De Re Language,De Re Eliminability,and the Essential Limits of Both

De re modality is eliminable if there is an effective translation of all wffs into non-de re equivalents. We cannot have logical equivalence unless logic has odd theses, but we can have material equivalence by banning all essences, something the non-de re facts let us do, or by giving everything such humdrum essences as self-identity and banning the more interesting ones. Eliminability cannot be got from weaker assumptions, nor independent ones of even modest generality. The net philosophical import is that, quite apart from the merits of essentialism, de re language has scant utility.     

Future Contradictions

A common and much-explored thought is ?ukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present.

The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3.     

Varieties of Reflection in Kant's Logic

For Kant, ‘reflection’ (Überlegung, Reflexion) is a technical term with a range of senses. I focus here on the senses of reflection that come to light in Kant's account of logic, and then bring the results to bear on the distinction between ‘logical’ and ‘transcendental’ reflection that surfaces in the Amphiboly chapter of the Critique of Pure Reason. Although recent commentary has followed similar cues, I suggest that it labours under a blind spot, as it neglects Kant's distinction between ‘pure’ and ‘applied’ general logic. The foundational text of existing interpretations is a passage in Logik Jäsche that appears to attribute to Kant the view that reflection is a mental operation involved in the generation of concepts from non-conceptual materials. I argue against the received view by attending to Kant's division between ‘pure’ and ‘applied’ general logic, identifying senses of reflection proper to each, and showing that none accords well with the received view. Finally, to take account of Kant's notion of transcendental reflection I show that we need to be attentive to the concerns of applied logic and how they inform the domain-relative transcendental logic that Kant presents in the first Critique.     

Possibilities,models, and intuitionistic logic: Ian Rumfitt’s The boundary stones of thought

AIan Rumfitt's new book presents a distinctive and intriguing philosophy of logic, one that ultimately settles on classical logic as the uniquely correct one–or at least rebuts some prominent arguments against classical logic. The purpose of this note is to evaluate Rumfitt's perspective by focusing on some themes that have occupied me for some time: (i) the role and importance of model theory and, in particular, the place of counter-arguments in establishing invalidity, (ii) higher-order logic, and (iii) the logical pluralism/relativism articulated in my own recent *Varieties of logic*.     

Negative Equivalence of Extensions of Minimal Logic

Two logics L₁ and L₂ are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L₁ if and only if it can be done in L₂. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.The author acknowledges support by the Alexander von Humboldt-StiftungPresented by Jacek Malinowski     

Early Examples of Resource-Consciousness

As with the development of several logical notions, it is shown that the concept of resource-consciousness, i. e. the concern over the number of times that a given sentence is used in the proof of another sentence, has its origin in the foundations of geometry, pre-dating its appearence in logical circles as BCK-logic or affine logic.