Constructing the World Week 3

1. Constructing the WorldWeek 3 • David Chalmers

2. Varieties of Scrutability • (1) Sentences, Propositions, Thoughts • (2)Empirical, Conditional, A Priori, Generalized Scrutability • (3) Scrutability, Knowability, and Determinacy

3. 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”.

4. 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.

5. 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.

6. 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.

7. 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).

8. 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.

9. 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.

10. 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.

11. 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?

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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’.

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. 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

25. 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.

26. 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.

27. 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...

28. 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.

29. 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.

30. 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.

31. 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.

32. 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.

33. 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).

34. 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.

35. 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!

36. 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.

37. 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!