Defending or attacking either functionalism or computationalism requires clarity on what they amount to and what evidence counts for or against them. My goal here is not to evaluate their plausibility. My goal is to formulate them and their relationship clearly enough that we can determine which type of evidence is relevant to them. I aim to dispel some sources of confusion that surround functionalism and computationalism, recruit recent philosophical work on mechanisms and computation to shed light on them, and (...) clarify how functionalism and computationalism may or may not legitimately come together. (shrink)

This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...) I argue that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analog of Mathematical CT. The correct physical analog of Mathematical CT is Modest Physical CT. I propose to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function. Finally, I suggest that proposed counterexamples to Physical CT are still far from falsifying it because they have not been shown to satisfy the usability constraint. (shrink)

I offer an explication of the notion of computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hard-wired versus programmable, general-purpose versus special-purpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system's mechanistic (...) properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind. (shrink)

A survey of more philosophical applications of Gödel's incompleteness results.

Despite its significance in neuroscience and computation, McCulloch and Pitts's celebrated 1943 paper has received little historical and philosophical attention. In 1943 there already existed a lively community of biophysicists doing mathematical work on neural networks. What was novel in McCulloch and Pitts's paper was their use of logic and computation to understand neural, and thus mental, activity. McCulloch and Pitts's contributions included (i) a formalism whose refinement and generalization led to the notion of finite automata (an important formalism in (...) computability theory), (ii) a technique that inspired the notion of logic design (a fundamental part of modern computer design), (iii) the first use of computation to address the mind–body problem, and (iv) the first modern computational theory of mind and brain. (shrink)

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)

Some philosophers have conflated functionalism and computationalism. I reconstruct how this came about and uncover two assumptions that made the conflation possible. They are the assumptions that (i) psychological functional analyses are computational descriptions and (ii) everything may be described as performing computations. I argue that, if we want to improve our understanding of both the metaphysics of mental states and the functional relations between them, we should reject these assumptions. # 2004 Elsevier Ltd. All rights reserved.

Alan Turing is often portrayed as a materialist in secondary literature. In the present article, I suggest that Turing was instead an idealist, inspired by Cambridge scholars, Arthur Eddington, Ernest Hobson, James Jeans and John McTaggart. I outline Turing’s developing thoughts and his legacy in the USA to date. Specifically, I contrast Turing’s two notions of computability (both from 1936) and distinguish between Turing’s “machine intelligence” in the UK and the more well-known “artificial intelligence” in the USA. According to my (...) proposed historical interpretation, Turing did not view computations in the real world to be exhaustively and deterministically characterized by his automatic machines from 1936. (shrink)

This paper revisits the often debated question Can machines think? It is argued that the usual identification of machines with the notion of algorithm has been both counter-intuitive and counter-productive. This is based on the fact that the notion of algorithm just requires an algorithm to contain a finite but arbitrary number of rules. It is argued that intuitively people tend to think of an algorithm to have a rather limited number of rules. The paper will further propose a modification (...) of the above mentioned explication of the notion of machines by quantifying the length of an algorithm. Based on that it appears possible to reconcile the opposing views on the topic, which people have been arguing about for more than half a century. (shrink)

Some philosophers have conflated functionalism and computationalism. I reconstruct how this came about and uncover two assumptions that made the conflation possible. They are the assumptions that (i) psychological functional analyses are computational descriptions and (ii) everything may be described as performing computations. I argue that, if we want to improve our understanding of both the metaphysics of mental states and the functional relations between them, we should reject these assumptions.

Computationalism has been the mainstream view of cognition for decades. There are periodic reports of its demise, but they are greatly exaggerated. This essay surveys some recent literature on computationalism. It concludes that computationalism is a family of theories about the mechanisms of cognition. The main relevant evidence for testing it comes from neuroscience, though psychology and AI are relevant too. Computationalism comes in many versions, which continue to guide competing research programs in philosophy of mind as well as psychology (...) and neuroscience. Although our understanding of computationalism has deepened in recent years, much work in this area remains to be done. (shrink)

According to pancomputationalism, everything is a computing system. In this paper, I distinguish between different varieties of pancomputationalism. I find that although some varieties are more plausible than others, only the strongest variety is relevant to the philosophy of mind, but only the most trivial varieties are true. As a side effect of this exercise, I offer a clarified distinction between computational modelling and computational explanation.<br><br>.

In this paper I argue that Turing’s responses to the mathematical objection are straightforward, despite recent claims to the contrary. I then go on to show that by understanding the importance of learning machines for Turing as related not to the mathematical objection, but to Lady Lovelace’s objection, we can better understand Turing’s response to Lady Lovelace’s objection. Finally, I argue that by understanding Turing’s responses to these objections more clearly, we discover a hitherto unrecognized, substantive thesis in his philosophical (...) thinking about the nature of mind. (shrink)

The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating misunderstandings about the relationship between CTT and computationalism, we deepen our appreciation of computationalism as an empirical hypothesis.

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

In 2003, philosopher Nick Bostrom presented the provocative idea that we are now living in a computer simulation. Although his argument is structured to include a “hypothesis,” it is unclear that his proposition can be accounted as a properly scientific hypothesis. Here Bostrom’s argument is engaged critically by accounting for philosophical and scientific positions that have implications for Bostrom’s principal thesis. These include discussions from Heidegger, Einstein, Heisenberg, Feynman, and Dreyfus that relate to modelling of structures of thinking and computation. (...) In consequence of this accounting, given that there seems to be no reasonably admissible evidence to count for the task of falsification, one concludes that the computer simulation argument’s hypothesis is only speculative and not scientific. (shrink)