The Computational Theory of Mind

A historical trend in the cognitive sciences has been to understand the brain as nature’s way of implementing a computer, a view often termed the Classical Computational Theory of Mind (CCTM).

Early roots of this idea can be found in the development of formal logics as a means for modeling laws of reason. A formal logic is a formal language consisting of a set of symbols, rules for combining these symbols into complex symbol structures, and purely syntactical rules of inference, i.e., rules that only make reference to the form of the symbols rather than their meaning. Through the application of these syntactical rules, true conclusions can be derived from true premises. This way, the syntax “tracks” the semantics: While the rules of transformation are purely syntactical, they are defined in such a way that truth is preserved across syntactical transformations – i.e., that syntactical operations satisfy semantical coherence.

For example, a syntactical rule could be specified that allows to derive the string “The sky is blue” from the string “The sky is blue and the sun is shining” due to the fact that the former is a constituent of the latter. This tracks the semantic fact that the proposition denoted by “The sky is blue” follows from the proposition denoted by “The sky is blue and the sun is shining”. This inference is valid, and it can be made without reference to the meaning of either “The sky is blue” or “The sun is shining”. As such, formal logics allow to account for reasoning processes without intrinsic reference to meaning. (For an introduction into the history of using formal logics to model inferences, see my article Gödel’s Incompleteness and its Implications for Artificial Intelligence.)

Formal logics introduce a liberalism regarding the actual physical shapes of the symbols, as long as the shapes are used consistently, and the rules of transformation are set up in accordance with these shapes. Thus, instead of using the symbol “and” for conjunction, we could use the symbol “#”, as long as we formulate the rules of inference in accordance, e.g., that the strings “A” and “B” can be derived from the string “A # B”.

Another milestone in the development of the CCTM was the formalization of the notion of computation by Turing (1936) in the form of the Turing machine, a hypothetical device that is able to execute any algorithm and solve any decidable problem. Importantly, its operations consist of the transformation of symbols, and these operations are sensitive to the syntactical structure (and only the syntactical structure) of those symbols. In combination with the work on formal logics, this showed that it is possible to construct an autonomous, syntax-driven machine whose state transitions satisfy semantical coherence – i.e., a reason-respecting machine.

McCulloch and Pitts (1943) were among the first to suggest that the human mind is nature’s way of implementing something that is similar in important respects to a Turing machine. The primary motivation for this view is its ability to account for the mental in naturalistic terms, and for how reason-respecting behavior can emerge from the interaction of physical matter. In the course of the 1960s, this stance was at the heart of the emerging field of cognitive science. It was widely believed that many of the higher cognitive functions like reasoning, decision making and problem solving are computations carried out in a fashion similar to a Turing machine. Research in mathematical modeling of cognition was thus closely intertwined with the emerging fields of computer science and artificial intelligence, and models of cognitive processes were often given in algorithmic terms.

One of the claims of the CCTM, maintained, e.g., by Fodor (1975), is that sensory input gets transformed into a symbolic representational format. These symbolic representations are stored and processed in systems that are separate from the brain’s modal systems for perception, action and introspection. Higher cognition is then the result of purely syntactical operations carried out on these symbolic representations, i.e., mechanistic operations that only make reference to the physical shape of the symbols, not to their meanings (Rescorla, 2017).

Importantly, these symbolic representations are believed to be amodal, i.e.,

“(1) they are arbitrarily related to their corresponding categories in the world and experience; and (2) they can stand alone without grounding to perform the basic computations underlying conceptual processing” (Barsalou,2016, p. 1125)

Here, grounding refers to the process by means of which a connection between a symbol and its meaning is established.

For example, the proposition “all humans are mortal” could be encoded as the symbol string

$$\forall x (\text{HUMAN}(x) \rightarrow \text{MORTAL}(x)).$$

Similarly, the proposition “Socrates is a human” could be encoded as the symbol string

$$\text{HUMAN}(\text{SOCRATES})$$

The CCTM claims that the conclusion that “Socrates is mortal”, which human beings draw with ease, is the result of a process that makes reference to the syntactic properties of the symbol strings alone. For instance, such a process could contain a rule that whenever a statement with the syntactic form

$$\forall x (\text{A}(x) \rightarrow \text{B}(x))$$

for arbitrary predicate symbols $\text{A}$ and $\text{B}$ is encountered in memory, and another statement with the syntactic form

$$\text{A}(\text{t})$$

for an arbitrary term symbol $\text{t}$ is encountered in addition, then the system should produce the statement

$$\text{B}(\text{t}).$$

This rule would lead the system to the conclusion

$$\text{MORTAL}(\text{SOCRATES})$$

from the premises, which states that “Socrates is mortal”. Importantly, this conclusion is drawn without any reference to the meanings of the symbols. The system does not imagine Socrates, nor humanity, nor mortality. It simply manipulates symbols without grounding their meaning.

The Language of Thought Hypothesis

While the core thesis of the CCTM is that the brain implements a Turing-style computational mechanism, many species of the CCTM include additional tenets. A common additional tenet is that the symbols manipulated in the computations are mental representations (Pitt, 2018). A mental representation is a structure with semantic properties – it represents something in the environment. Depending on one’s theory of mental representations, they may represent objects, categories of objects, properties, relations, states of affairs, or any combination of them. This tenet is often referred to as the Representational Theory of Mind (RTM).

