Causes and Counterparts

It follows from David Lewis's counterpart-theoretic analysis of modality and his counterfactual theory of causation that causal claims are relativized to a set of counterpart relations. Call this Shlewis's view. I show how Shlewis's view can provide attractively unified solutions to similar modal and causal puzzles. I then argue that Shlewis's view is better motivated, by his own lights, than the view Lewis actually held, and also better motivated than a similar approach which relativizes causal claims to sets of ‘contrast events’.     

Temporally Incongruent Counterparts

Despite its first page this paper is not yet another piece on Kant! Rather, the paper is a contribution to the literature on incongruent counterparts. Specifically, it concerns the question of whether we can construct a temporal version of the puzzle of incongruent counterparts—a question which (as far as 1 can tell) has been thoroughly neglected. I maintain that we can construct such a version of the puzzle, and that this temporal variant on the phenomenon has something to teach us about popular arguments for the possibility (or even actuality) of four-dimensional space.     

What Incongruent Counterparts Show

Abstract: In a recent paper, Robert Hanna argues that Kant's incongruent counterparts example can be mobilized to show that some mental representations, which represent complex states of affairs as complex, do so entirely non‐conceptually. I will argue that Hanna is right to see that Kant uses incongruent counterparts to show that there must be a non‐conceptual component to cognition, but goes too far in concluding that there must be entirely non‐conceptual representations that represent objects as existing in space and time. Kant is deeply committed to the thesis that no representation of a complex state of affairs as complex can be entirely non‐conceptual. For Kant, all representations of complex states of affairs as complex (including those of incongruent counterparts) are conceptually structured. I present an interpretation of the Transcendental Aesthetic according to which Kant not only aims at Leibnizian and Newtonian accounts of space and time, but also Hume's. Hume's account fails to make representations of complex states of affairs sufficiently determinate. Kant offers an account later in the Critique that is meant to correct this failing by requiring that all representations of complex states of affairs as complex be conceptually (inferentially) structured.     

Temporal Predication with Temporal Parts and Temporal Counterparts

If ordinary objects have temporal parts, then temporal predications have the following truth conditions: necessarily, (a is F) at t iff a has a temporal part that is located at t and that is F. If ordinary objects have temporal counterparts, then, necessarily, (a is F) at t iff a has a temporal counterpart that is located at t and that is F. The temporal-parts account allows temporal predication to be closed under the parthood relation: since all that is required to be F at t is to have a temporal part, a t, that is located at t and that is F, every object that has a t as a temporal part is F at t. Similarly for the temporal-counterparts account. Both closure under parthood and closure under counterparthood are shown to have unacceptable consequences. Then strategies for avoiding closure are considered and rejected.     

Deleuze's Use of Kant's Argument from Incongruent Counterparts

The aim of this paper is to explore Deleuze's use of Kant's argument from incongruent counterparts, which Kant uses to show the existence of what he calls an “internal difference” within things. I want to explore how Deleuze draws out an important distinction between the concept and the Idea, and provides an incisive account of his relationship to both the Kantian and Leibnizian projects. First, I look at Kant's use of the argument to provide a refutation of the Leibnizian account of space, before showing how this criticism in fact rests on the question of the conceptual determination of object. Second, I show how Deleuze develops a taxonomy of difference on the basis of his reading of Kant's argument. Finally, I look at what Deleuze sees as the limitations in Kant's understanding of this concept and Deleuze's attempt to overcome these limitations through the introduction of the notion of the Idea, which will provide a genetic and nonconceptual account of the object. In doing so, I show why Deleuze takes the formulation of an adequate account of difference to be one of the central aims of his own metaphysics.     

Models for Hylomorphism

Journal of Philosophical Logic - In a series of papers (Fine et al., 1982; Fine, Noûs28(2), 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his...     

Models for choice-reaction time

In the two-choice situation, the Wald sequential probability ratio decision procedure is applied to relate the mean and variance of the decision times, for each alternative separately, to the error rates and the ratio of the frequencies of presentation of the alternatives. For situations involving more than two choices, a fixed sample decision procedure (selection of the alternative with highest likelihood) is examined, and the relation is found between the decision time (or size of sample), the error rate, and the number of alternatives.     

Modal Correspondence for Models

This paper considers the correspondence theory from modal logic and obtains correspondence results for models as opposed to frames. The key ideas are to consider infinitary modal logic, to phrase correspondence results in terms of substitution instances of a given modal formula, and to identify bisimilar model-world pairs.     

Models,Models, and Models

Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a variety of modeling techniques that go beyond basic logic and elementary probability theory. What unifies this approach is a focus on what Alan Perlis called procedural literacy. This essay argues that the future spoils in philosophical research will disproportionally go to those who are procedurally literate.     

Trifactor Models for Multiple-Ratings Data

In this study we extend and assess the trifactor model for multiple-ratings data in which two different raters give independent scores for the same responses (e.g., in the GRE essay or to subset of PISA constructed-responses). The trifactor model was extended to incorporate a cross-classified data structure (e.g., items and raters) instead of a strictly hierarchical structure. we present a set of simulations to reflect the incompleteness and imbalance in real-world assessments. The effects of the rate of missingness in the data and of ignoring differences among raters are investigated using two sets of simulations. The use of the trifactor model is also illustrated with empirical data analysis using a well-known international large-scale assessment.     

Models for relevant modal logics

Semantics are given for modal extensions of relevant logics based on the kind of frames introduced in [7]. By means of a simple recipe we may obtain from a class FRM (L) of unreduced frames characterising a (non-modal) logic L, frame-classes FRM (L.M) characterising conjunctively regular modal extensions L.M of L. By displaying an incompleteness phenomenon, it is shown how the recipe fails when reduced frames are under consideration.     

Term Models for Abstraction Principles

Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, the method is poorly behaved unless the background second-order logic is predicative.     

Component Models for Fuzzy Data

The fuzzy perspective in statistical analysis is first illustrated with reference to the “Informational Paradigm” allowing us to deal with different types of uncertainties related to the various informational ingredients (data, model, assumptions). The fuzzy empirical data are then introduced, referring to J LR fuzzy variables as observed on I observation units. Each observation is characterized by its center and its left and right spreads (LR₁ fuzzy number) or by its left and right “centers” and its left and right spreads (LR₂ fuzzy number). Two types of component models for LR₁ and LR₂ fuzzy data are proposed. The estimation of the parameters of these models is based on a Least Squares approach, exploiting an appropriately introduced distance measure for fuzzy data. A simulation study is carried out in order to assess the efficacy of the suggested models as compared with traditional Principal Component Analysis on the centers and with existing methods for fuzzy and interval valued data. An application to real fuzzy data is finally performed. We would like to express our gratitude to the Editor, the Associate Editor, and the Referees whose comments and suggestions improved significantly the quality of the paper.