Truth-Makers and the Grounding Objection to Molinism

One of the most discussed topics on the nature of God, in Christian circles today, is the subject of God’s knowledge. There are a few popular positions today that are engaged in a serious debate as to what the true biblical and philosophical position on the nature of God’s knowledge is. One such position, which has become increasingly popular and has found support among many leading Christian philosophers, such as Alvin Plantinga, Thomas Flint, and William Lane Craig, is called Molinism. While Molinism does have an abundance of supporters, there are many detractors as well. Calvinist’s, Thomists and open theists like William Hasker have been waging a war against Molinism. One of the most popular objections to Molinism is the “grounding objection.” In this paper, I will argue that the grounding objection fails to defeat Molinism because it is based on a theory of the connection of truth and reality, called truth-maker theory, which is controversial. I will also show how, even if one were to accept truth-maker theory, a Molinist could still avoid the grounding objection

The cyclic coloring complex of a complete k-uniform hypergraph

In this paper, we study the homology of the cyclic coloring complex of three different types of $k$-uniform hypergraphs. For the case of a complete $k$-uniform hypergraph, we show that the dimension of the $(n-k-1)^{st}$ homology group is given by a binomial coefficient. Further, we discuss a complex whose $r$-faces consist of all ordered set partitions $[B_1, ..., B_{r+2}]$ where none of the $B_i$ contain a hyperedge of the complete $k$-uniform hypergraph $H$ and where $1 \in B_1$. It is shown that the dimensions of the homology groups of this complex are given by binomial coefficients. As a consequence, this result gives the dimensions of the multilinear parts of the cyclic homology groups of \C[x_1,...,x_n]/ \{x_{i_1}...x_{i_k} \mid i_{1}...i_{k} is a hyperedge of $H \}$. For the other two types of hypergraphs, star hypergraphs and diagonal hypergraphs, we show that the dimensions of the homology groups of their cyclic coloring complexes are given by binomial coefficients as well

Hyperoctahedral Eulerian Idempotents, Hodge Decompositions, and Signed Graph Coloring Complexes

Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperoctahedral Eulerian idempotents

Innovation Skills for the Self-Transformation of Underrepresented Engineering Students

Underrepresented engineering students typically face multiple challenges, for example, the lack of role models and familiar guidance during their studies. Successful students have specific characteristics (i.e. skills) that allow them to thrive. In this paper the authors explore the necessary skills that may allow students to self-transform and innovate into successful engineering students.Cockrell School of Engineerin

Small-scale morphologic properties of martian gullies: insights from analysis of HiRISE images

Abstract not available