The mereology of thermodynamic equilibrium

The special composition question (SCQ), which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, the thermodynamic composition principle (TCP): Multiple systems in (generalized) thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, might form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected.

Incompatibility and the pessimistic induction: a challenge for selective realism

Two powerful arguments have famously dominated the realism debate in philosophy of science: The No Miracles Argument (NMA) and the Pessimistic Meta-Induction (PMI). A standard response to the PMI is selective scientific realism (SSR), wherein only the working posits of a theory are considered worthy of doxastic commitment. Building on the recent debate over the NMA and the connections between the NMA and the PMI, I here consider a stronger inductive argument that poses a direct challenge for SSR: Because it is sometimes exactly the working posits which contradict each other, i.e., that which is directly responsible for empirical success, SSR cannot deliver a general explanation of scientific success.

Methodological Naturalism and Reflexivity Requirement

Methodological naturalists regard scientific method as the only effective way of acquiring knowledge. Quite the contrary, traditional analytic philosophers reject employing scientific method in philosophy as illegitimate unless it is justified by the traditional methods. One of their attacks on methodological naturalism is the objection that it is either incoherent or viciously circular: any argument that may be offered for methodological naturalism either employs a priori methods or involves a vicious circle that ensues from employing the very method that the argument is aimed to show its credentials. The charge of circularity has also been brought against the naturalistic arguments for specific scientific methods; like the inductive argument for induction and the abductive argument for the inference to the best explanation. In this paper, I respond to the charge of circularity using a meta-methodological rule that I call ‘reflexivity requirement.’ Giving two examples of philosophical works, I illustrate how the requirement has already been considered to be necessary for self-referential theories. At the end, I put forward a meta-philosophical explanation of the naturalism-traditionalism debate over the legitimate method of philosophy.

Reasons for the Method in Descartes’ Discours

In the practical philosophy of the Discours de la Méthode, before the theoretical metaphysics of Part Four and the Meditationes, Descartes gives us an inductive argument that his method, the procedure and cognitive psychology, is veracious at its inception. His evidence, akin to his Scholastic predecessors, is God, a maximally perfect being, established an ontological foundation for knowledge such that reason and nature are isomorphic. Further, the method, he tells us, is a functional definition of human reason; that is, like other rationalists during this period, he holds the structure of reason maps onto the world. The evidence for this thesis is given in what I call the groundwork to Descartes’ philosophical system, essentially the first half of the Discours, where, through a series of examples in the preamble of Part Two, he, step-by-step, ascends from the perfection of artifacts through the imposition of reason (the Architect Example) to the perfection of a constituent’s use of her cognitive faculties (the Wise-Lawgiver Example), to God perfecting and ordering reality (the Divine Artificer Example). Finally, he descends, establishing the structure of human reason, which undergirds and entails the procedure of the method (the Laws of Sparta Example).

Assessing Papal Probabilities: A Reply to Joseph E. Blado

Joseph Blado critiqued my probabilistic arguments against Roman papal doctrines by deploying probability arguments, particularly Bayesian arguments, in favor of the papacy. He contends that there are good C-inductive arguments for papal doctrine that, taken together, add up to a good P-inductive argument. I argue that his inductive arguments fail, and moreover that there are three good C-inductive arguments against papal doctrine in the neighborhood of his failed arguments. I conclude by critiquing his retreat to what he calls ‘skeptical papalism’ as a last ditch sort of move to defend papal doctrine.

Mary and Fátima: A Modest C-Inductive Argument for Catholicism

C-Inductive arguments are arguments that increase the probability of a hypothesis. In this paper, we offer a C-Inductive argument for the Roman Catholic hypothesis. We specifically argue that one would expect the Miracle of Fátima on Roman Catholicism more so than on alternative hypotheses. Since our argument draws on confirmation theory, we first give a primer for how confirmation theory works. We then, provide the historical facts surrounding the Miracle of Fátima. We offer up two competing naturalistic explanations that attempt to explain the historical facts, but then, argue that a supernatural explanation is superior. Having established that something miraculous likely occurred at Fátima, we move to argue for the overall thesis of the paper. Finally, we engage several objections to our argument.

Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators

We study fundamental solutions of elliptic operators of order $$2m\ge 4$$ 2 m ≥ 4 with constant coefficients in large dimensions $$n\ge 2m$$ n ≥ 2 m , where their singularities become unbounded. For compositions of second order operators these can be chosen as convolution products of positive singular functions, which are positive themselves. As soon as $$n\ge 3$$ n ≥ 3 , the polyharmonic operator $$(-\Delta )^m$$ ( - Δ ) m may no longer serve as a prototype for the general elliptic operator. It is known from examples of Maz’ya and Nazarov (Math. Notes 39:14–16, 1986; Transl. of Mat. Zametki 39, 24–28, 1986) and Davies (J Differ Equ 135:83–102, 1997) that in dimensions $$n\ge 2m+3$$ n ≥ 2 m + 3 fundamental solutions of specific operators of order $$2m\ge 4$$ 2 m ≥ 4 may change sign near their singularities: there are “positive” as well as “negative” directions along which the fundamental solution tends to $$+\infty $$ + ∞ and $$-\infty $$ - ∞ respectively, when approaching its pole. In order to understand this phenomenon systematically we first show that existence of a “positive” direction directly follows from the ellipticity of the operator. We establish an inductive argument by space dimension which shows that sign change in some dimension implies sign change in any larger dimension for suitably constructed operators. Moreover, we deduce for $$n=2m$$ n = 2 m , $$n=2m+2$$ n = 2 m + 2 and for all odd dimensions an explicit closed expression for the fundamental solution in terms of its symbol. From such formulae it becomes clear that the sign of the fundamental solution for such operators depends on the dimension. Indeed, we show that we have even sign change for a suitable operator of order 2m in dimension $$n=2m+2$$ n = 2 m + 2 . On the other hand we show that in the dimensions $$n=2m$$ n = 2 m and $$n=2m+1$$ n = 2 m + 1 the fundamental solution of any such elliptic operator is always positive around its singularity.

Birational Superrigidity and K-Stability of Singular Fano Complete Intersections

We introduce an inductive argument for proving birational superrigidity and $K$-stability of singular Fano complete intersections of index one, using the same types of information from lower dimensions. In particular, we prove that a hypersurface in $\mathbb{P}^{n+1}$ of degree $n+1$ with only ordinary singularities of multiplicity at most $n-5$ is birationally superrigid and $K$-stable if $n\gg 0$. As part of the argument, we also establish an adjunction-type result for local volumes of singularities.

Principles and Contraries

Contrary to readings that consider Physics I 5 as doxographical, this chapter argues that it is the first step of a constructive inquiry whose conclusions, paradoxical as they may seem, are never dismissed later. Its main thesis is that the contraries are principles of coming-to-be and passing-away, but it also endorses the stronger thesis that the principles are contraries. Although it appeals to doxographical considerations, its main section is an inductive argument which heralds the concept of privation, without mentioning it explicitly. This chapter studies the relationship between the opposition of contraries and that of possession and privation, as well as the way Aristotle reduces the intermediates to the contraries. Finally, it shows how the device of sustoikhia (‘series’) allows Aristotle to identify the opposition between possession and privation as the first pair of contraries and to organize the positions of his forerunners in respect of their proximity to the truth.