Rawleigh (2022)
Rawleigh, William. (2022) Reconceiving Scientific Mosaics: A New Formalization for Theoretical Scientonomy. In Barseghyan et al. (Eds.) (2022), 83-103.
| Title | Reconceiving Scientific Mosaics: A New Formalization for Theoretical Scientonomy |
|---|---|
| Resource Type | collection article |
| Author(s) | William Rawleigh |
| Year | 2022 |
| Collection | Barseghyan et al. (Eds.) (2022) |
| Pages | 83-103 |
Abstract
A central concept in scientonomy is the scientific mosaic, a concept intended to capture the state of an agent’s scientific knowledge at a given point in time. The currently accepted definition of the mosaic, “a set of all epistemic elements accepted and/or employed by an epistemic agent”, is a syntactic definition that fails to provide a theoretically robust investigational framework that allows scientonomists to explore mosaics and their minutiae fully and fruitfully. Pressingly, this definition leaves open some troubling semantic questions about the nature of deducibility and meaning within scientonomy’s theoretical framework. This paper tackles these problems by proposing a semantic foundation for theoretical scientonomy rooted in explicitly set-theoretic concepts. It begins by examining a problem of semantic recursion through self-reference posed by the current definition and shows how the syntactic definition is fundamentally unable to overcome this problem. Instead, it proposes a semantic definition of mosaics which, while recursive, is not viciously or self-referentially recursive. It argues that by formalizing mosaics semantically as natural language models for scientific communities, scientonomy can overcome its semantic problems while also illuminating how truth-value assignment, inference, and the operation of higher-order laws work within theoretical scientonomy. To that end, it shows how a semantic definition can solve an outstanding problem with the third law having to do with the concept of deducibility.
Theories
Here are all the theories formulated in Rawleigh (2022):
| Theory | Type | Formulation | Formulated In |
|---|---|---|---|
| Scientific Mosaic (Rawleigh-2022) | Definition | A model of all epistemic elements accepted or employed by the epistemic agent. | 2022 |
| The Law of Method Employment (Rawleigh-2022) | Descriptive | A method becomes employed only if it is derivable from a non-empty subset of other elements of the mosaic. | 2022 |
| The Law of Norm Employment (Rawleigh-2022) | Descriptive | A norm becomes employed only if it is derivable from a non-empty subset of other elements of the mosaic. | 2022 |
Suggested Modifications
Here are all the modifications suggested in Rawleigh (2022):
- Sciento-2022-0001: Accept a new model-theoretic definition of scientific mosaic, according to which, a scientific mosaic is a model of all epistemic elements accepted or employed by the epistemic agent. The modification was suggested to Scientonomy community by William Rawleigh on 28 February 2022.1 The modification was accepted on 21 February 2024. Nobody submitted opinions on this modification to the encyclopedia prior to the 2024 workshop. At the workshop, most of the discussion focused around the differences in wording between the earlier definition of scientific mosaic and the new one as formulated by Rawleigh. It was clarified that there is little difference in meaning between the definitions, but Rawleigh’s modification addressed the concern that the old language for describing a scientific mosaic was couched in terms of set theory, which Jamie Shaw pointed out would pose a problem for how we typically talk about mosaics (classifying mosaics by their number of elements is not particularly helpful for scientonomers). The new model-theoretic definition seemed more intuitive to some members of the community, even though neither definition commits to any syntactic view of theories. Some members of the community did not vote on the modification given their lack of experience with set theory, but overall the modification was accepted by over a two-thirds majority of voters. 13 out of 15 votes were to accept.
- Sciento-2022-0002: Accept the new law of norm employment that fixes some of the issues of the current law of method employment and makes it applicable to norms of all types. The modification was suggested to Scientonomy community by William Rawleigh on 28 February 2022.1 The modification was accepted on 21 February 2024. Prior to the 2024 workshop, Hakob Barseghyan commented on the encyclopedia with his opinion that the modification should be accepted given that the formulation seemed relatively future-proof: it would not have to change even if more elements are included into our ontology. Paul Patton and Cameron Scott raised some concerns about the differences between norm employment and norm acceptance, and about the derivability of norms from agents’ mosaics, given cases in the history of science where agents accept a norm that is derivable from their mosaic but do not act accordingly (that is, they fail to employ the norm). However, it was noted that this is a separate issue from what the modification aims to do: the law of norm employment does not describe what happens to norms that are already present in the mosaic, but merely describes how norms come to be part of the mosaic. Yet, the discrepancy in the community’s accepted definitions of norm acceptance (as a subtype of theory acceptance) and norm employment was highlighted as a pertinent issue for later focus. After this clarification, there were no further issues raised, and the modification was accepted by over a two-thirds majority of voters. 14 out of 16 votes were for acceptance.