Online research in philosophy

The importance of the Stability Problem in neurocomputing is discussed, as well as the need for the study of infinite networks. Stability must be the key ingredient in the solution of a problem by a neural network without external intervention. Infinite discrete networks seem to be the proper objects of study for a theory of neural computability which aims at characterizing problems solvable, in principle, by a neural network. Precise definitions of such problems and their solutions are given. Some consequences are explored, in particular, the neural unsolvability of the Stability Problem for neural networks.

We present a model for generating a kind of neural synchrony in which the individual spike trains of one neuron or group of neurons closely match the spike trains of another. This kind of neural synchrony has been observed in animals performing auditory, visual and attentional information processing tasks. Our model is realized in a system of functionally identical, refractory spiking neurons. Larger systems with more sophisticated information processing capabilities can be constructed from aggregated instances of the basic network.

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.

"Symbol Grounding" is beginning to mean too many things to too many people. My own construal has always been simple: Cognition cannot be just computation, because computation is just the systematically interpretable manipulation of meaningless symbols, whereas the meanings of my thoughts don't depend on their interpretability or interpretation by someone else. On pain of infinite regress, then, symbol meanings must be grounded in something other than just their interpretability if they are to be candidates for what is going on in our heads. Neural nets may be one way to ground the names of concrete objects and events in the capacity to categorize them (by learning the invariants in their sensorimotor projections). These grounded elementary symbols could then be combined into symbol strings expressing propositions about more abstract categories. Grounding does not equal meaning, however, and does not solve any philosophical problems.

``Neural computing'' is a research field based on perceiving the human brain as an information system. This system reads its input continuously via the different senses, encodes data into various biophysical variables such as membrane potentials or neural firing rates, stores information using different kinds of memories (e.g., short-term memory, long-term memory, associative memory), performs some operations called ``computation'', and outputs onto various channels, including motor control commands, decisions, thoughts, and feelings. We show a natural model of neural computing that gives rise to hyper-computation. Rigorous mathematical analysis is applied, explicating our model's exact computational power and how it changes with the change of parameters. Our analog neural network allows for supra-Turing power while keeping track of computational constraints, and thus embeds a possible answer to the superiority of the biological intelligence within the framework of classical computer science. We further propose it as standard in the field of analog computation, functioning in a role similar to that of the universal Turing machine in digital computation. In particular an analog of the Church-Turing thesis of digital computation is stated where the neural network takes place of the Turing machine.

Stevan Harnad correctly perceives a deep problem in computationalism, the hypothesis that cognition is computation, namely, that the symbols manipulated by a computational entity do not automatically mean anything. Perhaps, he proposes, transducers and neural nets will not have this problem. His analysis goes wrong from the start, because computationalism is not as rigid a set of theories as he thinks. Transducers and neural nets are just two kinds of computational system, among many, and any solution to the semantic problem that works for them will work for most other computational systems.

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.

Roughly speaking, computationalism says that cognition is computation, or that cognitive phenomena are explained by the agent‘s computations. The cognitive processes and behavior of agents are the explanandum. The computations performed by the agents‘ cognitive systems are the proposed explanans. Since the cognitive systems of biological organisms are their nervous 1 systems (plus or minus a bit), we may say that according to computationalism, the cognitive processes and behavior of organisms are explained by neural computations. Some people might prefer to say that cognitive systems are ―realized‖ by nervous systems, and thus that—according to computationalism—cognitive computations are ―realized‖ by neural processes. In this paper, nothing hinges on the nature of the relation between cognitive systems and nervous systems, or between computations and neural processes. For present purposes, if a neural process realizes a computation, then that neural process is a computation. Thus, I will couch much of my discussion in terms of nervous systems and neural computation.1 Before proceeding, we should dispense with a possible red herring. Contrary to a common assumption, computationalism does not stand in opposition to connectionism. Connectionism, in the most general and common sense of the term, is the claim that cognitive phenomena are explained (at some level and at least in part) by the processes of neural networks. This is a truism, supported by most neuroscientific evidence. Everybody ought to be a connectionist in this general sense. The relevant question is, are neural processes computations? More precisely, are the neural processes to be found in the nervous systems of organisms computations? Computationalists say ―yes‖, anti-computationalists say ―no‖. This paper investigates whether any of the arguments on offer against computationalism have a chance at knocking it off.2 Ever since Warren McCulloch and Walter Pitts (1943) first proposed it, computationalism has been subjected to a wide range of objections..

I argue that neural activity, strictly speaking, is not computation. This is because computation, strictly speaking, is the processing of strings of symbols, and neuroscience shows that there are no neural strings of symbols. This has two consequences. On the one hand, the following widely held consequences of computationalism must either be abandoned or supported on grounds independent of computationalism: (i) that in principle we can capture what is functionally relevant to neural processes in terms of some formalism taken from computability theory (such as Turing Machines), (ii) that it is possible to design computer programs that are functionally equivalent to neural processes in the same sense in which it is possible to design computer programs that are functionally equivalent to each other, (iii) that the study of neural (or mental) computation is independent of the study of neural implementation, (iv) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers. On the other hand, we need to gradually reinterpret or replace computational theories in psychology in terms of theoretical constructs that can be realized by known neural processes, such as the spike trains of neuronal ensembles.Â.