I lay down a system of structural rules for various notions of ground and establish soundness and completeness.

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of (...) problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)

This article develops the Pure Logic of Iterated Full Ground (PLIFG), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we (...) can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle. (shrink)

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many (...) case, giving rise to the Pure Logic of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one (...) that extends the rules of the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

I develop a graph-theoretic model theory for pure and iterative grounding logics.

I compare the semantic approach to the logic of worldly grounding put forward in my “Grounding and Truth-Functions” (2010) with the approach developed by Fine in “Guide to Ground” (2012a) and “The Pure Logic of Ground” (2012b). I argue that both are defective in some respects, and offer an alternative approach in the same spirit but based on a new semantic framework, which combines the best aspects of the frameworks within which the previous approaches were (...) developed. (shrink)

Though the study of grounding is still in the early stages, Kit Fine, in ”The Pure Logic of Ground”, has made a seminal attempt at formalization. Formalization of this sort is supposed to bring clarity and precision to our theorizing, as it has to the study of other metaphysically important phenomena, like modality and vagueness. Unfortunately, as I will argue, Fine ties the formal treatment of grounding to the obscure notion of a weak ground. The obscurity (...) of weak ground, together with its centrality in Fine’s system, threatens to undermine the extent to which this formalization offers clarity and precision. In this paper, I show how to overcome this problem. I describe a system, the logic of strict ground (LSG) and demonstrate its adequacy; I specify a translation scheme for interpreting Fine’s weak grounding claims; I show that the interpretation verifies all of the principles of Fine’s system; and I show that derivability in Fine’s system can be exactly characterized in terms of derivability in LSG. I conclude that Fine’s system is reducible to LSG. (shrink)

The difference between Hermann Cohen’s systematic philosophy and his philosophy of religion can be determined via the logical “Judgment of Contradiction,” viewed as an “Authority of Annihilation.” In Cohen’s Logic of Pure Knowledge the “Judgment of Contradiction” acts as a “means of protection” against “falsifications” that may have arisen on the pathway through the previous judgments of “origin” and “identity.” Cohen thematizes these operations in his Religion of Reason Out of the Sources of Judaism, too. However, there they (...) do not form the grounding for natural science but rather for the knowledge of nature as creation in a strict correlation to God’s uniqueness. Any admixture between God and nature is the falseness that must be excluded via the “Authority of Annihilation.” The Being of God places the world over against the possibility of its own radical Non-Being. Yet at the same time, a second mode of Negation, a relative Nothing providing continuity for the world’s being-there, grounded in the “Logic of Origin,” retains its validity. In Cohen’s view a Creation “in the beginning” stands side by side with a continuous “renewal of the world”. (shrink)

This paper is the first part of an exploration into the logical properties of relative identity. After providing the semantic grounds for various monadic logics of relative identity, I define the minimal system and its nine extensions. It is suggested that despite their purely formal origin at least some of them may contain nontrivial philosophical insights. All logics are axiomatized by means of sound and complete sequent calculi. I show their affinities with existing formalizations.

Kit Fine, in "The Pure Logic of Ground", has made a seminal attempt at formalizing the notion of ground. Fine ties the formal treatment of grounding to the notion of a weak ground. Formalization of this sort is supposed to bring clarity and precision to our theorizing. Unfortunately, as I will argue, it's not clear what weak ground is. I review five alternative explanations of the idea, and argue that none of them are ultimately (...) satisfactory. I close by outlining a more complicated explanation of the notion that turns out to be more satisfactory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 719 An Apology for Apologetics: A Study in the Logic of lnterreligious Dialogue. By PAUL J. GRIFFITHS. New York: Orbis, 1991. ISBN: 0 88344 761 4. pp. 113. Jesus Christ at the Encounter of World Religions. By J. DUPUIS. New York: Orbis, 1991 (ET: Robert R. Barr, from French, 1989). ISBN: 0 88344 723 1. pp. 301. Griffiths presents a rigorous argument for the possibility of (...) con· tradictory claims between different religious communities. His inspira· tion, as he acknowledges, is William Christian Snr. His basic argu· ment is: " If representative intellectuals belonging to some specific religious community come to judge at a particular time that some or all of their own doctrine-expressing sentences are incompatible with some alien religious claim(s), then they should feel obliged to engage in both positive and negative apologetics vis-a-vis these alien religious claim(s) and their promulgators" (3). He takes negative apologetics to be a critique of arguments made against one's own religious claims, showing that such arguments fail or are inconsistent or incoherent. Positive apologetics shows how a particular religious community's doctrines are cognitively superior, in some respect(s), to another religious community 's doctrines. It is essential for this enterprise that only methods of argumentation and criteria of knowledge acceptable to the adversary are employed. This requires the acceptance of natural theology. Griffiths is well aware of the lion's den he is entering, as his proposals run counter to much scholarship in the area of interreligious dialogue, so he spends three chapters apologetically tackling the lions. The objectors (who mainly remain in notes) include Derrida, Barthes, Winch, Lindbeck, Hick, Huxley, Nasr, Plantinga and others, although Mac· Intyre is curiously missing. This technique has the advantage of isolating and presenting arguments, without falling into problems of cor· rect exegesis of opponents. And this is also its weakness, as objectors will sometimes feel caricatured or misunderstood-as is surely the case with Plantinga and in one instance, Hick. First, he tackles objections that sentences from one tradition are either incomprehensible or incommensurable with those of another, convincingly showing that the strong versions of both claims are self· defeating and unsustainable. Weaker versions still allow for his proj· ect-or so he thinks. This is where Maclntyre's work should have been considered. Then he tackles various theories of religious language (following Lindbeck's typology). He argues against non-cognitive accounts that reduce beliefs to the credibility of causes for holding beliefs, a position incapable of asserting its truth over other views because of its 720 BOOK REVIEWS own presuppositions. He follows Lindbeck in criticizing experiental expressivism, and then turns upon Lindbeck's own form of rule theory (which is ambivalent regarding cognitive claims), arguing convincingly that to suggest that only sentences uttered confessionally and with performative function can possess ontological truth is confused (42). In a brief review it is not possible to rehearse Griffiths's careful argumentation. Griffiths then sets about tackling two types of universalists: Hick and Huxley. Of Hick, he argues that some criteria are required to discern true from false religions (e.g. Jim Jones) and in so doing such a position needs to support and develop such criteria, thereby effectively introducing apologetics. He neglects to deal with Hick's pragmatic criteria of beneficial ' fruits ' evident in adherents, but the logic of his argument can be applied to Hick's proposals. Using Katz and Zaehner, he argues against the esoteric universalism of the philosophia perennis. (The arguments of Robert Forman's recent book, The Problems of Pure Consciousness, are strangely neglected, despite Griffiths's being a contributor to that collection.) Finally, he tackles objections against positive apologetics-first, on the grounds that it has a negative effect on interreligious relations. Logically, this need not be the case, although Griffiths is well aware that the political context of apologetics can obscure its proper goal: deeper critical understanding, learning and problem solving. Then, in sustained dialogue with Plantinga, he argues against the objection that success is impossible. It is impossible only if " knockdown drag-out" (64) argumentative victory is expected. Griffiths suggests the cumulative -case argument and gives instances of such successful apologetics (medieval... (shrink)

