Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ (...) problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof. (shrink)

Benacerraf has presented two problems for the philosophy of mathematics. These are the problem of identification and the problem of representation. This paper aims to reconstruct the latter problem and to unpack its undermining bearing on the version of Ontic Structural Realism that frames scientific representations in terms of abstract structures. I argue that the dichotomy between mathematical structures and physical ones cannot be used to address the Benacerraf problem but strengthens it. I conclude by arguing that versions of OSR (...) that do not rely on mathematical frameworks for representational purposes need not be vulnerable to Benacerraf’s second problem. (shrink)

Social externalism is a thesis about the individuation-conditions of thoughts. Actually, the thesis applies only to a special category of ‘trained’ thoughts, thoughts which issue from trained thinking. It isn't that the thinker of such a thought has to have had special training about the subject-matter. It is rather that he or she needs to have acquired certain basic linguistic skills and values. For trained thoughts are thoughts whose contents are tailored to the demands of communication. Social externalism, as I (...) understand it, says that people who are competent in a public language are equipped to have certain thoughts whose contents are fixed by the lexical semantic norms of their language. (shrink)

What is an object? A prior question: What is objecthood? Au fond, and to logic’s eye, object is a role to be played with respect to a thought. It is to be a countable which that thought represent as being some way for such a countable to be; what restores the business of truth-of to that of truth outright. What plays that role for some given thought is then an object with respect to that thought. Given this, there are corresponding (...) absolute notions, to be fit for this role, and to be fit only for this role. So the fundamental task here is identifying the conditions on playing this role at all. All this is a contribution, however limited, to a topic called ‘ontology’. This last word also occurs in the plural in several contexts. The end of this essay considers how these notions might relate, and what assumptions underlie what some have seen them to. (shrink)

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There (...) are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not adequate to address these questions. Here I outline an alternative conception of computation, which I call the analog-model. The term ‘analog-model’ (...) does not mean continuous, non-discrete or non-digital. It means that the functional performance of the system simulates mathematical relations in some other system, between what is being represented. The brain-as-computer view is invoked to demonstrate that the internal cellular activity is appropriate for the pertinent information-processing task.Keywords: Computation; Computational neuroscience; Analog computers; Representation; Simulation. (shrink)

Elvira Schnabel; Wittgenstein on Rules: what follows and what does not, Journal of Philosophy of Education, Volume 25, Issue 1, 30 May 2006, Pages 83–94, https.

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes and (...) pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

Hilary Putnam's famous arguments criticizing Tarski's theory of truth are evaluated. It is argued that they do not succeed to undermine Tarski's approach. One of the arguments is based on the problematic idea of a false instance of T-schema. The other ignores various issues essential for Tarski's setting such as language-relativity of truth definition.

It is argued that, given certain reasonable premises, an infinite number of qualitatively identical but numerically distinct minds exist per functioning brain. The three main premises are (1) mental properties supervene on brain properties; (2) the universe is composed of particles with nonzero extension; and (3) each particle is composed of continuum-many point-sized bits of particle-stuff, and these points of particle-stuff persist through time.

The aim of this paper is to offer a formal criterion for physical computation that allows us to objectively distinguish between competing computational interpretations of a physical system. The criterion construes a computational interpretation as an ordered pair of functions mapping (1) states of a physical system to states of an abstract machine, and (2) inputs to this machine to interventions in this physical system. This interpretation must ensure that counterfactuals true of the abstract machine have appropriate counterparts which are (...) true of the physical system. The criterion proposes that rival interpretations be assessed on the basis of simplicity. Simplicity is construed as the Kolmogorov complexity of the interpretation. This approach is closely related to the notion of algorithmic information distance and draws on earlier work on real patterns. (shrink)

David Chalmers argues that virtual objects exist in the form of data structures that have causal powers. I argue that there is a large class of virtual objects that are social objects and that do not depend upon data structures for their existence. I also argue that data structures are themselves fundamentally social objects. Thus, virtual objects are fundamentally social objects.

