A tense logic for boethius

An interpretation in modal and tense logic is proposed for Boethius's reconciliation of God's foreknowledge with human freedom from The consolation of philosophy, Book V. The interpretation incorporates a suggestion by Paul Spade that God's special status in time be explained as a restriction of God's knowledge to eternal sentences. The argument proves valid, and the seeming restriction on omnipotence is mitigated by the very strong expressive power of eternal sentences.     

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.     

The Arabico-Islamic background of Al-Fārābī's logic

This paper examines al-Fārābī's logical thought within its Arabico-Islamic historical background and attempts to conceptualize what this background contributes to his logic. After a brief exposition of al-Fārābī's main problems and goals, I shall attempt to reformulate the formal structure of Arabic linguistics (AL) in terms of the ontological and formal characteristics that Arabic logic is built upon. Having discussed the competence of al-Fārābī in the history of AL, I will further propose three interrelated theses about al-Fārābī's logic, in terms of which I will attempt to redefine it: the logico-linguistic conception, the project of logicization, and nuclear logic. The final question that will arise is how Aristotle's logic could be built upon AL, which has a nature contrary to logic. The present paper also contributes to examining our traditional research habits in Arabic studies.     

Temporal necessity and the conditional

In [12] Richmond Thomason and Anil Gupta investigate a semantics for conditional logic that combines the ideas of [8] and [9] with a branching time model of tense logic. The resulting branching time semantics for the conditional is intended to capture the logical relationship between temporal necessity and the conditional. The central principle of this logical relationship is Past Predominance, according to which past similarities and differences take priority over future similarities and differences in determining the comparative similarity of alternative possible histories with respect to a given present moment.In this paper I will use ordinary possible worlds semantics (i.e. Kripke frames) to solve the completeness problem for a system of logic that combines conditional logic with temporal necessity in the context of Past Predominance. Branching time models turn out not to be necessary for the articulation of Past Predominance, and this means that one can axiomatize Past Predominance without first having to solve a much more difficult problem: the completeness problem for the logic of temporal necessity in the context of branching time.Thomason and Gupta argue in [12] that in addition to Past Predominance, temporal necessity and the conditional are logically related, by what have become known as the Edelberg Inferences, whose apparent validity motivates the very complicated theory presented at the end of [12]. I will conclude this paper by examining how the Edelberg inferences would be incorporated into the possible worlds based system presented in the earlier sections of this paper.This article is based on the second chapter of my doctoral dissertation Studies in the Semantics of Modality, University of Pittsburgh, 1985. I thank my adviser Richmond Thomason for his patient help throughout the course of that project.     

Gloria Anzaldúa's Affective Logic of Volverse Una

Although Gloria Anzaldúa's critical categories have steadily entered discussions in the field of philosophy, a lingering skepticism remains about her works’ ability to transcend the particularity of her lived experience. In an effort to respond to this attitude, I make Anzaldúa's corpus the center of philosophical analysis and posit that immanent to this work is a logic that lends it the unity of a critical philosophy that accounts for its concrete, multilayered character and shifting, creative force. I call this an “affective logic of volverse una.” Starting with the understanding of a situated modality of all subjectivity, Anzaldúa's work exhibits a logic of three moments distinguished by states of awareness. Each state of awareness is characterized by the generative degree of the subject's responses to its conditions: critical, individuating, and expansive. Led by her late concepts of conocimiento and nepantlera, I return to her earlier works and trace Anzaldúa's innovative exploration of undoing the oppressive condition of marginal subjectivities from “La Prieta” through Borderlands/La Frontera to her final published essay “now let us shift.” I find a liberatory schema of volverse una/becoming whole that is grounded in an active receptivity of sensibility and facilitated by affective technologies for transformation.     

Hume's Foundational Project in the Treatise

In the Introduction to the Treatise Hume very enthusiastically announces his project to provide a secure and solid foundation for the sciences by grounding them on his science of man. And Hume indicates in the Abstract that he carries out this project in the Treatise. But most interpreters do not believe that Hume's project comes to fruition. In this paper, I offer a general reading of what I call Hume's ‘foundational project’ in the Treatise, but I focus especially on Book 1. I argue that in Book 1 much of Hume's logic is put in the service of the other sciences, in particular, mathematics and natural philosophy. I concentrate on Hume's negative thesis that many of the ideas central to the sciences are ideas that we cannot form. For Hume, this negative thesis has implications for the sciences, as many of the texts I discuss make evident. I consider and criticize different proposals for understanding these implications: the Criterion of Meaning and the ‘Inconceivability Principle’. I introduce what I call Hume's ‘No Reason to Believe’ Principle, which I argue captures more adequately the link Hume envisions between his logic, in particular his examination of ideas, and the other sciences.     

