1. The physical reductive explainability of phenomenal consciousness and the logical impossibility of zombies Marco Giunti University of Cagliari (Italy) giunti@unica.it Paper (Zombies cannot be there) available at http://edu.supereva.it/giuntihome.dadacasa

2. Two concepts of reduction [1/21] Ontological reduction Facts of type T 1 (which hold in world w) do not exist independently of facts of type T 0 (which hold in the same world w). Epistemic reduction (or Reductive explanation) Facts of type T 1 (which hold in world w) are reductively explained by facts of type T 0 (which hold in the same world w).

3. How can we analyze either concept of reduction? [2/21] Standard answer By means of a relationship of entailment between types of facts or, equivalently, a relationship of supervenience between the corresponding types of properties. 1 Note Entailment between facts and supervenience between properties are interdefinable. Therefore, we can choose either concept as primitive. I choose the first one for convenience.

4. What is entailment between types of facts? [3/21] Standard answer It is the implication that holds in virtue of the meanings, or the intensions, of the properties involved in such types of facts. Since we can distinguish several different kinds of intensions, 1 we obtain a corresponding entailment for each kind. As a consequence, we get different analyses of ontological or epistemic reduction depending on which entailment is taken be appropriate.

5. What is my position on the analysis of ontological or epistemic reduction? [4/21] I just maintain that, probably, some kind of entailment is needed for an adequate analysis of ontological reduction. I am more doubtful about epistemic reduction. Epistemic reduction might be better analyzed in terms of representation relationships between models (isomorphisms, homomorphisms, or other concepts of a similar sort, like emulation or realization between dynamical systems).

6. Distinction between phenomenal and psychological consciousness [5/21] Let us stipulate that F* stands for the set of all physical facts that hold in the actual world w*, and CF* for the set of all phenomenal facts that hold in w*; I also call the latter set phenomenal consciousness (in the actual world). “First-person fact of consciousness”, “internal fact of consciousness”, and “conscious experience” are three synonyms for “phenomenal fact”. “Third-person fact of consciousness”, “external fact of consciousness”, and “conscious function” are three synonyms for “psychological fact”. Let us finally stipulate that CP* stands for the set of all psychological facts that hold in the actual world; I also call the latter set psychological consciousness (in the actual world).

7. What is my position on entailment between F* and CF*? [6/21] My view does not depend on any specific entailment. Terminology – Let us indicate with I an arbitrary kind of intensions and with |= I the corresponding entailment. My thesis on entailment between F* and CF* can be expressed as follows: Logical thesis – for any kind of intensions I, if F* |= I CP*, then F* |= I CF*. From the logical thesis, we obtain the following corollary. Philosophical thesis – if there is an adequate analysis of reduction (ontological or epistemic) in terms of some notion of entailment, then, if CP* is reducible to F* (ontologically or epistemically), CF* is reducible to F* as well (ontologically or epistemically).

8. How do I argue for either thesis? [7/21] My strategy consists of the following three steps. 1.Set up a formal possible world ontology where we can represent or express intensions of any kind, and thus any notion of entailment between types of facts. 2.Show how, within this ontology (equipped with  - abstraction), we can give a formal explication for each of the two concepts: (i) internal fact of consciousness (or conscious experience); (ii) external fact of consciousness (or conscious function). 3.On the basis of this analysis, prove that the two concepts individuate the same set of facts, i.e. prove that phenomenal consciousness is identical to psychological consciousness.  Both the logical and the philosophical theses are immediate consequences of 3.

9. What about zombies? [8/21] An easy consequence of the logical thesis is: Chalmers’ dilemma (logical version) – for any kind of intensions I, if F* |= I CP*, then a zombie copy of the actual world does not exist. 1 Also note that, from the logical version of Chalmers’ dilemma, it immediately follows: Chalmers’ dilemma (philosophical version) – if there is an adequate analysis of reduction (ontological or epistemic) in terms of some notion of entailment, then, if CP* is reducible to F* (ontologically or epistemically), a zombie copy of the actual world does not exist.

10. Step 1 – The formal ontology (1/4) Axioms [9/21] An intensional ontology is a structure (D, P, W, w*) that satisfies the following four axioms. 1.D is a non empty set; D is called domain; 2.P is a non empty set; each element of P is an ordered pair (P, n) such that 1  n; any such pair is indicated with the notation P n ; every element of P is called a property; the number n is called its arity (or its number of places). 3.W is a set of functions; each of them, to any property P n  P, associates a set {(x 1, …, x n )} of n-tuples of elements of D; every function w  W is called a possible world; the set of n-tuples assigned by w to P n is called the extension of P n in world w; 4.w*  W; w* is called the actual world.

11. Step 1 – The formal ontology (2/4) [10/21] It is then clear that any kind of intensions I can be expressed or represented within this formal ontology, for each I determines a specific model of this theory. 1 Given an arbitrary intensional ontology, we can then define facts, their holding in a world, and the entailment relationship relative to the given ontology.

12. Step 1 – The formal ontology (3/4) Definitions [11/21] Def. 1 [fact, predicate, subject] f is a fact iff: f is an ordered pair of the type (P n, (x 1, …, x n )), where P n  P and (x 1, …, x n ) is an n-tuple (n  1) of elements of D; the property P n is called the predicate of f; the n-tuple (x 1, …, x n ) is called the subject of f; we write for brevity P n (x 1, …, x n ) instead of (P n, (x 1, …, x n )).

