Constructing the World Week 2

1. Constructing the WorldWeek 2 • David Chalmers

2. Carnap’s Aufbau • (1) Carnap’s purposes in the Aufbau • (2)Carnap’s primitives • (3) Carnap’s derivation relation • (4) The vacuity problem for pure structuralism

3. Carnap’s Purposes • (1) Objectivity/communication in science • (2) Unity of science • (3) Clarifying philosophical problems • (4) Understanding concepts and meaning? • (5) Foundationalist epistemology? • (6) Epistemological optimism?

4. Objectivity in Science • “Science deals only with the description of structural properties of objects.” (10) • “Each scientific statement can be so transformed that it is nothing but a structure statement. But this transformation is not only possible, it is imperative. For science wants to speak about what is objective, and whatever does not belong to the structure but to the material is subjective.” (16) • “The problem of intersubjective reality.” (16)

5. Unity of Science • “Only if we succeed in providing such a unified system of all concepts will it be possible to overcome the separation of unified science into unrelated special sciences.” (2) • “If a constructional system is possible, then it follows that there is only one domain of objects and therefore only one science.” (4)

6. Clarification of Philosophical Problems • “A uniform ordering of concepts allows a clearer formulation of the question for each problem and thus brings us closer to a solution” (157) • Metaphysical theses “excluded from the domain of science” but not yet “condemned as pseudostatements” (preface) • Problems of essence, identity, causation, mind-body, self, reality, aims of science (158-183).

7. Concepts and Meaning? • “A step-by-step derivation of all concepts from fundamental concepts, so that a genealogy of concepts results in which each has its definite place.” (1) • “Rational reconstruction of the concepts of all fields of knowledge on the basis of concepts that refer to the immediately given”. (preface to 2nd edition)

8. Foundationalist Epistemology? • “We are here concerned with questions of epistemology...” (preface 1) • “This requirement for justification and conclusive foundation of each thesis will eliminate all speculative and poetic work from philosophy.” • “It must be possible to give a rational foundation for each scientific thesis.” • “The system form attempts to show order with respect to epistemic primacy. However...” (54)

9. Epistemological Optimism? • “The truth or falsity of each statement which is formed from scientific concepts can in principle be ascertained.” (180) • By translating into a relation statement whose truth can in principle be ascertained. • There may be “mere technical obstacles” • Q: Are there true non-scientific statements whose truth cannot be ascertained?

10. Carnap’s Primitives • Property descriptions [NO] • 1-place predicates allowed (plus logic) • Relation descriptions [YES, temporarily] • Only multi-place predicates allowed? • Structure descriptions [YES, ultimately] • No unbound predicates allowed • Logical expressions only

11. The Primitive Relation • Primitive relation: (recollected) phenomenal similarity • Holds between elementary experiences • I.e. total experiences (gestalt psychology) • Later suggests using domain of atomic elements of experience instead • Red sense-datum at location l in visual field • Various relations for color similarity, location similarity, etc.

12. Quasi-Analysis • Method of quasi-analysis: effectively “analyze” aspects of unanalyzed entities (e.g. elex’s) using relational structure (pair list) in the domain • “Synthesis which wears the garb of an analysis” • E.g. colors (e.g. blueness) = maximal similarity circles of entities standing in same-color relation • N.B. problems in “unfavorable circumstances” • e.g. if every yellow object is also blue

13. Quasi-Analysis of Experience • Qualia (e.g. red sense-datum at l) = maximal circle of elementary experiences standing in p-similarity to each other • Or (if p-similarity allows similar colors): maximal subclasses of these that are undivided by any similarity circle • “Unfavorable circumstances” if e.g. some non-red-l elex is similar to all red-l elex’s.

14. Goodman’s Critique • The Structure of Appearance, 1953 • Similarity circles needn’t yield qualia • One similarity circle for co-occurring red and blue: “companionship difficulties” • One similarity circle if every red object is similar in some other color to a blue object: “imperfect community”. • These “unfavorable circumstances” needn’t be rare.

