Constructing the World

Week 3

David Chalmers

Varieties of Scrutability

(1) Sentences, Propositions, Thoughts

(2) Empirical, Conditional, A Priori, Generalized Scrutability

(3) Scrutability, Knowability, and Determinacy

Varieties of Scrutability

• All truths are scrutable from base truths

• “Scrutable from”: definitional, empirical, conditional, a priori, ...

• “Base truths”: e.g. fundamental truths, phenomenal truths, compact class of truths, ...

• Definitional Phenomenal Scrutability, ...

• Defaults are “A Priori” and “Compact”.

Sentences, Propositions,

Thoughts• What are “truths”: true propositions,

true sentences, true thoughts?

• Natural interpretation: true propositions

• All true propositions are scrutable from true base propositions.

Theories of Propositions

• Russellian theory: propositions are composed from objects and properties

• Fregean theory: propositions are composed from Fregean senses

• Possible-worlds theory: propositions are sets of worlds.

Russellian Propositions

• On the Russellian theory: ‘Hesperus is Hesperus’ and ‘Hesperus is Phosphorus’ express the same proposition

• So we can’t associate them with different epistemological properties.

• If we went this way: An a priori scrutability base will arguably require singular propositions for every individual.

Possible-Worlds Theories

• On the possible-worlds theory: ‘2+2=4’ and Fermat’s Last Theorem (and ‘Hesperus = Phosporus’?) express the same proposition

• So we can’t associate them with distinct epistemological properties

• If we went this way: A scrutability base will arguably require just one proposition (containing our world).

Fregean Theories

• On a Fregean theory, these epistemologically different sentences will express distinct propositions

• So a Fregean theory is better-suited for our epistemological purposes

• But: we can’t just assume a Fregean theory, as grounding a Fregean theory of propositions is one of the project’s purposes.

Neutral on Theories?

• Can we formulate scrutability in terms of propositions while staying neutral on a theory of propositions?

• This is hard, because verdicts about scrutability look very different on different theories.

• Resulting scrutability theses will look quite different too.

Sentences• For our purposes, it’s better to formulate

scrutability in terms of sentences:

• All true sentences are scrutable from true base sentences

• Or better (because of context-dependence), in terms of sentence tokens, or utterances, or assertions, or sentences in contexts.

• All true sentence tokens (or true assertions) are scrutable from true base sentences.

Knowing Sentences

• This requires us to appeal to epistemological relations between subjects and sentences (or tokens/utterances/assertions):

• knowing S, being in a position to know S, believing S, being justified in believing S, ...

• How to make sense of this relation?

Knowing Propositions?

• It’s natural to understanding knowing S as knowing p, where S expresses p.

• This may be OK on a Fregean view of propositions, but on other views, will yield coarse-grained results:

• e.g. if someone knows ‘H=H’, they know ‘H=P’.

• We need a finer-grained understanding.

Fine-Grained Knowledge

• Claim: Everyone needs a fine-grained way of associating knowledge and belief with assertions, in order to explain phenomena such as

• sincere assertion, knowledgeable assertion, justified assertion, lying, norms of assertion, etc.

The Argument from Sincerity

• Mary knows that the morning star is a planet but believes that the evening star isn’t. Intending to deceive John, she says ‘Hesperus is a planet’.

(i) Mary’s assertion is not sincere (justified, knowledgeable, in accord with norms).

(ii) On Russellian views, Mary knows/believes the asserted proposition p.

(iii) So to explain sincerity (etc), the Russellian needs a finer-grained relation.

Accounts of Knowing

Sentences• On one view: knowing S = knowing p under the guise under which S expresses p.

• On another view: knowing S = knowing an associated descriptive proposition

• On a third view: knowing S = knowing that S is true.

• On a fourth view: knowing S = knowing p, where S expresses p.

• We can stay somewhat neutral on the correct account.

Sentences and Thoughts

• The account I’ll use:

• All nondefective assertions of sentences (or assertive sentence tokens) express thoughts.

• Thoughts are token occurrent mental states that can constitute belief, knowledge, etc.

• The expression relation is primitive.

• It is a priori that an assertion is true iff the thought it expresses is true.

Knowledge of Sentence Tokens• Then, for an asserted sentence token S:

the speaker knows S when S expresses a thought that constitutes knowledge.

• The speaker believes S when S expresses a belief.

• The speaker is justified (a priori) in believing S when S expresses a belief that is justified (a priori)

• N.B. Even on a Russellian view, ‘H=H’ can express a belief (that p) while ‘H=P’ expresses a thought (that p) that isn’t a belief.

Knowledge of Sentence Types

• For sentence types S: the speaker knows S when the speaker has knowledge expressible by an assertion of S.

• Likewise for belief, etc.

• The relevant sentence types (in a scrutability base) will always include only context-invariant expressions or primitive indexicals such as ‘I’ and ‘now’.

Formulating Scrutability

• We can then state scrutability claims: e.g.

• S is empirically scrutable from C if were one to know the members of C, one would be in a position to know S.

• I.e.: If one had knowledge expressible by each member of C, the thought expressed by S could then come (by idealized reflection) to constitute knowledge.

Scrutability Theses

• Empirical Scrutability: There is a compact class of sentences C such that for all true (nondefective, assertive) sentence tokens S, S is empirically scrutable from true sentences in C.

