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 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 Carnap's Conventionalism after all?

As is well known, Carnap's conventionalism was a rejection to Kant's view ofmathematics and was fully developed in his Logische Syntax der Sprache.The purpose of this article is to step back to Der Logische Aufbau der Weltto show that the Logical Syntax of Language is an attempt to solve difficultiesfound in the earlier construction. I first clarify the notion of conventionalism, whichplays a central role in the application of mathematics to the reconstruction of empiricalknowledge. By not strictly distinguishing between the intuitive notion and thetopological concept of dimension, Carnap is led to a construction which is highlyquestionable. To illustrate the constructive method developed in the Aufbauand some of its inherent difficulties, I consider the computational aspects of theconstruction of phenomenological space via the mathematical concept of dimension.Contrary to Carnap's conventionalism, a dual nature of mathematical statements isbrought into existence by his logical reconstruction. So, if Carnap wants to retainhis mathematics as devoid of content, he must make a clear-cut distinction betweenanalytic and synthetic statements. Thus the natural follow-up to the Aufbau isthe Logical Syntax of Language.     

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 a Relevant Connective?

Journal of Philosophical Logic - There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating...     

What is a Non-truth-functional Logic?

What is the fundamental insight behind truth-functionality? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known.A clear distinction can be drawn between logics characterizable through: (1) genuinely finite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truthtabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations respect the usual tarskian postulates. So, paradoxical as that might seem at first, it turns out that truth-functional logics may be adequately characterized by non-truth-functional semantics. Now, what feature of a given logic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantial semantic characterization?The present contribution will recall and examine the basic definitions, presuppositions and results concerning truth-functionality of logics, and exhibit examples of logics indigenous to each of the aforementioned classes. Some problems pertaining to those definitions and to some of their conceivable generalizations will also be touched upon.     

What is a Sophistical Refutation?

From Aristotle’s Sophistical Refutations the following classifications are put forward and defended through extensive excerpts from the text. (AR-PFC) All sophistical refutations are exclusively either ‘apparent refutations’ or ‘proofs of false conclusions’. (AR-F) ‘Apparent refutations’ and ‘fallacies’ name the same thing. (ID-ED) All fallacies are exclusively either fallacies in dictione or fallacies extra dictionem. (ID-nAMB) Not all fallacies in dictione are due to ambiguity. (AMB-nID) Not all fallacies due to ambiguity are fallacies in dictione. (AMB&ID-ME) The set of fallacies due to ambiguity and fallacies in dictione together comprise the set of arguments said to be “dependent on mere expression”. Being “dependent on mere expression” and “dependent on language” are not the same (instances of the latter form a proper subset of instances of the former). (nME-FACT) All arguments that are not against the expression are “against the fact.” (FACT-ED) All fallacious arguments against the fact are fallacies extra dictionem (it is unclear whether the converse is true). (MAN-ARG) The solutions of fallacious arguments are exclusively either “against the man” or “against the argument.” (10) (F-ARG) Each (type of) fallacy has a unique solution (namely, the opposite of whatever causes the fallacy), but each fallacious argument does not. However, each fallacious argument does have a unique solution against the argument, called the ‘true solution’ (in other words, what fallacy a fallacious argument commits is determined by how it is solved. However, if the solution is ‘against the man’ then this is not, properly speaking, the fallacy committed in the argument. It is only the ‘true solution’—the solution against the argument, of which there is always only one—that determines the fallacy actually committed).     

What is a chemical property?

Despite the currently perceived urgent need among contemporary philosophers of chemistry for adjudicating between two rival metaphysical conceptual frameworks—is chemistry primarily a science of substances or processes?—this essay argues that neither provides us with what we need in our attempts to explain and comprehend chemical operations and phenomena. First, I show the concept of a chemical property can survive the abandoning of the metaphysical framework of substance. While this abandonment means that we will need to give up essential properties, contingent properties can give us all the stability we need to account for chemical continuity as well as change. I then go on to show that this attention to clusters of contingent properties does not force us into the arms of an alternative process metaphysical framework either. Finally, I sketch a view I call particularism with respect to chemical properties on analogy with moral particularism. I conclude by sketching some of the implications for the field of philosophy of chemistry of my proposal that we abandon our interest in the metaphysical question of what chemistry is primarily about in favor of a broadly scientific particularism with respect to kinds and properties.     

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.