Truthmakers and modality

This paper attempts to locate, within an actualist ontology, truthmakers for modal truths: truths of the form <Possibly, p> or <Necessarily, p>. In Sect. 1 I motivate the demand for substantial truthmakers for modal truths. In Sect. 2 I criticise Armstrong’s account of truthmakers for modal truths. In Sect. 3 I examine essentialism and defend an account of what makes essentialist attributions true, but I argue that this does not solve the problem of modal truth in general. In Sect. 4 I discuss, and dismiss, a theistic account of the source of modal truth proposed by Alexander Pruss. In Sect. 5 I offer a means of (dis)solving the problem.     

Truthmakers and Normative Conflicts

Studia Logica - By building on work by Kit Fine, we develop a sound and complete truthmaker semantics for Lou Goble’s conflict tolerant deontic logic $$\mathbf {BDL}$$.     

Truthmakers and the direct argument

The truthmaker literature has recently come to the consensus that the logic of truthmaking is distinct from classical propositional logic. This development has huge implications for the free will literature. Since free will and moral responsibility are primarily ontological concerns (and not semantic concerns) the logic of truthmaking ought to be central to the free will debate. I shall demonstrate that counterexamples to transfer principles employed in the direct argument occur precisely where a plausible logic of truthmaking diverges from classical logic. Further, restricted transfer principles (like the ones employed by McKenna, Stump, and Warfield) are as problematic as the original formulation of the direct argument.     

Truthmakers and necessary connections

In this paper I examine the objection to truthmaker theory, forcibly made by David Lewis and endorsed by many, that it violates the Humean denial of necessary connections between distinct existences. In Sect. 1 I present the argument that acceptance of truthmakers commits us to necessary connections. In Sect. 2 I examine Lewis’ ‘Things-qua-truthmakers’ theory which attempts to give truthmakers without such a commitment, and find it wanting. In Sects. 3–5 I discuss various formulations of the denial of necessary connections and argue that each of them is either false or compatible with truthmaker theory. In Sect. 6 I show how the truthmaker theorist can resist the charge that they are committed to necessary exclusions between possible existents. I conclude that there is no good objection to truthmaker theory on the grounds that it violates the Humean dictum.     

Minimal Truthmakers

A minimal truthmaker for a given proposition is the smallest portion of reality which makes this proposition true. Minimal truthmakers are frequently mentioned in the literature, but there has been no systematic account of what they are or of their importance. In this article we shall clarify the notion of a minimal truthmaker and argue that there is reason to think that at least some propositions have minimal truthmakers. We shall then argue that the notion can play a useful role in truthmaker theory, by helping to explain the truth of certain propositions as precisely as possible.     

Truthmaker Theory without Truthmakers

Truthmaking without truthmakers (TWT, for short) is the thesis that although every true proposition is made true by reality, there need not be particular entities (like facts, states of affairs, or tropes) that make these propositions true. The first substantial part of this paper (section 2) is devoted to developing a particular version of TWT and at the same time defending TWT in general from arguments against it that have been advanced by orthodox truthmaker theorists. In the second part of the paper (section 3) I argue that talk about truthmakers within the theory can be understood as metaphoric and as conveying valuable information about something other than the supposed truthmakers: about truthmaking. The aim of this paper is therefore twofold. On the one hand, I intend to present the view on truthmaking, a version of TWT, that I find most plausible in the light of the arguments for and against truthmaker theory. On the other hand, I argue that friends of TWT have good reason to adopt a figuralist approach to truthmaker theory, rather than rejecting it outright.     

Truthmakers: a tale of two explanatory projects

Truthmakers are supposed to explain the truth of propositions, but it is unclear what kind of explanation truthmakers can provide. In this paper, I argue that ‘truthmaker explanations’ conflate two different explanatory projects. The first project is essentially concerned with truth, while the second project is concerned with reductive explanation. It is the latter project, I maintain, which is really central to truthmaking theory. On this basis, a general account of truthmaking can be formulated, which, when combined with a specific theory of reduction (the ‘conceptual entailment approach’), yields a new analysis of truthmaking. This analysis is intuitively appealing and avoids the problem of necessary truths, which poses a serious obstacle for standard accounts.     

Confirmation and the ordinal equivalence thesis

Synthese - According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the...     

Reasoning with exclusive disjunction arguments

An experiment was performed to determine the effects of negation in the major premise and/or conclusion of exclusive disjunction arguments on adults' abilities to apply two basic principles of exclusive disjunction. The component of the disjunctive premise that was referred to in the minor premise was varied systematically so that the influence of this factor could also be explored. The results indicated that arguments involving the confirmation of one of the components of the disjunctive premise followed by the denial of the other component of this premise were easier to evaluate than those in which this confirmation/denial sequence was reversed. In addition, arguments in which the disjunctive premise had two affirmative components were easier than those in which the disjunctive premise contained at least one negative component, but arguments with affirmative conclusions were more difficult than those with negative conclusions. Most importantly, an examination of subjects' errors and their response patterns revealed primitive response tendencies that paralleled those reported in previous studies of adults' propositional reasoning abilities.     

On maximal intermediate logics with the disjunction property

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.     

Algebraic logic for classical conjunction and disjunction

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties.Dedicated to our master, Francesc d'A. Sales, on his 75th birthday