kant’s first analogy

Kant’s first analogy is an argument connecting change with substance. A substance is a subject that is not a predicate of anything else, and when this concept is schematised it is assigned the temporal property of permanence. This generates a two-fold equivocation: the schematised concept does not apply univocally to either noumenal substance (which is outside time) or phenomenal substance (which ultimately remains a predicate of something else). For example, we may call the rainbow “appearance” and the rain “thing in itself”, but this is only comparatively speaking (A45/B63). In any case, this is a layer of complexity I am going to abstract away from here. I will focus primarily on James Van Cleve’s reconstruction of Kant’s argument.

The first analogy says: every change is an alteration of some substance. Van Cleve offers the following analysis:

  • Substance1 = bearer of properties + not a property of something else
  • Substance2 = exists at all times (i.e. schematised concept)
  • Substance = substance1 + substance2
  • Change = coming into or going out of being
  • Alteration = change of properties or determinations of a substance

Note that the last definition (of alteration) ascribes being to properties. This is Kant’s definition (A32/B48), which Van Cleve quotes, whilst providing his own slightly different gloss: for him an alteration occurs when a substance “acquires” or “loses” a property (p. 107). Defining alteration in terms of change is problematic if the goal is to offer a eliminative analysis of change. But is it possible to understand the occurrence of an alteration, the acquisition or loss of a property, without the concept of change? That is the question which it seems to me is left unaddressed in Van Cleve’s account.

Van Cleve holds that Kant is committed to the so-called Kant-Frege view (p. 117):

To say that something exists is to say that some concept is instantiated. 

The idea is that given this view it is hard to see how there could be changes that are not alterations of substance, i.e. hard to deny the first analogy. For any thing x to exist it is necessary (and sufficient given the Kant-Frege view) that it have some property or other. Minimally, we cannot say that x ceases to exist by its losing a property essential to it (specifically, the property of having properties), since that is in effect to say that there is a propertied x with no properties. Rather, x ceases to exist when something else loses a property essential to the existence of x. In other words, there cannot be change without alteration of substance.

From here Van Cleve goes on to make an interesting observation. What the Kant-Frege view really excludes is the possibility of change per se. That is, change is not really reduced to alteration, in the sense of being e.g. supervenient upon it; but rather eliminated altogether. There are only alterations (p. 117). However, alteration is characterised by Kant in terms of change, and thus in terms of being. This suggests that properties have being for Kant, so that alteration is the passing into and out of being of properties. However, this cannot be correct if Kant accepts the Kant-Frege view. Given the latter, we cannot say that e.g. the blush no longer exists, since that generates the same problem we are trying to escape from by translating talk of change into talk of alteration (on this reading). There is thus no change in alteration. If, however, there is no change in alteration, what is alteration? How to understand the acquisition of a property by a substance, for example in the case where John is not blushing at T1 and blushing at T2, without incurring commitment to the contingent being of the blush? Put rhetorically, how could there be alteration without change?

Since alterations are modes, Van Cleve himself gives the answer later in his book (p. 197):

Modes must… be accorded the status of mere constructions, not to be quantified over in an ontologically perspicuous language.

That is to say, if we are being ontologically perspicuous, then there is no alteration.


  • James Van Cleve, Problems From Kant, (OUP: 1999).
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