15. Carnapian Responses • Extensional adequacy • Psychology: we’d then perceive one quality • Similarity circles suffice for quasi-analysis in any case • Use multiple finer-grained/higher-order relations • Move to physical or other basis

16. Carnap’s Derivation Relation • The “ascension form” from primitive truths to non-primitive truths: • a rule for transforming statements with a non-primitive expression E into statements without E, and ultimately into statements in the basic vocabulary • Carnap’s ascension form involves definitions

17. Two Sorts of Definitions • Explicit definitions • e.g. 2 = 1+1 • Definitions in use • e.g. n is prime iff x has no divisors other than 1 and n. • Not: implicit definitions • e.g. lines are whatever make the following axioms true

18. Conditions of Adequacy • Definitions are required to be extensionally adequate • Preserving object (for singular terms), class of objects (predicates), ordered pairs of objects (2-place predicates) ... • Preserves “logical value”, not “epistemic value” • Requires only that definition statements be true. • Based on thesis of extensionality: language is extensional • Contrasts with intensional adequacy

19. Intensional Adequacy • Compare: intensional adequacy • Definitions must preserve sense, or intension • Preserve epistemic value, not logical value • Definitions should be a priori, or analytic, or necessary • Carnap thinks that intensional contexts involve senses as extensions, so can be handled extensionally (doesn’t say how)

20. Puzzle • How can mere extensional adequacy serve Carnap’s epistemological purposes? • E.g. say all renates = cordates is true, so we can define renate = creature with a heart. • Then does justifying X has a heart justify X is a renate? Prima facie, no. • In 2nd preface, Carnap suggests requiring that definitions aren’t true by accident. A weakly intensional criterion. Enough?

21. Iterated Definition • Carnap successively defines • Qualia (in terms of similarity) • Spacetime • Perceptual things • Physics • Other bodies • Behavior • Other minds • Intersubjective world • Cultural objects • Values

22. Quine’s Critique • In Carnap’s construction of spacetime, “Quality q is at point (x, y, z, t)” is not defined explicitly or in use. One is merely given 12 constraints on the is-at relation. • Simultaneously constraining is-at and points of view, lines of view, seen color spots, unseen color spots, world-lines, etc. • So Carnap violates his own rules, and we can’t translate into primitive sentences.

23. Carnap’s Response • Carnap (in preface to 2nd edition) suggests instead appealing to Ramsey-sentence method for defining theoretical terms: • E.g. is-at = that relation R that satisfies as many as possible of the constraints. Escapes Quine’s critique? • N.B. This requires a co-operative world with minimal illusion and hallucination • So can do limited epistemological work? • Doing better seems to require intensional adequacy, and thereby requires nonphenomenal primitives • E.g. causation, spacetime, ...

24. Pure Structuralism • Carnap ultimately requires a structure description • No primitive relations, just relational structure • E.g. ∃x, y, z ∃ R1,R2 R1(x,y) & R2 (y, z) &... • 153-55: Given world-sentence D(R) with primitive relation, define away R as that relation satisfying D(R): yielding ∃RD(R)?

25. Newman’s Problem • Newman (1928), on Russell’s Analysis of Matter • Pure structure descriptions are near-vacuous, only constraining cardinality. • Say set S1 and relation R satisfies D. Then if S2 has the same cardinality as S1, any 1-1 mapping from S1 onto S2 will yield S2, R* satisfying D. • N.B. the argument requires that there’s a relation for any set of ordered pairs.

26. Carnap on Newman’s Problem • Carnap (154) recognizes Newman’s problem • Proposes: relations must be “founded” (“experienceable, natural”). • Then world-sentence: ∃R Found(R) & D(R) • Cf. Lewis on Putnam’s paradox • Justification: “Foundedness” is a logical notion!

27. Whither Pure Structuralism? • This is in effect to give up on pure structuralism, introducing a primitive higher-order predicate of relations. • But once we can do this, why not other predicates or relations? • E.g. similarity? causation? spacetime? consciousness? • Moral: Move to impure structuralism, or give up structuralism.