Online research in philosophy

There is good reason to suppose that our best physical theories are false: In addition to its own internal problems, the standard formulation of quantum mechanics is logically incompatible with special relativity. There is also good reason to suppose that we have no concrete idea concerning what it might mean to claim that these theories are approximately or vaguely true. I will argue that providing a concrete understanding the approximate or vague truth of our current physical theories is not a task for traditional epistemology; rather, this is only possible in the context of ongoing empirical inquiry. [Note #1].

The dynamics/computation debate recalls a similar debate in the evolutionary biology community concerning the relative primacy of theories of structure versus theories of change. A full account of cognition will require a rapprochement between such theories and will include both computational and dynamical notions. The key to making computation relevant to cognition is not making it analog, but rather understanding how functional information-processing structures can emerge in complex dynamical systems.

Scientific Realists argue that it would be a miracle if scientific theories were getting more predictive without getting closer to the truth; so they must be getting closer to the truth. Van Fraassen, Laudan et al. argue that owing to the underdetermination of theory by data (UDT) for all we know, it is a miracle, a fluke. So we should not believe in even the approximate truth of theories. I argue that there is a test for who is right: suppose we are at the limit of inquiry. Suppose that we then have all the logically possible theories that are adequate to all the actual data. If they all resembled in their theoretical claims, since one of them must be true, all of them would then resemble it, whichever it is. We would thus be justified in saying they all approximated the truth in the degree to which they co-resembled. If they don't all co-resemble, the SRs are wrong; more predictive theories are not necessarily closer to the theoretical truth. Prior to the limit, if, in spite of our best efforts to the contrary, all the theories we can make adequate to current data tend to co-resemble, we have inductive warrant for thinking more predictive theories are closer to the truth. If they don't resemble, we have inductive warrant for thinking that more predictive theories are not necessarily closer to the truth.

This paper utilizes Scott domains (continuous lattices) to provide a mathematical model for the use of idealized and approximately true data in the testing of scientific theories. Key episodes from the history of science can be understood in terms of this model as attempts to demonstrate that theories are monotonic, that is, yield better predictions when fed better or more realistic data. However, as we show, monotonicity and truth of theories are independent notions. A formal description is given of the pragmatic virtues of theories which are monotonic. We also introduce the stronger concept of continuity and show how it relates to the finite nature of scientific computations. Finally, we show that the space of theories also has the structure of a Scott domain. This result provides an analysis of how one theory can be said to approximate another.

Aspects of a formal theory of approximate generalizations, according to which they have degrees of truth measurable by the proportions of their instances for which they are true, are discussed. The idealizability of laws in theories of fundamental measurement is considered: given that the laws of these theories are only approximately true "in the real world", does it follow that slight changes in the extensions of their predicates would make them exactly true?

Most scientific realists nowadays would endorse an argument like the following: The empirical and explanatory success of theories or theory-parts is a good indicator of their approximate truth. In turn, approximate truth is a good indicator of referential success. Successor theories typically preserve all of the empirical and explanatory success of their predecessors as well as add to it. They are thus in general strictly more approximately true than their predecessors. Moreover, by preserving their predecessors’ approximately true parts they preserve the referential success the predecessors probably enjoy. This implies that successor theories that are more approximately true than their predecessors are typically also referentially continuous with them.

There is good reason to suppose that our best physical theories, quantum mechanics and special relativity, are false if taken together and literally. If they are in fact false, then how should they count as providing knowledge of the physical world? One might imagine that, while strictly false, our best physical theories are nevertheless in some sense probably approximately true. This paper presents a notion of local probable approximate truth in terms of descriptive nesting relations between current and subsequent theories. This notion helps explain how false physical theories might nevertheless provide physical knowledge of a variety that is particularly salient to diachronic empirical inquiry.

The concept of approximate truth plays a prominent role in most versions of scientific realism. However, adequately conceptualizing ?approximate truth? has proved challenging. This article argues that the goal of articulating the concept of approximate truth can be advanced by first investigating the processes by which science accords theories the status of accepted or rejected. Accordingly, this article uses a path diagram model as a visual heuristic for the purpose of showing the processes in science that are involved in determining a theory's status. This ?inductive realist? model of theory status then serves as a starting point for explicating an inductive realist view of approximate truth that, it is argued, can explain instances of the success of science, but does not (1) require science's theories to be strictly true in any world or (2) require a metric for measuring how close an approximately true theory is to some strictly true theory. To show the advantages of the inductive realist approach to approximate truth, an example of a major success story of science, the successful eradication of smallpox, is reviewed and then explained.

This paper describes a theory of accuracy or approximate truth and applies it to problems in the realist interpretation of scientific theories. It argues not only that realism requires approximate truth, but that an adequate theory of approximation also presupposes some elements of a realist interpretation of theories. The paper distinguishes approximate truth from vagueness, probability and verisimilitude, and applies it to problems of confirmation and deduction from inaccurate premises. Basic results are cited, but details appear elsewhere. Objections are surveyed, including arguments by Miller, Laymon, and Laudan. Comparison is made with Niiniluoto's theory of verisimilitude, and the utility of his theory for realism assessed.

A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions of verisimilitude.