20th WCP: A Kantian Interpretation of Demonstrative Reference

A. The Semantic Content of "This"

It has been suggested that Kantian intuition is analogous to the demonstrative term "This." According to Sellars, "to intuit is to represent a this." The demonstrative "This" provides a semantic model for Kantian intuition, but with some restriction. We can certainly apply the demonstrative "This" to individual items which are not proper objects of intuition, e.g., "This theory," "This thought," or "This proposition." The singularity of "This" is insufficient to characterize Kantian intuition. Since space and time are the forms of intuition, an intuitable object must have a spatio-temporal location. Hence, the demonstrative "This" is a semantic model for Kantian intuition only if it is "spatio-temporized."

We can spatio-temporize "This" by performing a demonstrative act. The type of a demonstrative act can be characterized by a "2-placed de re ostension" as suggested by Howell. The function of a de re ostension is to indicate the presence of an object in our perceptual field.

Pointing at an object with a finger is an example of a 2-placed de re ostension par excellence. Melnick suggests that Kantian demonstrative is operational in which "the use of demonstratives involves besides affection by or sensation of things, accompanying gesturing behavior." Our gesturing behavior (e.g. pointing) "exhibits" the ostent that we intend to designate. It is the pointing activity which induces spatio-temporal significance to the demonstrative "This."

The function of "This" is to indicate the presence of material reality that is immediately given to us. What is immediately given to us is something we can point at right here and right now. The intensionality of an ostensive act entails the indexicality of <Here, Now>. Hence, the demonstrative statement "This is " is operationally interpreted as "This ostent is at <Here, Now>." Kant's theory of space and time entails that <Here, Now> is not represented conceptually but intuitively. The intensional content of <Here, Now> is operationally characterized in terms of the subject's intuiting act. The intensionality of <Here> is not defined conceptually, but is represented by a "spatial behavior introduced by the subject." Hence, the operational form of "This" is the pure intuition of <Here, Now>.

B. The Topological Complexities of "This"

An intuitive representation is non-instantaneous. We cannot point at an object at an instant, no matter how fast we move. Kantian intuition is an extensive magnitude a mathematical quantity of a non-zero dimensionality. Spatial points and temporal instants are non-extensive magnitudes and thus not intuitively constructible. It follows from the extensivity of intuition that space is not made up of points and time not of instants. Space and time are continuous quanta space is made up of spaces, and time of times. The continuity of space and time is derived from the flowing nature of intuition. Pointing is an example of a flowing activity par excellence. As we pointing with our finger we trace a continuous path in space. Hence, the kinematic idea of a continuous path provides a topological model for demonstrative reference.

Notice that space and time are not separable in a continuous flow. A spatial path in aflowing construction has to be traced out successively in time. An ostensive act as a flowing activity stretches out not only in space, but also in time. The flowing nature of intuition induces temporality upon the intensionality of "This." Since spatial points and temporal instants are unintuitable, the intuitive content of <Here, Now> has to be characterized as a neighborhoodwhich consists of a spatio-temporal spread <s, t> where s and t are non-degenerate extensive magnitudes. An intuitive act is topologically complex it consists of what Kant calls a manifold of intuition a non-degenerate spatio-temporal manifold.

C. The Ontological Status of "This"

Kantian intuition can be characterized as a pre-conceptual mode of singular reference. The demonstrative "This," as pointed out by Melnick, "is ontologically neutral, involving no divided reference in Quine's sense." Since ostension does not fix the ontology, the referent of "This" is characterized as a pre-ontological intuitive manifold. Our motivation is to come up with an operational characterization of referent without any ontological commitment to what the referent is. The idea is this: the referent in the pre-ontological mode is operationally defined in terms of the ostensive act as a "spatio-temporal-something-that-is-being-pointed-at." More precisely, the referent located at < s, t> can be characterized as a function of the ostensive act, i.e., = (< s, t>). The ostensive act refers to by mapping < s, t> onto, i.e.: < s, t> . Since the ostent has to be present when ostended, the ostensive act is local its scope is restricted to the immediate perceptual field of the intuiting subject.

Our topological characterization of the referent induces an ontological reduction the referent is reduced to a mere topological manifold which is a function of the ostensive act is ontologically-neutral because a mere topological manifold endorses different ontologies. Hence, we withhold judgment regarding the ontological status of . In stead, we make the following conditional claim: if is intuitable then must be spatio-temporizable. We make no ontological assumption about , except that it is intuitable. It is ontologically more correct to characterize as spatio-temporizable than spatio-temporal because the spatio-temporality of is derived from an intuiting act. An intuitive manifold is a topological manifold. In taking an intuitive stance toward, the ontological status of is left indeterminate.

