Anderson, R. L. (2015): Empirical concept formation and the systematic role of logical division

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  author = {Anderson, R Lanier},
  title = {Empirical Concept Formation and the Systematic Role of Logical Division},
  booktitle = {},
  shorttitle = {Empirical Concept Formation and the Systematic Role of Logical Division},
  editor = {},
  publisher = {Oxford University Press},
  address = {New York},
  pages = {333-372},
  year = {2015},
  file = {~/Library/Mobile Documents/iCloud~com~sonnysoftware~bot/Documents/be-library/anderson2015-ch13_empirical_concept_formation_and_the_systematic_role_of_logical_division.pdf},
  doi = {},
  url = {},
  langid = {},
  abstract = {The poverty of conceptual truth’ is based on a simple idea. Kant’s distinction between analytic and synthetic judgments underwrites a powerful argument against the metaphysical program of his Leibnizian-Wolffian predecessors-an argument from fundamental limits on its expressive power. In that tradition, metaphysics promised to reveal the deep rational structure of the world through a systematic philosophy consisting of strictly conceptual truths, which flow from a logically perspicuous relation of ‘containment’ among concepts. That is, all truths would be ‘analytic,’ in Kant’s sense. Kant’s distinction shows to the contrary that far reaching and scientifically indispensable parts of our knowledge of the world (including mathematics, the foundations of natural science, all knowledge from experience, and the central principles of metaphysics itself) are essentially synthetic and could never be restated in analytic form. Thus, the metaphysics of Kant’s predecessors is doomed, because knowledge crucial to any adequate theory of the world cannot even be expressed in the idiom to which it restricts itself (and which was the basis of its claim to provide a transparently rational account of things). Traditional metaphysics founders on the expressive poverty of conceptual truth. To establish these claims, R. Lanier Anderson shows how Kant’s distinction can be given a clear basis within traditional logic, and traces Kant’s long, difficult path to discovering it. Once analyticity is framed in clear logical terms, it is possible to reconstruct compelling arguments that elementary mathematics must be synthetic, and then to show how similar considerations about irreducible syntheticity animate Kant’s famous arguments against traditional metaphysics in the Critique of Pure Reason},
  keywords = {Kant, Immanuel; Metaphysics},

Three challenges for an account of empirical concept formation:

  1. Circularity
  2. Generality
  3. Empirical Constraint

Two other puzzles:

  1. Fixing identity conditions for concepts
  2. The relation between concept hierarchies and theoretical systematicity


The circularity problem seems to hinge on taking JL Logic §6, Ak. 9:94-5 as canonical, and also ignoring the difference between acquaintance, which Kant thinks is (or grounds) the ability to discriminate between similar and different things, and cognition, which kant thinks is (or grounds) the ability to grasp the basis of similarity and difference.

In my view, neither of these is tenable. This is especially clear with the acquaintance/cognition distinction, since if the circularity problem were a problem for Kant there would be no way for him to explain how it is that non-human animals are able to distinguish objects on the basis of similarities and differences, since these would all presuppose conceptual abilities. This suggests either that Kant thought association provided resources to resolve the problem, or that he thinks of conceptual representation in a more demanding way. My hunch is that the latter is correct.


Anderson approvingly cites Ginsborg’s connection of Kant’s conception of generality (Allgemeinheit) to Wittgenstein’s rule-following probelm:

the problem of attaining conceptual generality belongs with well-known puzzles concerning such rules. Any finite series of given perceptions is bound to remain compatible with more than one possible rule for extending it. How, then, can we move from a finite induction base of sensory inputs to a concept with full generality, which must serve as a rule determining the concept’s extension not just in the given instances but far beyond them, for an indefinite number of instances? [@anderson2015, 342]

This seems to me to only be correct if Kant conceives of generality in terms of repeatability, but why think this? Perhaps instead Kant conceives of generality in terms of systematicity of some kind.

