Defeasible Rules and Subsumption

If the rules that our concepts supply are defeasible in ways that are not encoded or anticipated in the rules themselves, then it seems that consistency in judgment – or, in Kant’s terms, agreement or unity – cannot be secured by subsuming particular cases under such rules. Consider how we might try to secure consistency in the Apple Tree case.

P1 If x is an apple tree, x has a completely impenetrable trunk.

P2 This is an apple tree.

C This has a completely impenetrable trunk.

If the rule in P1 is defeasible, if it holds in some but not all cases, then the inference

is formally invalid: the conclusion does not follow from the premises.159 So from the

point of view of those who accept the subsumptive conception of rationality, those who think that there is no consistency without formally valid inferences, our account of conceptual rules as defeasible must look problematic. But, as we will see, the sub- sumptive conception is not without alternatives. It is not the only way to make sense of Kant’s idea that we “cognize the particular in the universal through concepts” in order to secure “the highest unity of thinking” (CPR A299-300/B355-357).

Note that the subsumptive conception of rationality rests on an assumption. It assumes that, in saying “This is an apple tree”, I am not committing myself to any claim about the penetrability of its trunk. For if I did, if, in thinking “This is an apple tree”, I already thought “This has an impenetrable trunk”, then I would not need P1

to derive C from P2. So, according to the subsumptive conception, P2 (even when

combined with the claim that the circumstances are objective suitable) does not entail C. Instead, whether C is true is independent of whether P2 is true, each being a matter of

whether they correctly represent the properties of the object referred to. Knowing the rule in P1 might make it easier to figure out whether the trunk-part of the object

159 _{At this point, we might be tempted to add a hedging clause and restate the rule such that it does}

hold in all cases after all, e.g. as follows: “In objectively suitable circumstances, if x is an apple tree, x has a completely impenetrable trunk”. In that case, one would need a further premise to reach a determinate conclusion about whether one’s judgment about a particular (“This has a completely impenetrable trunk”) is consistent with one’s other judgments. One would need the premise that the circumstances at hand are objectively suitable. However, the rule itself provides no criterion on the basis of which one could decide whether a set of circumstances is objectively suitable or not. So this hedging strategy does not seem to get us closer to our goal.

in front of me is penetrable if I already know that it is an apple tree and cannot be bothered to touch it, or it might help me to predict what I will feel if I touch it, but none of this is required for either of the judgments to be true or objectively valid.

This assumption is in direct opposition to Kant’s view, as outlined in sect. 2.1 above. Recall that, according to Kant, we can only make objectively valid judgments, judgments that refer to and are true of objects, because we intuit and cognize these ob- jects through concepts, such as the concept of an apple tree, which, all by itself, serves as a rule, allowing me to infer what else can, cannot or must be true of an object that falls under it, given the circumstances in which it is embedded.160 This view, the view

that inference comes before reference, is a view that Kant shares with so-called infer- entialists in the theory of meaning.161 For this reason, it should not come as a surprise

that it is in their writings that we find an account of how defeasible rules can figure in valid inferences that secure consistency in judgment.

According to inferentialists, we have to extend the inferential role account of meaning, which is usually taken to cover logical terms only, to non-logical terms, i.e., to terms whose meaning is usually understood in referential terms (see e.g. Peregrin 2014: 25). Consider the material conditional as an example. There is broad agreement that the meaning of the material conditional can be articulated by saying that “If x is

160 _{Kant makes this point over and over again. He says, for example, that an “object is no more than}

that something, the concept of which expresses such a necessity of synthesis” (CPR A106) and that

“an object is that in the concept of which the manifold of a given intuition is united” (CPR B137).

Some commentators have read these remarks as indicating that Kant is a phenomenalist. James Van Cleve, for example, moves from the claim that “Kant defines an object as something the concept of which

plays a certain role” – a claim I agree with and highlight above – to the claim that Kant endorses a “reductive account of objects”. On this account, “to say that there is an apple before me is equivalent to saying that I am having certain sorts of experiences (intuitions), and that if I (or other observers simi- larly placed) were to perform certain actions, they would have further experiences of predictable sorts” (1999: 92-3). What Van Cleve is missing here is the normativity that concepts bring into the picture. To apply a concept, e.g. to say that the object before me is an apple, is not to predict that, if I perform certain actions, I will havecertain experiences, but to say that, if I perform these actions, I

ought to have these experiences, and that, if I don’t, something must have gone wrong. As I said earlier,

this is precisely how concepts make it possible for us to have experiences of objects.

