Chapter 3 Flashcards
Define: physical symbol system
It operates on a finite set of physical tokens called symbols, which are a component of a larger physical entity called a symbol structure or symbolic expression; it also consists of a set of operators that can create, modify, duplicate or destroy symbols; some sort of control is also required to select at any given time some operation to apply; a physical symbol system produces an evolving or changing collection of expressions which represent or designate entities in the world (as a result, the symbol manipulations performed by a PSS permit new meanings to be derived)
Where did the disembodied mind hypothesis originate, and what was its evidence?
From Descartes as a reaction against scholasticism; employing extreme scepticism, Descartes questioned ideas supported by the senses, because he claimed that the senses could be deceived – he eventually landed on the notion of “I think therefore I am”, but decided subsequently that there must be a mind and body divide. The body was divisible (lose a limb) but the mind was not. The mind was linked to the body however, and was responsible for the ‘think’ part of the ‘sense-think-act’ cycle of Cartesian philosophy. His idea is known as dualism.
What’s the key difference between dualism and materialism?
Dualism is a mind and body divide; materialism believes that the mind is caused by the brain.
What led Descartes to believe in dualism in re. to the human brain?
The infinity of language; a physical finite object (the brain) was supposedly responsible for an infinite range of expressions. While the technology of the time did not lend itself to prove this conundrum, modern day Turing machines and this notion of recursion proves that a finite machine can indeed produce an infinite volume of expressions (physical symbol systems).
» Descartes used language to separate man from machine
Define: the creative aspect of language
An essential property of language is that it provides the means for expressing indefinitely many thoughts and for reacting appropriately in an indefinite range of new situations
What is the arithmetisation of mathematics (the Dedekind-Peano axioms)?
An example of a recursive rule: the Successor Function;
mathematical theory defines three primitive notions: 0, number, and successor. It also defines five basic propositions: 0 is a number; the successor of any number is a number; no two numbers have the same successor; 0 is not the successor of any number; and the principle of mathematical induction. These basic ideas were sufficient to generate the entire theory of natural numbers (finite rules for an infinite expression).
When is a function recursive?
When it operates by referring to itself; recursion is one method where a finite system (ie. the Dedekind-Peano axioms) can produce infinite variety
How is the Tower of Hanoi problem solved using recursion?
It reduces it to a simpler problem by using recursion; it defines simpler subproblems, such that in order to solve the complex problem of ‘how to move x disks’ it first accomplishes ‘how to move x-1’ and so on (refers to itself)!
» MoveStack (N, Start, Spare, Goal)
» MoveStack (N-1, Start, Spare, Goal)
How are Sierpinski triangles an example of recursion?
Produces hierarchical, self-similar structures such as fractals; in this instance it starts with an equilateral triangle and inscribes three triangles (which are half the size as the original) into the original, so on and so forth to infinity; the original triangle can be found in any of the divisions, as they are all self-similar.
How is the structure of language produced using recursion, and what is the importance of this?
Sentence structure can be described using phrase markers; phrase markers can be produced using context-free grammar, which is a finite set of rewrite rules that can account for an infinite variety of phrase markers, since the rules can be applied recursively. For example, NP –> N is a rule, as is N –> AP + N; in theory, this recursiveness can repeat ad infinitum, which is why the infinite variety of language can be represented using finite rules (think embedded clauses that go on forever, which is what is being described above).
What type of information processing machines can handle recursion? What kind can’t?
Finite state automata cannot handle it, firstly because they only work in one direction, and as such have no memory (only S-R type response), and secondly because they cannot elaborate (don’t write); this essentially lays to rest the behaviourist argument on language acquisition.
Physical symbol systems, such as the Turing machine, permits recursive power, because it moves both left and right, and can rewrite the tape it works on. These devices can generate an infinite variety based on a finite set of rules, and thus shows how language may work in the human physical symbol system, the brain.
Describe a Turing machine
It consists of a machine head that manipulates the symbols on a ticker tape, where the ticker tape is divided into cells, and each cell is capable of holding only one symbol at a time. The machine head can move back and forth along the tape, one cell at a time. As it moves it can read the symbol on the current cell, which can cause the machine head to change its physical state. It is also capable of writing a new symbol on the tape
Define: informant learning
Learner is presented with either valid or invalid expression, and is then told about their validity
Define: text learning
Learner is presented only with expressions that are grammatical
Describe Gold’s algorithm for language learning
Learners are presented with an expression, and form a hypothesized grammar. The hypothesis is described as a Turing machine that can either accept the (hypothesized_ grammar or generate it, and therefore “learning a language” is now “selecting a Turing machine that represents a grammar”; according to this algorithm the language learner has a hypothesized grammar, and when encounter new expression either the grammar succeeds (and therefore remains) or it fails (and then a new grammar, or “Turing machine” would be selected); once the limit has been identified (new grammars fit the old system) language learning has occured
Outline the Chomsky hierarchy
- the simplest grammars are regular (can be accommodated by finite state automata)
- context-free grammars (can be processed by pushdown automata)
- context-sensitive grammars (can be processed with linear bounded automata, a device like a Turing machine, but with a ticker tape of bounded length)
- generative grammars (can be processed by a Turing machine)
What is Gold’s paradox?
Gold used formal methods to determine the conditions under which each class of grammars could be identified in the limit, and found that for context-sensitive and context-free grammars only informant learning would work; the paradox is that children learn most of their input in a text learning manner (this is an example of underdetermination)
Define: underdetermination
The information available from the environment is not sufficient to support a unique interpretation or inference
What is a solution to the underdetermination problem in language learning?
Classical cognitive scientists assume an innate structure (Chomsky’s UG; a universal base grammar so that learning a language is reduced to the task of learning the set of transformations that an be applied to phrase markers)
What are the three characteristics digital computers share?
- have a memory for the storage of symbolic structures
- have a mechanism separate from memory that is responsible for the operations that manipulate stored symbolic structures
- they have a controller for determining which operation to perform at any given time
What is the physical symbol system hypothesis?
that the necessary and sufficient condition for a physical system to exhibit general intelligent action is that it be a physical symbol system
Describe the dual nature of a physical symbol system
- the syntactic: their rules apply to symbols that have been identified as being of a particular type on the basis of their physical shape or form
- the semantic: these formal systems produce meaningful expression (two semantic properties: designation [an expression designates an object] and the rule-governed transition from one expression to another is also meaningful [in addition to the individual expressions])
» the application of rules cannot produce something which is meaningless aka. take care of the syntax and the semantics will take care of itself
What are the two senses in which a universal machine is maximally flexible?
- its behaviour is responsive to its inputs
- it must be able to compute the widest variety of input-output functions that is possible (known as the set of computable functions)
What is the intentional stance?
The reference to something as an object, using the presumed contents of someone’s mental states to predict their behaviour; as a result of assuming that another person possesses intentional mental states (beliefs, desires, or goals), the intentional stance involves describing other people with propositional attitudes (a statement that relates a person to a proposition or statement of fact).
The intentional stance involves using general, abstract laws to predict someone’s behaviour; the only problem here is that using logicism like this is undermined by the fact that people are often illogical