This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...) in his theory of axiomatics is presented. Specifically, it is shown that Carnap’s early model theory is based on a convention to simulate domain variation that is not identical but logically comparable to the modern account. (shrink)

The present paper attempts to show that a 1915 article by Erich Kretschmann must be credited not only for being the source of Einstein’s point-coincidence remark, but also for having anticipated the main lines of the logical-empiricist interpretation of general relativity. Whereas Kretschmann was inspired by the work of Mach and Poincaré, Einstein inserted Kretschmann’s point-coincidence parlance into the context of Ricci and Levi-Civita’s absolute differential calculus. Kretschmann himself realized this and turned the point-coincidence argument against Einstein in his second (...) and more famous 1918 paper. While Einstein had taken nothing from Kretschmann but the expression “point-coincidences”, the logical empiricists, however, instinctively dragged along with it the entire apparatus of Kretschmann’s conventionalism. Disappointingly, in their interpretation of general relativity, the logical empiricists unwittingly replicated some epistemological remarks Kretschmann had written before General Relativity even existed. (shrink)

Peter Van Inwagen argues that The Principle of Sufficient Reason (PSR) either leads to contradiction or it leads to necessitarianism. Although I agree with Van Inwagen that the relationship between the PSR and necessitarianism is close, I argue that the PSR is compatible with innocent versions of necessitarianism. In this project my main argument is that modal realism can account for the PSR and integrate it within an innocent version of necessitarianism. My main claim will be that each fact in (...) each possible world is grounded in the principle of plenitude. Also, while each fact is grounded in plenitude, it avoids rigid necessitarianism because (i) actuality is not captured by the PSR, (ii) things could be otherwise because there are other worlds, and due to the principle of recombination (iii) cardinality of possible worlds is maximized and (iv) there are no necessary connections between distinct individuals. As a result, the relationship between modal realism and the PSR is symbiotic. Through modal realism, the PSR also results as: having its scope extended to the realm of all possibilia rather than being confined to mere actuality; it solves indeterminacy problems like Leibniz’s problem of space or the hard problem of consciousness; it accounts for facts in lawless worlds etc. On the other hand, through the PSR, modal realism gets one more benefit in its inventory because it accounts for the PSR. Thus, modal realism still continues on Lewis’ paradoxical path of proving to be highly pragmatic but counterintuitive at the same time. If added benefits are worth the costs for modal realism is still an open question. (shrink)

Der Raum marks a transitional stage in Carnap’s thought, and therefore has both negative and positive implications for his further development. On the one hand, he is here largely a follower of Husserl, and a correct understanding of that background is important if one wants to understand what it is that he later rejects as “metaphysics.” On the other hand, he has already broken with Husserl in certain ways, in part following other authors. His use of Hans Driesch’s Ordnungslehre, in (...) particular, foreshadows the theme of so-called “voluntarism” which will characterize his later thought. (shrink)

Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...) significance of topological methods for philosophy, including the possible fruitfulness of a third conception of topology as a structure determining similarity. (shrink)