This is a non-technical version of "The Decision Problem for Effective Procedures." The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from the (...) notion of an effective procedure--without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis--that the class of effective procedures is undecidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. The proof does not appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though this undecidability result itself is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict. (shrink)

Horsten and Roelants have raised a number of important questions about my analysis of effective procedures and my evaluation of the Church-Turing thesis. They suggest that, on my account, effective procedures cannot enter the mathematical world because they have a built-in component of causality, and, hence, that my arguments against the Church-Turing thesis miss the mark. Unfortunately, however, their reasoning is based upon a number of misunderstandings. Effective mundane procedures do not, on my view, provide an analysis (...) of ourgeneral concept of an effective procedure; mundane procedures and Turing machine procedures are different kinds of procedure. Moreover, the same sequence ofparticular physical action can realize both a mundane procedure and a Turing machine procedure; it is sequences of particular physical actions, not mundane procedures, which enter the world of mathematics. I conclude by discussing whether genuinely continuous physical processes can enter the world of real numbers and compute real-valued functions. I argue that the same kind of correspondence assumptions that are made between non-numerical structures and the natural numbers, in the case of Turing machines and personal computers, can be made in the case of genuinely continuous, physical processes and the real numbers. (shrink)

Since the mid-twentieth century, the concept of the Turing machine has dominated thought about effective procedures. This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic. I show that Turing machines cannot live up to their billing as paragons of effective procedure; at best, they may be said to provide us with mere procedure schemas. I argue that the concept of an effective procedure crucially depends (...) upon distinguishing procedures as definite courses of action(- types) from the particular courses of action(-tokens) that actually instantiate them and the causal processes and/or interpretations that ultimately make them effective. On my analysis, effectiveness is not just a matter of logical form; `content' matters. The analysis I provide has the advantage of applying to ordinary, everyday procedures such as recipes and methods, as well as the more refined procedures of mathematics and computer science. It also has the virtue of making better sense of the physical possibilities for hypercomputation than the received view and its extensions, e.g. Turing's o-machines, accelerating machines. (shrink)

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a (...) given procedure is effective. This undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways (...) in the above areas, and discuss challenges and prospects for adopting a final foundational theory of (classical) ‘algorithms’. (shrink)

This paper develops my (BJPS 2009) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that "effectively computable" is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.

Turing's (1936) analysis of effective symbolic procedures is a model of conceptual clarity that plays an essential role in the philosophy of mathematics. Yet appeal is often made to the effectiveness of human procedures in other areas of philosophy. This paper addresses the question of whether Turing's analysis can be applied to a broader class of effective human procedures. We use Sieg's (1994) presentation of Turing's Thesis to argue against Cleland's (1995) objections to Turing machines and we evaluate (...) her proposal to understand the effectiveness of procedures in terms of their reliability and precision. A number of conditions for effectiveness are identified and these are used to provide a general argument against the possibility of a Leibnizian decision procedure. (shrink)

From an institutional perspective we contribute to corporate governance of firms by (1) proposing a procedurally fair mechanism that is ethically desirable, and (2) experimentally testing whether procedural fairness crowds-in ethical behavior of managers (on behalf of shareholders) and workers. The experiment sees one ‘manager’ and three ‘workers’ (possibly representing three sections of the firm) co-determining an efficiency-enhancing investment which could harm some workers. Firstly, the manager claims a share of the investment surplus, then workers ‘bid’ for the investment to (...) express their willingness to satisfy the manager’s claim in case the investment is implemented. If the sum of workers’ bids is less than the manager’s claim, the investment is not implementable, which means its surplus will be lost. Workers’ behavior is ‘ethical’ when they veto unfair managerial claims, because the workers have to sacrifice own earnings. Hence, a manager’s fair claim is the ethical response to the threat of workers’ veto. If the manager claims fairly, workers’ ethical behavior is to ‘truthfully’ bid their investment evaluations; by all doing so, they equally share whatever surplus the manager has left for them. The experimental results show ethical behavior of managers in the form of fair claims. Despite these fair claims, workers behave less ethically by strategically underbidding. So the procedurally fair mechanism only partially crowds-in ethical behavior. This study should interest theorists of stakeholder management, especially those engaged in designing the rules of corporate governance. (shrink)

This study investigated the effect of stroking vs. simple human presence on later reactions of dairy cows to routine veterinary handling. While in two groups of cows the experimenter stroked the ventral part of the neck or the withers for three consecutive weeks, the third group was exposed to close visual presence. After the treatment period the cows were subjected to rectal palpation. The three groups differed significantly in stepping during rectal palpation, which occurred less often in Neck- and Withers-animals (...) than in control animals. Heart rate increase was significantly higher in the control group than in the two stroking groups. Previous stroking led to fewer stress reactions during the rectal palpation, possibly due to a combined effect of improved relationship towards and thus perception of humans and lasting anti-stress effects of tactile stimulation. (shrink)

This study investigated the effect of stroking vs. simple human presence on later reactions of dairy cows to routine veterinary handling. While in two groups of cows the experimenter stroked the ventral part of the neck or the withers for three consecutive weeks, the third group was exposed to close visual presence. After the treatment period the cows were subjected to rectal palpation. The three groups differed significantly in stepping during rectal palpation, which occurred less often in Neck- and Withers-animals (...) than in control animals. Heart rate increase was significantly higher in the control group than in the two stroking groups. Previous stroking led to fewer stress reactions during the rectal palpation, possibly due to a combined effect of improved relationship towards and thus perception of humans and lasting anti-stress effects of tactile stimulation. Keywords: cattle; tactile stimulation; human–animal relationship; animal welfare. (shrink)

Efforts to improve patients’ understanding of their own medical treatments or research in which they are involved are progressing, especially with regard to informed consent procedures. We aimed to design a multisource informed consent procedure that is easily adaptable to both clinical and research applications, and to evaluate its effectiveness in terms of understanding and awareness, even in less educated patients.

Using data collected from 280 full-time employees from a variety of organizations, this study examined the effects of employee perceptions of the behavioral integrity (BI) of their supervisors on job tension. The moderating effect of procedural justice (PJ) on this relationship also was examined. Substitutes for leadership theory (Kerr and Jermier, 1978) and psychological contract theory (Rousseau, Empl Responsib Rights J 2:121–139, 1989) were used as the theoretical foundations for the hypothesized relationships. Results indicated a negative relationship between BI and (...) job tension. PJ moderated this relationship such that it was weakened under conditions of high PJ. Implications for research and managers are discussed. (shrink)