1. Conception

Conception is the process of linking concepts to percepts, such that a set of percepts are identified by some concept.

Conception is the process of creating referential associations between concepts and percepts. On the one hand, it may be viewed as the creation of a concept corresponding to some number of pre-existing percepts. On the other hand, it may be argued that concepts are to some extent responsible for creating individual or unified percepts out of the field of perception in the first place. In other words, it may be that the creation of perceptual things (percepts) is due in part to the atomic influence of concepts. This is similar to the nominalistic position, although nominalists make the further claim that the reason independent objects appear to exist in the world is that they correspond to individual concepts.

In comparison to percepts, concepts are primarily symbolic as opposed to sub-symbolic: they are categorical (atomic) as opposed to non-categorical (non-atomic). Note that this does not entail that mind as a whole is either categorical or not, which is a rather bold statement with a long history in both psychology and philosophy. Relative to one another, the perceptual mind is not categorical, and the conceptual mind is categorical (the degree to which the conceptual universe is necessarily categorical is debatable). In order to gain further insight into the nature of concept formation and categorical learning, this chapter introduces two prominent models of learning: conditioning and neural networks. The former is more of a symbolic paradigm, and the latter is (primarily) subsymbolic.

Conditioning is a popular (extrinsic) model of conception.

The conditioning (or stimulus/response) paradigm in the field of psychology, and in particular behaviorism, has produced a tremendous amount of information about how humans and animals learn and behave in the world. In order to remain objective, behaviorism limits itself to be a science of (externally observable) behavior, as opposed to a science of subjective phenomena. In other words, the organism under examination is treated as a black box, the mechanism of which is not explored. [88]

The psychological literature on conditioning (or stimuli and responses) is critically important to our understanding of learning and behavior. Much of this literature is relevant to the more subjective experience of cognition if we make the further assumption that the internal representation of the conditioned stimulus is identical to a concept. Hence, we assume that certain behavioral outputs (responses) are the result of certain perceptual inputs (stimuli), in virtue of the formation of concepts.[89]

Behaviorism categorizes learning by introducing two basic divisions: stimulus/response and conditioned/unconditioned. With respect to the first dichotomy, stimuli are the input to the organism, and responses are the output. With respect to the second dichotomy, conditioned inputs and outputs are those that have been trained, and unconditioned inputs and outputs are untrained (or innate). These two divisions are combined to produce the following four classes of things:

  • The Unconditioned Stimulus

  • The Unconditioned Response

  • The Conditioned Stimulus

  • The Conditioned Response

These four categories began taking shape in some of the earliest studies of conditioning, which were conducted by a Russian scientist named Ivan Pavlov. These experiments studied the relation between hungry dogs, salivation, food, and a bell.[90] Pavlov conducted studies of how stimuli became linked to responses (the observable results of a dog's learning process). Pavlov observed that dogs salivate just before, as well as during, their meal (salivation aides the digestion of food). After striking a dinner bell immediately prior to the presentation of the food (on a number of different occasions), dogs begin to salivate in response to the bell, even if the food is not subsequently presented. At this point, the dinner bell has become a conditioned stimulus, which elicits salivation independently of the unconditioned stimulus. In this way, the dinner bell has become a sign of food, and it elicits the same response that was originally elicited by the food itself.

Stimuli become linked to responses in virtue of their significance and desirability to the organism, as well as several other factors. The significance of the feeling or feature affects the rate of learning: if something is not significant, then there is little reason to learn it. For example, rewarding someone with food when they are in a state of hunger causes learning because it induces a change in a biologically-relevant dimension (i.e. being satiated). Punishing someone by removing food also causes learning because it induces a change in a biologically-relevant dimension. In this sense, reward and punishment are opposite ends of a single spectrum.[91]

In addition to the significance of a stimulus (as either a reward or punishment), there are several other factors which determine whether a conditioned stimulus will become associated with an unconditioned stimulus. One of the most important of these factors is the time of presentation: a stimulus will only be learned if it has predictive value. Clearly, for a conditioned stimulus to have predictive value, it must appear before the unconditioned stimulus: if it appears at the same time, then it has no predictive value (i.e. there is no information above and beyond the unconditioned stimulus itself). In other words, stimulus-response learning anticipates causality.

The predictive value of a stimulus decreases with time; it is difficult to notice the predictive ability of a conditioned stimulus if that stimulus occurs too long before the unconditioned stimulus. For example, if a dog's dinner bell were to ring exactly a year in advance, it is of little predictive value (unless the dog in question has a rather excellent memory). The frequency of the pairing of the conditioned and unconditioned stimuli is also an important variable: a certain amount of time after the stimulus appears, the response is expected to appear, based on the likelihood of past co-occurrence.[92]

In subjective terms, if hunger in the past has always been preceded by not eating (i.e. the absence of features which indicate eating), and fullness preceded by eating, the eating concept is learned, and this concept itself will acquire a positive value (which is transferred from the desirability of eating). This kind of learning depends on recognition of the stimulus: it must be possible (operationally) to tell when it is present, or have a cohesive concept of it. As experience with the stimulus increases, the stimulus is more precisely identified; irrelevant or coincidental features of the set are eliminated. For example, if a bell of a certain pitch is the stimulus, but bells with other pitches also ring, the concept “bell” is discriminated from other bells, and thereby becomes more narrowly defined.

