Relevant Robinson's arithmetic

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.This paper has been greatly influenced by the (largely unpublished) work of E. K. Meyer (cf. [7]) on relevant arithmetic, and I wish to thank him, and also N. D. Belnap, Jr. and D. Cohen for helpful advice. In fairness to Meyer it must be said that he finds my axioms 13 and 13(1) too strong (they are not theorems of his system R# - cf. §4 below). Meyer tells me be finds vindication for his view in my chief theorem of §2. For myself, I find the insights behind Meyer's work on R# to be both stable and fruitful, and if I now had to make a choice, I would follow Meyer in his rejection of my axioms. However, the systems I explore in this paper themselves have a surprising amount of internal consistency of motivation (cf. §5). Let a hundred formal systems bloom.     

On the Quinean-analyticity of mathematical propositions

This paper investigates the relation between Carnap and Quine??s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine??s own remarks, and set theory is at least defensibly analytic.     

Kontinentales Erbe Und Analytische Methode. Nelson Goodman Und Die Tradition

Goodman's most important contribution to philosophy seems to be his analysis of the relation between facts of science and fictions of art. His view can be seen as a kind of complementary pluralism. That is to say, science and art are two complementary forms of achieving cognition. This position overcame the positivistic view (of his teacher Carnap) according to which the value of art is restricted to the non-cognitive function of expressing emotions. In this paper I compare some of Goodman's fundamental ideas – especially his central conception of exemplification – with their counterparts in Baumgarten, Kant, and Cassirer. Based on this comparison I argue against the tendency to regard analytic and continental philosophy as two completely separated traditions.     

The structural theory and the representational world: developmental and biological considerations

Although the intriguing question of whether the division into two viewpoints within the structural theory is a theoretical convenience or whether it mirrors fundamental psychobiological truths is not capable of full resolution at the moment, fortunately that resolution is not required for our usual clinical purposes. I believe that analytic work presents us with data readily conceptualized now from one, now from the other, viewpoint, so that analytic understanding benefits from the analyst's shifting his frame of reference from moment to moment in listening and associating to the patient's material. I believe that in every event within the analytic situation or in a person's life, our understanding is deepened and made more complete by approaching the phenomena from both vantage points, bearing in mind that the same ego we conceptualize as testing, assessing, and evaluating emergent drives is also assessing the congruence or discrepancy between the wished-for and perceived states of the representational world. These processes are occurring both in the analysand and in the analyst who is attempting to resonate with and understand the intrapsychic functioning of his patient. They constitute two observational vantage points within the structural theory, organizations of motives (Friedman, 1980) either of which may offer the most immediate access to understanding a particular segment of clinical material. I believe our understanding is most often deepened, however, by subsequent scrutiny in the light of the other model. I have tried here to supplement my previous exposition of a representational world point of view (J.G. Jacobson, 1983) by providing some of its developmental, ethological, and psychophysiological landmarks and underpinnings.     

Føllesdal on the notion of the noema: A critique

Conclusion In this paper, I have demonstrated that Føllesdal's famous interpretation of Husserl's concept of the noema is mistaken due to a fundamental misunderstanding of Husserlian terminology. I have given what I consider to be a correct explanation of the notion of the noema and of Husserlian terminology and have backed my claims with direct references to the text. I have then compared and contrasted these with Føllesdal's interpretation and, thereby, have explained the nature of his mistakes with regards to terminology. I have also shown that two of Føllesdal's faithful followers, Smith and McIntyre, have walked a similarly erroneous path with regards to their interpretation of Husserl's theory of meaning in theIdeas.I do not know where the key to the reconciliation of phenomenology and analytic philosophy lies. But, I do know that it does not lie in the claim that Husserl shared Frege's view on the nature of meaning as an abstract intensionalSinn nor does it lie in the related view that Husserl radically changed his conception of the relation of meanings to intending acts. Hopefully, this paper has shed light on this widely debated issue and has clarified the nature of the mistakes in recent interpretations of Husserl's concept of the noema.     

Hume on space, geometry, and diagrammatic reasoning

Hume??s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume??s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume??s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working within this epistemological model, we cannot attain complete certainty about the continuum but only at most about discrete quantity. Geometry, in contrast to arithmetic, cannot be a fully exact science. A number of more recent commentators have offered sympathetic interpretations of Hume??s discussion aiming to correct the older tendency to dismiss this part of the Treatise as weak and confused. Most of these commentators interpret Hume as anticipating the contemporary idea of a finite or discrete geometry. They view Hume??s conception that space is composed of simple indivisible minima as a forerunner of the conception that space is a discretely (rather than continuously) ordered set. This approach, in my view, is helpful as far as it goes, but there are several important features of Hume??s discussion that are not sufficiently appreciated. I go beyond these recent commentators by emphasizing three of Hume??s most original contributions. First, Hume??s epistemological model invokes the ??confounding?? of indivisible minima to explain the appearance of spatial continuity. Second, Hume??s sharp contrast between the perfect exactitude of arithmetic and the irremediable inexactitude of geometry reverses the more familiar conception of the early modern tradition in pure mathematics, according to which geometry (the science of continuous quantity) has its own standard of equality that is independent from and more exact than any corresponding standard supplied by algebra and arithmetic (the sciences of discrete quantity). Third, Hume has a developed explanation of how geometry (traditional Euclidean geometry) is nonetheless possible as an axiomatic demonstrative science possessing considerably more exactitude and certainty that the ??loose judgements?? of the vulgar.     

Kant on justification in transcendental philosophy

Kant's claim that the justification of transcendental philosophy is a priori is puzzling because it should be consistent with (1) his general restriction on the justification of knowledge, that intuitions must play a role in the justification of all nondegenerate knowledge, with (2) the implausibility of a priori intuitions being the only ones on which transcendental philosophy is founded, and with (3) his professed view that transcendental philosophy is not analytic. I argue that this puzzle can be solved, that according to Kant transcendental philosophy is justified a priori in the sense that the only empirical information required for its justification can be derived from any possible human experience. Transcendental justification does not rely on any more particular or special observations or experiments. Philip Kitcher's general account of apriority in Kant captures this aspect of a priori knowledge. Nevertheless, I argue that Kitcher's account goes wrong in the link it specifies between apriority and certainty.     

EXAMINING THE BODHISATTVA'S BRAIN

Owen Flanagan's The Bodhisattva's Brain aims to introduce secular‐minded thinkers to Buddhist thought and motivate its acceptance by analytic philosophers. I argue that Flanagan provides a compelling caution against the hasty generalizations of recent “science of happiness” literature, which correlates happiness with Buddhism on the basis of certain neurological studies. I contend, however, that his positive account of Buddhist ethics is less persuasive. I question the level of engagement with Buddhist philosophical literature and challenge Flanagan's central claim, that a Buddhist version of eudaimonia is a common core conception shared by all Buddhists. I argue that this view is not only a rational reconstruction in need of argumentation but is in tension with competing Buddhist metaphysical theories of self, including the one Flanagan himself endorses.     

“Hall of Broken Mirrors”—Enactment in an Analytic Group of “Difficult Patients”

This article focuses on the transformation of dissociated self-states as a curative factor in an analytic group of “difficult patients.” Foulkes (1964) referred to the analytic group as a “curative hall of mirrors.” I would like to integrate group analytic theory with relational psychoanalytic concepts. I propose that when dissociated self-states are expressed in a group, this creates a “broken mirrors” experience that is sometimes expressed through enactment. I develop this idea, and argue that the group mirrors to the patient his image—distorted and defective—and forces him to cope with his “not me” states. I demonstrate, through three clinical vignettes, how dissociated states hinder the reflective space and create a “hall of broken mirrors” experience. I would argue that in a safe space, the patients’ “not me” states can be transformed, and the hall of broken mirrors can turn into a curative hall of mirrors.     

Intuition and Reflection in Arithmetic: Michael Potter

If arithmetic is not analytic in Kant's sense, what is its subject matter? Answers to this question can be classified into four sorts according as they posit logic, experience, thought or the world as the source, but in each case we need to appeal to some further process if we are to generate a structure rich enough to represent arithmetic as standardly practised. I speculate that this further process is our reflection on the subject matter already obtained. This suggestion seems problematic, however, since it seems to rest on a confusion between the empirical and the metaphysical self.     

Frege’s Unification

What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature.     

HACKER'S COMPLAINT

My goal in writing 'Philosophical Analysis in the Twentieth Century' was to identify and explain the most important achievements of analytic philosophy which every student of the subject should be aware of, as well as those of its failures from which we have the most to learn. I attempted to do this by constructing a history that was itself apiece of analytic philosophy in its emphasis on analysis, reconstruction and criticism of arguments. In rebutting Hacker's critique of it, I explain how my goal shaped my selection of topics, with special reference to the ordinary language period. I correct his misrepresentations of my treatment of the philosophers of this period, I demonstrate his failure to grasp, or understand the significance of, the Kripkean necessary a posteriori, and I reveal the misconceptions in his criticism of my interpretation of the 'Tractatus'.     

On Bolzano's Concept of a Sum

Alongside his groundbreaking work in logic, Bernard Bolzano (1781–1848) made important contributions to ontology, notably with his theory of collections. Recent work has done much to elucidate Bolzano's conceptions, but his notion of a sum has proved stubbornly resistant to complete understanding. This paper offers a new interpretation of Bolzano's concept of a sum. I argue that, although Bolzano's presentation is defective, his conception is unexceptionable, and has important applications, notably in his work on the foundations of arithmetic.     

The Capgras delusion: an integrated approach

Delusions are studied in two philosophical traditions: the continental or phenomenological tradition and the Anglo-American or analytic tradition. Each has its own view of delusions. Broadly stated, phenomenologists view delusions as a disturbed experience whilst most analytic researchers view them as beliefs. It is my contention that the most plausible account of delusions must ultimately incorporate valuable insights from both traditions. To illustrate the potential value of integration I provide a novel model of the Capgras delusion which describes how an analytic, cognitive neuropsychological two-factor account of the Capgras delusion and the phenomenological view of delusions might be integrated.     

Hegel on Kant's Analytic–Synthetic Distinction

In this paper, I argue, first, that Hegel defended a version of the analytic/synthetic distinction—that, indeed, his version of the distinction deserves to be called Kantian. For both Kant and Hegel, the analytic/synthetic distinction can be explained in terms of the discursive character of cognition: insofar as our cognition is discursive, its most basic form can be articulated in terms of a genus/species tree. The structure of that tree elucidates the distinction between analytic and synthetic judgments. Second, I argue that Hegel has an interesting and so far unexplored argument for the analytic/synthetic distinction: Hegel argues that the systematic relationship between concepts expressed in a genus/species tree can only be expressed through synthetic judgments. Third and finally, I explore some of the implications that the arguments in the first two parts of the essay have for understanding the way in which Hegel differs from Kant. I argue that Hegel accepts Kant's point that discursive cognition cannot be used to cognize the absolute. However, Hegel thinks that we can, nevertheless, cognize the absolute. I explore the character of this non‐discursive cognition and argue that we can understand Hegel's glosses on this form of cognition—as simultaneously analytic and synthetic and as having a circular structure—through contrasting it with his account of discursive cognition. As a consequence, I argue that we must give up on attempts to understand ‘the dialectical method’ and ‘speculative cognition’ on the model of discursive cognition.     

Merleau-Ponty’s Gordian knot: Transcendental phenomenology,science, and naturalism

In this paper I explore a series of fertile ambiguities that Merleau-Ponty’s work is premised upon. These ambiguities concern some of the central methodological commitments of his work, in particular his commitment (or otherwise) to transcendental phenomenology and how he transforms that tradition, and his relationship to science and philosophical naturalism and what they suggest about his philosophical methodology. Many engagements with Merleau-Ponty’s work that are more ‘analytic’ in orientation either deflate it of its transcendental heritage, or offer a “modest” rendering of its transcendental dimensions. This is also true, albeit perhaps to a lesser extent, of the work of the more empirically-minded phenomenological philosophers who engage very seriously with Merleau-Ponty—e.g. Hubert Dreyfus, Shaun Gallagher, Evan Thompson, Alva Noë, and others. At the same time, many other scholars contest these proto-scientific and more naturalistic uses of Merleau-Ponty’s work on hermeneutical and exegetical grounds, and they likewise criticise the deflated reading of his transcendental phenomenology that tends to support them. By working through some of the key passages and ideas, this paper establishes that the former view captures something pivotal to Merleau-Ponty’s philosophy. I also extend these interpretations by arguing that, at least around the time of Phenomenology of Perception, his philosophy might be reasonably regarded as a form of minimal methodological naturalism.     

Aesthetic Judging and The Intentionality of Pleasure

I point out some unclarities in Allison's interpretation of Kant's aesthetic theory, specifically in his account of the free play of the faculties. I argue that there is a tension between Allison's commitment to the intentionality of the pleasure involved in a judgment of beauty, and his view that the pleasure is distinct from the judgment, and I claim that the tension should be resolved by rejecting the latter view. I conclude by addressing Allison's objection that my own view fails to accommodate judgments of non-beauty or ugliness.     

On Sellars' exam question trilemma: are Kant's premises analytic,or synthetic a priori,or a posteriori?

ABSTRACT

Wilfrid Sellars argued that Kant’s account of the conceptual structures involved in experience can be given a linguistic turn so as to provide an analytic account of the resources a language must have in order to be the bearer of empirical knowledge. In this paper I examine the methodological aspects of Kant’s transcendental philosophy that Sellars took to be fundamental to influential themes in his own philosophy. My first aim here is to clarify and argue for the plausibility of what I claim is Sellars’ interpretation of Kant’s ‘analytic’ transcendental method in the first Critique, based ultimately on non-trivial analytic truths concerning the concept of an object of our possible experience. Kant’s ‘transcendental proofs’ thereby avoid a certain methodological trilemma confronting the candidate premises of any such proof, taken from Sellars’ 1970s undergraduate exam question on Kant. In part II of the essay I conclude by highlighting in general terms how Kant’s method, as interpreted in the analytic manner explained in part I, was adapted by Sellars to produce some of the more influential aspects of his own philosophy, expressed in terms of what he contends is their sustainable reformulation in light of the so-called linguistic turn in twentieth-century philosophy.     

Recasting Analytic Philosophy on the Problem of Evil

In his recent book, A Frightening Love: Recasting the Problem of Evil, Andrew Gleeson challenges a certain conception of justification assumed in mainstream analytic philosophy and argues that analytic philosophy is ill-suited to deal with the most pressing, existential, form of the problem of evil. In this article I examine some aspects of that challenge.