Kant had stated in the Deduction that appearances need not conform to the thought-forms of the understanding: "The categories of the understanding . . . do not represent conditions under which objects are given in intuition. Objects may, therefor, appear to us without their being under the necessity of being related to the functions of understanding; and understanding need not, therefore, contain their a priori conditions" (A89/B122). Mere appearances and pure categories have nothing in common, or in Kant's terminology are "heterogeneous". Appearances give us an unconnected manifold, while the categories are such general concepts that by themselves they do not determine any object. Thus, Kant called for a mediating element which would connect the pure concepts with appearances.
"This mediating representation must be pure, that is, void of all empirical content, and yet at the same time, while it must in one respect be intellectual, it must in another be sensible" (P. 181).
Kant claimed that there is only one way in which such a mediating element can be discovered, that is, by examining the single element which is present in all appearances, but at the same time is capable of being conceptualized: time. We must therefore discover various ways of thinking of time, and if we can discover the ways in which this must be done, we can say that they both conform to the conditions of thought (categories) and are present in all appearances. Kant calls these conceptualizations of time "schemata". "The schemata are thus nothing but a priori determinations of time in accordance with rules" (p. 185).
Not surprisingly, Kant found four fundamental modes of thinking time, one corresponding to each of the basic divisions of categories.
1. time-series, 2. time-content, 3. time-order, 4. scope of time.
Time-series. As a one-dimensional object, time is essentially successive: one moment follows another. Now in order to think time as a succession (rather than intuit it), we must generate the time-series -- we must think one moment as following another. At each point of the series up to that point (e.g. an hour or a day). Thus we always think time as a magnitude, and "the pure schema of magnitude (quantitates), as a concept of the understanding, is number, a representation which comprises the successive addition of homogeneous units" (p. 185). Since the categories of quantity are those of unity, plurality and totality, we can say that they apply to appearances in that all appearances must be thought as existing within a specific time- span which can be thought as momentary (unity), as a series of time spans (plurality) or as the completion of a series of time spans (totality, e.g., an hour as composed of sixty minutes).
Time-content. This is one of the fuzzier treatments, but we will have a go at it. The basic idea is that we can think of a given time as either empty or full, i.e. as having objects existing during that time or as having no objects so existing. In order to represent objects in time we must resort to sensation, so that in thinking a time we must always ask whether (and to what extent) that time is filled up.. Thus the schema of quality (which includes the categories reality, negation and limitation) is the filling of time. It would be natural to assume that the question whether-a time is full admits of a simple answer of yes or no. However, Kant claimed that reality and negation (complete filling of time and complete emptiness of time) must be conceived as two extremes or limits, between which exist infinitely many degrees. These degrees, which Kant calls "intensive magnitudes," may be illustrated by the brightness of alight source. Kant's real motivation for introducing this schema is its use in physics. He believed that as an object of physics, a body is composed of forces which vary in degree of intensity. We will return to this topic.
Time-order. The schemata for the categories of relation are treated separately. The reason for this is that unlike the mathematical categories which treat space and time in isolation, the relational categories treat them in respect to one another. Time considered of itself is successive but not simultaneous, and space is simultaneous but not successive. Thus there exist several ways in which we might think objects in a time-order.
1. as enduring through a number of times.
2. as in one state of affairs which succeeds another.
3. as co-existing with other objects.
The first of these time-determinations of objects is that of the permanence of substance, as "abiding while all else changes" (A143/B183).
The second is the schema of causality, that is, we think the states of substances as occupying a succession of times, in accordance with a rule.
The third is the schema of reciprocity or mutual simultaneous interaction. Here Kant really has in mind the Newtonian conception of the mutual attraction of bodies.
Scope of time. This is supposed to relate objects, not to one another, but to the understanding. That is, we can think an object in one of three ways.
1. as occupying some time or other, without specifying what part of time.
2. as existing in some definite time.
3. as existing at all times.
The first is the schema of possibility. We can think an object as possible in so far as we can think it as occupying some time or other, whether or not it actually occupies it.
The second is the schema of actuality. We think an object as actual when we claim that it exists in some specific part of time.
The third is the schema of necessity. An object is thought as being necessary if it is something which we must represent as occupying all times, in other words, that we could not think of a time which does not contain that object.