Online research in philosophy

In his 1961 paper "Tithenai ta Phainomena",1 G. E. L. Owen addressed the problem of the relationship between science as preached in the Analytics and the practice of the Aristotelian treatises. However, he gave this venerable crux a novel twist by focusing on a different aspect of the issue. According to the Prior Analytics , it appears that the first premises of scientific demonstrations must be obtained from collections (historiai) of facts derived from empirical observation. However, many of the treatises seem to make little use of empirical inquiry and instead concern themselves more with 'conceptual analysis.' This is especially true in the Metaphysics and the ethical treatises, but it is also very much characteristic of the Physics. How are these two kinds of inquiry related?

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

Whether a collection of scientific data can be explained only by a unique theory or whether such data can be equally explained by multiple theories is one of the more contested issues in the history and philosophy of science. This paper argues that the case for multiple explanations is strengthened by the widespread failure of Models in mathematical logic to be unique ie categorical. Science is taken to require replicable and explicit public knowledge; this necessitates an unambiguous language for its transmission. Mathematics has been chosen as the vehicle to transmit scientific knowledge, both because of its 'unreasonable effectiveness' and because of its unambiguous nature, hence the vogue of axiomatic systems. But Mathematical Logic tells us that axiomatic systems need not refer to uniquely defined real structures. Hence what is accepted as Science may be only one of several possibilities.

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth.

A plurality of axiomatic systems can be interpreted as referring to one and the same mathematical object. In this paper we examine the relationship between axiomatic systems and their models, the relationships among the various axiomatic systems that refer to the same model, and the role of an intelligent user of an axiomatic system. We ask whether these relationships and this role can themselves be formalized.

In this paper we examine Ellis and Bowman's argument, that simultaneity in inertial frames of reference is not conventional, from the axiomatic point of view. In Part I we examine the role of conventions in an axiomatic physical theory, and in Part II the relation of simultaneity in Reichenbach's axiomatization of the space-time theory of special relativity.

Formal theories, as in logic and mathematics, are sets of sentences closed under logical consequence. Philosophical theories, like scientific theories, are often far less formal. There are many axiomatic theories of the truth predicate for certain formal languages; on analogy with these, some philosophers (most notably Paul Horwich) have proposed axiomatic theories of the property of truth. Though in many ways similar to logical theories, axiomatic theories of truth must be different in several nontrivial ways. I explore what an axiomatic theory of truth would look like. Because Horwich’s is the most prominent, I examine his theory and argue that it fails as a theory of truth. Such a theory is adequate if, given a suitable base theory, every fact about truth is a consequence of the axioms of the theory. I show, using an argument analogous to Gödel’s incompleteness proofs, that no axiomatic theory of truth could ever be adequate. I also argue that a certain class of generalizations cannot be consequences of the theory.

During the Middle Ages and Rennaissance, it was commonly believed that Aristotle's biological studies reflected his theory of demonstrative science quite well. By contrast, most commentators in the twentieth century have taken it that this is not the case. This is largely the result of preconceptions about what a natural science modelled after the proposals of Aristotle's Posterior Analytics would look like. I argue that these modern preconceptions are incorrect, and that, while the Analytics leaves a variety of issues unanswered that a practicing biology must have answers to (hence Parts of Animals I), Aristotle's biological practice conforms to the Analytics model. It is further argued that establishing this claim requires reading philosophically through entire biological treatises--that is, one will miss the logical structure by following the usual practice of 'sampling' these treatises rather than reading them systematically.

More attention has been paid in recent years to the relationship between Aristotle’s science and his ethics, but little effort has been directed toward constructing a concrete model of a science of Aristotle’s ethics. I offer a proposal about how we might go about constructing a science of Aristotle’s ethics. I argue that constructing an axiomatic model for a portion of Aristotle’s ethics is not only possible, but helpful in making explicit relationships among concepts at the core of Aristotle’s theory. The model of an axiomatic approach to Aristotle’s ethics, which I propose in this paper, is only a small first step in constructing a full-blown science of Aristotle’s ethics, but taking this first step goes a long way toward showing that this project is promising.