ABSTRACTThis paper reconstructs and defends a Husserlian transcendental conception of intentionality. Initially, naturalistic conception of intentionality seems attractive, however, a naturalistic understanding conceals the true meaning of the puzzle and the nature of intentionality. Following Kant and primarily Husserl, this paper tries to determine the conditions a transcendental conception of intentionality must satisfy in order to be qualified as “transcendental”. Additionally, following Husserl, this paper argues that the alternative transcendental conception is not only possible, hence plausible; but also necessary, in (...) the sense that a thorough understanding of intentionality can only be achieved if a transcendental conception is adopted. (shrink)

Milner and Goodale's Two Visual Systems Hypothesis is regarded as common ground in recent discussions of visual consciousness. A central part of TVSH is a functional model of vision and action. In this paper, I provide a brief overview of these current discussions and argue that there is ambiguity between a strong and a weak version of PAM. I argue that, given a standard way of individuating computational mechanisms, the available evidence cannot be used to distinguish between these versions. This (...) not only has consequences for philosophical theories of the role of visual consciousness but also for the role of experimental evidence in model testing in cognitive neuroscience. (shrink)

Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of positive property. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes positive property as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" Pure attribution seems likely to be related to the Leibnizian concept of perfection.By a (...) careful examination of the formal semantics of third-order modal logic with property abstraction together with a Completeness result for third-order modal logic with property abstraction for faithful models that I previously developed in 2000 in my work, Gödel’s Ontological Argument, I argue that it is not possible to develop a sufficient applied third-order modal semantics for Gödel’s ontological argument. As I explore possible approaches for an applied semantics including anti-Realist accounts of the semantics of modal logic compatible with Actualism, I argue that Gödel makes implicit philosophical assumptions which commit him to both possibilism (the belief in merely possible objects) and modal realism (the belief in possible worlds). (shrink)

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply adhere to (...) Turing’s notion of computability . Classical computability theory studies what functions on the natural numbers are computable and what mathematical problems are undecidable. Whilst a mathematical formalism of computability may perform a methodological function of evaluating computational theories of certain cognitive capacities, concrete computation in physical systems seems to be required for explaining cognition as an embodied phenomenon . There are many non-equivalent accounts of digital computation in physical systems. I examine only a handful of those in this paper: (1) Turing’s account ; (2) The triviality “account”; (3) Reconstructing Smith’s account of participatory computation ; (4) The Algorithm Execution account . My goal in this paper is twofold. First, it is to identify and clarify some of the underlying key requirements mandated by these accounts. I argue that these differing requirements justify a demand that one commits to a particular account when employing the notion of computation in regard to physical systems. Second, it is to argue that despite the informative role that mathematical formalisms of computability may play in cognitive science, they do not specify the relationship between abstract and concrete computation. (shrink)

I reconstruct Aristotle’s reasons for thinking that the intellect cannot have a bodily organ. I present Aristotle’s account of the aboutness or intentionality of cognitive states, both perceptual and intellectual. On my interpretation, Aristotle’s account is based around the notion of cognitive powers taking on forms in a special preservative way. Based on this account, Aristotle argues that no physical structure could enable a bodily part or combination of bodily parts to produce or determine the full range of forms that (...) the human intellect can understand. For Aristotle, cognitive powers with bodily organs are always spatiotemporally limited, but the understanding is not. Aristotle claims that our understanding applies to all instances of the thing understood wherever and whenever they exist. On Aristotle’s own account the intellect in its nature is only “potential,” it does not actually possess any form. Thus nothing prevents it from possessing all forms. (shrink)

The initial argument presented herein is not significantly original—it is a simple reflection upon a notion of computation originally developed by Putnam and criticised by Chalmers et al. . In what follows, instead of seeking to justify Putnam’s conclusion that every open system implements every Finite State Automaton and hence that psychological states of the brain cannot be functional states of a computer, I will establish the weaker result that, over a finite time window every open system implements the trace (...) of FSA Q, as it executes program on input . If correct the resulting bold philosophical claim is that phenomenal states—such as feelings and visual experiences—can never be understood or explained functionally. (shrink)

When Putnam wrote Reason, Truth and History, he thought that whatever the truth was, it could not entirely outrun justification. He moved away from this epistemic conception of truth—of truth as idealized rational acceptability—and his later view appears to recognize the fact that there are truths that may well be recognition transcendent. Wright (J Philos 97(6):335–364, 2000) has correctly observed that this change in Putnam’s views raises the question of how his current natural realism is different from metaphysical realism, a (...) view that Putnam has always been at pains to distance himself from. After all, metaphysical realism is the admission of the fact that truths can be recognition transcendent. In this paper, I will reflect on the distinction between metaphysical realism and natural realism, hoping to lay out certain aspects of Putnam’s later views on truth which underwrite this crucial distinction. (shrink)