This paper advances an assessment of Kant’s Critique of Pure Reason made from a bird’s eye view. Seen from this perspective, the task of Kant’s work was to ground the spontaneity of human reason, preserving at the same time the strict methods of science and mathematics. Kant accomplished this objective by reviving an old philosophical discipline: the peirastic dialectic of Plato and Aristotle. What is more, he managed to combine it with logic. From this blend, Kant’s transcendental (...) idealism appeared as a new logic that paralleled Aristotle’s syllogistic logic. The first result of this move was that philosophy became a formal study that treats even such subjects as ethics with rigour. Another outcome was that it established philosophy as a professional – school – discipline. In the twentieth century academy, this development was echoed by the emergence of analytic philosophy, in which Kant’s new logic evolved into a philosophical logic. (shrink)

"And God said...." The author of this interesting study takes seriously the use of the italicized word in the biblical account of Creation. His thesis is that a modified version of the late J. L. Austin's analysis of "performatory" language can be used to reinterpret the traditional Christian claim that God "created" the world. The first half of the book is a purely philosophical analysis of self-involving language. Of particular importance is its clear distinction between, and logical mapping of, performative (...) and expressive language. In the second half this analysis is applied to biblical talk about Creation, an application which is made more valuable by the author's thorough grounding in biblical theology.—R. J. W. (shrink)

This article argues that the “_qua_ problem” for purely causal theories of reference grounding is an illusion. Reference _can_ be grounded via description and fit, but purely causal reference grounding is possible too. In fact, “arguments from ignorance and error” suggest that many of our terms have had their reference grounded purely causally. If the _qua_ problem is illusory, then there is no need to adopt a “hybrid” theory of reference grounding of the kind recently recommended by Amie Thomasson (Ontology (...) made easy, Oxford University Press, Oxford, 2015) and Ron Mallon (The construction of human kinds, Oxford University Press, Oxford, 2016). This opens the door to a “discovery model” of philosophical knowledge, a model we could then choose to accept. (shrink)

Throughout his entire career, Nishida Kitarō was, arguably, interested in challenging Immanuel Kant’s formulation of the moral will. In his first work, An Inquiry into the Good, he criticizes Kant’s pure practical reason as idealistic, arguing that the good should be understood not in terms of an abstract, formal relation of reason with itself, but in terms of personality as a single, unique, unifying power that is the true reality of the self. He echoes this language in his last (...) work, “The Logic of the Place of Nothingness and the Religious Worldview,” proposing that the personal self exists as a self-determining individual through creative expression. This article will investigate how Nishida’s development of this concept of the personal self grounds his proposal that the goal of the moral will is realization of the good as a personal, rather than abstract, ideal, through the intentional action of active intuition. (shrink)

Kant describes logic as “the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking”. (Bviii-ix) But what is the source of our cognition of such rules (“logical cognition” for short)? He makes no concerted effort to address this question. It will nonetheless become clear that the question is a philosophically significant one for him, to which he can see three possible answers: those representations are innate, derived from experience, or originally acquired a priori. (...) Although he gives no explicit argument for the third answer, he seems committed to it—especially given his views on the source of pure concepts of the understanding and on the nature of logic. It takes careful preparatory work to gather all the essential materials for motivating and reconstructing Kant’s “original acquisition” account of logical cognition. I shall proceed in two sections. In section 1, I analyze Kant’s argument that pure concepts of the understanding (or intellectual concepts)—as one kind of pure cognition—must be acquired originally and a priori. My analysis partly concerns his varied attitudes toward Crusius’s and Leibniz’s versions of the nativist account of such concepts. I give special attention to how Kant characterizes the nativist account and his own “original acquisition” account in terms of “preformation” and “epigenesis”. My goal is, firstly, to tease out the sense in which Kant grants that there must be an innate ground (or preformation) for the derivation of pure concepts and, secondly, to introduce—and pave the way for answering—the question about the source of logical cognition. In section 2, in light of Kant’s reference to Locke and Leibniz as the greatest reformers of philosophy (including logic) in their times (Log, AA 9: 32), I examine the Lockean and Leibnizian approaches to logic, respectively. Both approaches are “physiological” by Kant’s standard and are directly opposed to his own strictly critical method. I explain how this methodological move shapes Kant’s view that representations of logical rules must be originally acquired a priori. This acquisition involves a kind of radical epigenesis of pure reason: unlike the acquisition of pure concepts, it presupposes no further innate ground (or preformation). This view will have important consequences for issues such as the ground of the normativity of logical rules and the boundaries of their rightful use. (shrink)

