Online research in philosophy

Bransen takes the first question to pose “the problem of man’s uniqueness,” and his ultimate aim is to dissolve that problem. His method of dissolving it is by way of a detailed answer to the second question, which is the most fundamental. I want to show that Bransen’s answer to the second question actually provides an answer to each of the other questions, and that instead of dissolving the problem of man’s uniqueness (posed by question #1), what he offers is really a straightforward solution—albeit a partly normative one. To see this, we must look beyond Bransen’s answer to the metaphysical presuppositions on which, I believe, it rests.

According to standard mathematical platonism, mathematical entities (numbers, sets, etc.) are abstract entities. As such, they lack causal powers and spatio-temporal location. Platonists owe us an account of how we acquire knowledge of this inaccessible mathematical realm. Some recent versions of mathematical platonism postulate a plenitude of mathematical entities, and Mark Balaguer has argued that, given the existence of such a plenitude, the attainment of mathematical knowledge is rendered non-problematic. I assess his epistemology for such a profligate platonism and find it unsatisfactory because it lacks an adequate semantics, in particular, an adequate account of reference.

In the paper a question is explored whether human person possess something that may be called “a sense of uniqueness” (uniqueness in numerical sense). Uniqueness may be primarily related to individual experience of an episodic situation in an actual context. Only from such an experience one could derive an objective (or intersubjective) notion of uniqueness of concrete things and events. The sense of uniqueness is connected to the sense of spatiotemporal presence, sense of Self, and sense of sameness of episodes really lived through and their recollections. A question is posed of the nature of such connections.

Wentzel van Huyssteen's Gifford Lectures, published as Alone in the World? Human Uniqueness in Science and Theology, accomplish critical and constructive thinking about interdisciplinary reflection on science and religion and about the meaning of human uniqueness. One approach to discussion of van Huyssteen's text entails consideration of three issues: the contextual character of research on humans and animals, the difficult problem of defining uniqueness, and the important consequences of exploring human uniqueness. Evolutionary biology and primatology contribute specific scientific insights.

The Uniqueness Thesis, or rational uniqueness, claims that a body of evidence severely constrains one’s doxastic options. In particular, it claims that for any body of evidence E and proposition P, E justifies at most one doxastic attitude toward P. In this paper I defend this formulation of the uniqueness thesis and examine the case for its truth. I begin by clarifying my formulation of the Uniqueness Thesis and examining its close relationship to evidentialism. I proceed to give some motivation for this strong epistemic claim and to defend it from several recent objections in the literature. In particular I look at objections to the Uniqueness Thesis coming from considerations of rational disagreement (can’t reasonable people disagree?), the breadth of doxastic attitudes(can’t what is justified by the evidence encompass more than one doxastic attitude?), borderline cases and caution (can’t it be rational to be cautious and suspend judgment even when the evidence slightly supports belief?), vagueness (doesn’t the vagueness of justification spell trouble for the Uniqueness Thesis?), and degrees of belief (doesn’t a finegrained doxastic picture present additional problems for the Uniqueness Thesis?).

In this paper I argue for a version of the Total Evidence view according to which the rational response to disagreement depends upon one's total evidence. I argue that perceptual evidence of a certain kind is significantly weightier than many other types of evidence, including testimonial. Furthermore, what is generally called "The Uniqueness Thesis" is actually a conflation of two distinct principles that I dub "Evidential Uniqueness" and "Rationality Uniqueness." The former principle is likely true but the latter almost certainly false. Seeing why the Rationality Uniqueness fails opens the door to seeing how mutual reasonable disagreement is possible even among those who share the same evidence.

It is argued here that mathematical objects cannot be simultaneously abstract and perceptible. Thus, naturalized versions of mathematical platonism, such as the one advocated by Penelope Maddy, are unintelligble. Thus, platonists cannot respond to Benacerrafian epistemological arguments against their view vias Maddy-style naturalization. Finally, it is also argued that naturalized platonists cannot respond to this situation by abandoning abstractness (that is, platonism); they must abandon perceptibility (that is, naturalism).

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct.

Relationist theories of space or space-time based on embedding of a physical relational system A into a corresponding geometrical system B raise problems associated with the degree of uniqueness of the embedding. Such uniqueness problems are familiar in the representational theory of measurement (RTM), and are dealt with by imposing a condition of uniqueness of embeddings up to composition with an "admissible transformation" of the space B. Friedman (1983) presents an alternative treatment of the uniqueness problem for embedding relationist theories, developed independently of RTM. Friedman's approach differs from that of RTM in securing uniqueness by adding new primitives to the physical system A in contrast to the RTM approach which adds new axioms. Friedman's proposal has recently been developed and defended by Catton and Solomon (1988). This method of solving the uniqueness problem is here argued to be substantially inferior to the RTM method, both in practice and in principle. In practice we find that in none of the concrete examples offered to illustrate the method is the uniqueness problem actually solved in general. Moreover we find that in the most interesting case (addition to the system A of a finite number of relations of finite degree) the method is in principle incapable of success for mathematical reasons. In addition to these technical difficulties there are compelling methodological reasons for preferring the RTM method to the method of adding primitives.

A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist.