Proof vs Provability: On Brouwer’s Time Problem

Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies that Brouwer has invited us to introduce into mathematics.     

Knowledge’s Boundary Problem

Where is the justificatory boundary between a true belief’s not being knowledge and its being knowledge? Even if we put to one side the Gettier problem, this remains a fundamental epistemological question, concerning as it does the matter of whether we can provide some significant defence of the usual epistemological assumption that a belief is knowledge only if it is well justified. But can that question be answered non-arbitrarily? BonJour believes that it cannot be – and that epistemology should therefore abandon the concept of knowledge. More optimistically, this paper does attempt to answer that question, by applying – and thereby refining – a non-absolutist theory of knowledge.     

The Fictionalist’s Attitude Problem

According to John Mackie, moral talk is representational (the realists go that bit right) but its metaphysical presuppositions are wildly implausible (the non-cognitivists got that bit right). This is the basis of Mackie’s now famous error theory: that moral judgments are cognitively meaningful but systematically false. Of course, Mackie went on to recommend various substantive moral judgments, and, in the light of his error theory, that has seemed odd to a lot of folk. Richard Joyce has argued that Mackie’s approach can be vindicated by a fictionalist account of moral discourse. And Mark Kalderon has argued that moral fictionalism is attractive quite independently of Mackie’s error-theory. Kalderon argues that the Frege–Geach problem shows that we need moral propositions, but that a fictionalist can and should embrace propositional content together with a non-cognitivist account of acceptance of a moral proposition. Indeed, it is clear that any fictionalist is going to have to postulate more than one kind of acceptance attitude. We argue that this double-approach to acceptance generates a new problem – a descendent of Frege–Geach – which we call the acceptance–transfer problem. Although we develop the problem in the context of Kalderon’s version of non-cognitivist fictionalism, we show that it is not the non-cognitivist aspect of Kalderon’s account that generates the problem. A closely related problem surfaces for the more typical variants of fictionalism according to which accepting a moral proposition is believing some closely related non-moral proposition. Fictionalists of both stripes thus have an attitude problem.

On Norton’s dome

Norton’s very simple case of indeterminism in classical mechanics has given rise to a literature critical of his result. I am interested here in posing a new objection different from the ones made to date. The first section of the paper expounds the essence of Norton’s model and my criticism of it. I then propose a specific modification in the absence of gravitational interaction. The final section takes into consideration a surprising consequence for classical mechanics from the new model introduced here.     

On Love’s Robustness

Recently Philip Pettit (2015) has claimed that attachment, virtue, and respect are robust goods. Robust goods require not only the actual provision of certain associated ‘thin’ goods, but also the modally robust provision of these thin goods across a range of counterfactual situations. I focus my attention on Pettit’s account of the robust good of love, which, for Pettit, is the modally robust provision of care. I argue Pettit’s account provides neither necessary nor sufficient conditions for love. In place of Pettit’s account, I suggest an alternative account of love that distinguishes loving dispositions from loving actions.     

On Freedom’s Mystery

Philosophia - This paper argues that Peter van Inwagen’s argument for the mysteriousness of metaphysical freedom does not establish its conclusion. Van Inwagen’s argument involves the...     

On Parfit’s Ontology

Parfit denies that the introduction of reasons into our ontology is costly for his theory. He puts forth two positions to help establish the claim: the Plural Senses View and the Argument from Empty Ontology. I argue that, first, the Plural Senses View for ‘exists’ can be expanded to allow for senses which undermine his ontological claims; second, the Argument from Empty Ontology can be debunked by Platonists. Furthermore, it is difficult to make statements about reasons true unless these statements include reference to objects in reality. These arguments show the instability of Parfit’s claimed metaethical advantages over naturalism.     

Somatic Apprehension and Imaginative Abstraction: Cairns’s Criticisms of Schutz’s Criticisms of Husserl’s Fifth Meditation

Dorion Cairns correctly interprets the preconstituted stratum of Edmund Husserl’s Fifth Cartesian Meditation to be the primordial ego and not the social world, as was thought by Alfred Schutz, who considered Husserl to be insufficiently attentive to the social world’s hold upon us. Following Cairns’s interpretation, which involves recovering and reconstructing strata that may never exist independently, one better understands how the transfer of sense “animate organism” involves automatic association, or somatic apprehension. This sense-transfer extends to any animate organism, not just humans, and draws on extensive unreflected-upon similarities despite the distinctive fact that the other’s body is never given to oneself as is one’s own. Following Cairns’s interpretation, one can also understand the second epoché as an imaginative, reconstructive abstraction rather than as an example of failed ascesis. Consequently, Husserl appears as less intellectualized in his approach to empathy than often thought to be and more confident in the phenomenologist’s capacity to imagine and attend selectively to experience.     

On Hans Reichenbach’s inductivism

One of the first to criticize the verifiability theory of meaning embraced by logical empiricists, Reichenbach ties the significance of scientific statements to their predictive character, which offers the condition for their testability. While identifying prediction as the task of scientific knowledge, Reichenbach assigns induction a pivotal role, and regards the theory of knowledge as a theory of prediction based on induction. Reichenbach’s inductivism is grounded on the frequency notion of probability, of which he prompts a more flexible version than that of Richard von Mises. Unlike von Mises, Reichenbach attempts to account for single case probabilities, and entertains a restricted notion of randomness, more suitable for practical purposes. Moreover, Reichenbach developed a theory of induction, absent from von Mises’s perspective, and argued for the justification of induction. This article outlines the main traits of Reichenbach’s inductivism, with special reference to his book Experience and prediction.     

On Axiomatizing Shramko-Wansing’s Logic

This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ _t and ⊨ _f , determined via truth and falsity orderings on the trilattice SIXTEEN ₃ (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN ₃ as a twist-structure over the two-element Boolean algebra.     

On Recanati’s Mental Files

Abstract

In his book Mental Files (Oxford: Oxford University Press, 2012), Francois Recanati develops a theory of mind and language based on the idea that Fregean senses should be identified with ‘mental files’, mental representations whose primary function is to store information about objects. I discuss three aspects of Recanati’s book. The first concerns his use of acquaintance relations in individuating mental files, and what this means for ‘file dynamics’. The second concerns his comments on a theory that I have elsewhere advocated, the ‘sequenced worlds’ or ‘multi-centered worlds’ theory. The third concerns how the mental file approach handles non-doxastic attitudes like imagining.     

On Reichenbach’s Causal Betweenness

We characterize, by easily verifiable properties, abstract ternary relations isomorphic to the causal betweenness introduced by Hans Reichenbach.     

On Quine’s Translation Argument

Quine's translation argumnent figures centrally in his views on logic. The goal of this paper is to get clear on that argument. It can be interpreted as an argument to the effect that one should never translate somebody’s speech as going against a law of the translator’s logic. Key to this reading of the translation argument is the premise that one should never translate somebody's speech such that their speech is unintelligible. Ultimately, it is my aim to reject this reading. I argue that only a weaker conclusion—one that says “not most of the time” instead of the stronger “never”—should be attributed to Quine. Accordingly, I propose and defend a weaker version of the first premise that better coheres with the weaker conclusion of the translation argument. Instead of the claim that one should never translate somebody’s speech such that their speech is unintelligible I argue that we should only ascribe to Quine the claim that one should not most of the time translate somebody’s speech in a way that makes it unintelligible. I go on to  sum up the results of my discussion and respond to a criticism of my reading.

     

On Kim’s exclusion principle

In this paper we explore Jaegwon Kim’s principle of explanatory exclusion. Kim’s support for the principle is clarified and we critically evaluate several versions of the dual explananda response authors have offered to undermine it. We argue that none of the standard versions of the dual explananda reply are entirely successful and propose an alternative approach that reveals a deep tension in Kim’s metaphysics. We argue that Kim can only retain the principle of explanatory exclusion if he abandons his longstanding critique of nonreductive physicalism.     

On Luo Congyan’s Ethics

Luo Congyan put forward the idea that benevolence is the substance while righteousness is its function, which placed the intrinsic value of human beings on a more fundamental position and affirmed the unity of benevolent principle and universal norms from the perspective of the relationship between substance and function. The unity of benevolence and righteousness involves the connection between value and norms, and the latter relate to the relationship between morality and law in the broader sense. On the basis of the idea of using both benevolence and righteousness, Luo Congyan examined the relationship between morality and law. Corresponding to the emphasis on the role of both law and political power, Luo Congyan concerned himself with how to establish rational interpersonal relationships in various ways. Furthermore, Luo Congyan emphasized the significance of behavior in everyday life, while he affirmed that the universal principle should be followed. In this way, he developed the earlier Confucian thought. Translated from Studies in Ethics by Xiao Mo