“What is a class?”

Conclusion The argument of this paper suggests that for the last hundred years or so fundamental premisses of logic have been incorrect. From these premisses a vast superstructure has been developed which, it would seem, is no more meaningful than a game such as chess.The basic errors in current class theory, it seems to me, have impeded progress in the fields of mathematics and logic. I am certain that on the theory proposed, the correct definition of a natural number can be provided. I can, in fact, provide this. What benefits it will bring to logic only time will tell.Of the greatest importance is the fact that if the theory is true, at last, there will be a firm link between the Humanities and the Sciences.     

What is the “front” of a simple geometric form?

A total of 670 undergraduate Ss were tested in three studies conducted in an attempt to define a set of cues that minimally specify perceived “frontness” and “backness” of objects. In Experiment I, Ss were instructed to identify the “front” and “back” of printed squares to which no, one, or two circles were attached. In Experiment II, different Ss made the same kind of judgment to a wider range of geometric forms. In Experiment III, different Ss judged the direction of “imagined” movement of forms from Experiment I. The results indicated that the “front” and “back” are asymmetric opposite sides, with “front” the side most different from the rest and the side toward which the form is imagined to be moving.     

What is a Correspondence Theory of Truth?

It is often thought that instances of the T-schema such as snow is white is true if and only if snow is white state correspondences between sentences andthe world, and that therefore such sentences play a crucial role in correspondence theories oftruth. I argue that this assumption trivializes the correspondence theory: even a disquotationaltheory of truth would be a correspondence theory on this conception. This discussionallows one to get clearer about what a correspondence theory does claim, and toward the end of thepaper I discuss what a true correspondence theory of truth would involve.     

What is a Thing?

“Thing” in the titular question of this paper should be construed as having the utmost generality. In the relevant sense, a thing just is an entity, an existent, a being. The present task is to say what a thing of any category is. This task is the primary one of any comprehensive and systematic metaphysics. Indeed, an answer provides the means for resolving perennial disputes concerning the integrity of the structure in reality—whether some of the relations among things are necessary merely given those relata themselves—and the intricacy of this structure—whether some things are more or less fundamental than others. After considering some reasons for thinking the generality of the titular question makes it unanswerable, the paper propounds the methodology, original inquiry, required to answer it. The key to this methodology is adopting a singular perspective; confronting the world as merely the impetus to inquiry, one can attain an account of what a thing must be. Radical ontology is a systematic metaphysics—broadly Aristotelian, essentialist, and nonhierarchical—that develops the consequences of this account. With it, it is possible to move past stalemate in metaphysics by revealing the grounds of a principled choice between seemingly incommensurable worldviews.     

What is a City?

Cities are mysteriously attractive. The more we get used to being citizens of the world, the more we feel the need to identify ourselves with a city. Moreover, this need seems in no way distressed by the fact that the urban landscape around us changes continuously: new buildings rise, new restaurants open, new stores, new parks, new infrastructures… Cities seem to vindicate Heraclitus’s dictum: you cannot step twice into the same river; you cannot walk twice through the same city. But, as with the river, we want and need to say that it is the same city we are walking through every day. It is always different, but numerically self-identical. How is that possible? What sort of mysterious thing is a city? The answer, I submit, is that cities aren’t things. They are processes. Like rivers, cities unfold in time just as they extend in space, by having different temporal parts for each time at which they exist. And walking though one part and then again through another is, literally, walking through the same whole.

     

What is a Line?

Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed the revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”     

What is it to “B” a relation?

The purpose of this paper is two fold: first, I look to show Oaklander’s (The ontology of time. New York: Prometheus Books, 2004) theory of time to be false. Second, I show that the only way to salvage the B-theory is via the adopting of the causal theory of time, and allying this to Oaklander’s claim that tense is to be eliminated. I then raise some concerns with the causal theory of time. My conclusion is that, if one adopts eternalism, the unreality of time looks a better option than the B-theory. With thanks to Robin Le Poidevin, Robbie Williams, Andrew McGonigal, Peter Simons, Chris Timpson and an anonymous referee for this journal for comments on a previous draft.     

What is a Natural Conception of the World?

Continental philosophers such as Heidegger and Nicolai Hartmann and analytic philosophers such as Ryle, Strawson, and Jennifer Hornsby may be interpreted as using competing intellectual strategies within the framework of one and the same research programme, the programme of developing a natural conception of the world. They all argue that the Manifest Image of the world (to use Sellars's terminology) is compatible with, or even more fundamental than, the Scientific Image. A comparative examination of these strategies shows that Hartmann's strategy of stratification is superior to those of Heidegger, Ryle, and Strawson.     

What is “Intervention”?

I begin by noting that several theologians and others object to special divine action (divine intervention and action beyond conservation and creation) on the grounds that it is incompatible with science. These theologians are thinking of classical Newtonian science; I argue that in fact classical science is in no way incompatible with special divine action, including miracle. What is incompatible with special divine action is the Laplacean picture, which involves the causal closure of the universe. I then note that contemporary, quantum mechanical science doesn't even initially appear to be incompatible with special divine action. Nevertheless, many who are well aware of the quantum mechanical revolution (including some members of the Special Divine Action Project) still find a problem with special divine action, hoping to find an understanding of it that doesn't involve divine intervention. I argue that their objections to intervention are not sound. Furthermore, it isn't even possible to say what intervention is, given the quantum mechanical framework. I conclude by offering an account of special divine action that isn't open to their objections to intervention.     

What is a deep interpretation?

Important differences are emerging regarding the place where analysts believe the most meaningful analytic work takes place. One area that highlights these distinct ways of working is the analyst's view of deep interpretations. Models underlying the differing perspectives on this issue are presented, along with an extended clinical example that illustrates the importance of considering, in formulating analytic interventions, the concept of a structured mind. A view of the analytic process that accords the patient's perspective greater privilege is introduced.