54 3 A Patternist Philosophy of Mind B= ((1- ER.) 0 ) c(X) c(X) This degree is called the pattern intensity of P in X. It quantifies the extent to which P is a pattern in X. Supposing that F(P) = X, then the first factor in the definition equals 1, and we are left with only the second term, which measures the degree of compression obtained via representing X as the result of P rather than simply representing X directly. The greater the compression ratio obtained via using P to represent X, the greater the intensity of P as a pattern in X. The first time, in the case F(P) 4 X, adjusts the pattern intensity downwards to account for the amount of error with which F(P) approximates 4 X. If one holds the second factor fixed and thinks about varying the first factor, then: The greater the error, the lossier the compression, and the lower the pattern intensity. For instance, if one wishes one may take c to denote algorithmic information measured on some reference Turing machine, and F(X) to denote what appears on the second tape of a two-tape Turing machine ¢ time-steps after placing X on its first tape. Other more naturalistic computational models are also possible here and are discussed extensively in Appendix 1 of [Goe06a]. Definition 2 The structure of X € M is the fuzzy set Stx defined via the membership function Xstx(P) =e This lets us formalize our definition of “mind” alluded to above: the mind of X as the set of patterns associated with X. We can formalize this, for instance, by considering P to belong to the mind of X if it is a pattern in some Y that includes X. There are then two numbers to look at: .% and P(Y|X) (the percentage of Y that is also contained in X). To define the degree to which P belongs to the mind of X we can then combine these two numbers using some function f that is monotone increasing in both arguments. This highlights the somewhat arbitrary semantics of “of” in the phrase “the mind of X.” Which of the patterns binding X to its environm