Słupecki's Generalized Mereology and Its Flaws

One of the streams in the early development of set theory was an attempt to use mereology, a formal theory of parthood, as a foundational tool. The first such attempt is due to a Polish logician, Stanis?aw Le?niewski (1886–1939). The attempt failed, but there is another, prima facie more promising attempt by Jerzy S?upecki (1904–1987), who employed his generalized mereology to build mereological foundations for type theory. In this paper I (1) situate Le?niewski's attempt in the development of set theory, (2) describe and evaluate Le?niewski's approach, (3) describe S?upecki's strategy without unnecessary technical details, and (4) evaluate it with a rather negative outcome. The issues discussed go beyond merely historical interests due to the current popularity of mereology and because they are related to nominalistic attempts to understand mathematics in general. The introduction describes very briefly the situation in which mereology entered the scene of foundations of mathematics — it can be safely skipped by anyone familiar with the early development of set theory. Section 2 describes and evaluates Le?niewski's attempt to use mereology as a foundational tool. In Section 3, I describe an attempt by S?upecki to improve on Le?niewski's work, which resulted in a system called generalized mereology. In Section 4, I point out the reasons why this attempt is still not successful. Section 5 contains an explanation of why Le?niewski's use of Ontology in developing arithmetic also is not nominalistically satisfactory.     

Balashov on special relativity, coexistence, and temporal parts

Yuri Balashov has argued that endurantism isuntenable in the context of Minkowskispacetime. Balashov's argument runs through twomain theses concerning the relation ofcoexistence, or temporal co-location. (1)Coexistence must turn out to be an absolute or objective matter; and inMinkowski spacetime coexistence must begrounded in the relation of spacelikeseparation. (2) If endurantism is true, then(1) leads to absurd conclusions; but ifperdurantism is true, then (1) is harmless. Iobject to both theses. Against (1), I arguethat coexistence is better construed as beingrelative to a hyperplane of simultaneity.Against (2), I argue that the consequences of(1) given endurantism are no worse than theconsequences of (1) given perdurantism.     

A General Theory of Location Based on the Notion of Entire Location

It would be a good thing to have at our disposal a general theory of location that is neutral with respect to (i.e. that does not rule out or entail) (i) the view that some objects have more than one exact location, (ii) the view that some objects are located without having an exact location, and (iii) the view that some objects are “spanners”—where a spanner is an object exactly located at a region that has proper parts but which has no proper part exactly located at a proper part of the region. As far as I know, no theory of location that can be found in the literature has this feature. I put forward a new theory that does—or so I argue. The theory takes as its sole locational primitive the notion of being entirely located at.

     

How to endure presentism

Presentism and endurantism are natural bedfellows: arguments have been mounted from endurantism to presentism and vice versa. I generalise an argument against the compatibility between presentism and endurantism offered recently by Tallant (forthcoming. “Presentism, Persistence and Trans-temporal Dependence.” Philosophical Studies). I then show how to reformulate endurantism so that it is compatible with presentism. I demonstrate that this reformulated version of endurantism can do the same work with respect to the problem of temporary intrinsics as can standard definitions.     

Is Every Theory of Knowledge False?

Is knowledge consistent with literally any credence in the relevant proposition, including credence 0? Of course not. But is credence 0 the only credence in p that entails that you don't know that p? Knowledge entails belief (most epistemologists think), and it's impossible to believe that p while having credence 0 in p. Is it true that, for every value of ‘x,’ if it's impossible to know that p while having credence x in p, this is simply because it's impossible to believe that p while having credence x in p? If so, is it possible to believe that p while having (say) credence 0.4 in p? These questions aren't standard epistemological fare—at least in part because many epistemologists think their answers are obvious—but they have unanticipated consequences for epistemology. Let ‘improbabilism’ name the thesis that it's possible to know that p while having a credence in p below 0.5. Improbabilism will strike many epistemologists as absurd, but careful reflection on these questions reveals that, if improbabilism is false, then all of the most plausible theories of knowledge are also false. Or so I shall argue in this paper. Since improbabilism is widely rejected by epistemologists (at least implicitly), this paper reveals a tension between all of the most plausible theories of knowledge and a widespread assumption in epistemology.     

Against Fallibilism

In this paper I argue for a doctrine I call ‘infallibilism’, which I stipulate to mean that If S knows that p, then the epistemic probability of p for S is 1. Some fallibilists will claim that this doctrine should be rejected because it leads to scepticism. Though it's not obvious that infallibilism does lead to scepticism, I argue that we should be willing to accept it even if it does. Infallibilism should be preferred because it has greater explanatory power than fallibilism. In particular, I argue that an infallibilist can easily explain why assertions of ‘p, but possibly not-p’ (where the ‘possibly’ is read as referring to epistemic possibility) is infelicitous in terms of the knowledge rule of assertion. But a fallibilist cannot. Furthermore, an infallibilist can explain the infelicity of utterances of ‘p, but I don't know that p’ and ‘p might be true, but I'm not willing to say that for all I know, p is true’, and why when a speaker thinks p is epistemically possible for her, she will agree (if asked) that for all she knows, p is true. The simplest explanation of these facts entails infallibilism. Fallibilists have tried and failed to explain the infelicity of ‘p, but I don't know that p’, but have not even attempted to explain the last two facts. I close by considering two facts that seem to pose a problem for infallibilism, and argue that they don't.     

Does Universalism Entail Extensionalism?

Does a commitment to mereological universalism automatically bring along a commitment to the controversial doctrine of mereological extensionalism—the view that objects with the same proper parts are identical? A recent argument suggests the answer is ‘yes’. This paper attempts a systematic response to the argument, considering nearly every available line of reply. It argues that only one approach—the mutual parts view—can yield a viable mereology where universalism does not entail extensionalism.     

Assertion,Complexity, and Sincerity

The target of this paper is the ‘simple’ knowledge account of assertion, according to which assertion is constituted by a single epistemic rule of the form ‘One must: assert p only if one knows p’ (where p is a proposition). My aim is to argue that those who are attracted to a knowledge account of assertion should prefer what I call the ‘complex’ knowledge account, according to which assertion is constituted by a system of rules all of which are, taken together, constitutive of assertion. One of those rules—which, following John Searle, I call the ‘preparatory condition’—is of the form ‘One must: assert p only if one knows p.’ All else being equal, simple accounts are preferable to complex accounts. I argue in this paper that all else isn't equal. While the simple knowledge account provides an elegant explanation of certain data, it is hard to see how to integrate the simple knowledge account into a more general theory of illocutionary acts. Because the complex knowledge account avoids this objection while explaining the same data as the simple knowledge account does, I conclude that the complex knowledge account is superior to the simple knowledge account.     

GOD EMBODIED IN,GOD BODYING FORTH THE WORLD: EMERGENCE AND CHRISTIAN THEOLOGY

Abstract. I expand on Philip Clayton's application of emergence—in the context of a metaphysical position he calls emergent monism—to conceiving God's relationship to the world. Like Clayton, I adopt a panentheistic perspective, but in a way that I argue is consistent with classical philosophical theism and its grammatical analysis of Christian discourse about divine transcendence. In order to exploit further the analogical potential of an emergentist account of human mentality and agency, I argue that the standard panentheistic metaphor The world is the body of God should be complemented by the metaphor God is the body of the world.     

Distant Peers

What is the nature of rational disagreement? A number of philosophers have recently addressed this question by examining how we should respond to epistemic conflict with a so‐called epistemic peer—that is, someone over whom you enjoy no epistemic advantage. Some say that you're rationally required to suspend judgment in these cases—thereby denying the very possibility of a certain kind of rational disagreement. Others say that it's permissible to retain your beliefs even in the face of epistemic conflict. By distinguishing between close peers and distant peers, I argue that it's rational to respond to different types of peers in different ways. I also argue that remote peers—a particularly distant kind of distant peer—provide us with an important lesson in epistemic humility.     