The fact that symbols have meanings is usually formalized by a meaning function μ that maps symbols to meanings (Werning, 2005). For example, the symbol SWAN may represent the set of all swans in the world, i.e.,

$$\mu(\text{SWAN}) = \{x \; | \; x \text{ is a swan}\}.$$

Another common additional tenet is that the mental representations manipulated in mental computations have a part/whole constituency structure, i.e., that there are operations that allow to combine mental representations into more complex mental representations, which can be combined into yet more complex mental representations, etc. This is often referred to by saying that the mental representations themselves are “combinatorial” (Fodor & Pylyshyn, 1988).

The syntactical operations that allow to combine symbols into complex symbol structures are usually formalized as functions $\sigma : S^n \rightarrow S$ from a sequence of $n$ symbols into the set of symbols. For instance, there might be a syntactical operation that allows to combine adjective and noun symbols into a noun phrase symbol, which can be formalized as a function

$$
\sigma_\text{AdjectiveNounCombination} : \text{A} \times \text{N} \rightarrow \text{NP},\\
\sigma_\text{AdjectiveNounCombination}(a, n) = a \text{ } n
$$

from the Cartesian product of the set of all adjectives and the set of all nouns to the set of all noun phrases. This syntactical rule allows, e.g., to combine the symbols BLACK and SWAN into the combinatorial symbol BLACK SWAN:

$$\sigma_\text{AdjectiveNounCombination}(\text{BLACK}, \text{SWAN}) = \text{BLACK SWAN}$$

A third additional tenet, which goes hand in hand with the ability to combine symbols into combinatorial symbols, is the Principle of Compositionality (PoC), according to which the meaning of a combinatorial symbol structure is determined by the meanings of its parts and the way the parts are put together syntactically (Frege, 1897; Janssen et al., 2012).

For example, if the meanings of adjectives and nouns are sets of objects in the world to which the adjective or noun applies, then the meaning of a noun phrase may be given by the intersection of the set to which the adjective applies with the set to which the noun applies:

$$\mu_{\sigma_\text{AdjectiveNounCombination}}(\mu(a), \mu(n)) = \mu(a) \cap \mu(n)$$

Thus, if the meaning of the adjective BLACK is the set of all black things, i.e.,

$$\mu(\text{BLACK}) = \{x \; | \; x \text{ is black}\},$$

and the meaning of the noun SWAN is the set of all swans, i.e.,

$$\mu(\text{SWAN}) = \{x \; | \; x \text{ is a swan}\},$$

then the meaning of the combinatorial symbol BLACK SWAN is the set of all black swans, i.e.,

$$\mu(\text{BLACK SWAN})\\
= \mu_{\sigma_\text{AdjectiveNounCombination}}(\mu(\text{BLACK}), \mu(\text{SWAN}))\\
= \mu(\text{BLACK}) \cap \mu(\text{SWAN})\\
= \{x \; | \; x \text{ is black}\} \cap \{x \; | \; x \text{ is a swan}\}\\
= \{x \; | \; x \text{ is black and } x \text{ is a swan}\}.$$

The three additional tenets that (1) symbols are mental representations with (2) a part/whole constituency structure that (3) fulfill the PoC are at the heart of the Language of Thought Hypothesis (LOTH), a species of the CCTM put forward by Fodor (1975). An important feature of the LOTH is that the systems responsible for the higher cognitive functions are encapsulated modules that are independent from and cannot penetrate the sensory-motor systems (Fodor, 1983). Rather, perceptual representations are transformed into a completely new representational format, which is inherently symbolic and amodal. These amodal representations are fed into the systems responsible for higher cognition, and their output can be used to program motor commands.

One of the major attractions of the LOTH and derived views has been their ability to serve as fully functional conceptual systems that are able to account for many of the higher cognitive feats like memory, knowledge, reasoning, language, and thought.

The systems of symbols on which the brain is believed to operate under the CCTM and LOTH are often referred to as Amodal Symbol Systems to highlight two aspects of this view: (1) The relation between the symbols and their meaning is arbitrary, i.e., the symbols attain their meaning by convention, or by their role in the overall symbol system, but do not themselves resemble the objects in the world or the perceptual states that produced them. (2) The symbols enter into conceptual processing without grounding them in perception (Barsalou, 1999).

In the last few decades, the CCTM has been subject to widespread criticism. For instance,

• there is no direct empirical evidence for amodal symbols in the brain (Barsalou, 1999),
• the same brain regions that are responsible for perception and action are also involved in conceptual reasoning (Pulvermüller, 1999, 2005),
• there’s no satisfactory account for how amodal symbols can get mapped back to the perceptual and motor representations that gave rise to them, and for how a sense of understanding of one’s reasoning can come about (Harnad, 1990),
• the kinds of computations that neural populations can perform are significantly more limited than the kinds of computations that a Turing machine can perform (Richter, Lins, Schöner, 2017)

In an upcoming article, I am going to review this criticism and argue how it gave rise to the field of grounded cognition. Please subscribe to my blog to stay updated.

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