Anderson also falsely links rule-skepticism (i.e. meaning skepticism) with the problem of circularity.

if one already had a general empirical concept defining the relevant class, then that concept would impose “distributive unity” on its instances; that is, it would determine, for each of the indefinite range of potential instances, whether it fell into the extension of the concept or not (see B 40, A 644/B 672). So the unity of the indefinite class could easily be secured if the general concept could be presupposed. But if the task is to form the concept in the first place without circularity, by “moving up” from the instances to the general representation, then the rule-skepticism associated with the generality problem threatens. (343)

But rule-skepticism threatens meaning, it only thereby indirectly threatens any particular account of how meaning are acquired/learned.

Also, it doesn’t seem to me that Kant provides an explanation of what Anderson calls “commonality” (344), which is that we all mean the same thing by our use of a term. Kant seems to think that there is a right and wrong answer tot eh question of what a concept analytically contains, and that this is not determined by why a particular subject associates with a concept.

In general I find the entire line of thought that sees Kant account of concepts as supposed to resolve the ‘commonality’ issue and to show how a concept is applied in every possible circumstance totally implausible. The latter especially is clearly a function of the power of judgment.

Corrigibility (i.e. Empirical Constraint)

Here’s Anderson’s statement of the problem:

The issue concerns how the contents given via sense can constrain the content of concepts, and it raises a challenge for non-conceptualist readings, paralleling the circularity difficulty for conceptualists. The general demand of corrigibility is straightforward. Any plausible account of empirical concept formation needs to explain how sensory experience can be deployed to correct our emerging concepts. (348)

Obviously one problem here is with the conception of ‘content of sense’ that Anderson uses.

Putting that aside, I think I disagree with the general motivation for the position—that “experience should serve as a normative constraint on conceptual content (350).

Anderson’s Positive View

Anderson presupposes a conceptualist reading of the Deduction, and concludes that all perception depends on categorial synthesis. His reading seems to conflate ‘intuition’ and ‘perception’ as distinct mental kinds or acts. He then uses his conceptualism to motivate his positive view:

The initial proposal, then, would be that empirical concept formation secures its conceptual presuppositions by deploying the categories in a special role; the categories inject the wanted conceptual structure into experience without presupposing empirical concepts. (357)

Note that Anderson could hold this view even if he rejected conceptualism about intuition, since perception and experience rely on categorial synthesis.

Anderson then argues (358-61) that the proposal can resolve worries about circularity by appealing to the fact that the categories and some high-level concepts (e.g. <matter>, <organism>, <plant>) can be appealed to in generating empirical concepts. I don’t see why any part of this strategy requires appeal to conceptualism.

On the picture I am sketching, the system of empirical concepts forms a logical structure that determines the content of concepts, in that a concept has its content in virtue of occupying a definite node in that network. Experience can shape the content of an empirical concept through corrigibility—i.e., by “bending” the shape of the network and changing relations within it to accommodate the experienced content.) As we just saw, the proposal entails that in the end, properly formed empirical concepts ought to be related to one another in a logical system. (361)

I think it uncontroversial that Kant takes us to aim at a single unified conceptual network. There are clear problems for unifying <matter> and <organism> in that account. But this is Kant’s problem and not Anderson’s. HE sums up:

an adequate account of concept formation will involve each of the key aspects involved in the present sketch: 1) a special role for the categories in constituting the objective structure of experience, making possible the representation of stable objective properties for reflection into empirical concepts (see CPJ, First Intro., Ak. 20: 212n); and 2) an interconnected “logical system” of such concepts, affording a structure against the background of which experiences can assume determinate significance for concept formation (see CPJ, First Intro., Ak. 20: 212n and 214–15, 216); along with, finally, 3) an assumption of (some degree of) uniformity in the content of experience itself sufficient for general concepts to have bearing on it, an assumption which Kant thinks must be underwritten through a (regulative) a priori principle (CPJ, First Intro., Ak. 20: 213) (366)

Anderson addresses the issue of generality as follows:

the strategy does not need to extract conceptual generality from the radically particular contents of intuition and sense; on the contrary, empirical concepts are formed by using content gleaned from sense to specify higher concepts, and full generality is thereby communicated down, deriving ultimately from a priori sources in the understanding itself, as the faculty of general rules, with its Ur-concept (368)

Anderson resolves corrigibility by appeal to the holism of concepts. All general concepts admit of an in-principle further specification by lower concepts. This “exposes them to empirical correction and thereby endows all empirical concepts with an essential corrigibility” (369).

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