Hegel's real habits

Hegel frequently identifies ethical life with a “second nature.” This strategy has puzzled those who assume that second nature represents a deficient appearance of ethical life, one that needs to be overcome, supplemented, or constantly challenged. I argue that Hegel identifies ethical life with a second nature because he thinks that a social order only becomes a candidate for ethical life, if it provides a context conducive to the development of what I call “real habits.” First, I show that a criterion for a real habit can be found in Hegel's Anthropology, namely, that of liberation. Next, I explain how the state, as Hegel analyzes it in the Philosophy of Right, provides such an environment by enabling trust toward and within it. I then consider two literary examples of contexts that fail to be similarly supportive—Coates' Between the World and Me and Atwood's Handmaid's Tale—concluding with reasons for thinking that real habits are an integral part of ethical life.     

Emergentism and supervenience physicalism

I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of a composite as potentially outreaching the individual entities that are its parts. I sketch one formal system that allows things to have individual entities as parts multiple times over. This is particularly useful to David Armstrong, given Lewis's charge that his structural universals must do exactly that. I close by reflecting upon the nature and point of formal mereology.     

Nonconceptual apprehension and the reason-giving character of perception

I argue that the debate about the reason-giving character of perception, and, derivatively, the contemporary debate about the nature of the (non)conceptual content of perception, is best viewed as a confrontation with refined versions of the following three independently plausible, yet mutually inconsistent, propositions:

• Perceptual apprehension Some perceptions provide reasons directly

• Exclusivity Only beliefs provide reasons directly

• Bifurcation No perception is a belief

I begin with an evaluation and refinement of each proposition so as to crystallize the source of the difficulties that dominate our thinking about the reason-giving character of perception. I argue that the contemporary literature is broadly split between those denying Bifurcation and those denying Perceptual apprehension. Though Exclusivity, too, has been target to criticism, its grip on our thinking has all too often been underestimated. As a result, a proper denial or modification of Exclusivity is yet wanting. Overcoming Exclusivity involves a considerable challenge that has not been adequately acknowledged or met—to develop a substantive account of nonconceptual apprehension. Getting a clearer understanding of the nature, the source, and possible resolution of this challenge is the primary aim of this paper.

     

RECONSIDERING BARTH'S REJECTION OF PRZYWARA'S ANALOGIA ENTIS

Many interpreters argue that Barth's rejection of Erich Przywara's analogia entis is based upon a misinterpretation and that Barth actually incorporated a form of the analogia entis into his mature theology. Through an examination of records from Przywara's visit to Barth's seminar on Thomas Aquinas at the University of Münster in 1929 along with key texts from that period, I argue that Barth did not reject the analogia entis because he misinterpreted it. Rather, he did so on the basis of an accurate account of its meaning and content provided to him personally by Przywara. I also argue that, while Barth's response to the analogia entis did change over the course of his career, he never retracted, either explicitly or implicitly, his rejection of it—nor should he have done so.     

What's Wrong with Rex? Hegel on Animal Defect and Individuality

In his Logic, Hegel argues that evaluative judgments are comparisons between the reality of an individual object and the standard for that reality found in the object's own concept. Understood in this way, an object is bad (ugly, etc.) insofar as it fails to be what it is according to its concept. In his recent Life and Action, Michael Thompson has suggested that we can understand various kinds of natural defect (i.e., defects in living things) in a similar way, and that if we do, we can helpfully see intellectual and moral badness—irrationality and vice—as themselves varieties of natural defect. In this paper, I argue that Hegel's position on animal individuality denies the claim that irrationality and vice are forms of natural defect. Hegel's account of the individuality proper to the animal organism in the Philosophy of Nature clearly disallows evaluative judgments about animals and thereby establishes a well‐defined conceptual distinction between natural defect and intellectual or ethical—i.e., broadly spiritual or geistliche—defect. Hegel thus provides a way of maintaining the difference between nature and spirit within his broader commitment to a post‐Kantian conception of substantial form.     

