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For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics (1934–1951) grew from his Early (1912–1921) and Middle (1929–33) philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.
The Critique of Judgment is concerned with “judgment” as a power of the mind that is expressed in particular acts of judging. This is the sense we draw upon when we say of someone that they have good judgment, or when we put our trust in someone’s judgment. I consider Kant’s regress argument concerning judgment in the Analytic of the Principles of the first Critique. Kant has been read as concluding that if cognition is to be possible it must, on pain of infinite regress, bottom out in some non-rule-governed, “immediate” act or entity. I argue that this interpretation misconstrues the moral of Kant’s argument, as it does that of the rule-following passages in Wittgenstein’s Philosophical Investigations with which it is sometimes aligned. The point of Kant’s argument is that judgment must be exercised: this is its condition. Kant shares with Wittgenstein (properly read) an awareness of the desire that we may have to evade the exercise of judgment and the revelations of the self that it entails. Reflective judgment, as introduced in the third Critique, is a further development of the notion of judgment as necessarily exercised and reflective of a particular mind.
This paper discusses Claudine Verheggen's account of what she takes to be Donald Davidson's response to the sceptical paradox about rule-following and meaning developed in Saul Kripke's interpretation of Wittgenstein's ‘rule-following considerations.’ It focusses on questions about the normativity of meaning, the social character of meaning, and the role of triangulation in Davidson's account of the determination of meaning, and invites Verheggen to compare the non-reductionism she finds in Davidson with that developed in Crispin Wright's judgement-dependent account of meaning.
A core philosophical use of the term “objectivity” is to talk about a central metaphysical ideal. The term is employed to pick out aspects of the world that are there in the sense that any thinker who fails to register them can be said to be missing something. If we speak in this connection of a guiding concept of objectivity, we can ask what can be said about the nature of the things that fall under it. We might then speak in this further connection of different possible conceptions of objectivity. Today, thought about objectivity is dominated by a conception on which objectivity is taken to have as its hallmark the exclusion of everything subjective. Starting from a description of the relevant conception of objectivity, this chapter criticizes the kinds of considerations most commonly adduced in the conception’s favor. Along the way, the chapter uses passages from the later philosophy of Wittgenstein as its main reference points. A notable virtue of this method is that it sheds light on the transformative significance of Wittgenstein’s thought for how we construe the concept of objectivity.
What is the relation between meaning and use? This chapter first defends a non-reductionist understanding of Wittgenstein’s suggestion that ‘the meaning of a word is its use in the language’; facts about meaning cannot be reduced to, or explained in terms of, facts about use, characterized non-semantically. Nonetheless, it is contended, facts about meaning do supervene on non-semantic facts about use. That supervenience thesis is suggested by comments of Wittgenstein’s and is consistent with his view of meaning and rule-following. Semantic supervenience is then defended against two criticisms: first, John McDowell’s suggestion that the supervenience thesis falsifies the epistemology of meaning and fails to accommodate common-sense truths about meaning; second, a series of counter-examples proposed by Stephen Kearns and Ofra Magidor, who argue that worlds may differ semantically without differing non-semantically. It is argued that neither criticism is convincing: we should accept the thesis that semantic facts supervene on non-semantic facts.
In her seminal article ‘Modern Moral Philosophy’ (1958) Elizabeth Anscombe argued that we need a new ethics, one that uses virtue terms to generate absolute prohibitions against certain act-types. Leading contemporary virtue ethicists have not taken up Anscombe's challenge in justifying absolute prohibitions and have generally downplayed the role of rule-following in their normative theories. That they have not done so is primarily because contemporary virtue ethicists have focused on what is sufficient for characterizing the deliberation and action of the fully virtuous person, and rule-following is inadequate for this task. In this article, I take up Anscombe's challenge by showing that rule-following is necessary for virtuous agency, and that virtue ethics can justify absolute prohibitions. First, I offer a possibility proof by showing how virtue ethics can generate absolute prohibitions in three ways: by considering actions that directly manifest vice or that cannot be performed virtuously; actions that are prohibited by one's institutional roles and practical identities; and actions that are prohibited by the prescriptions of the wise. I then seek to show why virtue ethicists should incorporate rule-following and absolute prohibitions into their theories. I emphasize the central role that rules have in the development of virtue, then motivate the stronger view that fully virtuous agents follow moral rules by considering the importance of hope, uncertainty about consequences, and taking responsibility for what eventuates. Finally, I provide an account of what Anscombe called a ‘corrupt mind’, explaining how our understanding of virtue is corrupted if we think that virtue may require us to do vicious actions.
Most game-theoretic accounts of institutions reduce institutions to behavioural patterns the players are incentivized to implement. An alternative account linking institutions to rule-following behaviour in a game-theoretic framework is developed on the basis of David Lewis’s and Ludwig Wittgenstein's respective accounts of conventions and language games. Institutions are formalized as epistemic games where the players share some forms of practical reasoning. An institution is a rule-governed game satisfying three conditions: common understanding, minimal awareness and minimal practical rationality. Common understanding has a strong similarity with Ludwig Wittgenstein's concept of lebensform while minimal awareness and minimal practical rationality capture the idea that rule-following is community-based.
This paper defends Michel Foucault's notion of archaeology of knowledge against the influential and putatively devastating criticism by Dreyfus and Rabinow that Foucault's archaeological project is based on an incoherent conception of the rules of the discursive practices it purports to study. I argue first that Foucault's considered view of these rules as simultaneously implicit and historically efficacious corresponds to a general requirement for the normative structure of a discursive practice. Then I argue that Foucault is entitled to that view despite the charges to the contrary by Dreyfus and Rabinow. I also explain in detail how the argument by Dreyfus and Rabinow arises from a misunderstanding of Foucault's archaeological project as transcendental inquiry, while archaeology of knowledge is, in fact, a diagnostic project. The result is a novel understanding of the notion of archaeology of knowledge that enables a reassessment of Foucault's philosophical work in connection with current debates regarding the relationship between reflection and practice in the structure of thought.
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