Minds and Machines

Minds and Machines Summer 2011 Tuesday, 07/12

(Contemporary) Functionalist theories of consciousness • Global workspace theory. The job description of consciousness is “global broadcasting”.Perceptual systems supply representations that are consumed by mechanisms ofreporting, reasoning, evaluating, deciding, and remembering, which themselves produce representations that are further consumed by the same set of mechanisms. Once perceptual information is “globally broadcast” in frontal cortex this way, it is available to all cognitive mechanisms without further processing.

(Contemporary) Functionalist theories of consciousness • Integrated information theory. The job description of consciousness is to integrate information from multiple individual informational states. The level of consciousness of a system at a time is a matter of how many possible states it has at that time and how tightly integrated its states are.

(Contemporary) Functionalist theories of consciousness • (first order) Representational theory. The job description of consciousness is to represent the world in some specific way. • E.g. PANIC theory, on which conscious experience is “one and the same as” (1) Poised (2) Abstract (3) Non-conceptual (4) Intentional Representation.

(Contemporary) Functionalist theories of consciousness • (higher order) Representational theory. The job description of consciousness is to represent the subject’s mental states (which are themselves representations). Consciousness is higher-order representation/thought.

Biological vs. Functionalist theories of consciousness • According to the biological account (a version of the identity theory), global broadcasting, information integration and higher order thought are what consciousness does rather than what consciousness is. • The functional approach says consciousness is a role (or a job description), whereas the biological approach says consciousness is a realizer of that role. • “The key empirical difference comes down to the question of whether consciousness might sometimes exist without having its normal role or whether something else might in some circumstances play that role” (Block).

Biological vs. Functionalist theories of consciousness • Subjects may have visual experiences without any knowledge or access to the experiences. • There are unusual circumstances where the occipeto-temporal stream is activated at the level that is correlated with experience but in which the subject says he sees nothing.

Biological vs. Functionalist theories of consciousness • “Liss (1967) presented subjects with 4 letters in two circumstances, long, e.g. 40 msec followed by a “mask” known to make stimuli hard to identify or short, e.g. 9 msec, without a mask. Subjects could identify 3 of the 4 letters on average in the short case but said they were weak and fuzzy. In the long case, they could identify only one letter, but said they could see them all and that the letters were sharper, brighter and higher in contrast. This experiment suggests a double dissociation: the short stimuli were phenomenally poor but perceptually and conceptually OK, whereas the long stimuli were phenomenally sharp but perceptually or conceptually poor, as reflected in the low reportability.” (From Block)

Biological vs. Functionalist theories of consciousness • Consciousness may not really be a unitary phenomenon! In fact, there may be two concepts of consciousness: phenomenality (i.e. what it’s like to have an experience) and accessibility (i.e. availability for use in reasoning and rationally guiding speech and action). • Phenomenalitymay be best thought of in biological terms, whereas accessibility may best be thought of in functional terms, e.g. of global neuronal broadcasting.

Back to Machine Functionalism • To understand the mind as a computer, we need to have a sharp understanding of what computers really are. • And to understand computers, we first need to grasp the power and scope of formal systems. • For a highly entertaining historical narrative about the philosophical/mathematical developments in this area, check out Logicomix:

Some History

Formal Systems: Starting with Basics A Puzzle: Can you produce EL? You are supplied with a string of letters: EI. You are supplied with a set of rules (which I’ll shortly introduce) You can use the rules whenever they are applicable. But you must not do anything outside the rules!

Formal Systems: The ELI System • The ELI-system uses only three letters of the alphabet: E, L, I. • The only strings of the ELI-system are strings that are composed out of these letters. • Example strings: EL, ELI, IILE, ELLIE, LIEIE, LIELL, ILELLLLELIIIIILELLIIIILEEELLILLEE. • Although these are all legitimate, they are not in your possession yet. All you have so far is: EI

Formal Systems: The ELI System You can enlarge your private collection using the following rules: Rule 1: if you possess a string whose last letter is I, you can add on an L at the end. For example: EI  EIL, EILI  EILIL

Formal Systems: The ELI System You can enlarge your private collection using the following rules: Rule 2: If you have Ex, then you may add Exx to your collection. For example: EIEII, EIL  EILIL, EILIL  EILILILIL

