Online research in philosophy

Starting with the view that methodological constraints depend upon the nature of the system investigated, a tripartite division between theoretical, semitheoretical, and empirical discoveries is made. Many nanosystems can only be investigated semitheoretically or empirically, and this aspect leads to some nanophenomena being weakly emergent. Self-assembling systems are used as an example, their existence suggesting that the class of systems that is not Kim-reducible may be quite large.

It is commonly held that the change from the concrete view of the axiomatic method to the abstract one originated from the creation of non-Euclidean geometries and algebraic theories beyond the traditional theory of equations. Such explanation seems however to be too simple because, for instance, Lobačevskij presented his geometry not as an abstract system but as a concrete investigation of certain physical forces, and Boole presented his algebra not as an abstract system but as a concrete investigation of the operations of the mind by which reasoning is performed. Lobačevskij and Boole did not even present their systems as axiomatic systems. In this paper it is argued that a more plausible explanation is that the change was due to a somewhat late impact of Romanticism on mathematics.

The complex systems approach to cognitive science invites a new understanding of extended cognitive systems. According to this understanding, extended cognitive systems are heterogenous, composed of brain, body, and niche, non-linearly coupled to one another. In our previous work, we have argued that this view of cognitive systems, as non-linearly coupled brain-body-niche systems, promises conceptual and methodological advances on a series of traditional philosophical problems concerning cognition, reductionism, and consciousness. In this paper, we discuss agency and intentional action in light of this view of cognition.

Deterministic Chaos: Some Interesting Points of View from the Philosophy of Science. A comparatively simple example is used to present some of the main features of deterministic chaos. From the point of view of the philosophy of science, three questions are dealt with: if the equations of motion of chaotic systems are falsifiable in a strict sense; whether experiments on chaotic systems are reproducible; to what extent the development of chaotic systems is predictable. It emerges that in these respects chaotic systems, though being deterministic, behave essentially in the same way as stochastic (indeterministic) systems do.

Although resolution-based inference is perhaps the industry standard in automated theorem proving, there have always been systems that employed a different format. For example, the Logic Theorist of 1957 produced proofs by using an axiomatic system, and the proofs it generated would be considered legitimate axiomatic proofs; Wang’s systems of the late 1950’s employed a Gentzen-sequent proof strategy; Beth’s systems written about the same time employed his semantic tableaux method; and Prawitz’s systems of again about the same time are often said to employ a natural deduction format. [See Newell, et al (1957), Beth (1958), Wang (1960), and Prawitz et al (1960)]. Like sequent proof systems and tableaux proof systems, natural deduction systems retain..

Abstract I argue for the following, which I dub the ?fallibility syllogism?: (1) All systems of criminal punishment that inflict suffering on the innocent are unjust from a desert-based, retributivist point of view. (2) All past or present human systems of criminal punishment inflict suffering on the innocent. (3) Therefore, all such human systems of criminal punishment are unjust from a desert-based, retributivist point of view. My argument for the first premise is organized in the following way. I define what a human system of punishment is. I offer a distinction between retributive and utilitarian approaches to punishment. I distinguish between weak retributivism embodied in the second premise and strong retributivism, which I argue is the basis for the weak version. I argue that on retributivist grounds, each case of punishment is just when it matches the seriousness of the wrongdoing of the offender and that systems of punishment are just from a retributivist point of view when there are no exceptions to this match-up. In making my case, I will use Kant's retributivism as the version of my choice, so I will spend some time showing that recent reinterpretations of Kant (arguing that he was not a thoroughgoing retributivist), even if they are correct, are consistent with my view. Ultimately, however, I argue that the better view is that Kant was a thoroughgoing retributivist.

What is the simplest and most natural axiomatic replacement for the set-theoretic definition of the minimal fixed point on the Kleene scheme in Kripke’s theory of truth? What is the simplest and most natural set of axioms and rules for truth whose adoption by a subject who had never heard the word "true" before would give that subject an understanding of truth for which the minimal fixed point on the Kleene scheme would be a good model? Several axiomatic systems, old and new, are examined and evaluated as candidate answers to these questions, with results of Harvey Friedman playing a significant role in the examination.

Without introducing quantifiers, minimal axiomatic systems have already been constructed for Peirce's triadic logics. The present paper constructs a dual pair of axiomatic systems which can be used to introduce quantifiers into Peirce's preferred system of triadic logic. It is assumed (on the basis of textual evidence) that Peirce would prefer a system which rejects the absurd but tolerates the absolutely undecidable. The systems which are introduced are shown to be absolutely consistent, deductively complete, and minimal. These dual axiomatic systems reveal an interesting elegance, independent of their historical motivation.

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.

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.