161 _{The view that Kant is an inferentialist has recently been defended by David Landy (2015). Landy}

argues that this reading allows us to make sense of Kant’s case against Hume. In his view, Kant raises two objections against Hume’s theory of representation, namely, first, that Hume cannot account for the possibility of representing complex states of affairs as complex (Landy 2015: 62) and, second, that he cannot account for the unity of the proposition (2015: 91-2). Landy shows that, given these points of criticism, it is only be interpreting Kant as an inferentialist that we can see how his own theory of representation solves the problems that he finds in Hume. On this reading, Kant thinks of concepts as rules or functions that place intuitions in inferential relations, thus locating them in an inferentially structured system of cognitions (Landy 2015: 64-80, 92-101). Landy’s reading is inspired by Wilfrid Sellars’ reading of Kant and his talk of counterpart relations (see Sellars 1968: 26-30, 63-67). For other inferentialist readings of Kant, see Rosenberg 2005: 91-4 and O’Shea 2012: 128-32.

F, then x is G” is false, unless whenever “x is F” is true “x is G” is true as well. But many philosophers would argue that this is not how we should articulate the meaning of terms such as “apple tree”. Instead, they would suggest articulating the meaning of “apple tree” by citing the conditions that have to obtain in order for the claim “x is an apple tree” to be true. Here inferentialists disagree. In their view, we can articulate the meaning of “apple tree” by saying things like the following: in objectively suitable circumstances, “x is an apple tree” is false unless “x has a completely impenetrable trunk” is true.162 To say that the meaning of both logical and non-logical terms consists

in their inferential role is to say that inference (2) below is just as self-contained as inference (1), that it is not an enthymeme, and that we should not assume that there is some additional premise that has been omitted (see Sellars 1953, Brandom 1994: 95-105, 2000: 52-4, Peregrin 2014: 27-9).163

(1) If x is F, then x is G. x is F.

Therefore, x is G. (2) x is an apple tree.

Therefore, x has a completely impenetrable trunk.

If we think that (1) is valid as it stands, then this is only because we take the meaning of “if ... then ...” to be fixed. By the same token, we can treat the meaning of “apple tree” as fixed and regard (2) as valid and self-contained. Following Wilfrid Sellars (1953), inferentialists call the rule underlying (1) a formal rule of inference and the rule underlying (2) a material rule of inference. We need to highlight two implications of this broader conception of rules of inference.

The first concerns the issue that brought us here: the nexus between being an apple tree and having a completely impenetrable trunk is defeasible, so if we call the rule governing the inference in (2) a rule of inference,164 then we have to abandon the

idea that rules of inference are generally indefeasible. (However, as inferentialists are keen to emphasize, we might have good reasons to abandon this idea anyway, even

162 _{This, of course, is just a different way of saying what Kant says: that concepts serve as rules.} 163 _{In fact, according to inferentialists, if we thought that (2) relied on an implicit premise (as stated by}

Bertrand Russell in his 1914: 66), we would ultimately face the same infinite regress that Lewis Carroll (1895) cautioned against when reflecting on formal inferences such as (1).

when it comes to purportedly bulletproof rules of inference such as the rule in (1), i.e. modus ponens (McGee 1985)). Relatedly, we must abandon the idea that good inferences, i.e. inferences by means of which we can “cognize the particular in the universal” and thus secure consistency in judgment, have to be indefeasible, that they must survive the addition of any further premise whatsoever. I believe that we can abandon this idea. Recall what it takes for a judgment about a given particular to be consistent (in agreement, in unity) with our other judgments: it must fit in with what we know about objects of this kind. Note, further, that understanding which premises render a material inference (e.g. (2)) invalid is part of understanding the inferential role of the relevant term (e.g. “apple tree”). Thus, for an inferentialist, articulating the meaning of (at least) ordinary, non-logical terms, such as the term “apple tree”, is a matter of “construct[ing] ... inferential hierarchies with oscillating conclusions like [the following]” (Brandom 2000: 88).

