We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.

Many have bowed before the recently acquired powers of ‘new technologies’. However, in the shift from tekhnē to tekhnologia, it seems we have lost human values. These values are communicative in nature as technological progress has placed barriers like distance, web pages and ‘miscellaneous extras’ between individuals. Certain values, like the interpersonal pleasures of rendering service, have been lost as their domain of predilection has for many become fully commercially oriented, dominated by the cadence of profitability. Though the popular cultures (...) of the artificial have surged forth to deliver us from the twentieth century, they have enabled some very superfluous dreaming—Man has succumbed to the Godly role of simulating himself and creating other beings. Communication is replaced by machines, services are rendered via many automated devices, procreation has entered the public sphere, robots and entertainment agents educate our youth and mesmerising screen-integrating ‘forms of intelligence’ even think for us. As such, this so-called culture threatens the very values Man constructed in the nineteenth and twentieth centuries to guide himself into the future. But what if the phenomena mentioned just reflect our new values? The author presents an investigation into this cultural shift, its impact on human practices with regards the mind and the body and evokes some pros and cons of generally accepting the ‘Culture of the Artificial’. (shrink)

Related Works: Part II: C. T. Chong, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part II: Tame $\Sigma_2$ Coding and the Jump Operator. Ann. Pure Appl. Logic, vol. 87, no. 2, 103--116. Mathematical Reviews : MR1490049 Part III: C. T. Chong, Lei Qian, Theodore A. Slaman, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part III: Prompt Sets, Minimal Paries and Shoenfield's Conjecture. Mathematical Reviews : MR1818378.

We study the problem of existence of maximal chains in the Turing degrees. We show that: 1. ZF+DC+"There exists no maximal chain in the Turing degrees" is equiconsistent with ZFC+"There exists an inaccessible cardinal"; 2. For all a ∈ 2ω.(ω₁)L[a] = ω₁ if and only if there exists a $\Pi _{1}^{1}[a]$ maximal chain in the Turing degrees. As a corollary, ZFC + "There exists an inaccessible cardinal" is equiconsistent with ZFC + "There is no (bold face) $\utilde{\Pi}{}_{1}^{1}$ maximal chain of (...) Turing degrees". (shrink)

A scholium in codex Vaticanus graecus 156 provides evidence that Cassius Dio's Roman History once contained an explicit reference to the ludi saeculares of a.d. 204, something that has been denied in recent scholarship.

Discussion about the application of scientific knowledge in robotics in order to build people helpers is widespread. The issue herein addressed is philosophically poignant, that of robots that are “people”. It is currently popular to speak about robots and the image of Man. Behind this lurks the dialogical mind and the questions about the significance of an artificial version of it. Without intending to defend or refute the discourse in favour of ‘recreating’ Man, a lesser familiar question is brought forth: (...) “and what if we were capable of creating a very convincible replica of man (constructing a robot-person), what would the consequences of this be and would we be satisfied with such technology?” Thorny topic; it questions the entire knowledge foundation upon which strong AI/Robotics is positioned. The author argues for improved monitoring of technological progress and thus favours implementing weaker techniques. (shrink)

Professor Brenda Baker's recent critique of the Canadian Law Reform Commission's treatment of general standards for criminal liability adds to a growing body of critical theory concerning such standards and their relation to criminal justice. From within the perspective of this same critical movement, I assess the strengths and weaknesses of Professor Baker's efforts and of similar lines of argument in the work of Professor George Fletcher. I find two significant flaws in their shared approach. The first is confusion as (...) to the proper level for analysis of liability standards and, hence, for criticism of the "orthodox" view. This leads Professors Baker and Fletcher to concentrate on issues of culpability rather than responsibility (and to conflate these issues). The second flaw is an error in comprehension of the faults of the orthodox view and, hence, in recognition of the fundamental character of views opposed to that orthodoxy. This leads both theorists to overemphasize a suspect and unilluminating distinction between normative and descriptive approaches to liability problems. The rest of the article is devoted to an overview of my own approach to problems of liability and a general critique of the orthodox view in light of that approach. I argue that the fundamental issue is the relation of liability standards to a conception of agent responsibility. The primary fault of orthodoxy lies, then, in the cognitivist model of responsibility on which it relies. Against this, I propose use of a capacities model of responsibility as the basis for standards of liability. These two models are outlined and compared in final sections. (shrink)