent to which the politician was held responsible for the past event and was perceived as more convincing. In Study 2, counterfactual excuse and counterfactual justification were equally effective and led to a more positive evaluation of the politician than counterfactual concession. In Study 3, the higher effectiveness of counterfactual justification was independent from perceived ideological similarity with the politician, supporting the strength of this defence. These results show that counterfactual defences provide subtle communication strategies that effectively influence social judgements. Copyright © 2013 John Wiley & Sons, Ltd.     

Nietzsche and the Empirical: through the eyes of the term ‘Empfindung’

Abstract

This paper examines Nietzsche’s attitude to the empirical by concentrating on his concept of Empfindung (sensation, perception, feeling). In Section 1, five distinctive features of his use of ‘Empfmdung’ are described in relation to the philosophical tradition and some of his sources in 19^th Century physiology. All five features, I argue, point to Nietzsche’s philosophical concern to stake out the limits of ‘Empfmdung’ as an aspect of human finitude. In Section 2, my attention turns from the term ‘Empfmdung’ to Nietzsche’s actual argumentation. The bewildering variety of perspectives and arguments concerning ‘Empfmdung’ in his writings are broken down into three basic types of argument or discourse with radically different, incompatible presuppositions: a critical, epistemological discourse serving anti-metaphysical ends; a quasi-scientific discourse serving critical-epistemological ends; and a quasi-ontological discourse of life that looks to explain the results of Nietzsche’s critical epistemology. The value of this ‘contradictory’ practice, I contend, is twofold: Nietzsche makes epistemology fruitful for the philosophical problem of life; at the same time he offers a performative critique of epistemology by the manner in which he exceeds it.     

Demystifying Without Quining: Wittgenstein and Dennett on Qualitative States

Abstract

In his 1991 book Consciousness Explained, Daniel Deimett presents his “Multiple Drafts” model of consciousness. Central to his theory is the rejection of the notion of ‘qualia’ of the existence of the purported ‘qualitative character’ of conscious experience that many argue rules out the possibility of a purely materialist theory of mind. In eliminating qualia from his theory of consciousness, Dennett claims to be following in the footsteps of Wittgenstein, who also had much to say regarding the nature of ‘private’ experience. In this paper I reject this claim and argue that the elimination of qualia plays no part in Wittgenstein’s radical understanding of conscious experience.’¹     

Book notes

There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a dubious assumption about the linguistic expression of concepts. Successful revenge would require that there be a notion other than truth that plays the same role with respect to concept-expression that truth is naturally thought to play before we are confronted with the Liar paradox.

La vendetta, oh, la vendetta?Revenge, oh revenge

è un piacer serbato ai saggi.?is a pleasure reserved for the wise.

[…] il fatto è serio …?[…] the case is serious …

ma credete si farà.?but trust me, I'll take care of it.

Se tutto il codice dovessi volgere,?If I have to turn over the whole law-book,

se tutto l'indice dovessi leggere,?if I have to read through the whole index,

con un equivoco, con un sinonimo?with an equivocation, with a synonym

qualche garbuglio si troverà.?I'll find some way to tangle things up.

[…] il birbo Figaro vinto sarà.?[…] that rascal Figaro will be defeated.

Dr Bartolo, from da Ponte's libretto to Mozart's The Marriage of Figaro     

The enigmatic signifier and the decentred subject

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Three Twentieth-century Commonplaces about 'If'

The commonplaces, all grammatically confused, are that ‘conditionals’ are ternary in structure, have ‘antecedents’ and conform to the traditional taxonomy. It is maintained en route that ‘The bough will not break’ is consistent with ‘If the bough breaks …’, that there is no logical difference between “future indicatives” and “subjunctives”, and that there is a difference between the logic of propositions (e.g. ‘The bough broke’) and that of judgments (‘The bough will/might/could/should/must/needn't break’).     

The possibility of having knowledge of al‐wujūd al‐mahd ’sheer being’ according to ibn carabi's Kitab al‐jalal wa‐al‐jamal

Mysticism in general makes a distinction between ‘God‐for‐us’ and ‘God‐in‐him‐self. This paper attests that the Muslim mystic‐philosopher, Ibn ‘Arabi's concepts of ‘Sheer Possibility’ and ‘Sheer Being'; ‘Beauty’ and ‘Absolute Majesty’ parallel God‐for‐us and God‐in‐himself. The paper also attempts to examine the extent of possible human knowledge of God beyond the level ‘God‐for‐us'/'Beauty'/'sheer possibility’ and the relation of such developmental knowledge to the Qur'an, according to Ibn ^cArabi. The paper ends with a statement on the need to examine the hermeneutical mechanism supporting this sort of linking of human knowledge with the Qur'an and a need to discuss the possible motives behind traditionalization of developmental knowledge inputs.     

Actions That We Ought,But Can't

It is commonly assumed that ‘ought’ implies ‘can’, that is, that if we ought to do something, then it must be the case that we can do it. It is a frequent quip about this thesis that any account must specify three things: what is meant by the ‘ought’, what is meant by the ‘implies’, and what is meant by the ‘can’. ¹ Something is missed, though, when we state the thesis in its shortened, three‐word form. We overlook what it means to do something. It is, I think, not mere coincidence that nobody has discussed this issue: It is very difficult to specify what it means to do something in the relevant sense. This paper is devoted to fleshing out one way of doing something that is a problem for the thesis.