Categorization generated by extended prototypes—An axiomatic approach

We suggest a model of categorization based on prototypes. A set of entities, identified with some finite dimensional Euclidian space, is partitioned into a finite number of categories. Such a categorization is said to be generated by extended prototypes if there is a set of distinguished entities, one for each category, such that the categorization is determined by proximity to these prototypical entities. The prototypes are called extended since they are described by points in a higher dimensional space than the entities. Sufficient conditions for a categorization to be generated by extended prototypes are provided. These conditions are also necessary if the prototypes are in general position.     

The axiological solution to divine hiddenness

Philosophers have recently wondered whether the value impact of the existence of God on the world would be positive, negative, or neutral. Thus far discussions have distinguished between the value God's impact would have overall, in certain respects, and/or for particular individuals. A commonality amongst the various positions that have been taken up is to focus on the goods and drawbacks associated with both theism and atheism. Goods associated with atheism include things like privacy, independence, and autonomy. I argue that it is better overall and for everyone to prefer a hidden God to no God. This is because it is possible to experience many of the goods attributed to atheism if God is hidden even if they do not really obtain, while also gaining many of the additional goods connected to theism. This amounts to a new solution to the problem of divine hiddenness: God might hide in order to increase or maximize the axiological value of the world.     

Undermining the axiological solution to divine hiddenness

Lougheed (Ratio 31:331–341, 2018) argues that a possible solution to the problem of divine hiddenness is that God hides in order to increase the axiological value of the world. In a world where God exists, the goods associated with theism necessarily obtain. But Lougheed also claims that in such a world it’s possible to experience the goods of atheism, even if they don’t actually obtain. This is what makes a world with a hidden God more valuable than a world where God is unhidden (where it’s impossible to experience atheistic goods), and also more valuable than an atheistic world with no God (and hence no theistic goods). We show that Lougheed never considers the comparison between a world where God hides and an atheistic world. We argue that it’s possible for a person to experience theistic goods in a world where God does not exist, a possibility Lougheed never considers. If this is right it undermines his axiological solution to divine hiddenness. We conclude by showing how our discussion of the axiology of theism connects to the existential question of whether God exists; that is, we show that the axiological question is (partly) dependent on the existential question.

     

Magnitude comparison revisited: An alternative approach to binary choice under uncertainty

Two generations of psychologists have been interested in understanding binary choice under uncertainty. In the 1970s and 1980s, researchers assumed that people rely on a two-stage magnitude comparison process to make these decisions (Banks, 1977; Moyer & Dumais, 1978). More recently, the focus has shifted to approaches that rely on probabilistic cues and simple heuristics (Gigerenzer & Goldstein, Psychological Review 103, 650-669, 1996). Here, we test competing predictions derived from these two very different approaches and conclude that the magnitude comparison process plays a central role in this task. In support of this conclusion, we present an experiment in which participants were timed as they decided which of two vehicles was more expensive. Pairs composed of one luxury vehicle (e.g., BMW 323i) and one nonluxury vehicle (e.g., Toyota 4Runner) were critical because the magnitude comparison approach correctly predicted that reaction times would decrease with subjective distance, whereas the heuristics approach incorrectly predicted that there would be no relation.     

From an axiological standpoint

I maintain that intrinsic value is the fundamental concept of axiology. Many contemporary philosophers disagree; they say the proper object of value theory is final value. I examine three accounts of the nature of final value: the first claims that final value is non‐instrumental value; the second claims that final value is the value a thing has as an end; the third claims that final value is ultimate or non‐derivative value. In each case, I argue that the concept of final value described is either identical with the classical notion of intrinsic value or is not a plausible candidate for the primary concept of axiology.     

An axiomatic basis for distributional equality in utilitarianism

An axiomatic basis for a social preference ordering with interval-scaled utility levels satisfying the principles of anonymity and pareto superiority is elaborated. The ordering is required to be sensitive to distributional equality: Redistribution of utility income from poor to rich persons without changing their social rank should lead to a superior evaluation. The axiom of separability is weakened in order to make it compatible with distributional equality. We prove that every continuous ordering satisfying the upper axioms can be represented by a utility function which is positively linear on the convex cone of rank-ordered utility vectors. A modified unnormalized Gini coefficient is one possible choice, but it contradicts, as well as related proposals, the principle of adequacy of means for some distribution problems.     