As long as is ostensible, it must be intuitable, and thus, spatio-temporizable. What we have is an operational characterization of: is capable of being spatially and temporally represented. Space and time are not objective properties of, but modes of topologizing . is not posited as a 1-placed item which exists in absolute space and absolute time. The ontological status of is "free" from absolute space and absolute time, and is thus compatible to Kant's doctrine of space and time being the forms of intuition. Hence, the ontologically indeterminate is the objective correlate to our spatio-temporizing ostension. is defined in relation to an intuitive act (2-placed), and hence not a thing-in-itself. Our intuitive stance toward is thus ontologically neutral.

In order to fix the ontology we need to implement the categories. As Thompson says, "An empirical intuition by itself is blind insofar as it is simply an amorphous sensory manifold requiring unification through concepts in order to become intelligible." The topological manifold ostended by "This" is not structurally rich enough to be a Kantian object. Melnick points out that Kant's notion of an object is "contributed by the understanding and is not a matter of intuition per se." An object for Kant is a construction which involves both intuition and concept. In order to have a full-fledged object the intuitive manifold has be synthesized.

Since the intended referent of an ostension is a single object, the ostent must constitute a single-coherent whole. In Kant's language: must have synthetic unity. The intuiting subject must somehow synthesize over time (an integrative procedure) in order for singular reference to be possible at all. Even if we grant this synthesizing power to the intuiting subject, this still does not guarantee that the manifold we are synthesizing actually belong to a single object. The subjective unity of my synthesizing act does not necessarily yield the objective unity of a single object. The objective unity of the ostent cannot be fixed by the subjective unity of an ostensive act alone. The repeatability of ostension to a single object presupposes the re-identifiability of the object. The identity of the object across time is presupposed in order for its ostensive re-identification to be possible. In order for the ostent to be re-identifiable at all, its identity must persist through time.

D. Tracking a Moving Object

Since an ostensible object in the physical world is not just stationary but mobile, we take into consideration that the spatial locale of the referent can change over time. What we want is to extend our demonstrative reference to moving objects. As an object moves it traces a continuous path in space. In order to intuit a moving object we must be able to track the locus of its path. As Howell points out, "objects appearing in intuition can be traced and described to their places in demonstrative space ..." If a moving object is intuitable at all, the locus of its path must be trackable. Hence, our strategy is to incorporate the tracking capacity in the referential scheme of demonstrative reference.

Keeping track of a moving object as a mode of intuition is a spatio-temporal procedure. It is impossible to track motion at an instant time enters as a parameter to measure the change of spatial location. Evans points out that "we have to regard the static notion of having hold of an object at t as essentially an abstraction from the dynamic notion of keep track of an object from t to t." In order to keep track of a moving object we need to maintain an affection-relation with the object across time we have to keep being affected by the object as we track its motion. In order to track a moving object successfully, the intuiting subject must be capable of performing a certain set of tracking-procedures. Consider the following situation: "Suppose that one is watching a scene in which there are several similar objects moving about fairly rapidly, but not so rapidly as to prevent one's keeping track of one in particular ... Our eyes and heads move, perhaps we are also obliged to turn or move our bodies, but these changes are required to maintain contact with the same object over time. So one's thought at a time is dependent upon an ability which is necessarily manifested over time." The tracking capacity enables us to shift attention from one spatial region to another (sweeping out) along a continuous path.

The capacity to shift attention from here to there is necessary for tracking a moving object. Evans points out that "there could not be thoughts interpretable as It's here', if they were not entertained by a subject who had the propensity to entertain, as he moves about, thoughts expressed in the words It is there'." It is impossible to track a moving object if the intuiting subject is unable to shift attention from one spatial region to another. A stationary and passive intuiting subject is inadequate for tracking a moving object, especially if the object is moving away from its perceptual field. In order to track a moving object successfully, the intuiting subject has to rotate and to move about.

The operational meaning of "This" in a demonstrative reference consists of the canonical form of "keep pointing and keep tracking the referent continuously along its locus." The form of a tracking procedure is a continuous spatial path a topological structure which is homeomorphic to the path traced by the finger movement in a local ostension. Hence, we can consider tracking as an extension of the finger movement a kinematized ostensive act. The truth-condition for a successful tracking is thus formulated as follows: a moving object is successfully tracked if and only if there exists a surjection from the path of a kinematized ostensive act onto the locus of the moving object, wherever the object goes. It is not possible to refer to a moving object demonstratively with an ostensive act unless the intuiting subject is capable of shifting attention and moving about.

The intuiting subject is situated locally in the world at <Here, Now>. In order to discover what is out there in the world the intuiting subject has to move away from its locale. Since we are locally affected by an affecting reality, our referential strategy is to "keep being affected locally as we move about." In order to represent the world we have to move about in order to get affected. Our intuitive representation of the world is thus synthetic what is out there is apprehended along a path successively across time as we move about.

E. Pathing Toward a Remote Object

Our intuitive contact with reality in experience is local the immediate presence of an object is required. Since we do not have immediate contact with what is beyond our immediate perceptual field, demonstrative reference in regard to spatially remote objects seems problematic.

Recall that an object is intuitable if we can establish an affection-relation with it. Affection is a local phenomenon I have an immediate relation with what affects me here and now. In order to extend the referential scope to remote objects, what we have to do is to extend the affection-seeking capacity of intuition beyond our immediate perceptual field. But how can that be accomplished without violating the immediacy condition for Kantian intuition?

The empirical objects within our immediate perceptual field are appearances which we can point at. But what about spatially remote objects? They are neither actual appearances (the remote objects have not "appeared" yet), nor things-in-themselves (the referent has to be 2-placed). The ontological status of spatially remote objects is problematic. Kant's transcendental analysis of the possibility of experience gives us a hint spatially remote objects can be considered as possible appearances. Our semantic consideration becomes modal as we extend the scope of singular reference from actual experience to possible experience. The modal extension of actual experience to possible experience induces two different senses of "object": "That an object be given ... means simply that the representation through which the object is thought relates to actual or possible experience" (A156/B195). Hence, the possible appearances which lie beyond our actual experience (our immediate perceptual field) can be considered as objects of possible experience.

An object of possible experience, i.e. a possible appearance, must be spatio-temporizable its presence is ostensible at a certain spatio-temporal locale. The remote object that I could encounter in a possible experience is an intuitable (spatio-temporizable) manifold which I could enter an affection-relation with. Poincar points out to localize an object is "to represent to oneself the movements that would be necessary to reach it." Although I am not presently affected by in my local-neighborhood, I can certainly shift my location to a different neighborhood by taking a walk such that I could obtain an affection-relation with. If I get close enough to where can be located and sensed, I could then obtain an immediate relation with there. In initiating this contacting activity, we shift our location such that would fall within our immediate perceptual field. Once we get affected by , we will then be in a position to point at (locally) and say "This."

My actual experience as indexed by <Here, Now> is situational it is functionally dependent upon my location. As I keep being affected along my walk I extend my actual experience at <Here, Now> to some possible experience at <There, Then>. Topologically speaking, as I move about I shift the spatial locale of my immediate perceptual field. My path shifts the indices from <Here, Now> to <There, Then>. Suppose is located at a locale < s, t> which is remote for an intuiting subject at <Here, Now>. Since the referent of a local ostension is defined as a function of its locale, i.e. = (< s, t>), our referential strategy is to shift the indices <Here, Now> to < s, t> such that intuiting subject will be in a position to locally ostend at < s, t>.

The indexical shift can be operationally realized by a continuous path taken by an intuiting subject. Our semantics provides an operational shift of indices by a continuous path , where shifts <Here, Now> to < s, t>. The intuiting subject's path transforms its local perceptual field at <Here, Now> to the remote perceptual field at < s, t> such that becomes locally ostensible at < s, t>. Hence, is defined as follows: = ((<Here, Now>)), where (<Here, Now>) designates the location of, i.e. (<Here, Now>) = < s, t>. This formulation is an extension of local ostension by means of a continuous path, and we will call this a non-local, or global ostension.

But there is a further complication. Since could occupy different locations in its career, there are many possible situations in which the intuiting subject could locally ostend . Hence, we take into consideration all possible locales of in its career. We will call the locales of all possible appearances of a neighborhood-bundle N, defined as follows: N= {< si, ti>: can be locally ostended at < si, ti>}. Now is ostensible as long as there is a path which connects the intuiting subject to any local neighborhood in N. In other words, the intuiting subject can be connected to if there exists a path which shifts the location of the intuiting subject at <Here, Now> to some < si, ti>, where < si, ti> N. That path of an intuiting subject establishes a connection with a remote object. Hence, is ostensible via a connecting path.

The intuitive scope of demonstrative reference is globalized as we shift our location. In moving about, we put ourselves in a position to point at objects which are not immediately ostensible in our previous situation. The extension from local to global ostension is thus conservative with respect to affection-relation we continue to maintain an immediate relation with the referent as we move along in our path. Our path functions as what Marcus calls "the long finger of ostension." We are able to refer to spatially remote objects as we move along, yet without violating the immediacy condition. In taking a path, we find a way to represent the world.