Negative truths and truthmaker principles

This paper argues that a consideration of the problem of providing truthmakers for negative truths undermines truthmaker theory. Truthmaker theorists are presented with an uncomfortable dilemma. Either they must take up the challenge of providing truthmakers for negative truths, or else they must explain why negative truths are exceptions to the principle that every truth must have a truthmaker. The first horn is unattractive since the prospects of providing truthmakers for negative truths do not look good neither absences, nor totality states of affairs, nor Graham Priest and J.C. Beall’s ‘polarities’ (Beall, 2000; Priest, 2000) are up to the job. The second horn, meanwhile, is problematic because restricting the truthmaker principle to atomic truths, or weakening it to the thesis that truth supervenes on being, undercuts truthmaker theory’s original motivation. The paper ends by arguing that truthmaker theory is, in any case, an under-motivated doctrine because the groundedness of truth can be explained without appeal to the truthmaker principle. This leaves us free to give the ommonsensical and deflationary explanation of negative truths that common-sense suggests.     

Can There be A Priori Causal Models of Natural Selection?

I argue that Colin Cheyne and Charles Pigden's recent attempt to find truthmakers for negative truths fails. Though Cheyne and Pigden are correct in their treatment of some of the truths they set out to find truthmakers for (such as ‘There is no hippopotamus in S223’ and ‘Theatetus is not flying’) they over-generalize when they apply the same treatment to ‘There are no unicorns’. In my view, this difficulty is ineliminable: not every truth has a truthmaker.     

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.     

Necessity and Triviality

In this paper I argue that there are some sentences whose truth makes no demands on the world, being trivially true in that their truth-conditions are trivially met. I argue that this does not amount to their truth-conditions being met necessarily: we need a non-modal understanding of the notion of the demands the truth of a sentence makes, lest we be blinded to certain conceptual possibilities. I defend the claim that the truths of pure mathematics and set theory are trivially true, and hence accepting their truth brings no ontological commitment; I further defend the claim that the truths of applied mathematics and set theory do not demand the existence of numbers or sets. While the notion of a demand must not be reduced to anything modal, I nonetheless argue that sentences that are trivially true must also be necessary, lest we violate a very weak version of the principle that truth depends on the world. I further argue that all necessary truths are trivially true, lest we admit unexplained necessities. I end by showing one important consequence of this: I argue that if there are truthmakers for intrinsic predications, they must be states of affairs rather than tropes.     

Is there a dilemma for the truthmaker non-maximalist?

Mark Jago has presented a dilemma for truthmaker non-maximalism—the thesis that some but not all truths require truthmakers. The dilemma arises because some truths that do not require truthmakers by the non-maximalist’s lights (e.g., that Santa Claus does not exist) are necessitated by truths that do (e.g., that Barack Obama knows that Santa Claus does not exist). According to Jago, the non-maximalist can supply a truthmaker for such a truth only by conceding the primary motivation for the view: that it allows one to avoid positing strange ‘negative’ entities without adopting a non-standard account of the necessary features of ordinary things. In this paper, I sketch out and defend two plausible non-maximalist proposals that evade Jago’s dilemma.     

The cost of truthmaker maximalism

According to truthmaker theory, particular truths are true in virtue of the existence of particular entities. Truthmaker maximalism holds that this is so for all truths. Negative existential and other ‘negative’ truths threaten the position. Despite this, maximalism is an appealing thesis for truthmaker theorists. This motivates interest in parsimonious maximalist theories, which do not posit extra entities for truthmaker duty. Such theories have been offered by David Lewis and Gideon Rosen, Ross Cameron, and Jonathan Schaffer. However, it will be argued here that these theories cannot be sustained, and hence maximalism comes with a serious ontological cost. Neither Armstrong's invocation of totality facts nor the Martin-Kukso line on absences can meet this cost satisfactorily. I'll claim that negative facts are the best (and perhaps only) way out of the problem for the truthmaker maximalist.     

Setting the Facts Straight

Substantial facts (or states of affairs) are not well-understood entities. Many philosophers object to their existence on this basis. Yet facts, if they can be understood, promise to do a lot of philosophical work: they can be used to construct theories of property possession and truthmaking, for example. Here, I give a formal theory of facts, including negative and logically complex facts. I provide a theory of reduction similar to that of the typed λ-calculus and use it to provide identity conditions for facts. This theory validates truthmaker maximalism: it provides truthmakers for all truths. I then show how the usual truth-in-a-model relation can be replaced by two relations: one between models and facts, saying that a given fact obtains relative to the model, and the other between facts and propositions: the truthmaking relation.     

Modal truthmakers and two varieties of actualism

In this paper, I distinguish between two varieties of actualism—hardcore actualism and softcore actualism—and I critically discuss Ross Cameron’s recent arguments for preferring a softcore actualist account of the truthmakers for modal truths over hardcore actualist ones. In the process, I offer some arguments for preferring the hardcore actualist account of modal truthmakers over the softcore actualist one.     

Truthmaking without necessitation

I propose an account truthmaking that provides truthmakers for negative truths. The account replaces Truthmaker Necessitarianism with a ??Duplication Principle??, according to which a suitable entity T is a truthmaker for a proposition p just in case the existence of an appropriate counterpart of T entails the truth of p, where the counterpart relation is cashed out in terms of qualitative duplication. My account captures an intuitive notion of truthmakers as ??things the way they are??, validates two appealing principles about entailment and containment proposed by David Armstrong, and invalidates the controversial Disjunction Thesis.     