(2) x is an apple tree. Therefore, x has a completely impenetrable trunk.

(3) x is an apple tree. And x has become the nesting site of a woodpecker. There- fore, x does not have a completely impenetrable trunk.

(4) x is an apple tree. And x has become the nesting site of a woodpecker. And x has been patched up by a gardener. Therefore, x has a completely impenetrable trunk.

Etc.

This hierarchy expresses some of what we know about apple trees, namely what we know about the penetrability of their trunks, and therefore it is only in light of this hierarchy as a whole that a judgment about the penetrability of a particular apple tree trunk can be assessed for consistency.

With this in mind, we can restate a point from sect. 2.2 above in inferentialist terms. There we observed that the woodpecker exception is an exception that does not erode the distinction between objective and merely subjective combinations of the manifold of sense, because it is an exception that is intelligible from within the relevant system of rules as a whole. Now we can give the same explanation of why this exception is innocuous, albeit in slightly different terms: it is innocuous because the rule that “having become the nesting site of a woodpecker” is a defeater is part of

our shared understanding of the term “apple tree”, part of the meaning of this term. As such, it binds anyone who uses it. It is, in other words, not up to the individual user to treat this feature as a defeater. They ought to treat it as such, no matter what subjec- tive condition they are in (no matter if they have taken drugs or if they are having hallucinations, etc.).

The second implication of the view that the inferential role account of meaning should be extended to non-logical terms is that there is no sharp distinction between analytic and synthetic truths, at least not in the contemporary sense. In the context of an interpretation of Kant, this might seem particularly problematic, given that he is the one who first introduced the distinction. The attempt to examine this implication in full detail would take us far beyond the scope of this thesis, but let me indicate how one could go about overcoming this concern. To begin with, we should note that, for Kant, the difference between analytic and synthetic judgments is not that the former are made true by language, while the latter are made true by the world. Instead, he defines analytic judgments as those where “the predicate B is (covertly) contained in [the subject] concept A”, and synthetic judgments as those where “B lies entirely outside ... A, though to be sure it stands in connection with it” (CPR A6). This way of understanding the analytic-synthetic distinction leaves open the possibility that the manifold of sense (the “world-element”) enters into cognition not only as material that we synthesise in accordance with ready-made concepts (as a “truth-maker”),165

but also as something that shapes the formation of concepts (Sellars 1953: 336-7).166

Accordingly, we can attribute a given nexus, e.g. the nexus between apple trees and completely impenetrable trunks, to the world, without having to deny that this nexus has made its way into our language and become part of our shared understanding of a term.167 The judgment expressing this nexus will be synthetic, in Kant’s sense, if it

165 _{Strictly speaking, we should not use the term “truth-maker” in connection with Kant’s theory. This}

term is misleading because, for Kant, the manifold of sense, simply as such, has no objective purport at all. Prior to being synthesised, it cannot make anything true or false.

166 _{In fact, this is exactly what Kant says when he discusses the formation of empirical concepts. In his}

view, it is by comparing, reflecting on, and abstracting from our intuitions of particulars that we form concepts of empirical objects (JL 9:94).

167 _{For a detailed discussion of how it is possible that our empirical concepts are both derived from}

can only be established on the basis of a ground (or reason) that is not already con- tained in it, and analytic if it can be established without any such external ground.168

In fact, what initially seemed like a major drawback of the inferentialist reading, namely the blurring of the line between language-based and world-based truths, will turn out to be one of its most important advantages. For once we realize that even binding semantic norms are open to challenges, and that, in fact, we often challenge each other’s views about what to believe and how to live by challenging each other’s ways of speaking, we can see how it is possible to maintain that the intersubjective intelligibility of a domain depends on its being law-governed without denying that there is open-endedness and disagreement around the edges.169