A Return to the Analogy of Being

This chapter explores the metaphysics of what the author calls “analogous properties.” An analogous property is a non-specific property that is less natural than its specifications (called “analogue instances”) but is more natural as a merely disjunctive property. The author discusses and then applies two tests for being an analogous property: a property is analogous provided that it has more unity than a mere disjunction but yet systematically varies with respect to either its logical form or the axioms that govern its behavior. The notion of an analogous property is used to formulate several more versions of ontological pluralism. One kind of ontological pluralism appeals to a distinction between absolute and relative modes of existence. This distinction between modes of being is then used to articulate one kind of ontological superiority, which the author calls “orders of being.”

Burge on Perception and the Disjunction Problem

The Disjunction Problem states that teleological theories of perception cannot explain why a subject represents an F when an F causes the perception and not the disjunction F v G, given that the subject has mistaken G’s for F’s in the past. Without a suitable answer, non-veridical representation becomes impossible to explain. Here, I defend Burge’s teleological theory of perception against the Disjunction Problem, arguing that a perceptual state’s representing a disjunctive property is incompatible with perceptual anti-individualism. Because anti-individualism is at the heart of Burge’s theory, I conclude that Burgeans need not be concerned with the Disjunction Problem.

Quantum computaton from a quantum logical perspective

It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the information-processing in the three algorithms are presented from a different perspective, in terms of the way in which the algorithms exploit the non-Boolean quantum logic represented by the projective geometry of Hilbert space. From this quantum logical perspective, the XOR algorithm appears directly as a special case of Simon's algorithm, and all three algorithms can be seen as exploiting the non-Boolean logic represented by the subspace structure of Hilbert space in a similar way. Essentially, a global property of a function (such as a period, or a disjunctive property) is encoded as a subspace in Hilbert space representing a quantum proposition, which can then be efficiently distinguished from alternative propositions, corresponding to alternative global properties, by a measurement (or sequence of measurements) that identifies the target proposition as the proposition represented by the subspace containing the final state produced by the algorithm.