The Function is Unsaturated

An investigation of what Frege means by his doctrine that functions (and so concepts) are 'unsaturated'. We argue that this doctrine is far less peculiar than it is usually taken to be. What makes it hard to understand, oddly enough, is the fact that it is so deeply embedded in our contemporary understanding of logic and language. To see this, we look at how it emerges out of Frege's confrontation with the Booleans and how it expresses a fundamental difference between Frege's approach to logic and theirs

Texas Business Review, January 1967

The Business Situation in Texas; Texas Foreign Trade; Texas Building Construction Authorized in NovemberBureau of Business Researc

The Birth of Semantics

We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the appearance of critical reviews by members of the Boolean school

Texas Business Review, August 1967

The Business Situation in Texas; Climatology at Work in Texas; Texas Building Construction, January-June 1967; Texas Retail Sales, January-June 1967Bureau of Business Researc

Similarity of percolation thresholds on the hcp and fcc lattices

Extensive Monte-Carlo simulations were performed in order to determine the precise values of the critical thresholds for site ($p^{hcp}_{c,S} = 0.199 255 5 \pm 0.000 001 0$) and bond ($p^{hcp}_{c,B} = 0.120 164 0 \pm 0.000 001 0$) percolation on the hcp lattice to compare with previous precise measuremens on the fcc lattice. Also, exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth, first, and second moments of both lattices. When these series and the values of $p_c$ are compared to those for the fcc lattice, it is apparent that the site percolation thresholds are different; however, the bond percolation thresholds are equal within error bars, and the series only differ slightly in the higher order terms, suggesting the actual values are very close to each other, if not identical.Comment: 10 pages, 4 figures, submitted to J. Stat. Phy