God and the Argument from Consciousness: A Response to Lim

Recently, Daniel Lim has published a thoughtful critique of one form of my argument for the existence of God from consciousness (hereafter, AC).1 After stating his presentation of the relevant contours of my argument, I shall present the main components of his critique, followed by my response. Since one purpose of my publications of AC has been to foster discussion about a neglected argument for God’s existence, I am thankful to lim for his interesting article and the chance to further the discussion

A comment on "Intergenerational equity: sup, inf, lim sup, and lim inf"

We reexamine the analysis of Chambers (Social Choice and Welfare, 2009), that produces a characterization of a family of social welfare functions in the context of intergenerational equity: namely, those that coincide with either the sup, inf, lim sup, or lim inf rule. Reinforcement, ordinal covariance, and monotonicity jointly identify such class of rules. We show that the addition of a suitable axiom to this three properties permits to characterize each particular rule. A discussion of the respective distinctive properties is provided.Social welfare function; Intergenerational equity; Lim sup ; Lim inf

Zombies, Epiphenomenalism and Personal Explanations: A Tension in Moreland's Argument from Consciousness

In his so-called argument from consciousness (AC), J. P. Moreland argues that the phenomenon of consciousness furnishes us with evidence for the existence of God. In defending AC, however, Moreland makes claims that generate an undesirable tension. This tension can be posed as a dilemma based on the contingency of the correlation between mental and physical states. The correlation of mental and physical states is either contingent or necessary. If the correlation is contingent then epiphenomenalism is true. If the correlation is necessary then a theistic explanation for the correlation is forfeit. Both are unwelcome results for A

A maxmin problem on finite automata

AbstractWe solve the following problem proposed by Straubing. Given a two-letter alphabet A, what is the maximal number of states f(n) of the minimal automaton of a subset of An, the set of all words of length n. We give an explicit formula to compute f(n) and we show that 1= lim infn→∞nƒ(n)/2n≤lim supn→∞nƒ(n)/2n=2

A note on spherical maxima sharing the same Lagrange multiplier

In this paper, we establish a general result on spherical maxima sharing the same Lagrange multiplier of which the following is a particular consequence: Let $X$ be a real Hilbert space. For each $r>0$, let $S_r=\{x\in X : \|x\|^2=r\}$. Let $J:X\to {\bf R}$ be a sequentially weakly upper semicontinuous functional which is G\^ateaux differentiable in $X\setminus \{0\}$. Assume that $$\limsup_{x\to 0}{{J(x)}\over {\|x\|^2}}=+\infty\ .$$ Then, for each $\rho>0$, there exists an open interval $I\subseteq ]0,+\infty[$ and an increasing function $\varphi:I\to ]0,\rho[$ such that, for each $\lambda\in I$, one has $$\emptyset\neq \left \{x\in S_{\varphi(\lambda)} : J(x)=\sup_{S_{\varphi(\lambda)}}J\right\}\subseteq \{x\in X : x=\lambda J'(x)\}\ .$

On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix

Let $\{X, X_{k,i}; i \geq 1, k \geq 1 \}$ be a double array of nondegenerate i.i.d. random variables and let $\{p_{n}; n \geq 1 \}$ be a sequence of positive integers such that $n/p_{n}$ is bounded away from $0$ and $\infty$. This paper is devoted to the solution to an open problem posed in Li, Liu, and Rosalsky (2010) on the asymptotic distribution of the largest entry $L_{n} = \max_{1 \leq i < j \leq p_{n}} \left | \hat{\rho}^{(n)}_{i,j} \right |$ of the sample correlation matrix ${\bf \Gamma}_{n} = \left ( \hat{\rho}_{i,j}^{(n)} \right )_{1 \leq i, j \leq p_{n}}$ where $\hat{\rho}^{(n)}_{i,j}$ denotes the Pearson correlation coefficient between $(X_{1, i},..., X_{n,i})'$ and $(X_{1, j},..., X_{n,j})'$. We show under the assumption $\mathbb{E}X^{2} < \infty$ that the following three statements are equivalent: \begin{align*} & {\bf (1)} \quad \lim_{n \to \infty} n^{2} \int_{(n \log n)^{1/4}}^{\infty} \left( F^{n-1}(x) - F^{n-1}\left(\frac{\sqrt{n \log n}}{x} \right) \right) dF(x) = 0, \\ & {\bf (2)} \quad \left ( \frac{n}{\log n} \right )^{1/2} L_{n} \stackrel{\mathbb{P}}{\rightarrow} 2, \\ & {\bf (3)} \quad \lim_{n \rightarrow \infty} \mathbb{P} \left (n L_{n}^{2} - a_{n} \leq t \right ) = \exp \left \{ - \frac{1}{\sqrt{8 \pi}} e^{-t/2} \right \}, - \infty < t < \infty \end{align*} where $F(x) = \mathbb{P}(|X| \leq x), x \geq 0$ and $a_{n} = 4 \log p_{n} - \log \log p_{n}$, $n \geq 2$. To establish this result, we present six interesting new lemmas which may be beneficial to the further study of the sample correlation matrix.Comment: 16 page