According to truth pluralism, sentences from different areas of discourse can be true in different ways. This view has been challenged to make sense of logical validity, understood as necessary truth preservation, when inferences involving different areas are considered. To solve this problem, a natural temptation is that of replicating the standard practice in many-valued logic by appealing to the notion of designated values. Such a simple approach, however, is usually considered a non-starter for strong versions of truth pluralism, since (...) designation seems to embody nothing but a notion of generic truth. In this paper, I explore the analogy with many-valued logic by comparing the problem of mixed inferences with Suszko’s thesis, and argue that the strong pluralist has room to resist the commitment to a generic property of truth by undermining the semantic significance of Suszko’s reduction. (shrink)

I develop a new reading of Frege’s argument for the indefinability of truth. I concentrate on what Frege literally says in the passage that contains the argument. This literal reading of the passage establishes that the indefinability argument is an arguably sound argument to the following conclusion: provided that the Fregean conception of judgment—which has recently been countered by Hanks—is correct and that truth is a property of truth-bearers, a vicious infinite regress is produced. Given this vicious regress, Frege chooses (...) to reject that truth is a property of truth-bearers. Frege’s choice leads to a unique version of the Fregean conception of judgment. His unique conception of judgment can cope with Hanks’s recent criticisms against the Fregean conception. (shrink)

We will present a three-valued consequence relation for metainferences, called CM, defined through ST and TS, two well known substructural consequence relations for inferences. While ST recovers every classically valid inference, it invalidates some classically valid metainferences. While CM works as ST at the inferential level, it also recovers every classically valid metainference. Moreover, CM can be safely expanded with a transparent truth predicate. Nevertheless, CM cannot recapture every classically valid meta-metainference. We will afterwards develop a hierarchy of consequence relations (...) CMn for metainferences of level n. Each CMn recovers every metainference of level n or less, and can be nontrivially expanded with a transparent truth predicate, but cannot recapture every classically valid metainferences of higher levels. Finally, we will present a logic CMω, based on the hierarchy of logics CMn, that is fully classical, in the sense that every classically valid metainference of any level is valid in it. Moreover, CMω can be nontrivially expanded with a transparent truth predicate. (shrink)

Husserl claims that his phenomenological–epistemological system amounts to a “universal” form of empiricism. The present paper shows that this universal moment of Husserl’s empiricism is why his empiricism qualifies as a rationalism. What is empiricist about Husserl’s phenomenological–epistemological system is that he takes experiences to be an autonomous source of immediate justification. On top of that, Husserl takes experiences to be the ultimate source of justification. For Husserl, every justified belief ultimately depends epistemically on the subject’s experiences. These are paradigms (...) of empiricist claims and thus Husserl seems to subscribe to empiricism. However, what is universal about Husserl’s “empiricism” is that he does not limit the concept of experiences to sensory experiences or sensory experiences plus introspective intuitions but broadens the concept of experience such that also a priori intuitions are included. Husserl insists that logical, mathematical, and phenomenological intuitions such as ~, 2 + 2 = 4, and “Experiences necessarily bear the mark of intentionality” provide non-inferential justification analogous to how sensory experiences can non-inferentially justify beliefs such as “There is a table in front of me.” Importantly, Husserl makes clear that such a priori intuitions are not about our concepts but about reality. This is why Husserl’s universal empiricism is a rationalism. Husserl differs from traditional rationalism as he allows that a priori intuitions can be fallible and empirically underminable. This distinguishes Husserl’s rationalism from Descartes’ and makes him a proponent of moderate rationalism as currently championed by Laurence BonJour. (shrink)

Science is an activity of the human intellect and as such has ethical implications that should be reviewed and taken into account. Although science and ethics have conventionally been considered different, it is herewith proposed that they are essentially similar. The proposal set henceforth is to create a new ethics rooted in science: scientific ethics. Science has firm axiological foundations and searches for truth and knowledge. Hence, science cannot be value neutral. Looking at standard scientific principles, it is possible to (...) construct a scientific ethic, which can be applied to all sciences. These intellectual standards include the search for truth, human dignity and respect for life. Through these it is thence achievable to draft a foundation of a ethics based purely on science and applicable beyond the confines of science. A few applications of these will be presented. Scientific ethics can have vast applications in other fields even in non scientific ones. (shrink)

Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also introduced. In this alternative procedure (...) hidden variables are also used, but in this case to represent the degree of true or falsehood of propositions. (shrink)

In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for (...) developing paraconsistent logics. In Section 3, I’ll discuss what seem to me to be some promising applications of certain paraconsistent logics. In fact, however, I don’t think there’s all that much to the concept ‘paraconsistent’ itself; the collection of paraconsistent logics is far too heterogenous to be very productively dealt with under a single label. Perhaps that will emerge as we go. (shrink)

A sequent calculus for Odintsov’s Hilbert-style axiomatization of a logic related to the trilattice SIXTEEN3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cut-elimination theorem for . A first-order extension of and its semantics are also introduced. The completeness and cut-elimination theorems for are proved using Schütte’s method.

ABSTRACTWe will present 12 different mixed metainferential consequence relations. Each one of them is specified using two different inferential Tarskian or non-Tarskian consequence relations: or. We will show that it is possible to obtain a Tarskian logic with non-Tarskian inferential logics, but also a non-Tarskian logic with Tarskian inferential logics. Moreover, we will show how some of these metainferential logics work better than the corresponding inferential rivals. Finally, we will show how these logics prove that it is not enough to (...) work with inferences as pairs of sets of formulas to obtain a contractive logic. (shrink)

I highlight the importance of the notion of falsity for a semantical consideration of intuitionistic logic. One can find two principal (and non-equivalent) versions of such a notion in the literature, namely, falsity as non-truth and falsity as truth of a negative proposition. I argue in favor of the first version as the genuine intuitionistic notion of falsity.