The doctrine of divine aseity has played a significant role in the development of classical theism. However, very little attention has been paid in recent years to the question of how precisely aseity should be characterized. We argue that this neglect is unwarranted since extant characterizations of this central divine attribute quickly encounter difficulties. In particular, we present a new argument to show that the most widely accepted contemporary account of aseity is inconsistent. We then consider the prospects for developing (...) a new account of aseity which avoids the pitfalls we have highlighted. (shrink)

My two principal aims in this essay are interconnected. One aim is to provide a new interpretation of the ‘infinite modes’ in Spinoza’s Ethics. I argue that for Spinoza, God, conceived as the one infinite and eternal substance, is not to be understood as causing two kinds of modes, some infinite and eternal and the rest finite and non-eternal. That there cannot be such a bifurcation of divine effects is what I take the ‘infinite mode’ propositions, E1p21–23, to establish; E1p21–23 (...) show that each and every one of the immanent effects of an infinite and eternal God is an infinite and eternal mode. The other aim is to show that these propositions can be understood as part of an extended critical response to Descartes’s infamous doctrine that God creates eternal truths and true and immutable natures. If we have the correct (Spinozan) conceptions of what God is and how God works, we see that an eternal and infinite God can only be understood to cause ‘eternal truths,’ and that these eternal truths are infinite and eternal modes of God. (shrink)

Descartes famously endorsed the view that (CD) God freely created the eternal truths, such that He could have done otherwise than He did. This controversial doctrine is much discussed in recent secondary literature, yet Descartes’s actual arguments for CD have received very little attention. In this paper I focus on what many take to be a key Cartesian argument for CD: that divine simplicity entails the dependence of the eternal truths on the divine will. What makes this argument both important (...) and interesting is that Descartes’s scholastic predecessors share the premise of divine simplicity but reject the CD conclusion. To properly understand Descartes, then, we must determine precisely where he diverges from his predecessors on the path from simplicity to CD. And when we do so we obtain a very surprising result: that despite many dramatic prima facie differences, there is no substantive difference between the relevant doctrines of Descartes and the scholastics . Or so I argue. (shrink)

This paper argues that, for Bernard Nieuwentijt, mathematical reasoning on the basis of ideas is not the same as logical reasoning on the basis of propositions. Noting that the two types of reasoning differ helps make sense of a peculiar-sounding claim Nieuwentijt makes, namely that it is possible to mathematically deduce false propositions from true abstracted ideas. I propose to interpret Nieuwentijt’s abstracted ideas as incomplete mental copies of existing objects. I argue that, according to Nieuwentijt, a proposition is mathematically (...) deducible from an abstracted idea if it can be demonstrated that that proposition makes a true claim about the object that idea forms. This allows me to explain why Nieuwentijt deems it possible to deduce false propositions from true ideas. It also implies that logic and mathematics are not as closely related for Nieuwentijt as has been suggested in the existing secondary literature. (shrink)

(2013). Thomas Bradwardine on God and the Foundations of Modality. British Journal for the History of Philosophy: Vol. 21, No. 2, pp. 368-380. doi: 10.1080/09608788.2012.689754.

A cluster of similar trends emerging in separate fields of science and philosophy points to new opportunities to apply biosemiotic ideas as tools for conceptual integration in theoretical biology. I characterize these developments as the outcome of a “relational turn” in these disciplines. They signal a shift of attention away from objects and things and towards relational structures and processes. Increasingly sophisticated research technologies of molecular biology have generated an enormous quantity of experimental data, sparking a need for relational approaches (...) that could help to find recurrent patterns in the mass of data. Earlier conceptions of relational biology and cybernetics, once deemed too abstract and speculative, are now resurrected and applied by means of new computational and simulation tools. I think this receptivity should be extended to incorporate nets of semiotic relations as heuristic guides for discerning global patterns of interactions in living systems. In this article I review aspects of systems biology and new directions in evolutionary theory, focusing on the role of circular and downward causation in relational structures and dynamical networks. I also indicate promising avenues of integration of some ideas of biosemiotics with those emerging from these new currents in biology. Relational developments in biology bear a telling similarity to a parallel relational turn presently manifest in the philosophy of science, rooted in the philosophy of physics and mathematics and in different varieties of structural and informational realism. The recognition of the relational nature of reality within these disciplines entails a tacit repudiation of nominalistic biases in science that have hindered the reception of semitiotic conceptions in biology. In previous investigations I explored connections between two kinds of relational structures: the networks of self-referential circular loops that appear pervasively in living systems, and the triadic relational structures that Peircean semiotics places at the basis of all semiotic transactions. Current relational views in the sciences seem oblivious to the difference between dyadic and triadic relations. Incorporating this essential distinction from biosemiotics into other fields could be a first step in seizing the opportunities opened by the relational turn for a renewal of biology and of natural philosophy in general, across disciplinary boundaries. (shrink)

Descartes's claim that the eternal truths were freely created by God is fraught with interpretive difficulties. The main arguments in the literature are classified as concerning the ontological status or the modalities of possibility and necessity of the eternal truths. The views of the principal defenders of the Creation Doctrine – Robert Desgabets, Pierre Sylvain Régis, and Antoine Le Grand are contrasted with those of Nicolas Malebranche. In clarifying the theological, ontological, and logical terms of the debate we can see (...) that what was at stake was the objectivity and certainty of the truths of mathematics and physics. I conclude by suggesting that this issue might fruitfully be used to clarify the disparate discussions in the contemporary literature. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Central to Descartes’ philosophy is a view about immutable essences and eternal truths. After mentioning a Platonist account of recollection in Meditation V, Descartes declares that the ideas we have of mathematical notions “are not my invention but have their own true and immutable natures” (AT VII, 64/CSM II, 44).Descartes claims that other important philosophical notions, such as God, mind, body, and human free will (AT VII, 68; AT VIII-2, 348; AT III, 383; AT VII, 433, respectively), also have immutable (...) natures or essences. Although Descartes says a good many things about this view, nowhere does he offer definitive doctrine on the matter, and in fact frequently confuses his reader with apparently inconsistent pronouncements about immutable natures and eternal truths. In this essay, I focus on the immutable natures and propose a solution to two of the main problems associated with Descartes’ position, the metaphysical status of immutable natures and the purported indivisibility of their existence as ideas in the mind. (shrink)