Mahdi Mollakazemiha

Benacerraf's opacity objection to the Lucas-Penrose argument holds that even if a Turing machine governs mathematical judgment, we could never identify which one, and so could never construct its Gödel sentence. This paper grants the objection and argues without what it denies. Every $\Pi^1_1$-sound recursively enumerable theory has a proof-theoretic ordinal strictly below the Church-Kleene ordinal $\omega_1^{\mathrm{CK}}$, and this bound follows from the computational hypothesis and a soundness premise alone, whatever the machine may be. Against it stands a datum from the limit stages of reflective ascent: recognising a primitive recursive ordering to be well-founded is the same act at every ordinal height. If first-person experience is veridical concerning the structure of its own acts, and if soundness is given within understanding rather than established from outside, the order types so recognised are cofinal in $\omega_1^{\mathrm{CK}}$, contradicting the bound.

There are two approaches for simulating memory as well as learning in artificial intelligence; the functionalistic approach and the cognitive approach. The necessary condition to put the second approach into account is to provide a model of brain activity that contains a quite good congruence with observational facts such as mistakes and forgotten experiences. Given that human memory has a solid core that includes the components of our identity, our family and our hometown, the major and determinative events of our lives, and the countless repeated and accepted facts of our culture, the more we go to the peripheral spots the data becomes flimsier and more easily exposed to oblivion. It was essential to propose a model in which the topographical differences are quite distinguishable. In our proposed model, we have translated this topographical situation into quantities, which are attributed to the nodes. The result is an edge-weighted graph with mass-based values on the nodes which demonstrates the importance of each atomic proposition, as a truth, for an intelligent being. Furthermore, it dynamically develops and modifies, and in successive phases, it changes the mass of the nodes and weight of the edges depending on gathered inputs from the environment.