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)

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)

The Church-Turing thesis makes a bold claim about the theoretical limits to computation. It is based upon independent analyses of the general notion of an effective procedure proposed by Alan Turing and Alonzo Church in the 1930''s. As originally construed, the thesis applied only to the number theoretic functions; it amounted to the claim that there were no number theoretic functions which couldn''t be computed by a Turing machine but could be computed by means of some other kind of effective (...) procedure. Since that time, however, other interpretations of the thesis have appeared in the literature. In this paper I identify three domains of application which have been claimed for the thesis: (1) the number theoretic functions; (2) all functions; (3) mental and/or physical phenomena. Subsequently, I provide an analysis of our intuitive concept of a procedure which, unlike Turing''s, is based upon ordinary, everyday procedures such as recipes, directions and methods; I call them mundane procedures. I argue that mundane procedures can be said to be effective in the same sense in which Turing machine procedures can be said to be effective. I also argue that mundane procedures differ from Turing machine procedures in a fundamental way, viz., the former, but not the latter, generate causal processes. I apply my analysis to all three of the above mentioned interpretations of the Church-Turing thesis, arguing that the thesis is (i) clearly false under interpretation (3), (ii) false in at least some possible worlds (perhaps even in the actual world) under interpretation (2), and (iii) very much open to question under interpretation (1). (shrink)

A survey of the field of hypercomputation, including discussion of a variety of objections.

Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...) to a recent paper by Bringsjord, Bello and Ferrucci, however, the concept of an accelerating Turing machine cannot be used to shove up Searle's Chinese room argument. (shrink)

To compute is to execute an algorithm. More precisely, to say that a device or organ computes is to say that there exists a modelling relationship of a certain kind between it and a formal specification of an algorithm and supporting architecture. The key issue is to delimit the phrase of a certain kind. I call this the problem of distinguishing between standard and nonstandard models of computation. The successful drawing of this distinction guards Turing's 1936 analysis of computation against (...) a difficulty that has persistently been raised against it, and undercuts various objections that have been made to the computational theory of mind. (shrink)

What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We (...) will point to interesting examples of (ideal) physical machines that fall outside the class of Gandy machines and compute functions that are not Turing-machine computable. (shrink)

Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability.

To build a true conscious robot requires that a robot’s “brain” be capable of supporting the phenomenal consciousness as human’s brain enjoys. Operational Architectonics framework through exploration of the temporal structure of information flow and inter-area interactions within the network of functional neuronal populations [by examining topographic sharp transition processes in the scalp electroencephalogram (EEG) on the millisecond scale] reveals and describes the EEG architecture which is analogous to the architecture of the phenomenal world. This suggests that the task of (...) creating the “machine” consciousness would require a machine implementation that can support the kind of hierarchical architecture found in EEG. (shrink)

The Construction of Personal Identities Online Content Type Journal Article Category Introduction Pages 1-3 DOI 10.1007/s11023-011-9254-y Authors Luciano Floridi, Department of Philosophy, University of Hertfordshire, de Havilland Campus, Hatfield, Hertfordshire, AL10 9AB UK Journal Minds and Machines Online ISSN 1572-8641 Print ISSN 0924-6495.

Cognitive science uses the notion of computational information processing to explain cognitive information processing. Some philosophers have argued that anything can be described as doing computational information processing; if so, it is a vacuous notion for explanatory purposes.An attempt is made to explicate the notions of cognitive information processing and computational information processing and to specify the relationship between them. It is demonstrated that the resulting notion of computational information processing can only be realized in a restrictive class of dynamical (...) systems called physical notational systems (after Goodman's theory of notationality), and that the systems generally appealed to by cognitive science-physical symbol systems-are indeed such systems. Furthermore, it turns out that other alternative conceptions of computational information processing, Fodor's (1975) Language of Thought and Cummins' (1989) Interpretational Semantics appeal to substantially the same restrictive class of systems. (shrink)

