Under the standard modal explication of consequence, a conclusion is a consequence of some premises just in case necessarily, if the latter are true, so is the former. Notoriously, this explication yields some results that at first glance are counter-intuitive. In particular, a necessary truth is a consequence of arbitrary premises, and premises that cannot all be true together entail arbitrary conclusions. In his paper ‘On Ground and Consequence’ (Synthese, 2021), Benjamin Schnieder introduces a novel notion of web consequence, defined (...) on the basis of the concept of ground, which, he argues, fits our intuitive conception better. Building on his idea, the present paper examines the concept of web consequence in more detail. In particular, I provide three alternative, and simpler semantic characterizations of Schnieder’s propositional logic of web consequence, two within a form of truthmaker semantics, one within a many-valued setting. I then consider some natural variations on that logic and establish their connections to well-known subclassical logics such as FDE, $$\hbox {K}_3$$ K 3, and LP. Finally, I provide sound and complete tableaux-based proof systems for each of the logics of web consequence so obtained. (shrink)

I identify a notion of logical grounding, clarify it, and show how it can be used (i) to characterise various consequence relations, and (ii) to give a precise syntactic account of the notion of “groundedness” at work in the literature on the paradoxes of truth.

The present endeavour aims at the clarification of the concept of the logical consequence. Initially we investigate the question: How was the concept of logical consequence discovered by the medieval philosophers? Which ancient philosophical foundations were necessary for the discovery of the logical relation of consequence and which explicit medieval contributions, such as the notion of the formality (formal validity), led to its discovery. Secondly we discuss which developments of modern philosophy effected the turn from the medieval concept of logical (...) consequence to its most recent conceptions, such as the semantic, syntactic, axiomatic and natural deductive approaches? Thirdly we examine which are the similarities and the differences between the logical concepts of consequence, inference, implication and entailment? Furthermore, we ask what kind of relation signifies the concept of the logical consequence? That is to say, which is the analytic definition of the consequence relation R between the premises p1, p2...pn and the conclusion c of a formally valid argument? Finally, we focus on the respective answers given through the developments in proof theory by David Hilbert and Gerhard Gentzen. (shrink)

There is a well-documented Pre-Reflective Hostility against Machine Art (PRHMA), exemplified by the sentiments of fear and anxiety. How can it be explained? The present paper attempts to find the answer to this question by surveying a considerable amount of research on machine art. It is found that explanations of PRHMA based on the (alleged) fact that machine art lacks an element that is (allegedly) found in human art (for example, autonomy) do not work. Such explanations cannot account for the (...) sentiments of fear and anxiety present in PRHMA, because the art receiver could simply turn to human art for finding the element she is looking for. By contrast, an explanation based on the idea that machine art is “symbolically” a threat to human survival can be successful, since the art receiver’s turning from machine art to human art does not eliminate the (alleged) “symbolic” threat machine art poses for human survival. If there is a pre-reflective belief or feeling that machine art is such a threat, then it is perfectly understandable why humans exhibit a pre-reflective hostility against machine art. (shrink)