Abstract
In his theory of truthmaker content, Kit Fine has provided many insights concerning the relation of aboutness, allowing us to understand why a unique subject matter can be associated to a sentence, what is the relation between the subject matter of a sentence and its truth conditions, and why necessary sentences can be distinguished with respect to what they are about. The aim of this chapter is to consider these insights critically, compare them to the notion of subject matter developed by Lewis, and put forward a unified account giving us the resources to overcome some of their limits. The resulting theory characterizes the relation of aboutness by combining in a consistent framework Lewis’s intuition on how sentences are related to the questions they possibly answer with Fine’s intuition on how sentences are related to their truthmakers.
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Notes
- 1.
- 2.
In some theories, propositional contents and propositions are identified, since both propositional contents and propositions are assumed to coincide with what we grasp when we understand a sentence. In other theories, they are distinguished, since propositions are identified with other kind of entities. Thus, in Lewis (1988a), propositions are sets of possible worlds and, Fine (2017a), propositions are sets of truthmakers, the unilateral contents of sentences, or pairs of sets of truthmakers and falsemakers, the bilateral contents of sentences. See Barwise (1989, part one), Stalnaker (1999, part IV), and Recanati (2007, part 1), for a general introduction to the distinction between sentences, propositional contents, and propositions. See also Barwise and Perry (1981), Kratzer (1989, 2002), and Perry (1986, 1989) for a discussion of different conceptions of proposition in the context of possible worlds semantics and situation semantics.
- 3.
- 4.
The distinction between intensional and hyperintensional accounts is orthogonal with respect to the distinction between world-based and state-based semantics. A world-based semantics where both possible and impossible worlds are admitted can be hyperintensional. A state-based semantics where states are identified with sets of possible worlds can be intensional.
- 5.
To the best of my knowledge, there is no comprehensive general theory on the market. The most systematic attempt seems to be the one developed in Hawke (2018), which in turn is a refinement of Perry’s proposal.
- 6.
As we have seen before, a sentence like “\(5+7=12\)” can be about the sum of 5 and 7 in a certain context and about the difference of 12 and 5 in a different context.
- 7.
With slight variations with respect to the principles proposed in Fine (2018, pp. 8–10). The idea, see p. 10, is that “Without being too precise, we might call the theory that endorses these various compositional, logical and mereological principles the standard theory of subject matter. I am not suggesting that we should necessarily endorse such a theory. But it does provide us with a standard by which we may judge deviations from the norm; and it does seem that we should not deviate from this norm without strong and compelling reason.”.
- 8.
Note that this line of thought is consistent with both a classical and a constructivist point of view.
- 9.
See Hawke (2018, pp. 5–6). Here, I have made explicit constraints 3, which is accepted by Hawke but not inserted as one of the constraints on the connectives. Moreover, I have left out the constraint according to which a disjunction like \(\phi \vee \psi \) is about something but not necessarily about everything, since its first part follows from the implicit assumptions that \(\phi \) and \(\psi \) are usually about something and that the conjunction \(\phi \wedge \psi \) is usually not about everything.
- 10.
This is a line of argument that could have been followed by Lewis. See Lewis (1988a, pp. 164–165), where Lewis introduces a distinction between degenerate and genuine subject matters and suggests that the subject matter of a necessary proposition is not genuine, since necessary propositions provide no information about anything. Thus, he could have been content with assuming that logical validities and invalidities, being kinds of necessary propositions, are not genuine.
- 11.
See Hawke (2018, p. 702). I think this is a rather intuitive principle: books, reports, and papers are about specific subject matters, and are classified accordingly, based on library classification systems. Most of the propositions we find in them are typically about the same subject matters, and not about everything.
- 12.
See Lewis (1988a, p. 161): “We can think of a subject matter, sometimes, as a part of the world: the 17th Century is a subject matter, and also a part of this world. Or better, we can think of a subject matter as a part of the world in intension: a function which picks out, for any given world, the appropriate part-as it might be, that world’s 17th Century. (If for some reason the world had no 17th Century, the function would be undefined.)”. See also Lewis (1988b, p. 11).
- 13.
See Lewis (1988a, p. 161): “We can say that two worlds are exactly alike with respect to a given subject matter. For instance two worlds are alike with respect to the 17th Century iff their 17th Centuries are exact intrinsic duplicates (or if neither one has a 17th Century).” See also Lewis (1988b, p. 11).
