Debunking Logical Ground: Distinguishing Metaphysics from Semantics

Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of ground even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground

Debunking logical grounding: distinguishing metaphysics from semantics

Many philosophers take purportedly logical cases of ground (such as a true disjunction being grounded in its true disjunct(s)) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for (e.g.) first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of ground, even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground.Accepted manuscrip

Grounding rules and (hyper-)isomorphic formulas

An oft-defended claim of a close relationship between Gentzen inference rules and the meaning of the connectives they introduce and eliminate has given rise to a whole domain called proof-theoretic semantics, see Schroeder- Heister (1991); Prawitz (2006). A branch of proof-theoretic semantics, mainly developed by Dosen (2019); Dosen and Petric (2011), isolates in a precise mathematical manner formulas (of a logic L) that have the same meaning. These isomorphic formulas are defined to be those that behave identically in inferences. The aim of this paper is to investigate another type of recently discussed rules in the literature, namely grounding rules, and their link to the meaning of the connectives they provide the grounds for. In particular, by using grounding rules, we will refine the notion of isomorphic formulas through the notion of hyper-isomorphic formulas. We will argue that it is actually the notion of hyper-isomorphic formulas that identify those formulas that have the same meaning

Grounding rules and (hyper-)isomorphic formulas

An oft-defended claim of a close relationship between Gentzen inference rules and the meaning of the connectives they introduce and eliminate has given rise to a whole domain called proof-theoretic semantics, see Schroeder- Heister (1991); Prawitz (2006). A branch of proof-theoretic semantics, mainly developed by Dosen (2019); Dosen and Petric (2011), isolates in a precise mathematical manner formulas (of a logic L) that have the same meaning. These isomorphic formulas are defined to be those that behave identically in inferences. The aim of this paper is to investigate another type of recently discussed rules in the literature, namely grounding rules, and their link to the meaning of the connectives they provide the grounds for. In particular, by using grounding rules, we will refine the notion of isomorphic formulas through the notion of hyper-isomorphic formulas. We will argue that it is actually the notion of hyper-isomorphic formulas that identify those formulas that have the same meaning

Initial Draft of a Possible Declarative Semantics for the Language

This article introduces a preliminary declarative semantics for a subset of the language Xcerpt (so-called grouping-stratifiable programs) in form of a classical (Tarski style) model theory, adapted to the specific requirements of Xcerpt’s constructs (e.g. the various aspects of incompleteness in query terms, grouping constructs in rule heads, etc.). Most importantly, the model theory uses term simulation as a replacement for term equality to handle incomplete term specifications, and an extended notion of substitutions in order to properly convey the semantics of grouping constructs. Based upon this model theory, a fixpoint semantics is also described, leading to a first notion of forward chaining evaluation of Xcerpt program

Grounding Operators: Transitivity and Trees, Logicality and Balance

We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and logical operators. Without fixing a particular notion of grounding or grounding relation, we present inferential rules that define, once a base grounding calculus has been fixed, three grounding operators: an operator for immediate grounding, one for mediate grounding (corresponding to the transitive closure of the immediate grounding one) and a grounding tree operator, which enables us to internalise chains of immediate grounding claims without loosing any information about them. We then present an in-depth proof-theoretical study of the introduced rules by focusing, in particular, on the question whether grounding operators can be considered as logical operators and whether balanced rules for grounding operators can be defined

Three Reflections on Return: Convergence of form with regard to light, life, word

In this paper, I trace the three-fold essence of “return”—a generating trope of identity and difference, through which formal aspects of the theory of relativity, the movement of language and emergence in evolution might converge. The trope of return is contrasted with the more common two-fold structure of relatedness underwriting differential calculus, propositional semantics and reductionism, which privileges space over time, identity over difference, self over creation