Betting on conditionals

A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B, and conditional bets, I bet you that if A then B. The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional—true, false, or void for indicative conditionals and win, lose, or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgements in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis.     

Consequence and Normative Guidance

Logic, the tradition has it, is normative for reasoning. But is that really so? And if so, in what sense is logic normative for reasoning? As Gilbert Harman has reminded us, devising a logic and devising a theory of reasoning are two separate enterprises. Hence, logic's normative authority cannot reside in the fact that principles of logic just are norms of reasoning. Once we cease to identify the two, we are left with a gap. To bridge the gap one would need to produce what John MacFarlane has appropriately called a bridge principle, i.e. a general principle articulating a substantive and systematic link between logical entailment and norms of reasoning. This is Harman's skeptical challenge. In this paper I argue that Harman's skeptical challenge can be met. I show how candidate bridge principles can be systematically generated and evaluated against a set of well‐motivated desiderata. Moreover, I argue that bridge principles advanced by MacFarlane himself and others, for all their merit, fail to address the problem originally set forth by Harman and so do not meet the skeptical challenge. Finally, I develop a bridge principle that meets Harman's requirements as well as being substantive.     

A very obscure definition: Descartes’s account of love in the Passions of the Soul and its scholastic background

The definition of love given by Descartes in the Passions of the Soul (art. 79–84) has never stopped puzzling commentators. If the first Cartesian textbooks discreetly evoke or even fail to discuss Descartes’s account of love, Spinoza harshly criticizes it, pointing out that it is ‘on all hands admitted to be very obscure’. More recently several scholars have noticed the puzzling (or even paradoxical) character of the articles of the Passions of the Soul on love and hate. In this paper, I would like to propose a reassessment of the definition of love provided by the Passions of the Soul and the Letters to Elisabeth and Chanut. By tracing back Descartes’s scholastic sources (namely Aquinas’s treatises on the passions and charity in the Summa Theologiae), I will demonstrate how Descartes builds up his definition of love by displacing or subverting the meaning of several major elements of the thomistic vulgata on love. Hence, a significant part of the obscurity of the definition given by the Passions of the Soul possibly finds its ultimate rationale in this attempt to recover some traditional questions of the scholastic debate on love, while advancing new answers to them.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

A Logical Transmission Principle for Conclusive Reasons

Dretske's conclusive reasons account of knowledge is designed to explain how epistemic closure can fail when the evidence for a belief does not transmit to some of that belief's logical consequences. Critics of Dretske dispute the argument against closure while joining Dretske in writing off transmission. This paper shows that, in the most widely accepted system for counterfactual logic (David Lewis's system VC), conclusive reasons are governed by an informative, non-trivial, logical transmission principle. If r is a conclusive reason for believing p in Dretske's sense, and if p logically implies q, and if p and q satisfy one additional condition, it follows that r is a conclusive reason for believing q. After introducing this additional condition, I explain its intuitive import and use the condition to shed new light on Dretske's response to scepticism, as well as on his distinction between the so-called ‘lightweight’ and ‘heavyweight’ implications of a piece of perceptual knowledge.     

A Debate About Anderson's Logic

This article is about the history of logic in Australia. Douglas Gasking (1911–1994) undertook to translate the logical terminology of John Anderson (1893–1962) into that of Ludwig Wittgenstein's (1921) Tractatus. At the time Gilbert Ryle (1900–1976), and more recently David Armstrong, recommended the result to students; but it is reasonable to have misgivings about Gasking as a guide to either Anderson or Wittgenstein. The historical interest of the debate Gasking initiated is that it yielded surprisingly little information about Anderson's traditional (syllogistic or Aristotelian) logic and its relation to classical (first-order predicate or Russellian) logic, the ostensible topic; but the materials now exist to interpret Anderson's logic in classical logic, possibly as an algebra of classes. This would be of little interest to contemporary logicians, but it might shed some light on Anderson's philosophy.     

Divine Immutability,Divine Action and the God–World Relation

In his thought‐provoking critique of classical Christian theism, Isaak Dorner argues that a traditional understanding of God's immutability precludes any diversity in God's action and presence in the world. Dorner reasons that the view of God developed in scholastic thought entails a ‘uniform’ divine causality in which God cannot act in new and distinct ways according to the various circumstances of his creatures. This sort of critique elicits the question of whether God's immutability, if taken to include his pure actuality, flattens out his action such that he is no longer truly engaged in the lives of his creatures. In this article, I propose that a development of the virtual distinction found in scholastic theology proper will enable us to integrate (1) the pure actuality of God and (2) what we may call the formal and temporal diversity of God's action pro nobis that confirms his authentic involvement in the world. Unfolding the explanatory power of the virtual distinction will require considering its relationship to the concept of God's pure actuality and analyzing different aspects of divine action in which the diversity of that action might be located.     