- 14.
See Lewis (1988a, pp. 161–162): “This being exactly alike is an equivalence relation. So instead of thinking of a subject matter as a part of the world in intension, we can think of it instead as the equivalence relation.” See also Lewis (1988b, p. 12): “With any subject matter, we can somehow associate an equivalence relation on worlds: the relation of being exactly alike with respect to that subject matter. Now, unburdened of any contentious account of what that relation and its relata are, we proceed as before. A statement is entirely about a subject matter, iff, whenever two worlds are exactly alike with respect to that subject matter, then also they agree on the truth value of the statement.”
- 15.
See Lewis (1988a, p. 162): “The partition gives all the alternative complete answers to the question; the question asks which cell of the partition is the true one. (Which cell does our world fall into?) So a fourth way to think of a subject matter, again general, is as a question.”
- 16.
See Lewis (1988a, p. 163): “When we think of subject matters as partitions, we can say that P is about M iff each cell of M either implies or contradicts P. The cells are maximally specific propositions about the subject matter, and accordingly must imply or contradict any other proposition about the same subject matter.” As partitions, subject matters are connected by mereological relations. In addition, they can be orthogonal to each other. According to Lewis, \(\pi _{1}\) and \(\pi _{2}\) are orthogonal iff \(E_{1}(w)\cap E_{2}(v)\ne \varnothing \) for all \(w,v\in {\textbf {W}}\), where \(E_{1}\) and \(E_{2}\) are the equivalence relations induced by \(\pi _{1}\) and \(\pi _{2}\). The interesting idea behind this definition is that orthogonal subject matters are such that every cell of one of them intersects every cell of the other one. In terms of questions: propositions answering the question associated with one subject matter provide no information as to how the question associated with the other subject matter is to be answered. This notion is important in so far as it can be used for characterizing the relation of being completely off-topic: a sentence is completely off-topic when its subject matter is orthogonal with respect to the topic under discussion.
- 17.
These distinctions can be defined in terms of genuine properties and genuine counterpart relations, which are used in Lewis (2003) to characterize qua-objects. In effect, it is not difficult to develop a theory of genuine partitions based on an appropriate account of qua-objects.
- 18.
See Fine (2017a, pp. 646–647), where the system is presented in detail. The origin of this system traces back to the algebraic semantics proposed in Dunn (1966), where the connection with topics and the idea underlying the bilateral conception of a proposition is developed, and the facts semantics put forward in Van Fraassen (1969), where the unilateral conception of a proposition is advanced.
- 19.
See Fine (2017a, p. 628): “A proposition, at its simplest, may be identified with the set of its verifiers. Thus propositions with the same verifiers are taken to be the same. This is as it is with the possible worlds semantics, but with a more refined conception of the verifiers and of what it is for them to verify.”.
- 20.
Fine works with both unilateral and bilateral contents: see Fine (2017a, Sect. 2). The unilateral content of a sentence is the set \({\textbf {tm}}(\phi )\) of its truthmakers and coincides with a unilateral proposition, which is just a set of states. The bilateral content of a sentence \(\phi \) is the pair \(({\textbf {tm}}(\phi ),{\textbf {fm}}(\phi ))\) of the set of its truthmakers, its positive content, and the set of its falsemakers, its negative content. The bilateral content coincides with a bilateral proposition, which is a pair of sets of states. Here I propose a unified account based on the distinction between propositions and unilateral propositions. It is crucial to note that, for \(P=(P^{+},P^{-})\), the truthmakers of \(P^{+}\) coincide with the truthmakers of P, while the truthmakers of \(P^{-}\) coincide with the falsemakers of P.
- 21.
See Fine (2018, pp. 2–4). A similar idea is proposed in Yablo (2014), where the subject matter of a proposition is defined in terms of its matter, containing the truthmakers of the proposition, and antimatter, containing the falsemakers of the proposition. In Fine (2017a, pp. 647–648, 2017b, pp. 697–698), Fine defines the subject matter of a unilateral proposition P as \(\bigsqcup P\), so that \(sm(\phi )=\bigsqcup {\textbf {tm}}(\phi )\). The notion here defined corresponds to Fine’s notion of comprehensive subject matter of a bilateral proposition.
