An Epistemicist Solution to Curry's Paradox

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I aim, then, to provide a novel, epistemicist treatment to Curry's Paradox. The epistemicist solution that I advance enables the retention of both classical logic and the traditional rules for the alethic predicate: truth-elimination and truth-introduction

Abstracta and Possibilia: Modal Foundations of Mathematical Platonism

This paper aims to provide modal foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by Hale and Wright and examined in Hale (2013); and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics

Non-Transitive Self-Knowledge: Luminosity via Modal μ-Automata

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing self-knowledge on the model of fixed points in monadic second-order modal logic, i.e. the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- an epistemic interpretation of a $\mu$-automaton permits fixed points to entrain a principled means by which to account for necessary conditions on self-knowledge

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This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the axioms of a dynamic provability logic, which embeds GL within the modal $\mu$-calculus. Via correspondence results between modal logic and the bisimulation-invariant fragment of second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via four models, without a decision as to which model is to be preferred. The first model makes intuition sensitive to hyperintensional topics, i.e. subject matters. The second model is a hyperintensional truthmaker semantics, in particular a novel epistemic two-dimensional truthmaker semantics. The third model is a topic-sensitive non-truthmaker epistemic two-dimensional semantics. The fourth model is a topic-sensitive epistemic two-dimensional truthmaker semantics

Grothendieck Universes and Indefinite Extensibility

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in the category of sets is identifiable with the elementary embeddings of large cardinal axioms. A modal coalgebraic automata's mappings are further argued to account for both reinterpretations of quantifier domains as well as the ontological expansion effected by the elementary embeddings in the category of sets. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebraic automata are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility

The effect of data preprocessing on the performance of artificial neural networks techniques for classification problems

The artificial neural network (ANN) has recently been applied in many areas, such as medical, biology, financial, economy, engineering and so on. It is known as an excellent classifier of nonlinear input and output numerical data. Improving training efficiency of ANN based algorithm is an active area of research and numerous papers have been reviewed in the literature. The performance of Multi-layer Perceptron (MLP) trained with back-propagation artificial neural network (BP-ANN) method is highly influenced by the size of the data-sets and the data-preprocessing techniques used. This work analyzes the advantages of using pre-processing datasets using different techniques in order to improve the ANN convergence. Specifically Min-Max, Z-Score and Decimal Scaling Normalization preprocessing techniques were evaluated. The simulation results showed that the computational efficiency of ANN training process is highly enhanced when coupled with different preprocessing techniques