## Book Reviews

Additions to the Bibliography on Mind and Consciousness

compiled by Piero Scaruffi

(Copyright © 2000 Piero Scaruffi | Legal restrictions )

#### Zadeh Lotfi: FUZZY LOGIC APPLICATIONS (Kluwer Academics, 1992)

Zadeh's 1965 article "Fuzzy Sets" applied Lukasiewicz's multivalued logic to sets, so that elements belong to a set to different degrees.
In classical logic inference is performed symbolically, regardless of the meaning of the formulae. In fuzzy logic statements are translated into elastic constraints and the meaning is computer directly via nonlinear techniques.
The degree of truth is a measure of the coherence between a proposition about the world and the state of the world. The meaning of a proposition is the constraint that limits (explicitly or implicitly) the values of the variables in that proposition.
Zadeh defines a procedure to compute the meaning, i.e. that constraint, through non-linear programming techniques. A proposition can be true, false, partially known or vague with a degree of vagueness.
Zadeh's theory of fuzzy quantities assumes that things are not necessarily true or false, but things have degrees of truth. Fuzzy logic is a multi-valued logic that extends classical logic.
Fuzzy logic can explain paradoxes such as the one about removing a grain of sand from a pile of sand (when does the pile of sand stop being a pile of sand?). In fuzzy logic each application of the inference rule erodes the truth of the resulting proposition.
As for Duhem's principle of incompatibility, the certainty that a proposition is true decreases with any increase of its precision.
A fuzzy set is a set of elements that belong to a set only to some extent. Each element is characterized by a degree of membership. An object can belong (partially) to more than one set, even if they are mutually exclusive. Each set can be subset of another set with a degree of membership. A set can belong (partially) to one of its parts.
A distribution of possibilities (relative to a variable) projects the universe of discouse (relative to that variable) in the continous unitary interval. The distribution specifies what is epistemically possible, i.e. the values admissable for that variable. The value of the distribution for a term T of discourse expresses the degree of preference that is attributed to the expression "the value of the variable is T", i.e. the degree of possibility of T for that variable.

#### Zeeman Erich Christian: CATASTROPHE THEORY (Addison-Wesley, 1977)

A collection of papers on the subject. This is the book that made Thom's catastrophe theory famous worldwide.

#### Zeki Semir: A VISION OF THE BRAIN (Blackwell, 1993)

An investigation of the visual cortex from a neurobiological viewpoint lead Zeki to argue that perception and comprehension of the world occur simultaneously thanks to reentrant (reciprocal) connections between all the specialized areas of the visual cortex. Since the visual cortex constitutes a large part of the cerebral cortex, the same properties are likely to hold for the rest of the cortex. It appears then that the function of the sensory parts of the visual cortex is to categorize environmental stimuli.
The brain copes with a continually changing environment by focusing on a few unchanging characteristics of objects out of the numberless ever-changing bits of information that it receives from those objects. The brain basically is programmed to make itself as independent as possible from world changes. The brain cannot simply absorb information from the environment, it must process it to extract those constant features that represent the physical essence of objects.

#### Zimmermann Hans: FUZZY SET THEORY (Kluwer Academics, 1985)

A thorough introduction to the theory of fuzzy sets. The second part deals with applications in several fields.