Knowledge Attributions as Generic Sentences

Abstract

The Problem of Doxastic Shift may be stated as a dilemma: on the one hand, observations about the distribution of nominal complements strongly suggest that ‘that’-clauses cannot be univocally assigned propositional denotations.  For example, the sentence ‘x believes that p’ may be restated as ‘x believes the proposition that p’, but ‘x knows that p’ must instead be restated as ‘x knows the fact that p’.  On the other hand, facts about quantification strongly suggest that ‘that’-clauses must be assigned univocal denotations.  For example, it is a widely accepted philosophical principle that everything x knows, x believes. 

In previous work, I have argued that the best way of handling The Problem of Doxastic Shift is to make use of a systematic level-shifting operation, descriptive predication or predd, invoked in the analysis of kind-referring generic sentences.  In the present paper, I extend these results by taking the analogy between kind referring generics and knowledge attributions seriously.  In particular, I argue that treating knowledge attributions as a form of kind-referring generic sentence implies that they should be analyzed in terms of a counter-factual supporting modality.  This, in turn, provides an interesting explanation for the failure of the justified-true-belief analysis of knowledge.

1.  The Problem of Doxastic Shift

There is a something of a consensus in the philosophy of language that English ‘that’-clauses are singular terms.  However, Vendler (1967) and Bach (1997) have provided a strong prima facie case against the intuitively plausible view that ‘that’-clauses univocally denote propositions.  The argument derives from the observation that many so-called propositional attitude verbs cannot take nominal complements of the form ‘the proposition that p’ but can take ones of either the form ‘the fact that p’ or of the form ‘the possibility that p’ (among others).  So, for example, we get the following contrasts:

1a.     x knew/acknowledged that p

b.      *x knew/acknowledged the proposition that p

c.         x knew/acknowledged the fact that p

 

2a.     x feared/imagined that p

b.      *x feared/imagined the proposition that p

c.         x feared/imagined the possibility that p

 

As these examples show, Vendler’s and Bach’s observations hold for both factive contexts and nonfactive contexts.  Conversely, traditional propositional attitude verbs such as ‘believes’ allow nominal complements which explicitly invoke propositions, but are extremely awkward with either ‘the fact that p’ or ‘the possibility that p’.  Thus:

3a.     x believes the proposition that p

b.      *x believes the fact that p

c.       *x believes the possibility that p

 

Such observations suggest that ‘that’-clauses are ambiguous–denoting facts (or possibilities) in some occurrences and propositions in others.

            Unfortunately, the ambiguity thesis is itself open to serious prima facie objections.  The problem is that we can often quantify over objects of both types of verbs (Harman 2002; King forthcoming).  For instance, the following is a widely accepted philosophical principle:

4a.  Everything x knows, x believes.

According to the singular term theory, (4a) has the following logical form:

4b.  ("p)(K(x, p) ® B(x, p)).

But then, contrary to the ambiguity thesis, we seem to be committed to the claim that the same thing can be both known and believed.   

            We are thus faced with the following dilemma: on the one hand, observations about the distribution of nominal complements strongly suggest that ‘that’-clauses cannot be assigned univocal denotations; on the other hand, the facts about quantification strongly suggest that ‘that’-clauses must be assigned univocal denotations.  As a consequence, whether we take ‘that’-clauses to be univocal or not, we seem to be faced with a serious prima facie objection to our position. 

2. An Algebraic Solution

Arguably the best solution to this problem is to make use of a systematic level-shifting operation, descriptive predication or predd, invoked in the analysis of kind-referring generic sentences (Bealer 1993).  Specifically, let D-1 be the subdomain of D (i.e., the domain of discourse) containing individuals; D-2 be the subdomain containing conditions; and Dn (n ł 0) be the subdomain of D containing the n-ary relations-in-intension.  Then predd is an operation from D1 ´ D ® D0 such that, for all j Î D1 and y Î D:

ˇ(predd+j, y,) = 1 iff ($x)(x Î ˇy) & (("x Î ˇy: x Î ˇj)).

(Here I informally extend Montague’s 1973 extension operator ˇ as a function from entities to their extensions.)  This allows us to analyze a sentence such as “The lion has a mane” (also: “Lions have manes”) as follows:

predd+having a mane, the lion,

            We next make the following plausible ontological assumptions: (1) conditions are truth-makers for propositions, (2) if a condition obtains, it is a fact, and (3) the extension of a proposition is a condition (as opposed to a truth-value).  Given this, it is straightforward to analyze a sentence like “x knows that p” in terms of descriptive predication:

predd+being known by x, that p),.

As the reader can check, this proposition will be true just in case the fact in the extension of the proposition that p is known by x.  This provides a straightforward solution to the problem of doxastic shift.

3.  Knowledge Attributions as Generic Sentences

In the present section, I extend these results by taking the analogy between kind referring generics and knowledge attributions seriously.  As many people have noted, generic sentences exhibit a nomological or counterfactual-supporting characteristic.  For example, while (5a) is a true generic, (5b) is not–even if it turns out that every lion is, at the moment, asleep:

 5a.  The lion has a mane.

b.      The lion is asleep.

 

Let CFS be the relevant modal operator (from D0 ® D0).  Then we can represent (5a, b) as (5c ,d) respectively:

5c.  CFS(predd<having a mane, the lion>)

  d.  CFS(predd<being asleep, the lion>)

 

(5c) turns out true and (5d) false because of differences in how they are evaluated at nearby worlds.

            Moreover, the strength of the CFS operator in generic sentences depends on context.  Consider, for instance, the claim that the chimpanzee learns to use tools in the wild.  Relative to the default context, this claim is true.  But notice its counterfactual force is intuitively quite different from the counterfactual force of the claim that lions have manes.  In particular, it is certainly not a causally necessary characteristic of chimps that they learn to use tools in the wild (though this, or something like it, seems to be at play in the claim that lions have manes).

If we take seriously the suggestion that knowledge attributions really are a form of kind-referring generic sentence, then knowledge attributions should also involve the CFS operator.  This yields the following analysis:

CFS(predd+being known by x, that p),).

4. Implications for the JTB Analysis of Knowledge

This analysis is interesting because it effectively provides a semantic explanation for the failure of the justified-true-belief (JTB) analysis of knowledge (Gettier 1963).  According to the JTB analysis we have: for all x and p,

x knows that p iffdef (i) x believes that p

                               (ii) x is justified in believing that p, and

                              (iii) p is true.

 

But if as suggested above the left-hand side of this analysis involves the CFS operator, then it is clear why the JTB analysis fails–none of the conditions (i) through (iii) capture the counterfactual force of the CFS operator. 

            If this is correct, it suggests that the right fix-up for the JTB analysis is to invoke the CFS operator on the right-hand side as well.  Giving this operator widest scope yields the following extension of the JTB analysis: for all x and p,

x knows that p iffdef CFS[ (i) x believes that p

                                         (ii) x is justified in believing that p, and

                                        (iii) p is true].

 

According to this proposal, knowledge amounts to justified true belief where one continues to have a justified true belief in relevant nearby worlds. 

            On this view, the diagnosis of Gettier-style counterexamples is that they rely on justified true beliefs that are not (as we might say) counterfactually stable.  That is, such examples turn on the same sort of accidentalness that underlies generic sentences such as “The lion is asleep”.  In the case of the sleeping lions, the accidentalness seems to be captured roughly as follows: if we hold the relevant causal or nomological context fixed, there will be many nearby worlds in which not all the lions are asleep.  In Gettier-style cases, the analysis is similar: if we hold the relevant doxastic or epistemic context fixed, there will be many nearby worlds in which p is false.  Of course, spelling this proposal out in detail is a difficult task, for both standard generics and knowledge attributions.  Nevertheless, the current proposal helps to pinpoint precisely where the JTB analysis goes wrong and it provides a rough guideline for a solution.

References

Bach, Kent. 1997. Do belief reports report beliefs? Pacific Philosophical Quarterly, 78: 215-241

 

Bealer, George. 1993. A solution to Frege’s Puzzle. Philosophical Perspectives, 7: 17-60.

 

Gettier, Edmund. 1963. Is justified true belief knowledge? Analysis, 23: 121-123.

 

Harman, Gilbert. 2002. Category mistakes in M & E. Rutgers University, Rutgers Semantics Workshop, May 17.

 

King, Jeff. forthcoming. Designating propositions. In A. Bezuidenhout & M. Reimer (Eds.), Descriptions: Semantic and Pragmatic Perspectives. Oxford: Oxford University Press.

 

Montague, Richard. 1973. The proper treatment of quantification in ordinary English. In J. Hintikka, J. Moravcsik, & P. Suppes (Eds.), Approaches to Natural Language. Dordrecht: D. Reidel.

 

Vendler, Zeno. 1967. Linguistics in Philosophy. Ithaca, NY: Cornell University Press.