Very plausibly, nothing can be a genuine computing system unless it meets an input-sensitivity requirement. Otherwise all sorts of objects, such as rocks or pails of water, can count as performing computations, even such as might suffice for mentality—thus threatening computationalism about the mind with panpsychism. Maudlin in J Philos 86:407–432, ( 1989 ) and Bishop ( 2002a , b ) have argued, however, that such a requirement creates difficulties for computationalism about conscious experience, putting it in conflict with the (...) very intuitive thesis that conscious experience supervenes on physical activity. Klein in Synthese 165:141–153, ( 2008 ) proposes a way for computationalists about experience to avoid panpsychism while still respecting the supervenience of experience on activity. I argue that his attempt to save computational theories of experience from Maudlin’s and Bishop’s critique fails. (shrink)

Peter Ludlow presents the first book on the philosophy of generative linguistics, including both Chomsky's government and binding theory and his minimalist ...

On a modified view of embodied cognition, I argue that the conceptual structure of some present-day’s abstract artifact concepts such as PIECE OF MUSIC or PIECE OF ART can be effectively explained if it is taken into account that “visual recordings” of first observed result objects played a major role in developing abstract artifact concepts.

The new theory of reference has won popularity. However, a number of noted philosophers have also attempted to reply to the critical arguments of Kripke and others, and aimed to vindicate the description theory of reference. Such responses are often based on ingenious novel kinds of descriptions, such as rigidified descriptions, causal descriptions, and metalinguistic descriptions. This prolonged debate raises the doubt whether different parties really have any shared understanding of what the central question of the philosophical theory of reference (...) is: what is the main question to which descriptivism and the causal-historical theory have presented competing answers. One aim of the paper is to clarify this issue. The most influential objections to the new theory of reference are critically reviewed. Special attention is also paid to certain important later advances in the new theory of reference, due to Devitt and others. (shrink)

Saying that psychological states are functional states, the functionalist claims more than that psychological states have functions. Rather, functionalism is the theory that psychological states are defined and constituted by their functions. On this view, what it is to be a psychological state of a certain sort just is and consists entirely of having a certain function. Anything that has that function in a suitable system would therefore be that psychological state. If storing information for later use is the essential (...) function of memory, then anything that has that function counts as a memory. Similarly, one might say that anything that traps or kills mice counts as a mouse trap. (shrink)

In this paper, I want to deal with the triviality threat to computationalism. On one hand, the controversial and vague claim that cognition involves computation is still denied. On the other, contemporary physicists and philosophers alike claim that all physical processes are indeed computational or algorithmic. This claim would justify the computationalism claim by making it utterly trivial. I will show that even if these two claims were true, computationalism would not have to be trivial.

In this reply to James H. Fetzer’s “Minds and Machines: Limits to Simulations of Thought and Action”, I argue that computationalism should not be the view that (human) cognition is computation, but that it should be the view that cognition (simpliciter) is computable. It follows that computationalism can be true even if (human) cognition is not the result of computations in the brain. I also argue that, if semiotic systems are systems that interpret signs, then both humans and computers are (...) semiotic systems. Finally, I suggest that minds can be considered as virtual machines implemented in certain semiotic systems, primarily the brain, but also AI computers. In doing so, I take issue with Fetzer’s arguments to the contrary. (shrink)

The argument presented in this paper is not a direct attack or defence of the Chinese Room Argument (CRA), but relates to the premise at its heart, that syntax is not sufficient for semantics, via the closely associated propositions that semantics is not intrinsic to syntax and that syntax is not intrinsic to physics. However, in contrast to the CRA’s critique of the link between syntax and semantics, this paper will explore the associated link between syntax and physics. The main (...) argument presented here is not significantly original – it is a simple reflection upon that originally given by Hilary Putnam (Putnam 1988) and criticised by David Chalmers and others: instead of seeking to justify Putnam’s claim that, “every open system implements every Finite State Automaton (FSA)”, and hence that psychological states of the brain cannot be functional states of a computer, I will seek to establish the weaker result that, over a finite time window every open system implements the trace of a particular FSA Q, as it executes program (p) on input (x). That this result leads to panpsychism is clear as, equating Q (p, x) to a specific Strong AI program that is claimed to instantiate phenomenal states as it executes, and following Putnam’s procedure, identical computational (and ex hypothesi phenomenal) states (ubiquitous little ‘pixies’) can be found in every open physical system. (shrink)

