What does '&' mean?

Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist one based on introduction and elimination rules, and the representationalist one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my argument is that there are different notions of conjunction at play in standard first order logic, and that the technical and philosophical connections between them are far from well established

Linguistic Trust

In conversation we trust others to communicate successfully, to understand us, etc. because they have the adequate skills to be competent in the linguistic domain. In other words, to be trustworthy regarding an activity is nothing but to have the appropriate skills required for the activity. In the linguistic case, this means that being trustworthy regarding conversation is nothing but to have the capacity of partaking as a responsible participant in linguistic conversation, which requires having the appropriate linguistic skills. Now, to trust someone in conversation one better know that the person one trusts is trustworthy in the relevant sense, that is, one need to know that she has the relevant linguistic skills. Thus, in order to maintain mutual trust, participants in conversation must track not so much the linguistic successes of other participants, but their linguistic skills, i.e. they must be able to trace their successes to the agent and not to external circumstances. But lucky successes do not manifest skill and therefore show no evidence of the true capacities of performers and, therefore, are useless for building trust. This is as much true in the linguistic realm as outside of it. We care about successes because they provide us with defeasible evidence of skills, but this evidence is defeated if such successes cannot be attributed to the agent, but are instead the product of lucky. Therefore, if we care about trust, that is, if we care about agents and their skills, we need to be wary of lucky successes

Universalidad y aplicabilidad de las matemáticas en Wittgenstein y el empirismo logicista

//// Abstract: This paper studies the notions of universality and applicability of mathematics in the writings of Wittgenstein’s middle period. Against a common opinion, the author argues that mathematics is not a science of the most abstract and general. By focusing on the notion of grammar in Philosophical observations and Philosophical grammar , the author holds that one can account for the use of mathematics in extra mathematical contexts without resorting to what he calls the myth of universality

Mathematics as Grammar

Tésis de Doctorado en Filosofía, Universidad de Indiana, Bloomington, 2000This thesis makes sense of ‘grammar’s role in Wittgenstein's philosophy of mathematics during the early thirties. It constructs a formal model of Wittgenstein’s notion of grammar as expressed in his writings of that period, justifies the appropriateness of that model and then employs it to test Wittgenstein's claim that mathematical propositions are ultimately grammatical. Chapter 1 frames the dissertation’s topic in its historical and conceptual context. Chapter 2 traces the origins of Wittgenstein’s grammatical approach to mathematics in Frege’s philosophy of arithmetics. Chapter 3 explains the central role of calculation in Wittgenstein’s philosophy of mathematics. Chapter 4 presents Wittgenstein’s account of mathematical application [Anwendung]. Chapter 5 provides a formalized theory of grammatical analysis, and Chapter 6 applies it to a portion of language containing numerical expressions. It proves that if the object language contains the appropriate numerical expressions, the resulting grammar includes at least some rules which may be naturally interpreted as mathematical. In particular, it shows that Wittgenstein’s grammatical analysis of the ordinary use of numerical expressions yields familiar theorems of arithmetic.Chapter 7 rounds up Wittgenstein’s account of arithmetics in light of the formal results of the previous chapters. Finally, Chapter 8 explains Wittgenstein’s account of mathematical necessity as a special case of grammatical necessity

‘Grammar’ in Wittgenstein’s Philosophy of Mathematics during the Middle Period

Tésis de Doctorado en Filosofía, Universidad de Indiana, Bloomington, 2000This thesis makes sense of ‘grammar’s role in Wittgenstein's philosophy of mathematics during the early thirties. It constructs a formal model of Wittgenstein’s notion of grammar as expressed in his writings of that period, justifies the appropriateness of that model and then employs it to test Wittgenstein's claim that mathematical propositions are ultimately grammatical. Chapter 1 frames the dissertation’s topic in its historical and conceptual context. Chapter 2 traces the origins of Wittgenstein’s grammatical approach to mathematics in Frege’s philosophy of arithmetics. Chapter 3 explains the central role of calculation in Wittgenstein’s philosophy of mathematics. Chapter 4 presents Wittgenstein’s account of mathematical application [Anwendung]. Chapter 5 provides a formalized theory of grammatical analysis, and Chapter 6 applies it to a portion of language containing numerical expressions. It proves that if the object language contains the appropriate numerical expressions, the resulting grammar includes at least some rules which may be naturally interpreted as mathematical. In particular, it shows that Wittgenstein’s grammatical analysis of the ordinary use of numerical expressions yields familiar theorems of arithmetic.Chapter 7 rounds up Wittgenstein’s account of arithmetics in light of the formal results of the previous chapters. Finally, Chapter 8 explains Wittgenstein’s account of mathematical necessity as a special case of grammatical necessity