Foundations of Mathematics: Metaphysics, Epistemology, Structure

Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics.     

Virtue Epistemology: No New Cures

One version of virtue epistemology defines knowledge as belief whose truth arises from, or is explained by, the motives that produced it. This version is also intended to solve the Gettier problem, by shielding properly caused beliefs from double accidents. Unfortunately, there is no notion of "explains" or "arises from" which explains in the intended sense the truth of true beliefs.     

Robust Virtue Epistemology As Anti‐Luck Epistemology: A New Solution

Robust Virtue Epistemology (RVE) maintains that knowledge is achieved just when an agent gets to the truth through, or because of, the manifestation of intellectual virtue or ability. A notorious objection to the view is that the satisfaction of the virtue condition will be insufficient to ensure the safety of the target belief; that is, RVE is no anti‐luck epistemology. Some of the most promising recent attempts to get around this problem are considered and shown to ultimately fail. Finally, a new proposal for defending RVE as a kind of anti‐luck epistemology is defended. The view developed here turns importantly on the idea that knowledge depends on ability and luck in a way that is gradient, not rigid, and that we know just when our cognitive success depends on ability not rather, but more so, than luck.     

Towards a New Epistemology of Mathematics

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

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New Foundations for a Relational Theory of Theory-revision

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions ‘J is a contraction of K with respect to A’ and ‘J is a revision of K with respect to A’. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for AGM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions?     

Power and formation: New Foundations for a radical concept of Power

A radical concept of power identifies social processes which (whether as ‘ideology’, ‘false consciousness’, or ‘the spectacle') influence people's actions by moulding their beliefs or desires. However, seeing people as deluded is to risk treating them as less than fully autonomous beings. Despite his libertarian intentions, Lukes fails to guard against this paternalistic implication. His view still implies that it is the social critic who is in the best position to identify the real interests of an oppressed group. Here it is argued that power should be conceived as an intrusion on the ‘formative practices’ of people. It is possible to identify power as an unwanted influence on the processes in which people ‘form and discover’ interests, while maintaining that interests can only be self‐ascribed. This solution requires a concept of formation as both irreducibly social and yet potentially free. Neither Foucault nor Habermas can provide such a solution, despite some valuable insights. In the end, we must look at the influences of power on formative practices which are actual rather than idealized, productive rather than reflective, and which involve the whole person rather than merely the intellect.     

当代科学认识论的新视野

20世纪 50年代兴起的历史主义科学哲学瓦解了逻辑实证主义和证伪主义 ,但因历史主义强调科学理论的建构性和主观性 ,而逐步形成了相对主义和非理性主义为主导的科学哲学 ,从而导致了科学在文化中的权威性地位的丧失。所以 ,自 6 0年代开始 ,以Ｗ 塞拉斯和普特南为代表的科学实在论应运而生 ,他们对科学哲学历史主义学派的错误观点进行了批判 ,认为 ,科学理论的术语是有指称的 ,其指称的对象是客观存在的 ,成熟的科学理论比之以往的科学理论具有更多的真理性等实在论观点。 70年代末以来 ,美国科学哲学界出现了劳丹、范·弗拉森等人为代表的…     

The Attitudes About Reality Scale: A New Measure of Personal Epistemology

The Attitudes About Reality Scale (AAR) was constructed by Unger, Draper, and Pendergrass (1986) to measure implicit causal assumptions about the relationship between persons and their physical and social reality. The scale was presumed to assess a single dimension of personal epistemology, ranging from a social constructionist view of reality of a logical positivist view. The factor structure and convergent and discriminant validity of the AAR Scale were examined in this research. Results indicated that the AAR Scale measures at least two dimensions of personal epistemology, labeled societal determinism and individual determinism. A third dimension, labeled variable determinism, was also suggested by the results. Intercorrelations between AAR scale scores and measures of conceptually similar and conceptually distinct constructs supported the convergent and discriminant validity of the scale. Directions for future research on the predictive utility of the personal epistemology construct and on its socialization antecedents are discussed.     

Psychological Epistemology: Epistemological Psychology

In his 2010 book Being Human: Human Being, Rue Cromwell developed some key ideas for reforming psychology. These include resolving the conundrum of subject, object, and consciousness in science; sorting through the tangles of meaning in superficially similar but fundamentally different epistemologies; and reversing conflation of cultural, social, and economic values with those of science. This discussion applies those ideas to some particulars of clinical psychology, psychopathology and the treatment and rehabilitation of severe and disabling mental illness.     

New Foundations for Imperative Logic I: Logical Connectives,Consistency, and Quantifiers*

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me” is the conjunction of “kiss me” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, I argue. “If you love me, kiss me”, a conditional imperative, mixes a declarative antecedent (“you love me”) with an imperative consequent (“kiss me”); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three‐valued imperatives which mixes declaratives with imperatives. I develop such a logic.     

Foundations of Academic Freedom: Making New Sense of Some Aging Arguments

The article distinguishes between the various arguments traditionally offered as justifications for the principle of academic freedom. Four main arguments are identified, three consequentialist in nature (the argument from truth, the democratic argument, the argument from autonomy), and one nonconsequentialist (a variant of the autonomy argument). The article also concentrates on the specific form these arguments must take in order to establish academic freedom as a principle distinct from the more general principles of freedom of expression and intellectual freedom.     

Providing Foundations for Coherentism

We prove that four theses commonly associated with coherentism are incompatible with the representation of a belief state as a logically closed set of sentences. The result is applied to the conventional coherence interpretation of the AGM theory of belief revision, which appears not to be tenable. Our argument also counts against the coherentistic acceptability of a certain form of propositional holism. We argue that the problems arise as an effect of ignoring the distinction between derived and non-derived beliefs, and we suggest that the kind of coherence relevant to epistemic justification is the coherence of non-derived beliefs. This revised version was published online in July 2006 with corrections to the Cover Date.