Competitive equilibrium with intuitionistic agents

This paper studies an economy whose agents perceive their consumption possibilities subjectively, and whose preferences are defined on what they subjectively experience, rather than on those alternatives that are objectively present. The model of agents’ perceptions is based on intuitionistic logic. Roughly, this means that agents reason constructively: a solution to a problem exists only if there is a construction by which the problem can be solved. The theorems that can be proved determine how an agent perceives a set of alternatives. A dual model relates perceived alternatives to a shared language, which the agents use in trading. So perceptions relate objective alternatives to an agent’s subjective view of them, and reporting dually relates an agent’s subjective world to a shared language. It turns out that an appropriately modified notion of competitive equilibrium always exists. However, in contrast with standard results in economic theory, competitive equilibrium need not be efficient.     

Epistemic constraints on practical normativity

What is the relation between what we ought to do, on the one hand, and our epistemic access to the ought-giving facts, on the other? In assessing this, it is common to distinguish ‘objective’ from ‘subjective’ oughts. Very roughly, on the objectivist conception what an agent ought to do is determined by ought-giving facts in such a way that does not depend on the agent’s beliefs about, or epistemic access to, those facts; whereas on the subjectivist conception, what an agent ought to do depends on his beliefs. This paper defends the need for, and explicates, a third category of ‘ought’: ‘warranted oughts’. Section 1 introduces the distinction between objective and subjective ‘oughts’. Sections 2–3 draw attention to some serious problems with each. Section 4 examines, though rejects, a recent attempt to replace subjective ‘oughts’ with objective ‘wide-scope oughts’ operating on belief-action combinations. Section 5 explicates the notion of a warranted ‘ought’ and defends the account against some possible objections. The resulting a picture is one in which an adequate analysis of practical normativity requires both objective and warranted ‘oughts’. Section 6 concludes by responding to a worry about countenancing both.     

Ambiguous figures and representationalism

Macpherson (Nous 40(1):82–117, 2006) argues that the square/regular diamond figure threatens representationalism, construed as the theory which holds that the phenomenal character is explained by the nonconceptual content of experience. Her argument is the claim that representationalism is committed to the thesis that differences in the experience of ambiguous figures, the gestalt switch, should be explained by differences in the NCC of perception of these figures. However, with respect to the square/regular diamond and some other ambiguous figure representationalism fails to offer a unified account of how representational content makes them ambiguous. In this paper, I aim, first, to offer a representationalist account of ambiguous figures and, second, to examine and rebut Macpherson’s arguments. My main point is that in each ambiguous figure Macpherson discusses there are differences in representational content that can explain differences in phenomenal character or content. The representational differences are due to the ways the Cartesian frame of reference in which perceptual content is always cast cuts the figure, underlying different properties of the figure with respect to the axes of the Cartesian frame of reference.     

Reasoning defeasibly about probabilities

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&;R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus for prob(P/Q&;R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&;R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&;R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application.     

From data to phenomena: a Kantian stance

This paper investigates some metaphysical and epistemological assumptions behind Bogen and Woodward’s data-to-phenomena inferences. I raise a series of points and suggest an alternative possible Kantian stance about data-to-phenomena inferences. I clarify the nature of the suggested Kantian stance by contrasting it with McAllister’s view about phenomena as patterns in data sets.     

The scientistic stance: the empirical and materialist stances reconciled

van Fraassen (The empirical stance, 2002) contrasts the empirical stance with the materialist stance. The way he describes them makes both of them attractive, and while opposed they have something in common for both stances are scientific approaches to philosophy. The difference between them reflects their differing conceptions of science itself. Empiricists emphasise fallibilism, verifiability and falsifiability, and also to some extent scepticism and tolerance of novel hypotheses. Materialists regard the theoretical picture of the world as matter in motion as a true and explanatory account and insist on not taking ‘spooky’ entities or processes seriously as potential explanations of phenomena that so far lie outside the scope of successful science. The history of science shows us that both stances have been instrumental in the achievement of progress at various times. It is therefore plausible for a naturalist to suggest that science depends for its success on the dialectic between empiricism and materialism. A truly naturalist approach to philosophy ought then to synthesise them. Call the synthesized empiricist and materialist stances ‘the scientistic stance’. This paper elaborates and defends it.     

The rationality of metaphysics

In this paper, it is argued that metaphysics, conceived as an inquiry into the ultimate nature of mind-independent reality, is a rationally indispensable intellectual discipline, with the a priori science of formal ontology at its heart. It is maintained that formal ontology, properly understood, is not a mere exercise in conceptual analysis, because its primary objective is a normative one, being nothing less than the attempt to grasp adequately the essences of things, both actual and possible, with a view to understanding as far as we can the fundamental structure of reality as a whole. Accordingly, it is urged, the deliverances of formal ontology have a modal and epistemic status akin to those of other a priori sciences, such as mathematics and logic, rather than constituting rivals to the claims of the empirical sciences, such as physics.