Why does Frege claim that logical axioms are ‘self‐evident,’ to be recognized as true ‘independently of other truths,’ and then offer arguments for those axioms? I argue that he thinks the arguments provide us with the justification that we need for accepting the axioms and that this is compatible with his remarks about self‐evidence. This compatibility depends on philosophical considerations connected with the ‘critical method’: an interesting approach to the justification of axioms endorsed by leading philosophers at the time.

What, in Frege’s view, makes definitions fruitful? In Grundlagen §70, Frege offers an answer: Unfruitful definitions are definitions that “could just as well be omitted and leave no link missing in the chain of our proofs”. The §70 passage, however, poses an interpretive puzzle as its characterization of fruitfulness appears to conflict with other conditions that Frege imposes on definitions, namely, eliminability and conservativeness. It appears that the only way to resolve this conflict is to attribute to Frege a notion (...) of fruitfulness that is trivially satisfied and, hence, poorly motivated. I argue that this worry is misplaced. This is because Frege distinguishes between two roles of definitions, namely, between definitions qua explanations of concepts, and definitions qua resources of a proof system. I use this distinction to argue that a fruitful definition, for Frege, is a definition that plays both roles, and that to play both roles, the definition has to be used in the proof of sentences containing the term so defined. Starting from §70, I develop and defend this reading of Frege’s notion of fruitful definition. (shrink)

By playing a crucial role in settling open issues in the philosophical debate about logical consequence, logical evidence has become the holy grail of inquirers investigating the domain of logic. However, despite its indispensable role in this endeavor, logical evidence has retained an aura of mystery. Indeed, there seems to be a great disharmony in conceiving the correct nature and scope of logical evidence among philosophers. In this paper, I examine four widespread conceptions of logical evidence to argue that all (...) should be reconsidered. First, I argue that logical apriorists are more tolerant of logical evidence than empiricists. Second, I argue that evidence for logic should not be read out of natural language. Third, I argue that if logical intuitions are to count as logical evidence, then their evidential content must not be propositional. Finally, I argue that the empiricist proposal of treating experts' judgments as evidence suffers from the same problems as the rationalist conception. (shrink)

Studies of several languages, including Swahili [swa], suggest that realis (actual, realizable) and irrealis (unlikely, counterfactual) meanings vary along a scale (e.g., 0.0–1.0). T-values (True, False) and P-values (probability) account for this pattern. However, logic cannot describe or explain (a) epistemic stances toward beliefs, (b) deontic and dynamic stances toward states-of-being and actions, and (c) context-sensitivity in conditional interpretations. (a)–(b) are deictic properties (positions, distance) of ‘embodied’ Frames of Reference (FoRs)—space-time loci in which agents perceive and from which they contextually (...) act (Rohrer 2007a, b). I argue that the embodied FoR describes and explains (a)–(c) better than T-values and P-values alone. In this cognitive-functional-descriptive study, I represent these embodied FoRs using Unified Modeling Language (UML) mental spaces in analyzing Swahili conditional constructions to show how necessary, sufficient, and contributing conditions obtain on the embodied FoR networks level. (shrink)