Online research in philosophy

The concept of representation has been a key element in the scientific study of mental processes, ever since such studies commenced. However, usage of the term has been all but too liberal—if one were to adhere to common use it remains unclear if there are examples of physical systems which cannot be construed in terms of representation. The problem is considered afresh, taking as the starting point the notion of activity spaces—spaces of spatiotemporal events produced by dynamical systems. It is argued that representation can be analyzed in terms of the geometrical and topological properties of such spaces. Several attributes and processes associated with conceptual domains, such as logical structure, generalization and learning are considered, and given analogues in structural facets of activity spaces, as are misrepresentation and states of arousal. Based on this analysis, representational systems are defined, as is a key concept associated with such systems, the notion of representational capacity. According to the proposed theory, rather than being an all or none phenomenon, representation is in fact a matter of degree—that is can be associated with measurable quantities, as is behooving of a putative naturalistic construct.

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of zero-sets are elementarily equivalent then their respective rings of bounded continuous real-valued functions satisfy the same positive-universal sentences. The proof of this uses the technique of constructing ultraproducts as direct limits of products in a category theoretic setting.

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a variety of non-symbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent they lack a higher-level theory of representation. In this paper, conceptual spaces are suggested as an appropriate framework for non- symbolic models. Conceptual spaces consist of a number of 'quality dimensions' that often are derived from perceptual mechanisms. It will be outlined how conceptual spaces can represent various kind of information and how they can be used to describe concept learning. The connections to prototype theory will also be presented.

1. I think that by emphasizing theoretical spaces of representations, Andy has put his finger on an issue that is key to connectionism's success, and whose investigation will be a key determinant of the field's further progress. I also think that if we look at representational spaces in the right way, we can see that they are deeply related to classical phenomenon of systematicity in representation. I want to argue that the key to understanding representational spaces, and in particular their ability to capture the deep organization underlying various problems, lies in the idea of what I will call.

Clark & Thornton (C&T) have demonstrated the paradox between the opacity of the transformations that underlie relational mappings and the ease with which people learn such mappings. However, C&T's trading-spaces proposal resolves the paradox only in the broadest outline. The general-purpose algorithm promised by C&T remains to be developed. The strategy of doing so is to analyze and formulate computational mechanisms for known cases of recoding.

It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing-machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation.

Evolution is not like an exam in which pre-set problems need to be solved. Failing to recognise this point, Clark & Thornton misconstrue the type of explanation called for in species learning although, clearly, species that can trade spaces have more chances to discover novel beneficial behaviours. On the other hand, the trading spaces strategy might help to explain lifetime learning successes.

Although Clark & Thornton's “trading spaces” hypothesis is supposed to require trading internal representation for computation, it is not used consistently in that fashion. Not only do some of the offered computation-saving strategies turn out to be nonrepresentational, others (e.g., cultural artifacts) are external representations. Hence, C&T's hypothesis is consistent with antirepresentationalism.

It is widely appreciated that the difficulty of a particluar computation varies according to how the input data are presented. What is less understood is the effect of this computation/representation tradeoff within familiar learning paradigms. We argue that existing learning algoritms are often poorly equipped to solve problems involving a certain type of important and widespread regularity, which we call 'type-2' regularity. The solution in these cases is to trade achieved representation against computational search. We investigate several ways in which such a trade-off may be pursued including simple incremental learning, modular connectionism, and the developmental hypothesis of 'representational redescription'. In addition, the most distinctive features of human cognition- language and culture- may themselves be viewed as adaptions enabling this representation/computation trade-off to be pursued on an even grander scale.