In his impressive and welcome paper, Barsalou is at pains not to throw out some cherished symbolic babies with the amodal bathwater. Many of these babies, in their best-known incarnations, are the progeny of classical symbolic logic; they include the notions of proposition, truth, and abstraction. B sketches how the work that such notions do in classical theories can also be done in his theory, and this involves casting these theoretical terms in a new light. B does not focus specifically on the notion of an individual, but it figures persistently in his discussion, and it is clear that he does not want to throw it out. But his theory implies that we should take a radically different view from that of classical modern logics as to what individuals (alias particulars) are.
The classical modern logical view (e.g. Carnap (1958)) assumes an objectively given domain consisting of individual objects, typically exemplified as concrete (e.g. the sun, the moon, the person Charles). It usually goes without saying that each object in the domain is distinctive, and not identical to any other object. Furthermore, the objects in the domain are taken as the most basic elements of meaning. This is evidenced in the postulation by formal semanticists such as Montague (1973) of e as a basic ontological type, the type of individual entities. How such objects are known or perceived by people is not the concern of logicians.
The logical form of a specific, elementary proposition uses individual constants as arguments of predicates, and emphasizes the different functions in the logical system of predicates and individual constants. When B begins to discuss propositions (section 3.2), his examples are such as ABOVE(ceiling, floor) and BELOW(floor, ceiling). Clearly, these are not the propositions envisaged by logic, because, without being dazzled by the change from upper to lower case type, and interpreting floor and ceiling in a natural way, these latter terms are predicates, and not individual constants. I can point to something, and say of it (i.e. predicate of it) that it is a floor. When students in an introductory logic class confuse predicates with individual constants, we penalize them. But in the long run, I believe, such students and Barsalou are right, and classical modern logic has got it wrong.
B writes ``Perceptual symbols need not represent specific individuals ... we should be surprised if the cognitive system ever contains a complete representation of an individual. ... we should again be surprised if the cognitive system ever remembers an individual with perfect accuracy.'' (Section 2.3.3) This again shows the contrast with the logical approach, in which there can be no question of the completeness or accuracy of an individual constant term in denoting an individual; relative completeness is out of the question because an individual constant term is atomic, and accuracy is given by the logician's fiat.
At his most careful, B speaks of ``perceived individuals'' or ``individuals in the perceived world'', and this is where his version of proposition is based. ``Binding a simulator with a perceived individual ... constitutes a type-token mapping. ... this type-token mapping implicitly constitutes a proposition.'' (Section 3.2.1) Thus, in the very act of perceiving something as belonging to some pre-established mental category, I can entertain a proposition, because my attention at the moment of perception is fixed on this one particular thing. The argument of the predicate is given by my attention at the moment. The numerical singularity of the argument comes from the bottom up, because I am attending to just one thing; the predication comes from a match between some perceived property of the thing and top down information about a pre-existing mental category. Thus, a Barsalovian proposition is formed.
The numerical singularity of a perceived object is a product of the observer's attention at the time of perception. An observer may focus on a pile of rice, or on a single grain, on a pair of boots, attended to as a pair, or on two separate individual boots. If I attend to two objects, simultaneously but individually (say a man and his shaving mirror), my perception of them as two individual objects at the time provides slots for two arguments, and I can find a pre-established 2-place mental relation (say USE) to classify the perceived event. (The limit on how many individuals one can attend to at once may be similar to the limits of subitization in young children --- up to about four items.)
A classic formal semantic model (e.g. Cann (1993)) might contain a set of individual entities, each satisfying the predicate ANT; the denotation of the predicate ANT is the set. Each individual ant is the denotation of some individual constant (e.g. a1, a2, a3, ... ) in the logical language. Thus, a1 and a2 are distinguished by the fiat according to which the logician constructs his model. The proposition ANT(a1) is a different proposition from ANT(a2); and no further distinction, for example by a predicate applying to one ant but not to another, is necessary in the logical system. The representation of the proposition in the logical language tells us which ant the proposition is about.
By contrast, in terms of perception, I can attend to certain properties of an object and judge from these properties that it is an ant, but the perceived properties cannot tell me which ant it is. I know that the world contains more than one ant, because I have sometimes seen many together, but all I know is that I have seen some ant. B's account of the storing of a basic proposition in long-term memory decribes it as involving a ``type-token fusion'' (4.1.5). This fusion is not described further, but it must in fact result in the loss of identity of the token, the ``whichness'' of the originally perceived object.
B is usually careful to prefix `perceived' onto `individual'. We can see how an individual can be perceived, but can an individual be cognized, and if so how? If individuals lose their ``whichness'' during the process of storing a type-token fusion in long-term memory, how can the perceptual symbols (the simulators) in my mind for an ant and for my mother differ in a way that echoes the classical difference between a set and an individual (or between a property and an individual concept)?
A cognized individual (as opposed to a perceived individual) can be constructed by the process involving the three mechanisms which B claims are central to the formation of abstract concepts, namely framing, selectivity, and introspective symbols. I have many experiences of my mother, and form a simulator allowing me to recognize her, and anyone exactly like her. But I am never presented with evidence that there is anyone exactly like her, despite the thousands of opportunities for such a person to appear. Whenever I perceive my mother, there is never anyone else present with exactly her properties. The same can be said of the sun, or the moon, which I also represent as cognized individuals.
This account accords well with B's account of abstraction: ``First, an abstract concept is framed against the background of a simulated event sequence'' (3.4.2) In the case of my mother, the event sequence is drawn from all my experiences of her. ``Second, selective attention highlights the core content of an abstract concept against its even background'' (3.4.2) The selected core content of the abstract notion of a cognized individual is that this particular simulator is sui generis, that one has never encountered two perceived individuals together fitting this simulator. ``Third, perceptual symbols for introspective states are central to the representation of abstract concepts'' (3.4.2) An introspective state involved in the abstract notion of an individual is comparison of percepts.
Consider, briefly, classic cases of the identity relation as expressed by Clark Kent is Superman or The Morning Star is the Evening Star. Each such sentence seems to express a proposition equating two different cognized individuals. Before Lois Lane realized that Clark Kent is Superman, she had two distinct cognized individual simulators. She always and only saw Clark Kent wearing glasses and a baggy suit in the newspaper office; and she always and only saw Superman flying through the air in his red and blue cape and catsuit. On the day when she saw Clark Kent become Superman, these two individual concepts merged into a single, more complex cognized individual. If, at some later date, she actually explained to someone, in English, ``You see, Clark Kent IS Superman'', she was not thereby reflecting two separate individuals in her own cognition, but collaboratively assuming that her hearer would not yet have merged the two concepts.
There is no space to explore the role which language plays in establishing abstract cognized individuals. The grammaticalization of deictic terms into definite determiners, such as English the, and the fossilization of definite descriptions into proper names, like Baker and The Rockies, have given us devices for expressing the abstract notion `individual'. The existence of stable cognized individuals in our minds, as opposed to merely transient perceived individuals, in terms of which B mainly writes, must be central to the ability of humans to ``construct simulations jointly in response to language about nonpresent situations, thereby overcoming the present moment'' (4.2).
Identity, individuals, and the reidentification of particulars are classic problems in metaphysics and the philosophy of language. Barsalou has articulated a view of cognitive symbols which, if developed, can shed valuable light on these classic problems.