The concept of free will as an infinite metatheoretic recursion

It is argued that the concept of free will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two-stage model, which deconstructs free will into the causally open "free" stage with its closure in the "will" stage, is implicitly a move in this direction. However, to avoid the dilemma of determinism, free will additionally requires an infinite regress of causal meta-stages, making free choice a hypertask. We use this model to define free will of the rationalist-compatibilist type. This is shown to provide a natural three-way distinction between quantum indeterminism, freedom and free will, applicable respectively to artificial intelligence (AI), animal agents and human agents. We propose that the causal hierarchy in our model corresponds to a hierarchy of Turing uncomputability. Possible neurobiological and behavioral tests to demonstrate free will experimentally are suggested. Ramifications of the model for physics, evolutionary biology, neuroscience, neuropathological medicine and moral philosophy are briefly outlined.Comment: Accepted in INDECS (close to the accepted version

Solutions of the Diophantine Equation 7X2+Y7=Z27X^2+Y^7=Z^2 from Recurrence Sequences

summary:Consider the system $x^2-ay^2=b$, $P(x,y)= z^2$, where $P$ is a given integer polynomial. Historically, the integer solutions of such systems have been investigated by many authors using the congruence arguments and the quadratic reciprocity. In this paper, we use Kedlaya's procedure and the techniques of using congruence arguments with the quadratic reciprocity to investigate the solutions of the Diophantine equation $7X^2+Y^7=Z^2$ if $(X,Y)=(L_n,F_n)$ (or $(X,Y)=(F_n,L_n)$) where $\{F_n\}$ and $\{L_n\}$ represent the sequences of Fibonacci numbers and Lucas numbers respectively

Bartz-Marlewski equation with generalized Lucas components

summary:Let $\lbrace U_n\rbrace =\lbrace U_n(P,Q)\rbrace$ and $\lbrace V_n\rbrace =\lbrace V_n(P,Q)\rbrace$ be the Lucas sequences of the first and second kind respectively at the parameters $P \ge 1$ and $Q \in \lbrace -1, 1\rbrace$. In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation $$x^2-3xy+y^2+x=0\,,$$ where $(x,y)=(U_i, U_j)$ or $(V_i, V_j)$ with $i$, $j \ge 1$. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters

Solutions of the Markoff equation in Tribonacci numbers

In this paper, we determine all of the positive integer solutions of the so-called Markoff equation x2 + y2 + z2 = 3xyz in the sequence of Tribonacci numbers {Tn}, i.e. (x, y, z) = (Ti, Tj, Tk) such that i, j, k ≥ 2

Evolution of structural and magnetic properties in Ta/Ni_81Fe_(19) multilayer thin films

The interdiffusion kinetics in short period (12.8 nm) Ta/Ni81Fe19 polycrystalline multilayer films has been investigated and related to the evolution of soft magnetic properties upon thermal annealing in the temperature range 300-600-degrees-C. Small angle x-ray diffraction and transmission electron microscopy were used to estimate the multilayer period. Interdiffusion in the multilayers was directly computed from the decay of the satellites near (000) in a small angle x-ray diffraction spectrum. A kinetic analysis of interdiffusion suggests that grain growth is concurrent with grain boundary diffusion of Ta in Ni81Fe19. The evolution of soft magnetic properties of Ni81Fe19, i.e., lowering of 4piM(s) and increase in coercivity H(c), also lend support to the above analysis

An analysis of the relationship between the international economic-legal regime and the achievement of balanced and stable growth through the international economic cycle

The global economy is controlled by an 'international economic–legal regime' (hereinafter "IELR"), in which international economic institutions (hereinafter "IEIs") are the major nonstate actors. They provide the rules of the game for the interaction of the States in an international economic scenario. These IEIs, through their institutional capacity, enhance certainty and predictability within the IELR, thereby passively supporting stable and a balanced growth of global economy. This thesis argues that opportunities to achieve stable and balanced growth, in which both the financial and the real side of the economy grow, can be improved if the IEIs increase their focus on the relationship between the Economic Cycle and the IEIs' institutional role. This argument is developed by analysing the relationship between the IEIs' institutional role and the Economic Cycle, first describing the Economic Cycle, and then clarifying the functioning of the IEIs in their institutional role. To narrow the scope of this research, this thesis takes two IEIs as case studies; namely, the IMF and the WTO

Optical Properties Of Treated And Untreated Monocrystalline p- Si<L11>,p-Si<100>, n-Si<l11> and n-Si<100) Wafers In The Visible Region At Room Temperature.

Silicon only based materials have dominated the electronic applications for the past few decades and now the materials have almost reached its saturation point

Lesion size, latent period and sporulation on leaf discs as indicators of resistance of Hevea to Microcyclus ulei.

This study investigated lesion sizes, latent periods and sporulation of leaf discs as indicators of resistance of Hevea to Microcyclus ulei. There were clonal differences in the rate of development of mycelium and appearance of lesions, sizes of lesions, latent period and the quantity of conidia produced on discs of Hevea leaves. There was a positive correlation between conidial production and lesion size, and negative correlations existed between conidial production and latent period and lesion size and latent period. Latent period and sporulation are also important components for assessment of resistance. Clones GT 711, RRIM 501, CNS AM 7701, SIAL 842 and SIAL 263 possessed relatively smaller lesions, longer latent periods and reduced sporulation. On these clones, the differences in lesion size were significant between clonesbut not between races of Microcyclus ulei. However, diffences in conidial production between clones, races and the interaction between clones and races were significant

Responses of winged bean (Psophocarpus Tetragonolobus) to Mycorrhiza Inoculation in pot and field trials

Two greenhouse experiments and one field trial were conducted to provide information on the possibility of exploiting the beneficial effects of vesicular-arbuscular mycorrhizal fungi in Malaysian agriculture. In the first study, winged bean (Psophocarpus tetragonolobus) was grown in steam-sterilized Serdang soils and the development of the endophytes evaluated fortnightly. The second experiment was conducted in unsterilized Serdang and Munchong soils respectively with three levels ofP and/or inoculated with Acaulospora laevis, Glomus macrocarpum, Glomus mosseae, a mixture of Glomus species and Scutellospora calospora. All inocula, except for S. calospora, significantly enhanced growth throughout the course of the experiments and increased N, P and K concentrations in the plant tissues. G. mosseae was superior to the rest. In the field trial, Acaulospora laevis, Scutellospora calospora and Glomus mosseae were inoculated into winged bean grown in unsterilized field soil, with or without phosphate fertilizer. Inoculation of winged bean with G. mosseae significantly (P < 0.05) increased inflorescence formation (4.5/plant) , particularly at an intermediate level (60 kg ha-1 ) of P fertilizer