Brain Hammer

(I leave in a few hours to go see Jerry Fodor give a talk at the CUNY Graduate Center. I thought it appropriate, then, to post something on how awesome evolution and neural networks are.)

What makes analytical functionalists functionalists is their belief that what makes something a mental state is the role that it plays in a complex economy of causal interactions. What makes analytical functionalists analytical is their belief that which roles are essential is to be discovered by a consultation of common sense knowledge about mental states.

There are three serious related problems that arise for analytical functionalism. The first problem is that analytical functionalism appears to be committed to the existence of analytical truths and various philosophers inspired by Quine have been skeptical of analytical truths. As Prinz (20**) succinctly sums up this Quinean skepticism, the objection is that “[r]oughly, definitions of analyticity are either circular because they invoke semantic concepts that presuppose analyticity, or they are epistemically implausible, because they presuppose a notion of unrevisability that cannot be reconciled with the holistic nature of confirmation” (p. 92). There are two main ways in which analytic functionalism seems saddled with belief in analytic truths. The first is concerns the nature of psychological state types such as beliefs and desires. Analytical functionalism is committed to there being analytic truths concerning the necessary and sufficient conditions for being a belief. The second concerns the meaning of mental representations. The most natural theory of meaning for the analytic functionalist to adopt is that what makes one’s belief about, say, cows, have the meaning that it does, is the causal relations it bears to all other belief states. However, it is likely that no two people have all the same beliefs about cows. Thus, on pain of asserting that no one means the same thing when they think about cows, the functionalist cannot allow that every belief one has about cows affects the meaning of one’s cow thoughts. In order to allow that people with divergent beliefs about cows can both share the concept of cows, that is, both think about the same things when they think about cows, the analytic functionalist seems forced to draw a distinction between analytic and synthetic beliefs, eg., a distinction between beliefs about cows that are constitutive of cow concepts and beliefs that are not. But if Quinean skepticism about the analytic/synthetic distinction is correct, no such distinction is forthcoming.
The second problem arises from worries about how minds are implemented in brains. Many so-called connectionists may be seen to agree with analytical functionalists that mental states are defined in terms of networks. However, many connectionists may object that when one looks to neural network implementations of cognitive functions, it is not clear that the sets of nodes and relations postulated by common sense psychology will map on to the nodes and relations postulated by a connectionist architecture (see, e.g. Ramsey, et al., 1991). The question arises of whether folk-psychological states will smoothly reduce to brain states or be eliminated in favor of them. (I will not discuss further the third option that folk-psychological states concern a domain autonomous from brainstates.)
A third problem arises from worries about the evolution of cognition. If a mind just is whatever the collection of folk psychological platitudes are true of, then there seem not to be any simple minds, for a so called simple mind would be something that the folk psychological platitudes were only partially true of in the sense that only some proper subset of the platitudes were true of it. However a very plausible proposal for how our minds evolved is from simpler minds. It counts against a theory that it rules out a priori the existence of simpler minds than ours for it leaves utterly mysterious what the evolutionary forebears of our minds were. This third problem is especially pertinent to artificial life researchers.
One promising solution to these three problems involves appreciating a certain view concerning how information-bearing or representational states are implemented in neural networks and how similarities between states in distinct networks may be measured. Models of neural networks frequently involve three kinds of interconnected neurons: input neurons, output neurons, and neurons intermediate between inputs and outputs sometimes referred to as “interneurons” or “hidden-neurons”. These three kinds of neurons comprise three “layers” of a network: the input layer, the hidden layer, and the output layer. Each neuron can be, at any given time, one of several states of activation. The state of activation of a given neuron is determined in part by the states of activations of neurons connected to it. Connections between neurons may have varying weights which determine how much the activation of one neuron can influence the other. Each neuron has a transition function that determines how its state is to depend on the states of its neighbors, for example, the transition function may be a linear function of the weighted sums of the activations of neighboring neurons. Learning in neural networks is typically modeled by procedures for changing the connection weights. States of a network may be modeled by state spaces wherein, for example, each dimension of the space corresponds to the possible values of a single hidden neuron. Each point in that space is specified by an ordered n-tuple or vector. A network’s activation vector in response to an input may be regarded as its representation of that input. A state of hidden-unit activation for a three-unit hidden layer is a point in a three-dimensional vector-space. A cluster of points may be regarded as a concept (Churchland 19**).
Laakso and Cottrell (1999, 2000) propose a method whereby representations in distinct networks may be quantified with respect to their similarity. Such a similarity measure may apply even in cases where the networks in question differ with respect to their numbers of hidden units and thus the number of dimensions of their respective vector spaces. In brief the technique involves first assessing the distances between various vectors within a single network and second measuring correlations between relative distances between points in one network and points in another. Points in distinct networks are highly similar if their distinct relative distances are highly correlated.
Regarding the analytic/synthetic distinction related worries, the Laakso and Cottrell technique allows one to bypass attributions of literally identical representations to distinct individuals and make do instead with objective measures of degrees of similarity between the representations of different individuals. Thus if I believe that a cow once ate my bother’s hat and you have no such belief, we may nonetheless have measurably similar cow concepts. This is no less true of our psychological concepts such as our concepts of belief and concepts of desire. The so-called common-sense platitudes of folk psychology so important to analytic functionalism may very well diverge from folk to folk and the best we can say is that each person’s divergent beliefs about beliefs may be similar. And similarity measures are not restricted to the concepts that constitute various folk theories, we may additionally make meaningful comparisons between various folk theories and various scientific theories. This last maneuver allows us to retain one of the key insights of analytic functionalism mentioned earlier: that we are in need of some kind of answer to the question ‘how do you know that your theory is a theory of belief?” The answer will be along the lines of “because what I’m talking about is similar to beliefs.”
Regarding the question of simple minds, if there are no analytic truths, then there is no a priori basis (if any) for drawing a boundary between the systems that are genuine minds and those that are not. Similarity measurements between simple minds and human minds would form the basis for a (mind-body?) continuum along which to position various natural and artificial instances. How useful for understanding human minds will be the study of systems far away on the continuum? We cannot know a priori the answer to such a question.

Fig. 1. What are minds such that complex ones come from somewhere instead of nowhere? Photo by Pete Mandik.

References

Churchland, P. (19**)

Laakso, Aarre and Cottrell, Garrison W. (1998) How can I know what You think?: Assessing representational similarity in neural systems.(92k) In Proceedings of the Twentieth Annual Cognitive Science Conference, , Mahwah, NJ: Lawrence Erlbaum.
Laakso, Aarre and Cottrell, Garrison W. (2000) Content and cluster analysis: Assessing representational similarity in neural systems. Philosophical Psychology, 13(1):47-76.
Prinz, J. (****) “Empiricism and State-Space Semantics” in Keeley, ed. Paul Churchland.

Ramsey, W., Stich S. & Garon, J. (1991) Connectionism, eliminativism, and the future of folk psychology, in: W. Ramsey, S. Stich & D. Rumelhart (Eds.) Philosophy and Connectionist Theory. Hillsdale NJ: Lawrence Erlbaum.