Kant calls the Principle of the Synthetic Unity of Apperception the “highest point” to which we “must affix all use of the understanding, even the whole of logic and, after it, transcendental philosophy.” In this article, I offer an original interpretation of this “supreme principle.” My argument is twofold. First, I argue that the common identification of this principle with the “I think” or even the form of the I think misses the basis on which this principle is capable (...) of grounding Kant’s transcendental deduction. It must be understood as a purely formal, transcendental principle. Second, I argue that this highest principle must be understood as a purely formal principle of pure synthesis in order for Kant’s account of the mind to lay valid claim to such spontaneity without invoking the very dogmatic idealism that he critiques. The reduction of this principle to the real I think, or even to the Transcendental Unity of Apperception, undermines the basic distinction on which Kant’s deduction depends. I pay particular attention to important, recent arguments from Longuenesse on the TUA, Williams on the Original Unity of Apperception, Allison and Pollok on the status of a priori principles, and McLear on the claim that unity necessarily presupposes synthesis. (shrink)

The subject of metaphysics and traditional logic of confrontation is the subject of alienation - the object opposing the inevitable consequences of the theory, the tension between the two depends on the maintenance of the spirit of the times since the Enlightenment, that is the subject of support for the abstract. Once the main body of the abstract is dissolved, the main myth was exposed, the alienation of the natural transgression of ontological existence. Only out of Marx's historical dialectic (...) to the main body of subject-object dichotomy of alienation logic of confrontation with the traditional paradox. In the "Economic and Philosophical Manuscripts of 1844", Marx has been the traditional logic of alienation made ​​the initial breakthrough. The antinomy between the traditional theory of alienation and the metaphysics of subjectivity is the inevitable theoretic aftermath rooted into the dichotomy of subject-object, whose tension depends on the pure subjectivity-so called the spirit of time that initiated from the era of enlightenment. Once the pure subjectivity was cleared up and the myth of subject was exposed, the alienation must arrogate the reality. Only ground on the historical creation and transcendent of the capitalism mode of production exposed by Marx can we walk out the paradox of the dichotomy of subject- object. (shrink)

In the 1787 Transcendental Deduction of the Categories Kant indicates the only possible ways by which one can account for a necessary agreement of experience with the concepts of its objects (B166), using analogies between modes of explanation and biological theories about the origin of life. He endorses epigenesis as a model for his system of pure reason (B167). This paper examines various interpretive claims about the meaning of this theory of generation and its significance for Kant’s philosophy (Section (...) 1), showing that, after his Critical shift in perspective, in 1775/77 Kant already combined preformed elements and their purposively oriented formation by natural forces (Section 2). Contrary to the standard view, Kant’s theory of race appears to constitute the background to assess Blumenbach’s later (1799/1781) shift to epigenesis after supporting Haller’s preformism (Section 3). In Section 4, I argue that the ground of affinity between epigenesis and formal idealism rests in tracing the first origin of these conformities: externala posterioriclimate conditions and predisposed germs and dispositions within the generative power of the human body; and externala posterioriexperience and spontaneousa prioriconcepts of its objects, within pure sensory intuiting and pure thinking. In both cases the external empirical conditions would function as occasioning propelling factors affecting internal pre-established forms of generation. (shrink)

This paper advances an assessment of Kant’s Critique of Pure Reason made from a bird’s eye view. Seen from this perspective, the task of Kant’s work was to ground the spontaneity of human reason, preserving at the same time the strict methods of science and mathematics. Kant accomplished this objective by reviving an old philosophical discipline: the peirastic dialectic of Plato and Aristotle. What is more, he managed to combine it with logic. From this blend, Kant’s transcendental (...) idealism appeared as a new logic that paralleled Aristotle’s syllogistic logic. The first result of this move was that philosophy became a formal study that treats even such subjects as ethics with rigour. Another outcome was that it established philosophy as a professional – school – discipline. In the twentieth century academy, this development was echoed by the emergence of analytic philosophy, in which Kant’s new logic evolved into a philosophical logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Avicenna's Theory of Science: Logic, Metaphysics, Epistemology by Riccardo StrobinoThérèse-Anne DruartRiccardo Strobino. Avicenna's Theory of Science: Logic, Metaphysics, Epistemology. Oakland: University of California Press, 2021. Pp. xvi + 428. Hardback, $95.00.Strobino's remarkable book does not simply present Avicenna's theory of science; it also highlights the importance of demonstration not only for logic but also for metaphysics and epistemology. Hence, Strobino's work is essential to appreciate (...) and better understand Avicenna's philosophy as a whole.Strobino grounds his research on Avicenna's theory of science in his Book of Demonstration in the Shifā', which focuses on Aristotle's Posterior Analytics. Taking into account the lack of any translation into English or any other main modern language as well as the lack of a full medieval Latin translation (only chapter 7 of book 3 exists in a medieval Latin version) of Avicenna's text, Strobino kindly provides in appendix C (357–71) a detailed "map" of this text, useful not only to readers who cannot handle Arabic but even to those who can, as the [End Page 326] text is so rich and complex. A simple but careful look at this map confirms what Strobino makes clear and insists upon: Avicenna greatly develops, enriches, completes, and even outgrows some of Aristotle's views. The Book of Demonstration is far more than a commentary on the Posterior Analytics; it is a complete reworking of it.Strobino shows that Avicenna grounds his theory of demonstration and science on two basic notions—conception (tasawwur) and assertion (tasdīq, which some other scholars translate as "assent")—and so gives a unified approach to his theory. Scientific conceptions require better understanding of definition and description. Avicenna builds definitions and descriptions on essentialism and, therefore, grounds them in metaphysics. As for scientific assertions, in contradistinction to nonscientific ones, they must be necessary and give the cause. Therefore, Avicenna places great importance on modality and develops modal syllogisms, whereas Aristotle focused on categorical syllogisms and neglected hypothetical and disjunctive syllogisms. Avicenna also elaborates a sophisticated account of modality and its metaphysical implications. Furthermore, he broadens and enriches the appreciation of causality and explanation. These developments, according to Strobino, lead Avicenna to set forth an intricate division and hierarchy of the sciences under metaphysics, which provides their ultimate principles and allows for a unified understanding of the sciences while respecting their particularities.According to Strobino, Avicenna is keen to develop a theory of science that gives a good account of science as it is practiced. Strobino carefully shows how Avicenna's theory better reflects this practice than does Aristotle's.Strobino does not simply highlight how much Avicenna distances himself from Aristotle and goes far beyond what the Posterior Analytics yields, but also shows how much Avicenna relies on points adumbrated by his predecessor al-Fārābī in his own Book of Demonstration.The way Strobino through his analysis of demonstration links Avicenna's understanding of logic, epistemology, and metaphysics underscores the coherence and unity of Avicenna's philosophy. Scholars were aware of the importance of demonstration for Avicenna in various philosophical fields, but until the release of this book, they seemed not to have fully grasped the centrality and essential role played by the Avicennian understanding and focus on demonstration.Of course, Strobino does not limit himself to an analysis of passages in the Book of Demonstration. He has an encompassing knowledge of Avicenna's texts and uses them well to flesh out and enrich what remains terse in the Book of Demonstration. He even takes into account the way one of his successors, al-Tūsī, reads him. He also shows an extensive and wide-ranging knowledge of Aristotle's texts and of Aristotelian scholarship, as well as an interest in the Greek commentators and Galen and their relevance for interpreting Avicenna.Avicenna's Theory of Science is not an easy book to read, as it is often very technical, particularly when dealing with purely logical points or issues, but reading it is rewarding if one does so slowly and meditatively. The author, in fact, illuminates difficult matters but does not waste words. From... (shrink)

The concept of grounding - of a fact obtaining in virtue of other facts - has been a topic of intensive philosophical and logical investigation over roughly the past two decades. Many philosophers take grounding to deserve a central place in metaphysical theorizing, in great part because it is thought to do a better job than other concepts - for example, reduction and supervenience - at capturing certain phenomena. Studies on the logic of grounding have largely been conducted with (...) this philosophical background in mind. In this Element, the author tries to give a faithful picture of the contemporary development of the logic of grounding in a way that is both reasonably comprehensive and reasonably systematic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant and the Capacity to Judge; Sensibility and Discursivity in the Transcendental Analytic of the Critique of Pure Reason by Beatrice LonguenesseMichelle GreerBeatrice Longuenesse. Kant and the Capacity to Judge; Sensibility and Discursivity in the Transcendental Analytic of the Critique of Pure Reason. Translation by Charles T. Wolfe. Princeton, NJ: Princeton University Press, 1998. Pp. xv + 420. Cloth, $59.50.Kant and the Capacity to Judge is (...) a translation of Longuenesse’s Kant et Pouvoir de juger, although Longuenesse has revised and added to the original version. The central argument seeks to demonstrate the essential role played by the logical forms of judgment in the arguments of Kant’s first Critique. Longuenesse emphasizes straight away Kant’s efforts (in the Metaphysical Deduction) to deduce a set of pure concepts from the logical forms of judgment. Against many standard readings, she aims to reveal the very “tight” connection between this attempt and subsequent arguments in the Transcendental [End Page 372] Analytic. That Kant takes the functions of judgment to be relevant to these arguments is hardly a novel claim. The originality of Longuenesse’s work, however, stems both from the central and pervasive role she assigns to the logical forms of judgment, and from the impressive, painstaking effort she makes to sustain the close connection between these forms and Kant’s subsequent arguments. According to Longuenesse, any proper understanding of the arguments of the Transcendental Analytic absolutely depends upon relating these “down to the minutest details of their proofs,” to the role of the logical forms (5).These minute details do not escape Longuenesse in her subsequent elaboration on this original thesis. Given the length and detail of her work, I can only highlight a few of the central points and strategies. One should note from the outset, however, that the detail and the scholarship evinced to support her claims constitute much of what is of value in the book. Many of these “supporting arguments” and discussions, which include efforts to trace Kantian conceptions back to their historical/philosophical origins, stand in their own right as independent contributions to Kant scholarship and interpretation.The work is divided into three parts. The first part is essentially propaedeutic. Longuenesse begins by drawing a distinction between the potential or capacity to judge and judgement itself (i.e., the “actualization” of this judgmental capacity under [externally grounded] sensory stimulation) (7). Taking this distinction as her cue, Longuenesse seeks to reveal the way in which the line of argumentation in the transcendental analytic presents an extended investigation into the formal capacity (ibid). The centrality of the logical forms of judgment is secured early on by assigning them a substantive role in the very presentation of something in intuition “as” an “object.” Insofar as she assigns this role to the logical forms themselves, her account clearly undercuts the primary function of the categories in this regard. Relevant here is Longuenesse’s construal of “appearances” as the intentional correlates of our representational capacities and activities (cf. 20–21). Given this, the problem now motivating the transcendental deduction is how to make sense of the relation between this “internalized” object of (indeterminate) empirical intuition (the appearance) and the object corresponding to intuition which concepts allow one to think in a determinate way (the phenomenon). This ability to think the object in a determinate fashion appears to be the essential contribution made by judgement.These preliminary considerations ground Longuenesse’s efforts (in Part Two) to isolate and examine the discursive activity of judgment. Longuenesse stresses the reflective (and not simply the determinative) role of judgment and its forms. Indeed, she suggests that concepts (not merely empirical concepts, but also the pure concepts of the understanding themselves) are formed by reflecting (through acts of comparison, reflection, and abstraction) on the “sensible given.” Drawing extensively from the Logic, she interestingly argues that the form of judgment itself carries with it some inherent claim to objectivity. Thus, objectivity is folded into the formal activity of judging by being identified as a “normative propensity” inherent in every judgment by virtue of its form alone (87–88). Longuenesse accordingly eschews efforts to downplay the role of the logical use of the... (shrink)

I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ‘Guide to Ground.’ This logic, I argue, generates many plausible principles which Fine’s system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It’s elegant, parsimonious (...) and explanatorily powerful. Yet, so I suggest, adopting it has important consequences. First, it means we should think of ground as a type of identity. Second, it means we should reject much of Fine’s logic of strict ground. I also show how the logic I develop connects to other systems in the literature. It is definitionally equivalent both to Angell’s logic of analytic containment and to Correia’s system G. (shrink)

Accuracy in the philosophical theory of rationality demands that we recognize particular beliefs as arising within the context of larger units, the cultural or conceptual schemes, patterns, or practices, involvement in which itself provides standards and grounds for their rational evaluation. At the same time, though, a satisfactory account of rationality cannot hold the standards, values, or commitments of one particular culture, practice, or conceptual scheme, even one’s own, immune from rational criticism. In order to accurately and responsibly picture the (...) shape of our commitments and the dynamics of their revision over time, in other words, the theory of rationality must reconcile the immanence of reason to particular cultural and conceptual units with its transcendence of them. This raises a deep and far-ranging problem of perspective. In his perspicuous presentation of it, Hilary Putnam put the problem this way: There are two points that must be balanced, both points that have been made by philosophers of many different kinds: (1) talk of what is ‘right’ and ‘wrong’ in any area only makes sense against the background of an inherited tradition; but (2) traditions themselves can be criticized … On the one hand, there is no notion of reasonableness at all without cultures, practices, procedures; on the other hand, the cultures, practices, procedures we inherit are not an algorithm to be slavishly followed. As Mill said, commenting on his own inductive logic, there is no rule book which will not lead to terrible results ‘if supposed to be conjoined with universal idiocy.’ Reason is, in this sense, both immanent (not to be found outside of concrete language games and institutions) and transcendent (a regulative idea that we use to criticize the conduct of all activities and institutions). (p. 431). As Putnam argues, it is difficult to find a standpoint of theory from which the contrasting claims of immanence and transcendence can be reconciled.. (shrink)

I here defend logical atomism. This defense rests on reinterpreting logical atomism as a search for logical forms. This reinterpretation has two parts comprising six chapters. In the first part, I do some historically-driven recovery. In the introduction, I review the literature on Russell's logical atomism. In Chapter 1, I argue that the dominant interpretation of logical atomism is wrong on historical grounds: it accounts for neither the history of logical atomism nor for crucial elements of the logical atomist texts. (...) In Chapter 2, I then use Russell's writings to recover what I argue is the core of logical atomism. I explicate the critical notions and essential ingredients of logical atomism using "Principia Mathematica" as the archetype of logical atomism. I argue that logical atomsts are term busters. The essential ingredient of a logical atomist's term busting practice is a higher-order logic with the power of impredicative comprehension. In Chapter 3, I discuss the widespread view that Wittgenstein held a version of logical atomism. Focusing on his pre-"Tractatus" writings and changes in his earlier views, I argue that Wittgenstein embraced a philosophy of logic incompatible with emulating impredicative comprehension in April 1914. As such, Wittgenstein was a logical atomist, if ever, in October 1913, possibly through April 1914. In the second part, having clarified what logical atomism is, I present a modern logical atomism. In Chapter 4, I develop a philosophy of logic for logical atomism based on the notion of a pure logic. I critically discuss normativity in logic, the epistemology of pure logic, and logical pluralism. In Chapter 5, I propose a formal logic for logical atomism. I argue for the logic of logical atomism being an infinitely-descending and infinitely-ascending simple type theory with impredicative comprehension compatible with a domain empty of particulars. In Chapter 6, I critically discuss what the ontology of logical atomism should be, that is, what the ontology of the logical atomist's logic must be. This includes an ontology of logical concepts and of logical forms as completely-general, necessarily-existing logical facts with no constituents. I conclude by indicating avenues for new work on logical atomism. (shrink)

Justified belief is a core concept in epistemology and there has been an increasing interest in its logic over the last years. While many logical investigations consider justified belief as an operator, in this paper, we propose a logic for justified belief in which the relevant notion is treated as a predicate instead. Although this gives rise to the possibility of liar-like paradoxes, a predicate treatment allows for a rich and highly expressive framework, which lives up to the (...) universal ambitions of investigating epistemological concepts. We start with a base theory for justified belief, and then systematically present putative additional axioms for justified belief. We provide an overview of consistency results when the additional principles are added to the base theory, and discuss their philosophical plausibility. (shrink)

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than (...) each would individually. (shrink)

This paper is concerned with the semantics for the logics of ground that derive from a slight variant GG of the logic of (Fine, 2012) that have already been developed in (deRosset and Fine, 2023). Our aim is to outline that semantics and to provide a comparison with two related semantics for ground, given in (Correia, 2017) and (Kraemer, 2018). This comparison highlights the strengths and difficulties of these different approaches.

This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual settheoretical interpretation. (ii) A proof format may (...) display an internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity). (iii) A monotonic logic may have a non-monotonic characterization. (shrink)

Inspired by Bermúdez’s notion of proto-logic, I would like to fathom what the true proto-logic could be like. But this will be approached only in a negative way of figuring out what it could not be. I shall argue that it could not be purely deductive by exploiting the recent researches in logic of maps. This will allow us to reorient the search for proto-logic, starting with animal abduction. I will also suggest that proto-logic won’t (...) get off the ground without proto-geometry. These negative results will shed some lights on some further conceptual and historical issues around the language of thought hypothesis to arrive at the true proto-logic. (shrink)

In this paper our aim is twofold: on the one hand, to present in a clear and faithful way two recent contributions to the logic of grounding, namely Correia, and Fine ; on the other hand, to argue that some of the formal principles describing the notion of grounding proposed by these logics need to be changed and improved.

This essay examines the possibility that phenomenological laws might be implemented by a computational mechanism by carefully analyzing key passages from the Prolegomena to Pure Logic. Part I examines the famous Denkmaschine passage as evidence for the view that intuitions of evidence are causally produced by computational means. Part II connects the less famous criticism of Avenarius & Mach on thought-economy with Husserl's 1891 essay 'On the Logic of Signs (Semiotic).' Husserl is shown to reaffirm his earlier (...) opposition to associationist (Humean) and adaptationist (Darwinian) explanations of our thought-machine on the ground that they cannot reconstruct the notion of truth and its syntactic mental preservation in symbolic thought-trains. Part III reveals Husserl's interesting commitment to the idea that descriptive sciences necessarily transform into explanatory sciences on pain of contradicting the essence of science as a rational ideal. Since explanation in relation to phenomenology means causal explanation, and causal explanation in the form of the Denkmaschine accounts for phenomenological intuition, it is inferred that the rationally compelling ideal of explanatory science requires a computationalist reading of the subsequent logical investigations. (shrink)

Kant is the last classical practitioner of foundationalist epistemology in the Cartesian tradition, a tradition which saw the major problem of the theory of knowledge as one of providing a metaphysical account of the way in which the subjective contents of the individual mind come to have indubitable objective reference. But he is also the inaugurator of a very different approach to epistemology, one that sees methodology or rules of cognitive procedure as fundamental in determining the objectivity of knowledge. An (...) examination of Kant's reconstruction of the traditional form-matter distinction and his application of it to the manifold of intuition in the Critique of Pure Reason brings out the transitional character of his philosophy with particular force, and shows the immense impact of his work on the central epistemological issues of representation, explanation, and justification. While Kant continues to employ the traditional term Vorstellung , he extends its signification beyond that of a subjective mental content to an intersubjectively shared scheme of description. Where he adopts scholastic usage in referring to categories as concepts, he does not regard them as highest genera, but interprets them as rules of connection, thereby providing a logical framework suitable for functional, rather than essentialist explanation. Finally, while retaining in his transcendental psychology the conception of mental activity derivative of the older empirical psychology, Kant still manages to distinguish successfully the previously conflated questions of the causal origins vs. the grounds of justification of knowledge. Consideration of subsequent developments in regard to these issues in the light of Kant's work not only lends a certain amount of support to pragmatic conceptions of the nature of knowledge and its justification, but also suggests some promising directions for future epistemological investigation along evolutionary lines. (shrink)

Many philosophers have been attracted to the idea of using the logical form of a true sentence as a guide to the metaphysical grounds of the fact stated by that sentence. This paper looks at a particular instance of that idea: the widely accepted principle that disjunctions are grounded in their true disjuncts. I will argue that an unrestricted version of this principle has several problematic consequences and that it’s not obvious how the principle might be restricted in order to (...) avoid them. My suggestion is that, instead of trying to restrict the principle, we should distinguish between metaphysical and conceptual grounds and take the principle to apply exclusively to the latter. This suggestion, if correct, carries over to other prominent attempts at using logical form as a guide to ground. (shrink)

Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an (...) important collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99. 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In the third Critique Kant details an aesthetic operation of judgment that is surprising considering how judgment functioned in the first Critique. In this book, I defend an understanding of Kant’s theory of Geschmacksurteil as detailing an operation of the faculties that does not violate the cognitive structure laid out in the first Critique. My orientation is primarily epistemological, elaborating the determinations that govern the activity of pure aesthetic judging that specify it as a "bestimmte" type of judgment without (...) transforming it into "ein bestimmendes Urteil". I focus on identifying how the logical functions from the table of judgments operate in the pure aesthetic judgment of taste to reveal "the moments to which this power of judgment attends in its reflection". In the course of doing so, a picture emerges of how the world is not just cognizable in a Kantian framework but also charged with human feeling, acquiring the inexhaustible, inchoate meaningfulness that incites "much thinking". The universal communicability of aesthetic pleasure serves as the foundation that grounds robust intersubjective relations, enabling genuine connection to others through a shared a priori feeling. (shrink)

I show that the assumption of highly structured propositions can be leveraged to provide a unified semantics for various propositional logics of impure ground in a very expressive and flexible way. It is shown, in particular, that the induced models are capable of capturing an infinitude of grounding facts that follow from unrestricted logics of ground, but, due to certain artificial restrictions, are left unaccounted for by the existing semantics in the literature. It is also shown that our (...) models, unlike the ones in the literature, are easily extendable to capture certain distinct views about iterated as well as identity grounding. (shrink)

