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 cant 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 Fermats Last Theorem (and Hesperus = Phosporus?) express the same proposition So we cant 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 cant just assume a Fregean theory, as grounding a Fregean theory of propositions is one of the projects 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, its 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? Its 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 isnt. Intending to deceive John, she says Hesperus is a planet. (i) Marys 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 Ill 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 isnt 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 dont 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: Theres 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 (theres only one world in which theyre all true, and thats 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: Theres 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 subjects 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 Ill 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 doesnt entail VT, as base truths may be unverifiable. Is ST scrutable? (cf. Is VT verifiable?). Yes!