Formal Systems: The ELI System You can enlarge your private collection using the following rules: Rule 3: If III occurs in one of the strings in your collection, you may make a new string with L in place of III. For example: ELIIILEELLLE, EIIIIEIL (or ELI)

Formal Systems: The ELI System You can enlarge your private collection using the following rules: Rule 4: If LL occurs inside one of your strings, you can drop it. For example: ELL  E, ELLLLIILELLIIL

Formal Systems: The ELI System So here are all the rules: Rule 1: if you possess a string whose last letter is I, you can add on an L at the end. Rule 2: If you have Ex, then you may add Exx to your collection. Rule 3: If III occurs in one of the strings in your collection, you may make a new string with L in place of III. Rule 4: If LL occurs inside one of your strings, you can drop it. Now try to make EL. The only string now in your collection is EI. Remember: you must not do anything outside the rules!(which also means that you can’t run these rules backwards!)

Describing Formal Systems • Theorems: the strings that you produce by following the rules. • Axioms: A free theorem that you may use at any point without having to derive it using the system’s rules. The Eli system has only one axiom: EI. Other formal systems may include any number of axioms. • Derivations: line-by-line demonstrations of how to produce theorems according to the formal system’s rules.

Formal Systems: PQ− system • Has an infinite number of axioms: Definition: xP−Qx−is an axiom, whenever x is composed of hyphens only. Since x is not part of the PQ− system, this definition is an axiom schema rather than an axiom.

Formal Systems: PQ− system • But only one rule of production: Rule: Suppose x, y and z all stand for particular strings containing only hyphens. And suppose that xPyQz is known to be a theorem. Then xPy−Qz− is a theorem. For example: If −−P−−−Q− turns out to be a theorem, then so will −−P−−−−Q−−

Formal Systems: PQ− system Axiom Schema: xP−Qx−is an axiom, whenever x is composed of hyphens only. Rule: Suppose x, y and z all stand for particular strings containing only hyphens. And suppose that xPyQz is known to be a theorem. Then xPy−Qz− is a theorem. Generate 10 theorems in the PQ− system. Notice any patterns?

Formal Systems: PQ− system Do the theorems in this system mean anything?

Formal Systems: PQ− system Do the theorems in this system mean anything? A very natural interpretation is this: P means Plus Q means Equals − means 1 −− means 2 −−− means 3 (and so on)

Formal Systems: PQ− system Do the theorems in this system mean anything? A bizzare interpretation is this: P means horse Q means happy − means apple • On this interpretation −P−Q−− means apple horse apple happy apple apple rather than one plus one equals two.

Isomorphism What makes the first interpretation more appropriate than the second? One answer is that there is an isomorphism between pq-theorems and additions. The word “isomorphism” applies when two complex structures can be mapped onto each other in such a way that to each part of one structure there is a corresponding part in the other structure, where “corresponding” means that the two parts play similar roles in their respective structures. (This is a bit vague, but there’s a more precise mathematical characterization)

Syntax and Semantics • Semantic properties are “meaning-involving” properties, e.g. the property of meaning plus, the property of meaning two plus two equals four, etc. −−P−−Q−−−− (arguably) means two plus two equals four. It (arguably) has this semantic property.

Syntax and Semantics • Syntactic properties are nonsemantic properties of expressions (i.e. of any kinds of inscriptions of meaningful items). • “−−P−−Q−−−−” (arguably) means the same as “two plus two equals four”, but the two expressions have different syntactic properties. The first contains dashes, the second does not. • Two uses of the word “bank” may be syntactically identical but semantically distinct. • This inclusive use of the term “syntax” is differentfrom a more narrow one used in Linguistics.

Formal Systems: PQ− system Unfortunately, there’s another equally good “semantic theory” or interpretation of the symbols: P means equals Q means taken from − means 1 −− means 2 −−− means 3 (and so on) This shows that the PQ− system imitates both additions and subtractions. In this case, there is no single appropriate interpretation.

Applications: Formal Logics • Formal systems comprising sets of symbols, ways of joining the symbols so as to express complex propositions, and rules for how to legally derive new symbol complexes from old ones. • The application of the rules guarantees that you will never legally infer a false conclusion from true premises, even if you don’t know what the strings of symbols mean. (Similarly to how you can never infer something that violates the laws of arithmetic if you follow all the rules of the PQ− system.)

Minds and Machines