Jonas Raab

Carnap introduced his notion of explication to arrive at concepts that are precise enough for scientific purposes. As Carnap wants to precisify concepts, his notion of explication targets less precise concepts so that explications within mature mathematics are not possible. We argue that explications of mature mathematical concepts are both possible and widespread. We focus on foundational work, especially as done in the context of interactive theorem proving. Taking foundational work seriously necessitates explicit decisions which are generally ignored in mathematical practice—and such developments are not captured by our usual notions of explication. To see this, we introduce Carnapian and Quinean explication and argue that they are not capable of accounting for intra-mathematical conceptual changes. We argue that these changes are best understood as explications and so need a different notion of explication. We suggest one candidate, called tolerant explication, and sketch how it handles the intra-mathematical cases.

Carnap introduced his notion of explication to arrive at concepts that are precise enough for scientific purposes. As Carnap wants to precisify concepts, his notion of explication targets less precise concepts so that explications within mature mathematics are not possible. We argue that explications of mature mathematical concepts are both possible and widespread. We focus on foundational work, especially as done in the context of interactive theorem proving. Taking foundational work seriously necessitates explicit decisions which are generally ignored in mathematical practice - and such developments are not captured by our usual notions of explication. To see this, we introduce Carnapian and Quinean explication and argue that they are not capable of accounting for intra-mathematical conceptual changes. We argue that these changes are best understood as explications and so need a different notion of explication. We suggest one candidate, called tolerant explication, and sketch how it handles the intra-mathematical cases.

I develop a modal extension of the QUantified ARgument Calculus (QUARC) - a novel logical system introduced by Hanoch Ben-Yami. QUARC is meant to better capture the logic of natural language. The purpose of this paper is to evaluate this claim by considering how modal QUARC (M-QUARC) handles the Barcan and Converse Barcan Formulas and how this correlates to surrounding debates. To do so, I develop a variable domain semantics for M-QUARC and show that even if the usual domain conditions are imposed on models with variable domains, simple M-QUARC-analogues of the Barcan and Converse Barcan Formulas are not valid. I introduce new conditions and show that they validate the formulas. I go on to extend the language of M-QUARC to simulate unrestricted quantification and show that in this setting the domain conditions validate the Barcan and Converse Barcan Formulas. Based on these results, I evaluate the relationship of the formal systems M-QUARC and standard quantified modal logic with respect to one another and to natural language. I argue that if M-QUARC does capture the logic of natural language, then natural language is capable to express neither the Barcan and Converse Barcan Formulas nor counterexamples to them. Given that, I raise doubts that M-QUARC captures quantification as it occurs in natural language.

Aristotle counts as the founder of formal logic. The logic he develops dominated until Frege and others introduced a new logic. This new logic is taken to be more powerful and better capable of capturing inference patterns. The new logic differs from Aristotelian logic in significant respects. It has been argued by Fred Sommers and Hanoch Ben-Yami that the new logic is not well equipped as a logic of natural language, and that a logic closer to Aristotle's is better suited for this task. Each of them developed their own formalism - Sommers in form of term logic, Ben-Yami in form of his Quantified Argument Calculus (QUARC). I discuss Aristotle's logic - a term logic - and attempt a comparison between Aristotelian logic and (i) the new logic, (ii) Sommers' term logic, and (iii) Ben-Yami's QUARC. I consider differences between the systems, and show how they are related to and diverge from the new logic.

The main goal of this paper is to work out Quine's account of explication. Quine does not provide a general account but considers a paradigmatic example which does not fit other examples he claims to be explications. Besides working out Quine's account of explication and explaining this tension, I show how it connects to other notions such as paraphrase and ontological commitment. Furthermore, I relate Quinean explication to Carnap's conception and argue that Quinean explication is much narrower because its main purpose is to be a criterion of theory choice.

In this paper, I argue that Amie Thomasson’s Easy Ontology rests on a vicious circularity that is highly damaging. Easy Ontology invokes the idea of application conditions that give rise to analytic entailments. Such entailments can be used to answer ontological questions easily. I argue that the application conditions for basic terms are only circularly specifiable showing that Thomasson misses her self-set goal of preventing such a circularity. Using this circularity, I go on to show that Easy Ontology as a whole collapses.