We introduce an Automatic Theorem Prover (ATP) of a dual tableau system for a relational logic for order of magnitude qualitative reasoning, which allows us to deal with relations such as negligibility, non-closeness and distance. Dual tableau systems are validity checkers that can serve as a tool for verification of a variety of tasks in order of magnitude reasoning, such as the use of qualitative sum of some classes of numbers. In the design of our ATP, we have introduced some (...) heuristics, such as the so called phantom variables, which improve the efficiency of the selection of variables used un the proof. (shrink)

This paper presents some considerations about the relationship between languages and computer systems from a pragmatic, user-centered point of view.

People increasingly form beliefs based on information gained from automatically filtered Internet ‎sources such as search engines. However, the workings of such sources are often opaque, preventing ‎subjects from knowing whether the information provided is biased or incomplete. Users’ reliance on ‎Internet technologies whose modes of operation are concealed from them raises serious concerns about ‎the justificatory status of the beliefs they end up forming. Yet it is unclear how to address these concerns ‎within standard theories of knowledge and justification. (...) To shed light on the problem, we introduce a ‎novel conceptual framework that clarifies the relations between justified belief, epistemic responsibility, ‎action, and the technological resources available to a subject. We argue that justified belief is subject to ‎certain epistemic responsibilities that accompany the subject’s particular decision-taking circumstances, ‎and that one typical responsibility is to ascertain, so far as one can, whether the information upon which ‎the judgment will rest is biased or incomplete. What this responsibility comprises is partly determined by ‎the inquiry-enabling technologies available to the subject. We argue that a subject’s beliefs that are ‎formed based on Internet-filtered information are less justified than they would be if she either knew how ‎filtering worked or relied on additional sources, and that the subject may have the epistemic ‎responsibility to take measures to enhance the justificatory status of such beliefs.‎. (shrink)

I address whether neural networks perform computations in the sense of computability theory and computer science. I explicate and defend
the following theses. (1) Many neural networks compute—they perform computations. (2) Some neural networks compute in a classical way.
Ordinary digital computers, which are very large networks of logic gates, belong in this class of neural networks. (3) Other neural networks
compute in a non-classical way. (4) Yet other neural networks do not perform computations. Brains may well fall into this last class.

This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations. A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule that applies to all relevant strings and depends on the input strings and (possibly) internal states for its application. This account is motivated by reasons endogenous to the philosophy of computing, namely, doing (...) justice to the practices of computer scientists and computability theorists. It is also an application of recent literature on mechanisms, because it assimilates computational explanation to mechanistic explanation. The account can be used to individuate computing mechanisms and the functions they compute and to taxonomize computing mechanisms based on their computing power. (shrink)

If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. They (...) have infinitely complex bodies. Transfinite games anchor their social relations. (shrink)

This paper proposes an extensionalist analysis of computer simulations (CSs). It puts the emphasis not on languages nor on models, but on symbols, on their extensions, and on their various ways of referring. It shows that chains of reference of symbols in CSs are multiple and of different kinds. As they are distinct and diverse, these chains enable different kinds of remoteness of reference and different kinds of validation for CSs. Although some methodological papers have already underlined the role of (...) these various relationships of reference in CSs and of cross-validations, this diversity is still overlooked in the epistemological literature on CSs. As a consequence, a particular outcome of this analytical view is an ability to classify existing epistemological theses on CSs according to what their authors choose to select and put at the forefront: either the extensions of symbols, or the symbol-types, or the symbol-tokens, or the internal denotational hierarchies of the CS or the reference of these hierarchies to external denotational hierarchies. Through the adoption of this extensionalist view, it also becomes possible to explain more precisely the reasons why some complete reduction of CSs to classical epistemic paradigms such as “experiment” or “theoretical argument” remains doubtful. On this last point, in particular, this paper is in agreement with what many epistemologists already have acknowledged. (shrink)