What''s computation? The received answer is that computation is a computer at work, and a computer at work is that which can be modelled as a Turing machine at work. Unfortunately, as John Searle has recently argued, and as others have agreed, the received answer appears to imply that AI and Cog Sci are a royal waste of time. The argument here is alarmingly simple: AI and Cog Sci (of the Strong sort, anyway) are committed to the view that cognition (...) is computation (or brains are computers); butall processes are computations (orall physical things are computers); so AI and Cog Sci are positively silly.I refute this argument herein, in part by defining the locutions x is a computer and c is a computation in a way that blocks Searle''s argument but exploits the hard-to-deny link between What''s Computation? and the theory of computation. However, I also provide, at the end of this essay, an argument which, it seems to me, implies not that AI and Cog Sci are silly, but that they''re based on a form of computation that is well beneath human persons. (shrink)

Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers, this position-argument pair, while based on a seminal insight that program verification, despite its Platonic proof-theoretic airs, is plagued by the inevitable unreliability of messy, real-world causation, is demonstrably self-refuting. As I soon show, Fetzer is like the person who claims: ‘My sole claim is that every claim expressed by an English sentence and (...) starting with the phrase “My sole claim” is false’. Or, more accurately, such thinkers are like the person who claims that modus tollens is invalid, and supports this claim by giving an argument that itself employs this rule of inference. (shrink)

In an effort to uncover fundamental differences between computers and brains, this paper identifies computation with a particular kind of physical process, in contrast to interpreting the behaviors of physical systems as one or more abstract computations. That is, whether or not a system is computing depends on how those aspects of the system we consider to be informational physically cause change rather than on our capacity to describe its behaviors in computational terms. A physical framework based on the notion (...) of causal mechanism is used to distinguish different kinds of information processing in a physically-principled way; each information processing type is associated with a particular causal mechanism. The causal mechanism associated with computation is pattern matching, which isphysically defined as the fitting of physical structures such that they cause a simple change. It is argued that information processing in the brain is based on a causal mechanism different than pattern matching so defined, implying that brains do not compute, at least not in the physical sense that digital computers do. This causal difference may also mean that computers cannot have mental states. (shrink)

This paper argues that at least one of the following propositions is true: the human species is very likely to go extinct before reaching a "posthuman" stage; any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history ; we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently (...) living in a simulation. A number of other consequences of this result are also discussed. (shrink)

I argue that at least one of the following propositions is true: the human species is very likely to become extinct before reaching a ’posthuman’ stage; any posthuman civilization is extremely unlikely to run a significant number of simulations of its evolutionary history ; we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we shall one day become posthumans who run ancestor-simulations is false, unless we are currently living (...) in a simulation. I discuss some consequences of this result. (shrink)

Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a (...) system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind. (shrink)

I. Recent years have witnessed a great resurgence of interest in the writings of the later Wittgenstein, especially with those passages roughly, Philosophical Investigations p)I 38 — 242 and Remarks on the Foundations of mathematics, section VI that are concerned with the topic of rules. Much of the credit for all this excitement, unparalleled since the heyday of Wittgenstein scholarship in the early IIJ6os, must go to Saul Kripke's I4rittgenstein on Rules and Private Language. It is easy to explain why. (...) To begin with, the dialectic Kripke uncovered from Wittgenstein's.. (shrink)

David Marr's three-level method for completely understanding a cognitive system and the importance he attaches to the computational level are so familiar as to scarcely need repeating. Fewer seem to recognize that Marr defends his famous method by criticizing the “reductionistic approach.” This sets up a more interesting relationship between Marr and reductionism than is usually acknowledged. I argue that Marr was correct in his criticism of the reductionists of his time—they were only describing, not explaining. But a careful metascientific (...) account of reductionistic neuroscience over the past two decades reveals that Marr's criticisms no longer have force. Contemporary neuroscience now explains cognition directly, although in a fashion—causal-mechanistically—quite different than Marr recommended. So while Marr was correct to reject the reductionism of his day and offer an alternative method for genuinely explaining cognition, contemporary cognitive scientists now owe us a new defense of Marr's famous method and the advantages of its explanations over the type now pursued successfully in current reductionist neuroscience. There are familiar reasons for thinking that this debt will not be paid easily. (shrink)

