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Studia Neoaristotelica

A Journal of Analytic Scholasticism

Volume 11, Issue 2, 2014

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1. Studia Neoaristotelica: Volume > 11 > Issue: 2
Dale Jacquette Toward a Neoaristotelian Inherence Philosophy of Mathematical Entities
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The fundamental idea of a Neoaristotelian inherence ontology of mathematical entities parallels that of an Aristotelian approach to the ontology of universals. It is proposed that mathematical objects are nominalizations especially of dimensional and related structural properties that inhere as formal species and hence as secondary substances of Aristotelian primary substances in the actual world of existent physical spatiotemporal entities. The approach makes it straightforward to understand the distinction between pure and applied mathematics, and the otherwise enigmatic success of applied mathematics in the natural sciences. It also raises an interesting set of challenges for conventional mathematics, and in particular for the ontic status of infinity, infinite sets and series, infinitesimals, and transfinite cardinalities. The final arbiter of all such questions on an Aristotelian inherentist account of the nature of mathematical entities are the requirements of practicing scientists for infinitary versus strictly finite mathematics in describing, explaining, predicting and retrodicting physical spatiotemporal phenomena. Following Quine, we classify all mathematics that falls outside of this sphere of applied scientific need as belonging to pure, and, with no prejudice or downplaying of its importance, ‘recreational’, mathematics. We consider a number of important problems in the philosophy of mathematics, and indicate how a Neoaristotelian inherence metaphysics of mathematical entities provides a plausible answer to Benacerraf’s metaphilosophical dilemma, pitting the semantics of mathematical truth conditions against the epistemic possibilities for justifying an abstract realist ontology of mathematical entities and truth conditions.
2. Studia Neoaristotelica: Volume > 11 > Issue: 2
Miguel García-Valdecasas Givens and Foundations in Aristotle’s Epistemology
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Aristotle’s epistemology has sometimes been associated with foundationalism, the theory according to which a small set of premise-beliefs that are deductively valid or inductively strong provide justification for many other truths. In contemporary terms, Aristotle’s foundationalism could be compared with what is sometimes called “classical foundationalism”. However, as I will show, the equivalent to basic beliefs in Aristotle’s epistemology are the so-called first principles or “axiómata”. These principles are self-evident, but not self-justificatory. They are not justified by their act of understanding, but by the arguments that satisfactorily prove them. In addition, these principles are intellectual, rather than perceptual, so that no basic belief that is about our immediate experience or sensorydata is apt to provide the required foundation of knowledge. In spite of this, I argue that Aristotle’s foundationalism has no givens, and that his epistemology resists the objections usually leveled against givens.
3. Studia Neoaristotelica: Volume > 11 > Issue: 2
Walter Redmond De ontologico logicae fundamine meditatio
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I wish to reflect briefly on what logic “is” and what the “is” is founded upon. Logic has traditionally been linked with argumentation. I shall examine a simple argument relative to a “miniworld”, and with the help of current logic and traditional ontology, extract from it a modest theory of logical entities and relations. “Current logic” involves modal semantics and the “traditional ontology” is that of Plato, Bonaventure and Thomas Aquinas, and some later philosophers.
discussion articles
4. Studia Neoaristotelica: Volume > 11 > Issue: 2
Louis Groarke Response to “Hildebrand vs. Groarke” by Vlastimil Vohánka
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I defend an Aristotelian account of induction against an analytic challenge that recommends Bernoulllian satistics as a more rigorous foundation for inductive reasoning. If Aristotle defines metaphysical necessity as a causal relation produced by the form inherent in a substance, the modern Humean account construes metaphysical necessity as a matter of exceptionless statistical regularity. I argue that Humean epistemology cannot move beyond relations of ideas to a description of the true nature of things in the world and that Aristotelian realism offers, in comparison, a metaphysical perspective that can serve as a firm foundation for science. Any attempt to prove the validity of induction using mathematical probability is bound to fail for basic principles of all mathematics begin ininduction. Any such strategy is viciously circular. In the course of the paper, I argue that logic must begin in an immediate leap of reason, that intuitive insights can be tested in hindsight, that metaphysical essentialism can account for the accidental (or contingent) properties of things, and that phenomenological distinctions between metaphysical, natural, and empirical necessity can be mapped onto Aristotelian categories.