The Most General Factive Mental State Operator

Last week I re-read the first chapter of Timothy Williamson's Knowledge and Its Limits. TW argues that 'knows' is the most general factive mental state operator. To be a factive mental state operator (FMSO) is to be a factive semantically unanalyzable expression that attributes a propositional attitude to a subject. The semantic unanalyzability claim is that, by definition, an FMSO is never synonymous with a complex expression whose meaning is composed of the meanings of its parts. So, for instance, 'could hear' is a FMSO. There is a reading of it such that the presumption of truth is not cancelable, as is revealed by the deviance of


(1) She could hear that the volcano was erupting, but it was not erupting.


Moreover, the meaning of 'could hear' is not composed of the meanings of 'could' and 'hear', for that would assimilate 'could hear' to something like 'it is merely possible that s heard that p', which is not factive.

Additionally, 'could hear' is further evidence that 'knows' is the most general FMSO, since 's could hear that p' implies 's knows that p'.

Let's explore the properties of other FMSOs. I want to argue that there is a more general FMSO than 'knows'.

Consider the ambiguity in each of the following expressions:

'could see that'

'could hear that'

'could feel that',


'can't believe that'

'is not happy that'

'is not surprised that'

'failed to realize that'

'is not impressed that'

'is not able to taste that'

Each of these has a factive and a non-factive reading. For instance, 'cannot believe' is factive in

(2) I cannot believe that you are smoking again,

but is not factive in

(3) I cannot believe that I don't have any beliefs.


Now the non-factive readings of the above list items are semantically decomposable. They may be paraphrased roughly as


'it is false that s believes/is happy/is surprised/realizes/is impressed/is able to taste that'

or

'it is (merely) possible that the subject s sees/hears/feels that'.



Exactly analogous remarks may be made about knowability- and ignorance-attributions. More carefully, 'could have known that' and 'does not know that' both have a factive and a non-factive reading. Let's discuss 'could have known that'. The non-factive reading, perhaps not common in ordinary English, is that it is merely possible that s knows that p. The other reading carries a presumption of truth as in 's was in a position to know that p'. Notice that the presumption of truth is not cancelable. This is demonstrated by the deviance of the following claims:


(4) Andy could have known that grandmother was ill, even though she was not ill.

and

(5) Sally was in a position to know that Andy was cheating, but he was not cheating.

The deviance of the claims suggests that the presumption of truth is semantic and not cancelable.

As with the factive readings of the items on the above list, we should expect that the factive readings of 'could have known that' and 'is not known that' are not analyzable. My hypothesis is that they are not analyzable. And I suggest that the burden is on one who thinks otherwise to show that 'could have known' is different from all of our other factive operators of the form 'could have ___ed'.

Incidentally, the non-factive readings of all of the aforementioned expressions fail to attribute a propositional attitude to a subject. They either outright deny the presence of the attitude or affirm merely its possibility of obtaining. The factive readings of the above operators, on the other hand, all attribute a propositional attitude to a subject (with the exception of 'does not know that').

According to Williamson, when a propositional attitude that p is attributed, so is a grasp of the concepts in p. Since the factive reading of 'does not know' fails to attribute grasp of meaning, we may conclude that it is not a mental state operator. A fortiori it is not an FMSO. Importantly, 'could have known' does attribute grasp of meaning. Consider,

(6) Andy doesn't understand high-energy physics, yet he could have known that there are top quarks in pp collisions.

Or

(7) Andy doesn't grasp any of the rules of Chess. He was nevertheless in a position to know that his King was about to be mated.

The oddities of (6) and (7) suggest that knowability is a mental state---that 'to s it is knowable that p' implies 's has an attitude that p'---minimally, it implies 's grasps the meaning that p'. Similar things can be said about 's failed to realize that p'. It wouldn't be a failure to realize that p, if the subject didn't have a grasp of the concepts in p.

It would seem then that 'knowable' or 'could have known' is an FMSO. The problem for Williamson's account is that 's could have known that p' does not entail 's knows that p'. Hence, 'knows' is not the most general FMSO. Instead, the entailment goes the other way. Are we to conclude that 'could have known' is the most general FMSO?

Löb's Legacy

Richard Zach's Log Blog has brought to my attention the recent death of Martin Löb. It is fitting that we think here about his work. The famous Löb Theorem (in "Solution of a Problem of Leon Henkin" JSL, 1955) generates Löb's paradox (ibid.), which goes something like this:

(*) If this sentence is true, then so is A.
Notice that (*) is provable for an arbitrary proposition A. Here's the proof. Suppose (*) is true. Then it satisfies its own antecedent. So it follows that A. By conditional proof, if (*) is true then so is A. And that is just to say that (*) is true.

Notice also, that the provability of (*) underwrites the truth of any proposition A. For this reason and since both (*) and its proof are negation-free, Löb offers (*) as a test for inconsistency of negation-free languages (that allow self-reference).

Löb credits an anonymous referee for extracting the paradox and the insight about how to test for inconsistency without negation. Curry (1942), and not Löb (1955), usually gets credit for the above insights. Johan van Benthem ("FourParadoxes" JPL 1978), however, argues that the Löb+Referee insights were developed independently of Curry's work. Moreover, the Curry paradox is treated by Curry and his students as a feature of formal systems only, whereas Löb's paradox is a natural language paradox.

An interesting loose-end is the identity of the 1955 anonymous referee that extracted the paradox from Löb's Theorem.

Call for Papers: Knowability and Beyond

CALL FOR PAPERS (May 1, 2007)

Knowability & Beyond
Special issue of Synthese

• Can there be non-actual knowledge of what is actually the case?
• Is the concept of knowability basic or is it semantically decomposable into knowledge and (alethic) possibility?
• Should an intuitionist find a way to express an existential commitment to some ignorance and undecidedness?
• Are there more truths than knowables?

These are possible topics for a special issue of Synthese that I will be editing. For a description of the issue and further details please go here.

Visitors at Knowability

Sporadically one will find here at Knowability a post authored by someone not identical to me. The explanation is that, although this is not currently a guest blog, I will be hosting visitors now and again. I look forward to these visits.

The Logical Necessity of Some Ignorance

Modest modal epistemic reasoning reveals the equivalence of the following two principles:


(1) Any truth can be known.


(2) All truths are known.


Jon Kvanvig, in his latest book The Knowability Paradox (2006), poses a challenge to anyone who accepts the validity of the reasoning---viz., explain the loss of the apparent logical distinction between these two principles. Here's one way to go.

It is logically necessary that each of the above propositions is false. Logically necessary propositions often appear to express different thoughts, especially if one involves a concept not involved in the other.

Why think that the above propositions are necessarily false? An appendix to Nicholas Rescher's Epistemic Logic (2005) inspires an answer. It is a logical fact that there are more truths than knowables. Knowledge requires thought, and we could at most think a countable number of propositions. However, the true propositions themselves are uncountable. A diagonalization argument is required to make this stick, but it shouldn't be difficult to construct one for, say, a class of truths about the rational numbers. So if (i) there are more truths about the rational numbers than things that can be known about the rational numbers and (ii) the proof of this rests on no non-logical facts, then it is logically necessary that there is an unknown truth. (2) is logically false. And by the same reasoning so is (1).

The apparent logical distinction is explained by the fact that (2) seems on first glance to be stronger than (1). But the appearance is the result of not immediately recognizing that both propositions are logical falsehoods.