The Integrative Role of Sacrifice in the Theology of Henri de Lubac

At key junctures in his theologies of spiritual exegesis, the Eucharist and the church, Henri de Lubac appeals to the notion of Christ's sacrifice as providing the pivotal content for the topic at hand. Despite this, de Lubac scholarship has devoted scant attention to the role of sacrifice in his thought. Using the fourfold sense of Scripture and the scholastic categories of res and sacramentum to establish a formal structure for de Lubac's thought, I demonstrate that sacrifice provides an integrative motif for these disparate areas of de Lubac's thought, better accounting for the ‘organic unity’ of his theology.     

John Plaifere (d.1632) on conditional predestination: a well-mixed version of scientia media and resistible grace

This article argues that John Plaifere's doctrine of predestination appearing in Appello Evangelium (1651) can be labelled as ‘conditional predestination’, since it embodies two Arminian features: scientia media and resistible grace. His conditional predestination needs to be considered as recognizing at least five different variations of predestination in his time. It is distinctive in English Arminianism, but not because Plaifere introduces scientia media and resistible grace or because he is unique in adopting these notions (as is not the case). Rather, Plaifere's doctrine of predestination is distinctive because it is a hybrid version embracing core tenets of Molina, Arminius, Arminianism, and the Remonstrants. Although not every English Arminian or Dutch Remonstrant had much concern for scientia media, Plaifere's conditional predestination advances resistible grace, which is substantially based on the notion of scientia media as its metaphysical foundation. In analyzing Plaifere's Appello Evangelium, one can gain a sense of the specific technical-theological components with which English Arminianism was constructed.     

GARRETT ON THE THEOLOGICAL OBJECTION TO HUME'S COMPATIBILISM

Between 1927 and 1936, Martin Heidegger devoted almost one thousand pages of close textual commentary to the philosophy of Immanuel Kant. This article aims to shed new light on the relationship between Kant and Heidegger by providing a fresh analysis of two central texts: Heidegger's 1927/8 lecture course Phenomenological Interpretation of Kant's Critique of Pure Reason and his 1929 monograph Kant and the Problem of Metaphysics. I argue that to make sense of Heidegger's reading of Kant, one must resolve two questions. First, how does Heidegger's Kant understand the concept of the transcendental? Second, what role does the concept of a horizon play in Heidegger's reconstruction of the Critique? I answer the first question by drawing on Cassam's model of a self-directed transcendental argument (‘The role of the transcendental within Heidegger's Kant’), and the second by examining the relationship between Kant's doctrine that ‘pure, general logic’ abstracts from all semantic content and Hume's attack on metaphysics (‘The role of the horizon within Heidegger's Kant’). I close by sketching the implications of my results for Heidegger's own thought (‘From Heidegger's Kant to Sein und Zeit’). Ultimately, I conclude that Heidegger's commentary on the Critical system is defined, above all, by a single issue: the nature of the ‘form’ of intentionality.     

Non‐Classical Knowledge

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely‐held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single‐premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker‐than‐classical K₃ logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to—whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non‐classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities.     

Cartesian Method and the Aristotelian-Scholastic Method

In book one of the Consolation of Philosophy, Boethius is portrayed as a man who suffers because he forgot philosophy. Scholars have underestimated the significance of this portrayal and considered it a literary device the goal of which is simply to introduce the discussion that follows. In this paper, I show that this view is mistaken since it overlooks that this portrayal of Boethius is the key for the understanding of the whole text. The philosophical therapy that constitutes the core of the ‘Consolation’ can in fact be properly evaluated only if we recognize the condition it is designed to cure. Through the portrayal of Boethius's forgetfulness, the ‘Consolation’ illustrates that it is the very nature of philosophical knowledge that makes it susceptible to being forgotten. Philosophical knowledge can (i) turn into misology, when it appears unable to solve certain problems, and (ii) be overrun by strong emotions. The therapy offered in the ‘Consolation’ is designed to make Boethius aware of the ‘fragility’ of philosophical knowledge and show him how to ‘strengthen’ it. He is taught how to more fully embody philosophy's precepts and that philosophy's inability to solve certain problems reveals not its failures but its limits.     

A Lewisian Semantics for S2

This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory.