This paper explores the centrality of self-affirmation in Bernard Lonergan’s Insight and is specifically concerned with the role of bias in relation to self-appropriation and genuineness. I begin with an explication of the process of self-affirmation and the model of knowledge it involves. I then discuss the nature of bias and its relation to genuineness in Insight. My analysis concludes that bias is never “overcome,” in the sense of being eliminated. Thus, genuine self-appropriation is never complete. Rather, being true to (...) oneself is the struggle to recognize one’s biases while still affirming what is reasonable and choosing responsible action. I also conclude that total resistance to self-affirmation is a disingenuous refusal to engage one’s biases; it is an act of evasion, or a fear of genuineness and its accompanying responsibilities. I end by briefly addressing some of these tensions in relation to Catholicism, specifically raising questions concerning our thinking and acting from within a Catholic faith. (shrink)

This paper explores the centrality of self-affirmation in Bernard Lonergan’s Insight and is specifically concerned with the role of bias in relation to self-appropriation and genuineness. I begin with an explication of the process of self-affirmation and the model of knowledge it involves. I then discuss the nature of bias and its relation to genuineness in Insight. My analysis concludes that bias is never “overcome,” in the sense of being eliminated. Thus, genuine self-appropriation is never complete. Rather, being true to (...) oneself is the struggle to recognize one’s biases while still affirming what is reasonable and choosing responsible action. I also conclude that total resistance to self-affirmation is a disingenuous refusal to engage one’s biases; it is an act of evasion, or a fear of genuineness and its accompanying responsibilities. I end by briefly addressing some of these tensions in relation to Catholicism, specifically raising questions concerning our thinking and acting from within a Catholic faith. (shrink)

Robert Talisse argues that a Peircean epistemic basis for democracy is "thin" enough to allow for reasonable pluralism while being "thick" enough to justify the preferability of democracy. This brief critical engagement with Talisse's argument asks, first, whether or not it is fair to employ Peirce's doubt-belief model of inquiry as the basis of a "thin" philosophy of democracy. Additionally, it asks whether such a justification of democracy can do any real work without also employing Peirce's more comprehensive philosophical views (...) concerning the conditions necessary for developing the epistemic character required for actual democratic practices. Lastly, it questions whether Talisse's philosophy of democracy is best called "Peircean" at all. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly (...) precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

In this paper, we argue that the characteristics of digital platforms challenge the fundamental assumptions of value sensitive design (VSD). Traditionally, VSD methods assume that we can identify relevant values during the design phase of new technologies. The underlying assumption is that there is onlyepistemic uncertaintyabout which values will be impacted by a technology. VSD methods suggest that one can predict which values will be affected by new technologies by increasing knowledge about how values are interpreted or understood in context. (...) In contrast, digital platforms exhibit a novel form of uncertainty, namely,ontological uncertainty: even with full information and overview, it cannot be foreseen what users or developers will do with digital platforms. Hence, predictions about which values are affected might not hold. In this paper, we suggest expanding VSD methods to account for value dynamism resulting from ontological uncertainty. Our expansions involve (1) extending VSD to the entire lifecycle of a platform, (2) broadening VSD through the addition of reflexivity, i.e. second-order learning about what values to aim at, and (3) adding specific tools of moral sandboxing and moral prototyping to enhance such reflexivity. While we illustrate our approach with a short case study about ride-sharing platforms such as Uber, our approach is relevant for other technologies exhibiting ontological uncertainty as well, such as machine learning, robotics and artificial intelligence. (shrink)

Geach's problem, the problem of accounting for the fact that judgements expressed using moral terms function logically like other judgements, stands in the way of most noncognitive analyses of moral judgements. The non-cognitivist must offer a plausible interpretation of such terms when they appear in conditionals that also explains their logical interaction with straightforward moral assertions. Blackburn and Gibbard have offered a series of accounts each of which interprets such conditionals as expressing higher order commitments. Each then invokes norms for (...) the coherent acceptance of attitudes to explain why we hold certain combinations inconsistent. Against these accounts the paper presses two related objections: (1) The norms needed to do the explanatory work cannot be strong enough to do that work without also ruling clearly consistent attitudes inconsistent. And (2), the norms of rational attitude acceptance do not neatly track the distinction between consistent and inconsistent attitudes. (shrink)

Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...) choice sequences is defective on several counts. (shrink)

Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...) choice sequences is defective on several counts. (shrink)

Motivational internalism about moral judgments is the plausible view that accepting a moral judgment is necessarily connected to motivation motivation. However, it conflicts with the Humean theory that motives must be constituted by desires. Simple versions of internalism run into problems with people who do not desire to do what they believe right. This has long been urged by David Brink. Hence, many internalists have adopted more subtle defeasible views, on which only rational agents will have a desire to act. (...) I will argue that more complex versions run into problems with self-effacing values of the sort Parfit highlights in another context. Such values can only be attained indirectly. After proposing a general account of motivation suited to the internalist thesis, I argue that Anti-Humeanism is better suited to accommodating the internalist insight. (shrink)

Brouwer and Husserl both aimed to give a philosophical account of mathematics. They met in 1928 when Husserl visited the Netherlands to deliver his Amsterdamer Vorträge. Soon after, Husserl expressed enthusiasm about this meeting in a letter to Heidegger, and he reports that they had long conversations which, for him, had been among the most interesting events in Amsterdam. However, nothing is known about the content of these conversations; and it is not clear whether or not there were any other (...) exchanges between them. The following is an attempt at some remarks on Husserl’s Philosophy of Arithmetic from an intuitionistic, by which I mean a Brouwerian, point of view. I will confine myself specifically to some intuitionistic musings on Husserl’s analysis of the concept of finite number, which he developed in his Habilitationsschrift of 1887, “On the Concept of Number,” and presented again in 1891 in the first four chapters of the Philosophy of Arithmetic. It will turn out that the intuitionistic account of number is very different from Husserl’s. For instance, they strongly disagree about the number 2. On the other hand, the roots of the projects of Husserl and Brouwer have much in common. Since this fact makes their disagreement pressing and lends it much of its significance, I will begin there. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly (...) precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

Over the last decade there have been various attempts to use empirical data about people’s dispositions to choose to undermine various moral positions by arguing that our judgements about what to do are unreliable. Usually they are directed at non-consequentialists by consequentialists, but they have also been directed at all moral theories by skeptics about morality. Walter Sinnott-Armstrong has been one of the leading proponents of such general skepticism. He has argued that empirical results particularly undermine intuitionist moral epistemology. This (...) paper is an attempt to look at what intuitionists should say in response. Consider the following argument : Regress (R1) If any person S is ever justified in believing a normative claim that p then S must be able to infer p from other beliefs of S. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly (...) precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers,mandxover natural numbers, andstands for ⟨α(0), α(1), …, α(m− 1)⟩, the initial segment of α of lengthm.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is (probably) the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

In his text 'The modern development of the foundations of mathematics in the light of philosophy' from around 1961, Go¨del announces a turn to Husserl's phenomenology to find the foundations of mathematics. In Go¨del's archive there are two draft letters that shed some further light on the exact strategy that he formulated for himself in the early 1960s. Transcriptions of these letters are presented, together with some comments.

Gödel once offered an argument for the general reflection principle in set theory that took the form of an analogy with Leibniz' Monadology. I discuss the mathematical and philosophical background to Gödel's argument, reconstruct the proposed analogy in detail, and argue that it has no justificatory force.

Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part. The refutation of this argument by Russell and others is equally well known. In this note, I argue (against positions recently defended by Arthur, Breger, and Brown) for the following three claims: (1) Leibniz himself had all the means to devise and accept this refutation; (2) This refutation does not presuppose the consistency of Cantorian set (...) theory; (3) This refutation does not cast doubt on the part-whole axiom. Hence, should there be an obstacle to Gödel's wish to integrate Cantorian set theory within Leibniz' philosophy, it will not be this famous argument of Leibniz'. (shrink)

The dialectical approach to teaching critical thinking is centred on a comparative evaluation of contending arguments, so that generally the strength of an argument for a position can only be assessed in the context of this dialectic. The identification of fallacies, though important, plays only a preliminary role in the evaluation to individual arguments. Our approach to fallacy identification and analysis sees fallacies as argument patterns whose persuasive power is disproportionate to their probative value.

This book is a good idea, well-executed. The setup of the book mirrors one way of dividing up normative ethics. We divide theorists into Kantians, consequentialists and virtue theorists on the assumption that these are distinct and incompatible approaches to ethics. Each position is represented by one of the co-authors with Baron representing Kantians, Pettit consequentialists and Slote virtue theorists. What emerges is that each approach has virtues, but also that the division is neither neat nor exhaustive. As Pettit notes, (...) the issue that divides consequentialists from non-consequentialists is whether it is always right to promote agent-neutral value. While Kantians answer no where the consequentialists answer yes, a consequentialist can agree with Kantians about many other issues. And while Kantians are often portrayed as being exclusively interested in the rightness of actions, their actual emphasis on motivation and reasons for action make it difficult to distinguish their views from virtue theories that focus on the way an agent’s character and practical wisdom is reflected in her choices. The complexity of the positions defended by the authors highlight these difficulties for the standard division of the terrain. (shrink)

Joint Session of the two Divisions of the International Union for History and Philosophy of Science.

We compare Gödel’s and Brouwer’s explorations of mysticism and its relation to mathematics.