Abstract
Using the tools of universal algebra, it is shown that oscillatory networks realize systematic cognitive representations. It is argued (i) that an algebra of propositions and concepts for objects and properties is isomorphic to an algebra of brain states, neuronal oscillations and sets of oscillations related to clusters of neurons, (ii) that the isomorphism, in a strong sense, preserves the constituent relations of the conceptual algebra, and (iii) that the isomorphism transfers semantic compositionality. Oscillatory networks are neurobiologically plausible. They combine the virtues and avoid the vices of classical and connectionist architectures.
Research for this paper was sponsored by the National German Merit Foundation. It was enabled by a one-year research scholarship at Rutgers University and the Rutgers Center of Cognitive Science. I owe many of the presented insights to discussions with Andreas Engel, Wolf Singer, Jerry Fodor, Ernie LePore, Brian McLaughlin, Bruce Tesar, Thomas Metzinger, and Gerhard Schurz. I have benefitted from comments by a number of colleagues on various occasions where parts or earlier stages of this material were presented. I am grateful, in particular, to participants at the Berlin Colloquium Philosophy Meets Cognitive Science, FotFS II, CogSci2001, and ESPP2001. I would, also, like to thank an anonymous referee for very helpful remarks.
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References
I take Smolensky’s approach only as a representative for a variety of models that pursue a similar strategy. For a survey of related models see [Wer01].
I do not intend to make any substantial statements about idioms, here. In an objection to the received view, which is reflected in [NunSagWas94] and according to which some idioms violate semantic compositionality, Westerståhl [Wes02] argues that idioms can always be embedded in compositional languages. He proposes three ways of doing so: (i) extend the set of atomic expressions by a holophrastic reading of the idiom, (ii) extend the list of syntactic operations so that the literal and the idiomatic reading of the idiom turn out to be outcomes of different syntactic operations, or (iii) take the components of the idiom as homonyms of their occurrences in its literal reading and add them to the set of atomic expressions. None of the three options afflict our argumentation, though, because in each case a child with an old coat is distracted by a red herring would no longer be a syntactic re-combination of a child with a red coat is distracted by an old herring. This, however, would simply negate the assumption that it is. The assumption has been made for the sake of the argument with the intention to show that syntactic re-combination is not sufficient for systematicity.
This point is made in a more elaborate way by Dretske [Dre88a].
This holds even if the mapping is an isomorphism rather than a homomorphism.
Fodor and McLaughlin [FodMcL90,Fod97] also see a connection between the ideas of cormpositionality, co-variation and constituency.
Oscillatory networks are dynamical systems in the sense that they are described by systems of differential equations that involve time-dependent functions (cf. [vGe98]).
The degree of synchrony, so defined, corresponds to the cosine of the angle between the vectors a and b. Alternative measures for synchrony (respectively temporal coherence) are available, in particular for discrete functions of spiking activity.
The assumption that the class of possible worlds is a set may impose some restrictions on the universe. It is debatable, furthermore, whether it makes sense to say that every set of possible worlds is a proposition. An analogous objection may apply to the view that identifies every set of time slices of brains with a brain state. Notice, however, that only the sets of possible worlds (and their intersections) —and the sets of time slices of brains (and their intersections), respectively— which are in the ranges of the first three algebraic operations matter for our considerations, anyway. For an appropriate restriction of the algebras, cf. p. 274.
A crucial difference between the notions of expressing and referring should not be overlooked here. In the English sentence “this is the same as that”, “this” and “that” do not refer to concepts, but to objects. They, nevertheless, express the concepts this and that.
The topographical arrangement in the in-module does not have any representational function. The surrounding neurons with simplex activity may, however, help drive the embedded neurons to show duplex activity (cf. [May01]).
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© 2003 Springer Science+Business Media Dordrecht
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Werning, M. (2003). Synchrony and Composition: Toward a Cognitive Architecture between Classicism and Connectionism. In: Löwe, B., Malzkom, W., Räsch, T. (eds) Foundations of the Formal Sciences II. Trends in Logic, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0395-6_19
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DOI: https://doi.org/10.1007/978-94-017-0395-6_19
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