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ontologically real properties. After Descartes, a speculative atomism was thought to supply a new foundation for physics. Neither the original mechanistic atomism nor the nineteenth century revision, atomistic mechanism, succeeded in achieving a coherent reductive account of classical physics in terms of the properties of atoms. Yet, the effort had a distinct role in integrating physics and left a linguistic residue, the primacy accorded mechanical concepts. The concepts ‘space’, ‘time’, ‘mass’, ‘force’, ‘energy’, and ‘momentum’ are anchored in mechanics but function in all branches of physics. To round out the core concepts one must add two distinctively thermodynamic concepts, temperature and entropy, and one electrodynamic concept, charge. The concept of a classical field became, after its ontological foundations dissolved, a phenomenological concept based on measurement. The classical/quantum boundary makes classical physics a closed system in a special sense.

This categorial framework supports an increasingly complex network of quantitative concepts. According to Mary Hesse's (1974) network model, which I am adapting, any new quantitative concept is under a double constraint. It must fit into a network of concepts in a coherent fashion and it must support a mathematical representation. Quine's great sphere of knowledge supplies a useful analogy for understanding the way coherence is achieved. Reality intrudes on the periphery through the excitations of nerve endings. For the core, Quine proposed first order sentential calculus with or without identity. Between the core and the periphery Quine posited layers, with fuzzy borders: numbers, sets, and various mathematical structures; general principles like symmetry and simplicity; general physical laws; and particular assumptions. The pragmatic strategy for handling the contradictions that routinely rise up is to move contradictions as far from the core as possible and then resolve them by whatever expedient causes the least overall incoherence.

The key difference between this and LCP concerns the core. Quine admitted that spatio-temporal objects with properties is at the conceptual core of our ordinary language, but considered this a remnant of muddy savagery. The logical core he proposed was an anticipation of a reformed future science. For various reasons, including the well-known incompatibilities between standard logic and quantum mechanics, this anticipation does not fit present physics or its foreseeable extensions. The anticipation of such a core reflects a goal Quine shared with many philosophers of science. The reasoning involved in interpreting physics should be formal, mathematics, logic, and the interpretation of formal systems. The conceptual core of LCP features spatio-temporal objects with the basic quantitative properties just listed. The network of concepts it supports plays an inferential role that is neglected in more formal approaches to interpreting physics. However, it is important both for understanding the functioning of classical physics and the complementary role between classical and quantum physics.

2.21  Material Inferences.

Consider the muddy alternative to Quine's sanitized core. The categorial structure of LCP supports two distinct, but interrelated, types of inferences, which we will simplistically label 'material' and 'formal'.  Instead of attempting to develop either I will simply indicate some compatible sources and focus on two points of more immediate concern. First, when material inferences become widely accepted they effectively cease to function as inferences. They become matters of 'objective fact'. Second, we must

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