You meta believe it

Because of the privileged place of beliefs in explaining behaviour, mismatch cases—in which agents sincerely claim to believe that p, but act in a way that is inconsistent with that belief—have attracted a great deal of attention. In this paper, I argue that some of these cases, at least, are at least partially explained by agents believing that they believe that p, while failing to believe that p. Agents in these cases do not believe that ~p; rather, they have an indistinct first‐order, beliefy, representation that p. The indistinctness of this first‐order representation provides the leeway for the inconsistency seen in their behaviour.     

The Courage of Conviction: Andreia as Precondition for Philosophic Examination in Plato's Protagoras and Republic

There are at least two apparently conflicting views of courage found in Plato's dialogues: the intellectualist view exemplified by Socrates’s identification of courage with wisdom as found in the Protagoras; and the dispositional view of courage as a natural temperament to overcome fear in situations of danger, the necessary qualification for the auxiliary class in the Republic. In this paper I argue that these views are complementary, dispositional courage being a necessary precondition for the pursuit of the proper human excellence of wisdom. I demonstrate this by considering the role opinion plays in each understanding of courage, showing both that dispositional courage is necessary to ensure that proper opinions be retained in the pursuit of wisdom and that wisdom is necessary to guarantee these opinions are the proper ones. Finally, I argue that not only is this relationship of the two understandings of courage present in the Republic, but even in the Protagoras Socrates’s method of conducting the elenchus betrays awareness on his part of the importance of dispositional courage in the pursuit of wisdom     

Does Freudian Theory Resolve “The Paradoxes of Irrationality”?*

This paper consists of two related parts: I. A detailed critique of Donald Davidson's thesis—in his “The Paradoxes of Irrationality”—that “…any satisfactory [explanatory] view [of irrationality] must embrace some of Freud's most important theses” (p. 290). I argue that this conclusion is doubly flawed: (i) Davidson's case for it is logically ill‐founded, and (ii) its Freudian plaidoyer is also factually false. II. Relatedly, in the second part, I confute the recent arguments given by Marcia Cavell, Thomas Nagel, et al. to establish that psychoanalytic causal explanations of irrationality are epistemically justified, because they are extensions of the desire‐cumbelief pattern of accounting for intentional actions. As a corollary, it becomes clear that these authors have failed to undermine my epistemological strictures on the foundations of psychoanalysis.     

Endurantism vs. Perdurantism?: A Debate Reconsidered

One of the central debates in contemporary metaphysics has been the debate between endurantism and perdurantism about persistence. In this paper I argue that much of this debate has been misconstrued: most (if not all) of the arguments in the debate crucially rely on theses which are strictly orthogonal to the endurantism/perdurantism debate. To show this, I note that the arguments in the endurantism/perdurantism debate typically take the following form: one presents a challenge that endurantists (/perdurantists) allegedly have some trouble addressing, and to which perdurantism (/endurantism) apparently has a straightforward response. I argue, however, that in each case, there are versions of endurantism (/perdurantism) that can offer precisely the same (or at least a highly analogous) response to the challenge, and thus the ability to provide this particular solution does not directly tell in favour of one the two views. In §1, I elaborate two views which will be particularly prominent in the discussion: liberal endurantism and restrictive perdurantism. In §2–6 I discuss in turn the central pro‐perdurantism arguments: the argument from anthropocentricism, the argument from vagueness, the argument from recombination, the argument from temporary intrinsics, and the argument from coincidence. In §7–8, I discuss the main pro‐endurantism arguments: the arguments from motion, and the argument from permanent coincidence. Finally, in §9, I discuss what conclusion can be drawn from this discussion.