The Hard Road to Presentism

It is a common criticism of presentism – the view according to which only the present exists – that it errs against truthmaker theory. Recent attempts to resolve the truthmaker objection against presentism proceed by restricting truthmaker maximalism (the view that all truths have truthmakers), maintaining that propositions concerning the past are not made true by anything, but are true nonetheless. Support for this view is typically garnered from the case for negative existential propositions, which some philosophers contend are exceptions to truthmaker maximalism. In this article, we argue that a ‘no truthmakers’ approach to the truthmaker objection is critically flawed.     

Causal grounds for negative truths

Among truthmaker theorists it is generally thought that we are not able to use the entailment principle (i.e. the principle according to which truthmaking distributes across entailment) to ground negative truths. But these theorists usually only discuss truthmakers for truth-functional complexes, thereby overlooking the fact that there are non-truth-functional complexes whose truth values are not solely determined by the truth or falsity of their atomic propositions. And once we expand the class of truths that require their own bespoke truthmakers to also include these, there is no reason to exempt negative truths from grounding. For given that truthmaking is closed under entailment and every negative truths is entailed by some non-truth-functional complex or other, any resources rich enough to ground the truth of the latter will do the same job for the former.     

Absences as Latent Potentialities

Absences, i.e., agential omissions and forbearances, but also ‘natural’ negative states and events beyond the sphere of human agency, seem to be part and parcel of the real world. Yet, it is exactly the putative reality of absences that strikes many philosophers as utterly mysterious, if not entirely unintelligible. As a promising approach towards solving the problem of real absences, I wish to explore the idea that absences are latent potentialities. To this end, I shall investigate what potentialities are, what kinds of potentiality exist, and what it means for a potentiality to remain latent. I will also discuss whether the framework of latent potentiality is able to meet the extensional constraints imposed on the theory of absences by our intuitions about the reach of negative acts and events, i.e., whether latent potentialities can account for all real absences.     

Existential Import in Cartesian Semantics

The paper explores the existential import of universal affirmative in Descartes, Arnauld and Malebranche. Descartes holds, inconsistently, that eternal truths are true even if the subject term is empty but that a proposition with a false idea as subject is false. Malebranche extends Descartes’ truth-conditions for eternal truths, which lack existential import, to all knowledge, allowing only for non-propositional knowledge of contingent existence. Malebranche's rather implausible Neoplatonic semantics is detailed as consisting of three key semantic relations: illumination by which God's ideas cause mental terms, creation by which God's ideas cause material substances by a kind of ‘ontic privation’, and sensation in which brain events occasion states of mental awareness. In contrast, Arnauld distinguishes two types of propositions – necessary and contingent – with distinct truth-conditions, one with and one without existential import. Arnauld's more modern semantics is laid out as a theory of reference that substitutes earlier causal accounts with one that adapts the medieval notion of objective being. His version anticipates modern notions of intentional content and appeals in its ontology only to substances and their modes.     

Absence Causation and a Liberal Theory of Causal Explanation

For the framework of event causation—i.e. the framework according to which causation is a relation between events—absences or omissions pose a problem. Absences, it is generally agreed, are not events; so, under the framework of event causation, they cannot be causally related. But, as a matter of fact, absences are often taken to be causes or effects. The problem of absence causation is thus how to make sense of causation that apparently involves absences as causes or effects. In an influential paper, Helen Beebee offers a partial solution to the problem by giving an account of causation by absence (i.e. causation in which absences are supposed to be causes). I argue that Beebee's account can be extended to cover causation of absence (i.e. causation in which absences are supposed to be effects) as well. More importantly, I argue that the extended Beebeeian account calls for a major modification to David Lewis's theory of causal explanation, usually taken as standard. Compared to the standard theory, the result of this modification, which I shall call ‘the liberal theory of causal explanation’, has, among other things, the advantage of being able to accommodate causal explanations in which the explananda are not given in terms of events.     

Constructive Empiricism and the Closure Problem

In this paper I articulate a fictionalist solution to the closure problem that affects constructive empiricism. Relying on Stephen Yablo’s recent study of closure puzzles, I show how we can partition the content of a theory in terms of its truthmakers and claim that a constructive empiricist can believe that all the observable conditions that are necessary to make a part of her theory true obtain and remain agnostic about whether or not the other truthmakers for the other parts of her theory obtain. This can be done even though she asserts her theory as if it was wholly true.     

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.     

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.     

Why Truthmaking Is Not a Case of Grounding

Truthmaker theorists often express their core commitment by saying that truth is grounded in being, and grounding theorists often take truthmaking to be a paradigm case of grounding. But I will argue that truthmaking is not a case of grounding. What is crucial for understanding truthmaking is not grounding but rather meaning (in a broad sense including reference). Truth is still constrained by how things are, so even if (so-called) truthmakers don't play a role in grounding truths, the methodological program of truthmaker theory survives. Here I lay out my understanding of truth and truthmaking, and distinguish two conceptions of grounding. I argue that truthmaking is not plausibly seen as a case of grounding on either conception. I argue further that treating truthmaking as grounding threatens to violate a plausible irreflexivity principle, and makes trouble for the view that grounding is transitive. I then suggest that there is no genuine relation of truthmaking (which there would have to be if it were a true case of grounding). Finally, I show how the core insights of truthmaker theory are preserved by the understanding of truthmaking that I favor.