Neural networks are a popular (intrinsic) model of conception.

The conditioning paradigm described in the previous section is incomplete as a general cognitive model for at least two reasons. One is the claim that behaviorism, as formulated, is insufficient to account for the richness of language and verbal behavior. Another is the fact that behaviorism does not describe the biological mechanisms of conditioning (which it avoids on purpose by considering the organism to be a black box). In this section, we summarize a few details from the neural network paradigm, which offers a complementary point of view from which to understand concepts.

The basic principle behind a neural network is quite simple: take a small computing element (a neuron), define its operation, and replicate that neuron in an organized fashion a large number of times, thereby mimicking the structure of a brain. The operation of networks built in this way is often astounding: the exhibited behavior is difficult to predict based on knowledge knowledge of the responsible mechanism. Of course, the mechanism itself is not exactly transparent if the model consists of large numbers of massively interconnected neurons.

The earliest model of the neuronal processing element, the Perceptron , is roughly equivalent to a propositional function. This neuron operates on some number of inputs (a quantified input space), and yields a single bit of information, either true or false, as a result. In doing so, the Perceptron creates a dichotomy in the input space: every point in the input space maps to either true or false (later neuronal models typically have a larger range of output values). This output value can in turn be processed by other neurons. This organization, where multiple neurons are neighbors that operate on input at the same time, leads naturally to a layered network implementation: neurons in one layer send their output to a subsequent layer, where it is used as input.[93]

A powerful geometric analogy for the operation of these simple, binary-output neurons is that of separating hyperplanes. A hyperplane is a division in a hyperspace, or a high-dimensional space (the prefix hyper , in this context, indicates the multi-dimensionality of the thing to which it is applied). In order for the separation (or boundary) created by these neurons to be meaningful, some of the inputs must be on one side of the neuron's decision boundary, and some must be on the other side. The location of this decision boundary is altered by the process of learning, which amounts to a binary classification problem.

In the following picture, a decision boundary is shown with a dotted line. The line approximately separates observations marked ‘x’ from observations marked ‘o’ :

The ability to classify individual points (or observations) in the diagram above is equivalent to being able to discriminate the conditioned stimulus: some percepts correspond to the stimulus object, and some do not. To use the Pavlovian example, this boundary might represent a discrimination in auditory feature space between bell and non-bell sounds.[94] In order for this discrimination to be meaningful, we need more than the experience of the bell; we also need the experience of non-bell (otherwise the dividing line would not actually do any dividing). In other words, if everything in the world was a bell, then a bell could not be effective as a stimulus.

Early models of neurons such as the Perceptron are often biologically inaccurate in light of current knowledge. One of the most obvious inaccuracies is the mapping of single neurons to single concepts. Current research indicates that concepts have a distributed representation in the brain. In other words, there is no single neuron that corresponds to the concept “apple” : rather, the concept “apple” has a distributed representation across a large number of neurons. So, even though concepts may be atomic from a conceptual point of view, they have distributed physical representations.

[88] Historically, examination of internal states could not be done objectively as it could only come from subjective report: behavior, on the other hand, can be directly observed and verified by multiple observers. In an age when we are able to directly observe much of what is going on inside a subject's head with various machines, this restriction of the field of study is less warranted.

[89] Talking of concepts violates the behavioral dictum of treating organisms like black boxes. On the other hand, limiting the examination of subjective experience to concepts does not venture arbitrarily far into the territory of subjective report. Further, from a nominalist point of view, behaviorism is already a subjective science in that the CS is a single object only in virtue of being unified in the mind of an observer. In any case, the formalism presented here is an attempt to open the Pandora's box of subjectivity without unleashing complete pandemonium.

[90] In these studies, salivation is the unconditioned response to the unconditioned stimulus (eating food). The bell acts as the conditioned stimulus; by ringing it just before food is served, it comes to elicit salivation (the conditioned response).

[91] Punishment and reward occupy a single dimension from a cognitive perspective. From a physiological perspective, they may be mediated by different mechanisms (neurons, neurotransmitters, etc.).

[92] The strength of the connection is determined by this likelihood, or the correlation of the conditioned stimulus with the unconditioned stimulus. In fact, there is a significant difference here between the correlation of the conditioned stimulus and the unconditioned stimulus, and the informative value of the conditioned stimulus. In particular, the presentation of the conditioned stimulus, if it is not followed by the unconditioned stimulus, will weaken the association between these two stimuli. However, the presentation of the unconditioned stimulus, when it is not associated with a prior presentation of the conditioned stimulus, will not weaken the association.

[93] Incidentally, this division of neurons into layers appears to mimic the organization of the visual cortex. The visual cortex consists of layers at the back of the brain stacked like five or so pancakes; neurons in one layer receive input from previous layers and project their output to subsequent layers.

[94] The type of discrimination that we have shown above is very simple: it is a line. It generalizes easily to multiple dimensions: in three dimensions, it is a separating plane, and more generally, it is known as a separating hyperplane. There are numerous other types of basis functions: in two dimensions, sigmoids (or s-shaped curves) and radial basis functions (which select circular groups) are commonly used.