13. Step 1 – The formal ontology (4/4) Definitions [12/21] Def. 2 [holding in a world] f holds in w iff: f = P n (x 1, …, x n ) is a fact, w  W, and (x 1, …, x n )  w(P n ). Def. 3 [entailment between sets of facts] F 1 |= F 2 iff: for any w  W, if for any f 1  F 1, f 1 holds in w, then for any f 2  F 2, f 2 holds in w.

14. Step 2 (1/7) – Formal explication The analysis strategy [13/21] INTERNAL FACT OF CONSCIOUSNESS INTERNAL FACT OF CONSCIOUSNESS FOR SOMEONE INTERNAL FACT FOR SOMEONE FACT OF CONSCIOUSNESS EXTERNAL FACT OF CONSCIOUSNESS EXTERNAL FACT OF CONSCIOUSNESS FOR SOMEONE FACT OF CONSCIOUSNESS EXTERNAL FACT FOR SOMEONE

15. Step 2 (2/7) – What is an internal or an external fact for someone? [14/21] The fact f = George is running is an experience (internal fact) for George, but f is an external fact for anybody else. Why? Because George, and nobody else, is the subject of the fact, i.e., only George is located internally to f in the role of bearer of the predicate of f. Thus, let us define: Def. 4 f is an internal fact for x iff: f is a fact and x is the subject of f. Def. 5 f is an external fact for x iff: f is a fact and x is not the subject of f and, for some n, x is an n ‑ tuple of elements of D.

16. Step 2 (3/7) – What is a fact of consciousness? [1/3] [15/21] Typical examples 1.Mary is conscious of her running; 2.Mary is conscious of John’s speaking. Note Mary is seeing a red spot is not a typical example, because in this case the logical form of the fact of consciousness is disguised. 1 By observing the two typical examples, we notice: i.in each of them, the binary property x is conscious of f occurs; this is a relation between an element x of the domain and a fact f; ii.the subject of each fact of consciousness is x (Mary in the examples).

17. Step 2 (4/7) – What is a fact of consciousness? [2/3] [16/21] To formalize the examples so that conditions i and ii be satisfied, we need I.a binary property C, for which we assume that it may only hold between elements of the domain and facts (axiom 5). Intuitively, C is to be identified with the relationship being conscious of; II.the abstraction operation ; is governed by straightforward adaptations of two standard principles of the ‑ calculus (axiom 6 – abstraction, and axiom 7 – instantiation).

18. Step 2 (5/7) – What is a fact of consciousness? [3/3] [17/21] By employing C and, we get: Mary is conscious of her running = [ (m)C(m, f 0 )](m), where f 0 = Mary is running = R(m); the form of this fact satisfies i and ii. Intuitively, the facts of consciousness are all those facts with a form like the one of the fact above. Let us thus define: Def. 6 f is a fact of consciousness iff: there is x  D, there is a fact f 0, such that f = [ (x)C(x, f 0 )](x).

19. Step 2 (6/7) – What is an internal or an external fact of consciousness for someone? [18/21] Def. 7 f is an internal fact of consciousness for x iff: f is an internal fact for x and f is a fact of consciousness. Def. 8 f is an external fact of consciousness for x iff: f is an external fact for x and f is a fact of consciousness.

20. Step 2 (7/7) – What is an internal or an external fact of consciousness? [19/21] Def. 9 f is an internal fact of consciousness iff: there is x such that f is an internal fact of consciousness for x. Def. 10 f is an external fact of consciousness iff: there is x such that f is an external fact of consciousness for x.

21. Step 3 (1/2) – The proof that CF* = CP* [20/21] Suppose f is an internal fact of consciousness. Then, by def. 9, 7 and 4, f is a fact and f is a fact of consciousness. Since f is a fact, let x be its subject. Then, by def. 5, f is an external fact for the pair (x, x). Since f is a fact of consciousness, it follows from def. 8 that f is an external fact of consciousness for the pair (x, x). Therefore, by def. 10, f is an external fact of consciousness. Hence, CF*  CP*.

22. Step 3 (2/2) – The proof that CF* = CP* [21/21] Conversely, suppose f is an external fact of consciousness. Then, by def. 10, 8 and 5, f is a fact and f is a fact of consciousness. Since f is a fact, let x be its subject. Then, by def. 4, f is an internal fact for x. Since f is a fact of consciousness, it follows from def. 7 that f is an internal fact of consciousness for x. Therefore, by def. 9, f is an internal fact of consciousness. Hence, CP*  CF*. Q.E.D.

23. That’s all Thank you

24. Three main kinds of intensions, and corresponding entailments [1A/4] 1.A ‑ priori intensions – the primary intensions in Chalmers’ sense, indicated by I 1 ; A ‑ priori entailment – indicated by |= 1. 2.Weak a ‑ posteriori intensions – the secondary intensions in Chalmers’ or Kripke’s sense, indicated by I 2 ; Weak a ‑ posteriori entailment – indicated by |= 2. 3.Strong a ‑ posteriori intensions – they determine strong metaphysical necessities and cannot be described within Chalmers’ two dimensional framework. Indicated by I 3 ; Strong a ‑ posteriori entailment – indicated by |= 3.

25. Different analyses of ontological or epistemic reduction depending on which entailment is taken be appropriate [2A/4]

26. Does physics entail phenomenal consciousness? Different answers depending on the kind of entailment [3A/4]

27. Analysis of sensory facts of consciousness [4A/4]  Mary is seeing a red spot =  Mary is conscious of her being in neurophysiologic state r =  [(m)C(m, f 0 )](m), where  f 0 = Mary is in neurophysiologic state r = [(m)S(m, r)](m)