Explanations in the life sciences frequently involve presenting a model of the mechanism taken to be responsible for a given phenomenon. Such explanations depart in numerous ways from nomological explanations commonly presented in philosophy of science. This paper focuses on three sorts of differences. First, scientists who develop mechanistic explanations are not limited to linguistic representations and logical inference; they frequently employ diagrams to characterize mechanisms and simulations to reason about them. Thus, the epistemic resources for presenting mechanistic explanations are (...) considerably richer than those suggested by a nomological framework. Second, the fact that mechanisms involve organized systems of component parts and operations provides direction to both the discovery and testing of mechanistic explanations. Finally, models of mechanisms are developed for specific exemplars and are not represented in terms of universally quantified statements. Generalization involves investigating both the similarity of new exemplars to those already studied and the variations between them. (shrink)

The original proof of the four-color theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depend heavily for their soundness on large amounts of computation-intensive custom-built software. Contra Tymoczko, we argue that the justification provided by certain computerized mathematical proofs is not fundamentally different from that provided by surveyable (...) proofs, and can be sensibly regarded as a priori. We also show that the aforementioned impression is mistaken because it fails to distinguish between proof search (the context of discovery) and proof checking (the context of justification). By using mechanized proof assistants capable of producing certificates that can be independently checked, it is possible to carry out complex proofs without the need to trust arbitrary custom-written code. We only need to trust one fixed, small, and simple piece of software: the proof checker. This is not only possible in principle, but is in fact becoming a viable methodology for performing complicated mathematical reasoning. This is evinced by a new proof of the four-color theorem that appeared in 2005, and which was developed and checked in its entirety by a mechanical proof system. (shrink)

I. The function of models in the empirical sciencesII. Structure and purpose: conditions of a structural nature which models should satisfy in order to accomplish their function.III. Generalisation and specialisation of the classical definition of model, in view of the above requirements:the algebraic model conceptthe semantic model conceptthe syntactical model conceptIV. Attempt towards reunification: the concept of model on a pragmatic basis.

This paper takes part in the methodological debate concerning the nature and the justification of hypotheses about computational systems in software engineering by providing an epistemological analysis of Software Testing, the practice of observing the programs’ executions to examine whether they fulfil software requirements. Property specifications articulating such requirements are shown to involve falsifiable hypotheses about software systems that are evaluated by means of tests which are likely to falsify those hypotheses. Software Reliability metrics, used to measure the growth of (...) probability that given failures will occur at specified times as new executions are observed, is shown to involve a Bayesian confirmation of falsifiable hypotheses on programs. Coverage criteria, used to select those input values with which the system under test is to be launched, are understood as theory-laden principles guiding software tests, here compared to scientific experiments. Redundant computations, fault seeding models and formal methods used in software engineering to evaluate test results are taken to be instantiations of some epistemological strategies used in scientific experiments to distinguish between valid and non-valid experimental outcomes. The final part of the paper explores the problem, advanced in the context of the philosophy of technology, of defining the epistemological status of software engineering by conceiving it as a scientifically attested technology. (shrink)

Model checking, a prominent formal method used to predict and explain the behaviour of software and hardware systems, is examined on the basis of reflective work in the philosophy of science concerning the ontology of scientific theories and model-based reasoning. The empirical theories of computational systems that model checking techniques enable one to build are identified, in the light of the semantic conception of scientific theories, with families of models that are interconnected by simulation relations. And the mappings between these (...) scientific theories and computational systems in their scope are analyzed in terms of suitable specializations of the notions of model of experiment and model of data. Furthermore, the extensively mechanized character of model-based reasoning in model checking is highlighted by a comparison with proof procedures adopted by other formal methods in computer science. Finally, potential epistemic benefits flowing from the application of model checking in other areas of scientific inquiry are emphasized in the context of computer simulation studies of biological information processing. (shrink)