• To strengthen the thesis: extend to nomologically possible true sentence tokens, scrutable from true sentences in C, with truth relative to world of assertion.

Notions of Scrutability

• “Scrutable from”: empirical, conditional, a priori scrutability

• A priori scrutability is perhaps the central notion

• Empirical and conditional scrutability are useful preliminary notions that don’t require the notion of apriority, and that can be used to help argue for a priori scrutability.

Empirical Scrutability

• S is empirically scrutable from C if were one to know the members of C, one would be in a position to know S.

• Empirical Scrutability thesis: There’s a compact class C such that all truths are empirically scrutable from the class of true sentences in C.

Fitchian Problems

• (1) It is impossible to know all truths in C (there’s only one world in which they’re all true, and that’s a world in which no-one knows them).

• (2) Empirical Scrutability seems to imply that all truths are knowable. But some sentences are unknowable: e.g. q and no-one knows q, where q is a truth that no-one ever knows.

Ways Out

• (i) Allow non-vacuous counterfactuals with impossible antecedents [obscure]

• (ii) Require only knowledge of a subclass of C [partial]

• (iii) Require only knowledge whether S [partial]

• (iv) Exclude Fitchian truths [heuristically useful]

• (v) Move to Conditional Scrutability

Conditional Scrutability

• S is conditionally scrutable from C for a subject iff the subject is in a position to know that if the members of C are true, then S is true.

• Conditional scrutability: There’s a compact class C such that all truths are conditionally scrutable from the class of true sentences in C.

• This avoids the Fitchian problems.

• Apriority not required: use of armchair background knowledge is allowed.

Conditional Knowledge

• This invokes the notion of conditional knowledge

• I know that if it rains today, my car will get wet.

• Conditional knowledge stands to knowledge as conditional belief stands to belief.

• N.B. not merely knowledge of a material conditional; more like knowledge of an indicative.

Conditional Credence

• Conditional belief is often analyzed in terms of conditional credence:

• S believes that if P, then Q iff cr(Q|P) is sufficiently high.

• “Sufficiently high” is vague, context-dependent, variable between propositions...

Conditional Knowledge and

Credence• Conditional knowledge requires at least justified conditional belief

• A subject knows that if P then Q only if the subject has a high justified credence cr(Q|P).

• S is conditionally scrutable from C only if the subject’s rational conditional credence cr’(S|C) is high.

• Choices: Take this as (i) a gloss [taking conditional knowledge as primitive], (ii) a stipulative definition, or (iii) a definition, once an anti-Gettier condition etc is added.

The Anti-Arithmetic Drug

• D = ‘I have been given an anti-arithmetic drug that renders my arithmetical reasoning entirely unreliable.’

• M = ‘57+65=122’

• Then arguably the ideal rational credence cr’(M | D) = 0.5.

• But then, in a world where D is true, M will not be conditionally scrutable from base truths.

• Christensen: this affects certainty in logical truths. For logical truths L, cr’(L) is not 1.

Insulated Idealization

• Solution: Invoke an insulated idealization.

• Insulated mode of cognition = cognition insulated from practical impact of higher-order beliefs about cognitive capacity, and with no use of introspection or perception.

• An ideal insulated cognizer will have cr(L) = 1 and cr (M|D) = 1.

• Then define conditional scrutability in terms of insulated rational credences.

A Priori Scrutability

• S is a priori scrutable from C iff S is a priori entailed by a conjunction of members of C.

• I.e. if the thought T expressed by S is such that a disjunction of it with the negation of C’ (a thought apt to be expressed by the conjunction) is justifiable a priori, yielding a priori knowledge.

Generalized Scrutability

• Generalizing scrutability beyond the actual world.

• Say that S is epistemically possible if the truth of S cannot be ruled out a priori.

• Generalized scrutability: There is a compact class C of sentences such that all epistemically possible sentences are scrutable from some epistemically possible subclass of C.

Scrutability and Vagueness

• Inconsistent triad:

(i) Scrutability Thesis: For all S, if S then scrut(S)

(ii) Excluded Middle: For all S, S or ~S

[so: For all S, scrut(S) or scrut(~S)]

(iii) There are borderline cases of vague expressions such that ~scrut(S) and ~scrut(~S).

Ways Out

(i) Deny excluded middle

(ii) Hold that borderline cases of truth are borderline cases of scrutability

(iii) Reformulate scrutability: If det(S) then scrut(S).

• All have some virtues, but I’ll go with (iii): Scrutability of determinate truth.

Scrutability and the Liar

• S: ‘This sentence is not scrutable from D.’

• If S is false, it is not scrutable, so true.

• If S is indeterminate, it is not scrutable, so true.

• So S is true, and inscrutable.

• A counterexample to the scrutability thesis!

Ways Out• A problem like this applies to any thesis of

the form S is true iff phi(S).

• A counterexample to any naturalization or substantive general thesis about truth?

• Better: hold that such sentences are relevant akin to the Liar, or Strengthened Liar. Truth-value is the same as that of the Strengthened Liar.

• These sentences should be handled by whatever mechanisms best handle Liar sentences.

Scrutability and Verifiability

•Verification Thesis: S is true iff S is verifiable

•Scrutability Thesis: S is true iff S is scrutable

•ST doesn’t entail VT, as base truths may be unverifiable.

•Is ST scrutable? (cf. Is VT verifiable?). Yes!