Part III: Synthetic Judgments (Overview)
- Analytic and Synthetic Judgments
- Synthetic Judgments a posteriori and empirical intuitions
- Synthetic Judgments and construction of ideal objects by way of a priori intuitions (space and time)
- Results for the Ontological Status of Bodies and the Scientific Status of Physics
Synthetic Judgments (a priori and a posteriori)
Starting from the possibility of experience—understood as empirical knowledge of objects—we can see what Kant means in distinguishing between analytic judgments and synthetic judgments.
Analytic judgments start with some concept and articulate one or more of the characteristics that we use to ‘pick out’ any of the (indeterminately many) objects that are referred to by that concept (or that are subsumed under the concept).
- The judgment ‘water is clear’ is analytic, assuming we already understand that water is a clear liquid; i.e., if we use the description ‘clear liquid’ as a way of determining that some object = x that we come across in the course of our experience is water.
- The judgment ‘gold is a metal’ is analytic, assuming we already understand that gold is a yellow metal; i.e., if we use the description ‘yellow metal’ as a way of determining that some object = x that we come across in the course of our experience is gold.
Synthetic judgments involve attributing some property to one or more of the objects that are subsumed under some general concept = X in cases where this property is not already attributed to all objects of that kind as one of the characteristics that we use to ‘pick out’ these objects.
- The judgment ‘this water is cold’ is synthetic, assuming that what we understand about water does not tell us anything specific about its temperature; i.e., if the description of the characteristics that we use to identify some object = x as water does not include the term ‘cold’.
- The judgment ‘gold is rare’ is synthetic, assuming that what we understand about gold does not tell us anything specific about its prevalence in nature; i.e., if the description that we use to determine that some object = x is gold enables us to do this without any appeal to a concept of rarity.
We can also see how synthetic judgments that we justify by appeal to our actual experience (synthetic a posteriori judgments) operate.
- My sensible awareness of the changes in my body when I put my toe in this particular bath of water (i.e., my intuitions in relation to the given individual that I subsume under the concept ‘water’) allows me to determine something about it that is left indeterminate by the general concept. The connection between the concept ‘water’ and the concept ‘cold’ in my judgment ‘this water is cold’ is justified by way of actual sensible intuitions that are simultaneously intuitive representations of water and intuitive representations of something cold.
- My experience (or my learning from the experience of others) concerning the various naturally occurring metals and their distribution across the earth allows me to determine something about gold that is left indeterminate by the concept of it as a yellow metal. Here, the intuitive representations that lead to claims about different kinds of metals are necessary for our empirical judgments—i.e., we have to have the synthetic judgments that determine that there are yellow metals and there are grey metals and there are black metals. Then we need to determine the relative frequency of individuals of these various kinds—which also involves intuitive representations that go beyond the mere concepts of the things we are investigating.
What we don’t yet see is how we can make judgments that are synthetic, but that we justify by appeal to something other than our actual experience (either my own empirical judgments or the complex system of empirically grounded judgments that constitute empirical sciences). The main question that Kant sees Hume’s challenge raising for metaphysics is: How are synthetic a priori judgments possible?
Part of Kant’s answer can be understood by returning to the discussion of analytic and synthetic methods in geometry that we started in discussing Descartes. That is, we can analyze existing areas of a priori knowledge (like geometry and the mathematical part of natural philosophy, aka, pure physics), to determine what it is that allows us to make synthetic claims with demonstrative certainty there. The answer, in Kant’s view, involves recognizing that the constructive activities through which geometers and physicists provide models that can be used for their analytical purposes (i.e., demonstrations that proceed logically, i.e., via the law of non-contradiction) involve us in the use of formal ontological concepts (categories) as well as formal intuitions (space and time). If we couldn’t imaginatively represent a space (as a region of the space) and determine that region of space through the construction of an ideal thing, we couldn’t then ‘look’ at that thing and derive cognition concerning its features through analysis. Similarly, if we couldn’t start with the empirical concept of matter, and then ‘apply’ geometrical considerations to determine the formal features of bodies (qua existing things that fill space and that change spatial dimensions and locations), we couldn’t have knowledge of the mathematical laws governing the motion of bodies that we have. A priori (i.e., demonstrative and certain) knowledge in mathematics and physics requires both a priori intuitions and a priori concepts.
The drawback of this kind of answer, however, is that it is incomplete as a response to the question. If it’s right, it shows that synthetic a priori judgments are possible (because we actually do make them), but it doesn’t show how they are possible. The Prolegomena proceeds analytically to the discovery of these kinds of judgments, but the account of their possibility has to proceed synthetically from the elements of judgment we discover in this way to the construction of the kinds of judgment and cognition that these elements make possible.
Results of this view of Synthetic a priori Judgments in Geometry and Physics for the Ontological Status of Bodies
This means that Kant agrees with Leibniz, against Descartes and Spinoza, concerning the idea of body as geometrical extension. It does not constitute a purely intellectual idea of a substance; i.e., the primary attribute of something that exists in itself and can be conceived through itself. Instead the representation of body as extended in three dimensions requires the intuitive representation of space provided by the imagination. Considered purely geometrically, there is no distinction between body and space–to represent a particular kind of body geometrically is just to imagine a particular way of determining some part of space; i.e., it is a way of introducing a distinction, within the imagined whole of space, between the space internal to the body and the space external to the body. The particular physical bodies we come across in nature, according to Kant’s somewhat Leibnizean view, are not extended substances (they don’t exist in themselves); nor are they composed out of extended substances (physical atoms); nor are they finite modes of the infinite extension of the one extended substance (Descartes and Spinoza). If they were, Kant claims, it would impossible to explain how the a priori knowledge we have concerning the formal features of bodies could hold of those bodies in themselves (at least, without bringing in some less than certain claims about God creating our minds and creating our bodies–which might explain that, but not how, this fit between our representations and their objects is achieved.)
Bodies are well-founded phenomena, which require a grounding in the causal powers of some thing-in-itself that we cannot have any direct knowledge of, but that we can think indeterminately through the intellect as the supersensible (or non-empirical) substrate of the sensibly discovered capacities and states of bodies. This is a central feature of Kant’s Transcendental Idealism, which derives some of its argumentative support from its ability to articulate how pure mathematics can be applied to empirically given bodies, through geometry and physics, in ways that secure the scientific status of the new approach to natural philosophy initiated in the modern period.