- 22.
See Fine (2018, pp. 16–20) for a finer analysis of different possibilities of definition. Fine works with the relation of being relevant to the truth of a proposition and concludes that \(\bigsqcup P\) is the subject matter to be assigned to a unilateral proposition P, while \(\bigsqcup P^{+}\sqcup \bigsqcup P^{-}\) is the comprehensive subject matter to be assigned to a bilateral proposition \((P^{+},P^{-})\).
- 23.
See Fine (2017b, p. 680): “We may say, for example, that a proposition P is entirely about the subject-matter s if the subject-matter p of P is part of s. Thus the proposition that it is snowing or raining is entirely about the weather since the verifiers of the proposition, snow or rain, are part of the weather”.
- 24.
See Fine (2017b, pp. 679–680): “I suspect that it has often been thought, if only implicitly, that a compositionally adequate account of subject-matter could only be achieved by adopting a structural conception of propositions, under which the subject-matter of a proposition is somehow discerned from its structure. Adopt the more usual ‘extensional’ conception of propositions, under which a proposition is identified with a set of verifiers, and some compositional principles must perforce be given up. [...] The present truthmaker account of propositions shows this line of thought to be mistaken. Once relevance is built into the very conception of verification, the notion of subject-matter will be reasonably well-behaved. The defects and distortions of the intensional approach arise, not from its embrace of an extensional conception of content, but from its indifference to considerations of relevance.”
- 25.
See Hawke (2018, p. 721): “But it defies intuition to claim that, say, “Jane is a lawyer” is about the impossible situation in which Jane is both a lawyer and not, in every conceivable way. And since impossible situations cannot be actualized, so much for the guiding rationale that meaningful claims are directed at facts.”
- 26.
The following principle is stated in terms of knowledge, but any other appropriate epistemic modality could be used.
- 27.
As highlighted by an anonymous referee, the argument just proposed can be resisted. In fact, it can be argued that the move from possible/impossible truths to possible/impossible worlds is only justified in so far as a convincing account of what possible/impossible worlds are is provided. Yet, while Lewis has put forward a well-developed theory of possible worlds, Fine provides no clue as to what impossible states are. It is also worth noting that Fine’s states are not like situations or portions of the actual world, since the possibility of non-obtaining states is admitted. In addition, states are not constructible by using propositions or sentences, since propositions are defined in terms of states and sentences are expressions having propositions as contents.
- 28.
See Berto and Jago (2019, ch. 3), for an overview and a critical assessment of the ways in which possible and impossible worlds can be built from ersatz entities like states, properties, propositions, or sentences.
- 29.
See Lewis (1988a, pp. 172–173).
- 30.
In pursuing this strategy some delicate issues arise that are related to the ontological status of impossible worlds. At a first sight, two options seem to be open. The first one is to adopt Lewis’s metaphysical standpoint and try to justify the existence of impossible worlds as ways the world cannot possibly be. The second option is to adopt Fine’s metaphysical standpoint and rephrase the distinction between possible and impossible states in terms of possible and impossible worlds. Both options present problems, mainly due to the fact that it should be intuitive to assume that it is impossible for impossible entities to exist, but see Franz and Jago (2019) and Priest (2006) for a comprehensive discussion, in particular with respect to the existence of intentionalia, i.e., intentional entities, which I take to be the best candidates for the role of impossible entities.
- 31.
As intermediate steps, I first introduce two other kinds of spaces: \({\textbf {W}}\)-state spaces and classical \({\textbf {W}}\)-state spaces. Classical \({\textbf {W}}\)-state spaces also appear in Fine (2017a, pp. 665–667): they are \({\textbf {W}}\)-spaces equipped with classical propositions.
- 32.
In general, given Definition 16, \(s_{a}^{G}\sqcup s_{a}^{Y}\sqcup s_{a}^{R}\sqcup s_{b}^{G}\sqcup s_{b}^{Y}\sqcup s_{b}^{R}\) is the subject matter of any combination of basic predications.
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Giordani, A. (2023). On the Notion of Aboutness in Logical Semantics. In: Faroldi, F.L.G., Van De Putte, F. (eds) Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Outstanding Contributions to Logic, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-031-29415-0_19
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