Engaging with Kant’s transcendental logic seems to be a question of mere scholarly historical interest today. It is most commonly regarded a mixture between logic and psychology or epistemology, and by that, not a serious form of logic. Transcendental logic seems to be of no systematical impact on the concept of logic. My paper aims to disclose a different account on the endeavour of Kant’s transcendental logic in particular and of the “Critique of (...) class='Hi'>Pure Reason” (CPR) in general. Kant’s fundamental question is in a revolutionary way aiming to ground the character of necessity of knowledge, which means to justify the claim that thinking in accordance with the forms and principles of formal logic does not lead to sheer tautologies or an unsolved contradiction, but to knowledge that is objectively valid. In a first part, I shall demonstrate the necessity and the significance of this new fundamental question of the CPR with respect to its genesis out of pre-Kantian metaphysics. A brief outline of Kant’s answer to this question, with special emphasis on his revolutionary new comprehension of logical form, will be given as well. A second part shall open up a perspective that lies beyond Kant’s standpoint with reference to Nietzsche and eventually to Hegel. I will answer the question: What knowledge do we achieve about being or actuality by means of formal logic? I will argue that Kant shows that formal logic is the logic of all technical-practical conduct but also, at least indirectly, the limitation of the technical-practical knowledge and its legitimate sphere of application. (shrink)

In the Critique of Fure Reason Kant distinguishes two sorts of conditions of knowledge. First, there are the space and time of pure intuition, introduced in the Transcendental Aesthetic. They are grounded in our dependence on a special sort of perceptual field for the location of objects. Second, there are pure concepts of the understanding, or categories, introduced in the Analytic. In one respect these are grounded in the logical function of the understanding in judgements, introduced in the (...) first chapter of the analytic of concepts: Clue to the Discovery of All Pure Concepts of the Understanding; in another respect, they are grounded in transcendental unity of apperception, which is introduced in the second chapter: Deduction of the Pure Concepts of the Understanding, or Transcendental Deduction. I shall be concerned with the latter and its contribution to the overall strategy of argument in the analytic. Within the Analytic, Kant distinguishes between an Analytic of Concepts and an Analytic of Principles. This corresponds to a traditional distinction between a doctrine of concepts and judgement. It is arguable that Kant's theory of concepts undermines this distinction. However, I shall not deal with that general issue, but with a more specific issue related to the first two chapters of the Analytic of Principles: the Schematism and the System of Principles. (shrink)

What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...) Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains. (shrink)

In this essay, I argue for a view that inclusive positivists share with Ronald Dworkin. According to the Moral Incorporation Thesis (MIT), it is logically possible for a legal system to incorporate moral criteria of legality (or “grounds of law,” as Dworkin puts it). Up to this point, the debate has taken the shape of attacks on the coherence of MIT with the defender of MIT merely attempting to refute the attacking argument. I give a positive argument for MIT. I (...) begin with an explanation of the logic of establishing possibility claims, such as MIT. At the outset, it is worth noting that the logic of establishing possibility claims is very different from the logic of establishing contingent descriptive claims or necessary claims. For this reason, some explication of the relevant features of the semantics of modal logic will be necessary here. Once the structural framework is adequately developed, the argument for MIT will be grounded on the strength of a thought experiment of a surprisingly simple kind. Indeed, the argument is inspired by a Razian argument for the possibility of a legal system without coercive enforcement machinery; on his view, a society of angels could still have a system of law without any coercive machinery. My argument will possess two theoretically important qualities that are also possessed by Raz’s powerfully simple, but ultimately unsuccessful, argument. (shrink)

Husserl and Frege did not criticize psychologism on the ground that it deduced the norms of logic from non-normative premises (naturalistic fallacy), as is often supposed. Rather, their refutation of psychologism assumes that such a deduction is possible. Husserl compared the rules of logic to those of technology, on the supposition that they have a purely theoretical basis. This conception of logic is critically examined, and it is argued (contra Follesdal) that Frege held a similar view.

This exceedingly rich book can be understood as an attempt to grasp the nature of Hegel’s system, specifically the relationship obtaining between that system and its vaunted "transitions." This attempt is carried out through a study of Hegel’s account of Vorstellung and thought. The operational point d'appui of the study is what Clark identifies as the central paradox essentially inherent in his subject, which may be variously formulated as: how language can be the "other" of thought and yet sublated in (...) thought; how pure thought can abide an other; how the Logic can from within itself develop its categories to absolute fulfillment and yet refer beyond itself to its fulfillment; how Hegel can be understood to have "completed" philosophy in the first quarter of the nineteenth century; how one makes sense of the notion of an essentially temporal eternality; how the Logic and the Phenomenology of Mind can each presuppose the other. The developing treatment of this paradox constitutes almost an object lesson in the "preserved" aspect of aufhebung—The or a methodological enactment of the second book of the Logic—for Clark wrestles with the tacky conceptual framework upon which rests the topic under investigation. The whole is deftly handled. Particularly inspired is the close analysis of the Theoretical Mind chapter of the Philosophy of Spirit and its bearing upon the Logic’s "Essence." This coupling, together with a treatment of the Philosophy of Religion constitutes one of the two foci of the book. What comes clear from this extended study is an appreciation of the fundamental difficulties connected with any philosophical explanation that has failed to resolve satisfactorily the relationship between ground and consequent and treats them either as being simply different or from the standpoint of a simply presumed totality. Clark’s considered position is that Hegel’s thought is paradoxical precisely in its intelligibility. Ultimately, he can only reiterate the paradox one final time: "The paradox of a Logic that is at once the whole and but a part of experience is thus a systematic expression of the need for reconciliation of a standpoint that is simply accomplished and a standpoint that is ever accomplishing itself." Now for the misgivings, which are for the most part issues of form. There is an obstinate problem of indistinctness running through the work. The recurrent summaries, both internal and thematic, the forecasts, the exhaustively particularized table of contents, are all tacit concessions to the existence of this problem. Seldom do positions come ringing through with conviction; often, notwithstanding the above-mentioned signposts, their origin, their precise connection to the text, is obscure. This is particularly true of the truncated final passages, where interpretation converts to criticism. In short, a fuller statement of significance might well have been supplied. A second problem, or at the least an annoying inconvenience, is the decision not to translate most of the abundant quotations from Hegel’s works into English. Some of the quotations are, for no apparent reason, in fact translated; and with well over 900 footnotes in a 200-page text anyway, translations would hardly constitute a stylistic blemish.—R. J. G. (shrink)

