Luis F. Bartolo Alegre

Priest's theory of motion is based on Leibniz's Continuity Condition (LCC), which states that any state that exists at each instant in a continuous set of moments also exists at its temporal limit. If we accept the CCL, a free-falling pen would have to be simultaneously in motion and at rest at the instant of change: the critical moment when it hits the ground, thus passing from the state of motion to that of rest. This seems to be a contradictory state of affairs, which is precisely what Priest claims to be the case. In this article, I discuss the logical possibility of empirically testing whether such a contradictory state of affairs occurs.

In this paper we will review the history of Quechua in the Peruvian territory (including the eras of the Inca empire, the viceroyalty, and the republic) and consider the challenges it faces in order to survive from the bicentenary of our republic onwards. I begin by showing that most varieties of Quechua are in a process of extinction and reflect on the causes that may have determined this trend in the republican era. I defend the thesis that it was the progressive increase in opportunities for social mobility in the republic that motivated an increasing adoption of Spanish by Quechua speakers, since such opportunities depended on mastering Spanish. The paper closes by discussing about the possibilities to reverse the trend towards the extinction of Quechua.

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

The standard definition of “argument” is satisfied by any series of statements in which one (of the statements) is marked as the conclusion of the others. This leads to the counter-intuitive result that “I like cookies, therefore, all swans are white” is an argument, since “therefore” marks “all swans are white” as the conclusion of “I like cookies”. This objection is often disregarded by stating that, although the previous sequence is an argument, it fails to be a good one. However, when we compare our previous argument with a definitely bad argument like “this swan is white, therefore, all swans are white”, we see that there is an important difference between them. Whereas the former fails to fulfil our intuition of what an argument is, the latter does qualify as an argument, but as a bad one. In this talk, I will sketch a definition that better captures this feature of our intuition of what an argument is in three steps. Following Díez and Moulines (1999), I first reduce inductive validity to deductive validity through what we may call the method of deductivisation. Second, through epistemic predicates (cf. Thompson 2002), I introduce a broader concept of validity that accounts not only for deductive and inductive validity, but also for a weaker type of validity that may be called pseudo-validity. I show that these pseudo-valid arguments can also be deductivised with the help of the above-mentioned epistemic predicates. Finally, I re-define the concept of argument as any series of statements that is at least pseudo-valid, which leaves the “cookies argument” outside of this definition.

In this paper, I propose a formal framework for modelling the process of testing empirical statements, hypotheses, theories, and research programmes. Unlike the diverse forms of falsificationism, this framework does not require any commitment to classical logic or to any specific system of logic, as it aims to be useful regardless of the logic we presuppose. On this regard, the paper will focus on how this framework applies to two logical contexts: the classical and the paraconsistent contexts. I will show that this framework converges with falsificationism for consistent classical theories, and that it has very interesting consequences for the variety of paraconsistent cases. Concerning the latter cases, what may be called "empirical dialetheism" will be severely undermined as I will show that not even in our quite liberal framework it is possible to reject an "observable contradiction."

Logic systems that can handle contradictions were being used for some time without having a general technical name. One of the main proposers of these systems, Newton da Costa, asked Francisco Miró Quesada to suggest him a name for those systems. In the historical letter that here we translate into English for the first time, Miró Quesada suggests three names to da Costa for this purpose: ‘ultraconsistent’, ‘metaconsistent’, and ‘paraconsistent’; explaining their pros and cons. Paper based on a letter by Francisco Miró Quesada Cantuarias to Newton da Costa, edited, translated, and annotated by Luis Felipe Bartolo Alegre.

This paper discusses the logical possibility of testing inconsistent empirical theories. The main challenge for answering this affirmatively is to avoid that the inconsistent consequences of a theory both corroborate it and falsify it. I answer affirmatively by showing that we can define a class of empirical sentences whose truth would force us to abandon such inconsistent theory: the class of its potential rejecters. Despite this, I show that the observational contradictions implied by a theory could only be verified (provided we make some assumptions), but not rejected. From this, it follows that, although inconsistent theories are rejectable, they cannot be rejected qua inconsistent.

From the apparently trivial problem of homonyms, I argue that proper names as they occur in natural languages cannot be characterised as strings of sounds or characters. This entails, first, that the proper names philosophers talk about are not physical entities, like strings, but abstractions that, second, may be better characterised as triples (s, m, C), where s is the string that conveys the meaning m in a set of contexts C. Third, the generality principle of compositionality may be put into question, for apparently its converse holds in some cases. Finally, the prominence of context for determining the meaning expressed by a sign suggests a strong connection between proper names and indexicals. This connection has been largely overlooked by the analytic tradition, in spite that both proper names and indexicals have been among their hottest topics. This may be because the analytic literature about proper names has been decisively influenced by Frege’s work, which was better suited for formal languages. Izydora Dąmbska and Jerzy Pelc, with their semiotic background, were able to have a finer understanding of this quasi-indexical character of proper names.

This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. We say, instead, that Ƭ is non-trivial iff there is at least one α such that Ƭ ⊢ α, otherwise we say that it trivial. This happens because classical logic satisfies the principle of explosion, according ex contradictione sequitur quodlibet (from a contradiction anything follows). Under these conditions inconsistent classical theories would be compatible with any well-formed formula, which makes them useless for science. There are, however, so-called paraconsistent logics in which the principle of explosion does not generally hold and in which a theory can be (simply) inconsistent, but also absolutely consistent. It is in this logical framework that we can prove that some inconsistent theories can be falsifiable.

Popper restricted his definition of falsifiability to consistent theories through what we may call his requirement of consistency. His main argument was that an inconsistent theory does not distinguish the sentences that corroborate it from those that contradict it, for all sentences follow from it. I propose to replace this requirement by the more basic requirement that the classes of potential corroborators and falsifiers of a theory do not overlap. This results not only in an unrestricted definition of falsifiability but also in some inconsistent theories being falsifiable whenever that inconsistency is not located among its observational statements. Although this assumes a restriction of the principle of explosion or ex contradictione sequitur quodlibet (ECQ), it does not depend on any particular system or approach of paraconsistent logic. Finally, I propose to define the class of potential refuters of a theory, which is obtained by subtracting the class of potential corroborators from the class of potential falsifiers. Given that, by definition, the classes of potential refuters and corroborators of a theory do not overlap, it immediately follows that some observationally inconsistent theories are refutable in this sense. This establishes the bases for a new and more general formal theory of falsifiability of scientific factual/empirical theories.

According to falsificationism, a theory is scientific if it can be incompatible with some empirically testable statements. This epistemological approach has been criticized because, in practice, it is impossible to decide when a particular fact should be considered incompatible with a theory. These criticisms, however, neglect the fact that the Popperian sense of falsification is a “logical sense.” Thus, the Popperian criterion of falsifiability only requires that, assuming certain auxiliary hypotheses, the theory in question be logically incompatible with some empirically testable statements. This paper presents a reassessment of these criticisms, justifying that the criterion of falsifiability is unrenounceable insofar as our best theories should aspire to satisfy it.

In this paper I formalise the falsificationist proposal omitting Popper’s requirement of consistency. This omission results in (i) trivial theories being falsifiable in an inappropriate sense of the term, but also in (ii) some inconsistent non-trivial theories being so in an appropriate one. This justifies a slight alteration of the definition of falsifiability that excludes (i) but allows (ii). Instead of requiring that a falsifiable theory be consistent, my proposal only requires that the intersection of its classes of potential corroborators and falsifiers be empty.