Automated Software Testing (AST) using Model Checking is in this article epistemologically analysed in order to argue in favour of a model-based reasoning paradigm in computer science. Preliminarily, it is shown how both deductive and inductive reasoning are insufficient to determine whether a given piece of software is correct with respect to specified behavioural properties. Models algorithmically checked in Model Checking to select executions to be observed in Software Testing are acknowledged as analogical models which establish isomorphic relations with the (...) target system’s data set. Analogical models developed in AST are presented as abductive models providing hypothetical explanations to observed executions. The model assumption—algorithmic check—software testing process is understood as the abduction—deduction—induction process defining the selective abduction and turned to isolate a set of model-based hypotheses concerning the target system behaviours. A manipulative abduction process is finally recognized in the practice of adapting, abstracting and refining models that do not provide successful predictions. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as Aristotelian (...) abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)

One of the most lasting contributions of Marr's posthumous book is his articulation of the different “levels of analysis” that are needed to understand vision. Although a variety of work has examined how these different levels are related, there is comparatively little examination of the assumptions on which his proposed levels rest, or the plausibility of the approach Marr articulated given those assumptions. Marr placed particular significance on computational level theory, which specifies the “goal” of a computation, its appropriateness for (...) solving a particular problem, and the logic by which it can be carried out. The structure of computational level theory is inherently teleological: What the brain does is described in terms of its purpose. I argue that computational level theory, and the reverse-engineering approach it inspires, requires understanding the historical trajectory that gave rise to functional capacities that can be meaningfully attributed with some sense of purpose or goal, that is, a reconstruction of the fitness function on which natural selection acted in shaping our visual abilities. I argue that this reconstruction is required to distinguish abilities shaped by natural selection—“natural tasks” —from evolutionary “by-products”, rather than merely demonstrating that computational goals can be embedded in a Bayesian model that renders a particular behavior or process rational. (shrink)

Should cognitive scientists be any more embarrassed about their lack of a discipline-fixing definition of cognition than biologists are about their inability to define “life”? My answer is “no”. Philosophers seeking a unique “mark of the cognitive” or less onerous but nevertheless categorical characterizations of cognition are working at a level of analysis upon which hangs nothing that either cognitive scientists or philosophers of cognitive science should care about. In contrast, I advocate a pluralistic stance towards uses of the term (...) ‘cognition’ that eschews the urge to treat cognition as a metaphysically well-defined “natural” kind. (shrink)

In this paper I argue that whether or not a computer can be built that passes the Turing test is a central question in the philosophy of mind. Then I show that the possibility of building such a computer depends on open questions in the philosophy of computer science: the physical Church-Turing thesis and the extended Church-Turing thesis. I use the link between the issues identified in philosophy of mind and philosophy of computer science to respond to a prominent argument (...) against the possibility of building a machine that passes the Turing test. Finally, I respond to objections against the proposed link between questions in the philosophy of mind and philosophy of computer science. (shrink)

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

Raymond Turner first provides a logical framework for specification and the design of specification languages, then uses this framework to introduce and study ...

Editorial preface to the fourth edition and modified translation -- The text of the Philosophische Untersuchungen -- Philosophische untersuchungen = Philosophical investigations -- Philosophie der psychologie, ein fragment = Philosophy of psychology, a fragment.

The aim of this book is to advance our understanding of how humans think. It seeks to do so by putting forth a theory of human problem solving, along with a body of empirical evidence that permits assessment of the theory.

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.

There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind.

Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

Software is a ubiquitous artifact, yet not much has been done to understand its ontological nature. There are a few accounts offered so far about the nature of software. I argue that none of those accounts give a plausible picture of the nature of software. I draw attention to the striking similarities between software and musical works. These similarities motivate to look more closely on the discussions regarding the nature of the musical works. With the lessons drawn from the ontology (...) of musical works I offer a novel account of the nature of software. In this account, software is an abstract artifact. I elaborate the conditions under which software comes into existence; how it persists; how and on which entities its existence depends. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

What psychological and philosophical significance should we attach to recent efforts at computer simulations of human cognitive capacities? In answering this question, I find it useful to distinguish what I will call "strong" AI from "weak" or "cautious" AI. According to weak AI, the principal value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion. (...) But according to strong AI, the computer is not merely a tool in the study of the mind; rather, the appropriately programmed computer really is a mind, in the sense that computers given the right programs can be literally said to. (shrink)

This is a welcome reprint of a book that continues to grow in importance.

1st ser. The four historical conceptions of being.--2d ser. Nature, man, and the moral order.

Traditionally, many writers, following Kleene (1952), thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing’s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis, what Turing (1936) calls “argument I,” has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, essentially presupposed by Turing (...) himself in what he calls “argument II.” The idea is that computation is a special form of mathematical deduction. Assuming the steps of the deduction can be stated in a first order language, the Church-Turing thesis follows as a special case of Gödel’s completeness theorem (first order algorithm theorem). I propose this idea as an alternative foundation for the Church-Turing thesis, both for human and machine computation. Clearly the relevant assumptions are justified for computations presently known. Other issues, such as the significance of Gödel’s 1931 Theorem IX for the Entscheidungsproblem, are discussed along the way. (shrink)

The paper explores the distinction between two doctrines, both of which inform theory construction in much of modern cognitive psychology: the representational theory of mind and the computational theory of mind. According to the former, propositional attitudes are to be construed as relations that organisms bear to mental representations. According to the latter, mental processes have access only to formal (nonsemantic) properties of the mental representations over which they are defined.The following claims are defended: (1) That the traditional dispute between (...) “rational” and “naturalistic” psychology is plausibly viewed as an argument about the status of the computational theory of mind. Rational psychologists accept a formality condition on the specification of mental processes; naturalists do not. (2) That to accept the formality condition is to endorse a version of methodological solipsism. (3) That the acceptance of some such condition is warranted, at least for that part of psychology which concerns itself with theories of the mental causation of behavior. This is because: (4) such theories require nontransparent taxonomies of mental states; and (5) nontransparent taxonomies individuate mental states without reference to their semantic properties. Equivalently, (6) nontransparent taxonomies respect the way that the organism represents the object of its propositional attitudes toitself, and it is this representation which functions in the causation of behavior.The final section of the paper considers the prospect for a naturalistic psychology: one which defines its generalizations over relations between mental representations and their environmental causes, thus seeking to account for the semantic properties of propositional attitudes. Two related arguments are proposed, both leading to the conclusion that no such research strategy is likely to prove fruitful. (shrink)

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...) with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics. (shrink)

Under the banner of "hypercomputat ion" various claims are being made for the feasibility of modes of computation that go beyond what is permitted by Turing computability. In this article it will be shown that such claims fly in the face of the inability of all currently accepted physical theories to deal with infinite precision real numbers. When the claims are viewed critically, it is seen that they amount to little more than the obvious comment that if non-computable inputs are (...) permitted, then non-computable outputs are attainable. (shrink)

Elegance in software is widely recognized by professionals, but not well articulated. Program elegance rests on not only efficiency, as widely acknowledged, but other features that reflect the notion in other creative endeavors where artifacts are built under constraints, such as architecture. We suggest a compendium of minimality, accomplishment, modesty, and revelation, discussion of which reveals some subtleties. Programming experience enhances appreciation of these features, especially the last. Together, they can viewed as a program’s degree of “fit” to the task, (...) raising other questions in common with any problem of the philosophy of aesthetics. (shrink)

(Citation/Reference) Williams, S. H. Lewis Carroll handbook.