Donald Davidson and John Searle famously differ, among other things, on the issue of animal thoughts. Davidson seems to be a latter-day Cartesian, denying any propositional thought to subhuman animals, while Searle seems to follow Hume in claiming that if we have thoughts, then animals do, too. Davidson’s argument centers on the idea that language is necessary for thought, which Searle rejects. The paper argues two things. Firstly, Searle eventually argues that much of a more complex thought does depend on (...) language, which reduces a distance between himself and Davidson. Secondly, some of Davidson’s suggestions are promising – in particular the idea that we may lack a vocabulary to capture the contents of animal thoughts. Based on this insight, one might, pace Davidson, grant thoughts to animals. However, this does not mean, pace Searle, that it should be possible to construe even the simplest of such thoughts as propositional. Perhaps we need to move beyond Davidson and Searle by developing a theory of nonpropositional thought for animals. (shrink)

SOMMAIRE 1. Deux questions préalables à toute théorie de l?intentionnalité Où est le contenu intentionnel ? L?intentionnalité est-elle nécessairement conceptuelle ? 2. Premiers arguments pour et contre la conceptualisation du noème 3. Quelque part entre le conceptualisme et le Mythe du donné 4. Trois contre-arguments de Searle 5. Réponse aux contre-arguments de Searle 6. Perspectives Contenu perceptuel et signification Significations propres et schèmes perceptuels Les schèmes perceptuels sont intrinsèques Problèmes généraux.

The structuralist heritage in linguistics continues to obscure the essential properties of natural language as an empirical phenomenon. It is argued that the new framework of autopoiesis possesses a greater explanatory power, as it assumes the connotational na-ture of language. The key notions of representation, sign and signification, interpreta-tion, intentionality and communication, and reciprocal causality, approached from the autopoietic angle, allow for deeper insights into the essence of language which is as a kind of adaptive behavior of an organism involving (...) a system constituted by signs of signs. (shrink)

The recent development of the research field of Computing and Philosophy has triggered investigations into the theoretical foundations of computing and information. This thesis consists of two parts which are the result of studies in two areas of Philosophy of Computing and Philosophy of Information regarding the production of meaning and the value system with applications. The first part develops a unified dual-aspect theory of information and computation, in which information is characterized as structure, and computation is the information dynamics. (...) This enables naturalization of epistemology, based on interactive information representation and communication. In the study of systems modeling, meaning, truth and agency are discussed within the framework of the PI/PC unification. The second part of the thesis addresses the necessity of ethical judgment in rational agency illustrated by the problem of information privacy and surveillance in the networked society. The value grounds and socio-technological solutions for securing trustworthiness of computing are analyzed. Privacy issues clearly show the need for computing professionals to contribute to understanding of the technological mechanisms of Information and Communication Technology. The main original contribution of this thesis is the unified dual-aspect theory of computation/information. Semantics of information is seen as a part of the data-information-knowledge structuring, in which complex structures are self-organized by the computational processing of information. Within the unified model, complexity is a result of computational processes on informational structures. The thesis argues for the necessity of computing beyond the Turing-Church limit, motivated by natural computation, and wider by pancomputationalism and paninformationalism, seen as two complementary views of the same physical reality. Moreover, it follows that pancomputationalism does not depend on the assumption that the physical world on some basic level is digital. Contrary to many believes it is entirely compatible with dual quantum-mechanical computing. (shrink)

A computational theory of consciousness should include a quantitative measure of consciousness, or MoC, that (i) would reveal to what extent a given system is conscious, (ii) would make it possible to compare not only different systems, but also the same system at different times, and (iii) would be graded, because so is consciousness. However, unless its design is properly constrained, such an MoC gives rise to what we call the boundary problem: an MoC that labels a system as conscious (...) will do so for some – perhaps most – of its subsystems, as well as for irrelevantly extended systems (e.g., the original system augmented with physical appendages that contribute nothing to the properties supposedly supporting consciousness), and for aggregates of individually conscious systems (e.g., groups of people). This problem suggests that the properties that are being measured are epiphenomenal to consciousness, or else it implies a bizarre proliferation of minds. We propose that a solution to the boundary problem can be found by identifying properties that are intrinsic or systemic: properties that clearly differentiate between systems whose existence is a matter of fact, as opposed to those whose existence is a matter of interpretation (in the eye of the beholder). We argue that if a putative MoC can be shown to be systemic, this ipso facto resolves any associated boundary issues. As test cases, we analyze two recent theories of consciousness in light of our definitions: the Integrated Information Theory and the Geometric Theory of consciousness. (shrink)