This guide accompanies the following article: ‘Logic and Divine Simplicity’. Philosophy Compass 6/4 : pp. 282–294, doi: Author’s IntroductionFirst‐order formalizations of classical theistic doctrines are increasingly used in contemporary work in philosophy of religion and philosophical theology, as a means for clarifying the conceptual structure of the doctrines and their role in inferential procedures. But there are a variety of different ways in which such doctrines have been formalized, each representing the doctrines as having different conceptual structures. Moreover, the (...) adequacy of such formalizations as such has, at least with respect to some classes of doctrines, been disputed. One reason for disputing their adequacy derives from the conceptual impact of classical theism’s doctrine of divine simplicity.Author RecommendsFrege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. The preface contains interesting remarks about the purpose of formalization as understood by the chief pioneer of modern formal logic. These remarks are also connected by Frege to his views on the relation between thought and language more generally.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press.The preface and first section of the long introduction contain remarks on the purpose and advantages of formalization. Chapter 1 of the introduction contains what is probably one of the first formalizations ever of a theistic doctrine, and is given in terms of a definite description analysis.Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Clear and concise discussion of some of the advantages of formalization in philosophical inquiry, written by a prominent contemporary American philosopher‐logician.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9.A valuable paper that narrates, among other things, the programme of formalizing theistic doctrines that emerged in Poland in the 1920s under the influence of the Lvov‐Warsaw School. Various examples of formalizations are also given.Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press.In Section 27 of this classic study, Quine offers a formalization of theistic doctrines which seeks to avoid the difficulties of earlier formalizations by means of a subtle extensional singleton set analysis. The proposal has not won many adherents, but is worthy of careful study nonetheless.Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.A concise but lucid survey of some attempts to formalize theistic doctrines and some problems besetting these attempts. Woleński also proposes his own method of formalization, which could be described as a simplified version of Quine’s method in Mathematical Logic.Bocheński, Joseph The Logic of Religion. New York: New York University Press.The first book‐length treatment of the relation between modern logic and theism. It covers much ground, and remains very readable.Alston, William P. ‘Religious Language and Verificationism,’ in The Rationality of Theism, eds. Paul Moser and Paul Copan. London: Routledge, pp. 17–34.Identifies some problems with attempts at articulating theistic doctrines by means of subject‐predicate language. Highly relevant to formalizations of theistic doctrines, even though this topic is not dealt with explicitly.Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass.Offers a survey of three main methods of formalizing theistic doctrines, and of some variants of these methods. Argues that certain formalizations of theistic doctrines are bound to be rejected as conceptually inadequate by all who understand the doctrines at hand within the framework provided by the traditional doctrine of divine simplicity.Sample Syllabus Week I: The Idea of Formalization and the Project of Formalizing Theistic Doctrines Reading:Frege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9. Week II: Formalizing Theistic Doctrines: Three Alternative Methods Reading:Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press. Week III: Arguments for and Against Some Formalizations of Theistic Doctrines Reading:Bocheński, Joseph The Logic of Religion. New York: New York University Press. Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass, Vol. 6, No. 4, pp. 282–94.Focus Questions1 What do Frege, Russell and Whitehead, and Suppes understand the purpose or purposes of logical formalization to be, and why do they think formalization can achieve these purposes?2 Woleński sketches some simple ways of formalizing theistic doctrines such as ‘God exists’ or ‘God is almighty’ in terms of 1‐place predicates which he subsequently abandons in favour of other methods. What reasons lead him to abandon these more simple methods of formalization?3 What are the advantages of the definite description formalization of theistic doctrines offered by Russell and Whitehead?4 Quine offers a subtle formalization of the theistic doctrine ‘God exists’ in terms of singleton sets. What problems are Quine’s formalization intended to accommodate, and how does it seek to accommodate them?5 Which relative merits or demerits are there in Bocheński’s and Kraal’s respective arguments for and against the adequacy of certain formalizations of theistic doctrines? (shrink)

In this paper I address the question 'How is knowledge of logical truths possible'. The sought-after explanation should be independent of what the true story about logical truth is. In particular, I try to account for the epistemic warrant that is conferred upon logical beliefs when they are neither inferred from other beliefs nor grounded on empirical evidence or testimony. The need for such an account is motivated by the apparent failure of the notions ofanalyticity on the one hand and (...) intuition on the other in addressing the relevant question. I end up defending an account according to which warranted logical beliefs can be grounded on pure reasoning: they can be inferentially formed on the basis of pieces of suppositional reasoning. (shrink)

I introduce a distinct challenge to religious belief: the Ethical Argument from evil. By this argument, paradigmatic forms of religious practice constitutively involve failures of ethical acknowledgement with respect to the reality of evil. I show how standard discussions of the problem of evil, as a purely logical or epistemic issue, abstract away from its fundamentally ethical dimensions. Drawing on an analogy with Moore’s paradox, I argue that the Ethical Argument presents a genuine theoretical problem, not merely a practical or (...) pastoral one: the problem of how religious devotion can be compossible with properly acknowledging the reality of evil. I further argue that, in order properly to address this problem, the philosophy of religion needs to take a phenomenological turn. To illustrate this approach, I focus on the case of thankful prayer and draw out from Kierkegaard’s writings a religious ideal of unconditional gratitude. Developing the relevant notion of a failure of ethical acknowledgement in terms of two vices—wishful self-deception and spiritualized self-absorption—I show how Kierkegaard’s account can help us to assess whether expressions of religious devotion are objectionable on these grounds. (shrink)