An axiomatic theory of conjoint,expected risk

This paper presents an axiomatization of subjective risk judgments that leads to a representation of risk in terms of seven free parameters. This is shown to have considerable predictive ability for risk judgments made by 10 subjects. The risk function retains many of the features of the expectation models—e.g., a constant number of parameters independent of the number of outcomes—but it also allows for asymmetric effects of transformations on positive and negative outcomes. This arises by axiomatizing independently the behavior with respect to gambles having entirely positive outcomes and those with entirely negative outcomes. Complex gambles are decomposed into these, and zero outcomes, using the expected risk property. The resulting risk function compares favorable with other functions previously suggested. It is also demonstrated that preference judgments are distinct from risk judgments, and that the theory does not apply as well to the former.     

An axiomatic formulation and generalization of successive intervals scaling

A formal set of axioms is presented for the method of successive intervals, and directly testable consequences of the scaling assumptions are derived. Then by a systematic modification of basic axioms the scaling model is generalized to non-normal stimulus distributions of both specified and unspecified form.     

An approach to why-questions

The purpose of this paper is to give a semantical analysis of why-questions. Why-questions will be construed as requests for knowledge. Special attention will be paid to considering what the conditions for conclusive answerhood are in the case of why-questions. Since explanations can often be thought of as answers to why-questions, we also discuss some topics in the theory of explanation.This study was supported by the Academy of Finland (Valtion humanistinen toimikunta) and by NSF grant No. IST-8310936 (Information Science and Technology), principal investigators Jaakko Hintikka and C. J. B. Macmillan. Scholarships from the Emil Aaltonen Foundation and the Finnish Academy of Sciences (Suomalainen Tiedeakatemia) are gratefully acknowledged.     

An ecological approach to disjunctivism

In this paper I claim that perceptual discriminatory skills rely on a suitable type of environment as an enabling condition for their exercise. This is because of the constitutive connection between environment and perceptual discriminatory skills, inasmuch as such connection is construed from an ecological approach. The exercise of a discriminatory skill yields knowledge of affordances of objects, properties, or events in the surrounding environment. This is practical knowledge in the first-person perspective. An organism learns to perceive an object by becoming sensitized to its affordances. I call this position ecological disjunctivism. A corollary of this position is that a case of perception and its corresponding case of hallucination—which is similar to the former only in some respects—are different in nature. I show then how the distinguishability problem is addressed by ecological disjunctivism.

     

An approach to intensional logic

A system of tensed intensional logic excluding iterations of intensions is introduced. Instead of using the type symbols (for ‘sense’), extensional and intensional functor types are distinguished. A peculiarity of the semantics is the general acceptance of value-gaps (including truth-value-gaps): the possible semantic values (extensions) of extensional functors are partial functions. Some advantages of the system (relatively to R. Montague's intensional logic) are briefly indicated. Also, applications for modelling natural languages are illustrated by examples.     

An ecological approach to learning

This paper introduces a special journal issue devoted to the study of learning in ecological and developmental contexts. In the past, the dominant approach to the study of learning has depended upon the choice of arbitrary problems, stimuli, and responses to guarantee the generality of principles discovered in the laboratory. Recently, though, there has been considerable interest in integrating an ecological (functional) account of learning with the strengths of the classic laboratory approach. One form of integration is to use the technology of the laboratory to look for the operation of general learning laws in ecological problems. The approach favored here is to treat learning as a biological phenomenon by first placing it within a functional system of behavior, and then by analyzing where and how learning modifies the operation of that system. Because the results of such analyses are defined with respect to functioning systems rather than procedural paradigms, the ecological approach readily makes contact with issues in evolution, development, and physiology, an ability not completely shared by the classic general-process approach. Concerns about laboratory versus field, function versus mechanism, generality of results, and adaptive “storytelling” can be resolved or further clarified by the present approach. The papers in this issue represent a cross-section of research stemming from an ecological approach to learning, and provide specific analyses of how learning modifies and is expressed in functional systems of behavior.