Abstract
It is almost universally accepted that the Frege–Geach Point is necessary for explaining the inferential relations and compositional structure of truth-functionally complex propositions. I argue that this claim rests on a disputable view of propositional structure, which models truth-functionally complex propositions on atomic propositions. I propose an alternative view of propositional structure, based on a certain notion of simulation, which accounts for the relevant phenomena without accepting the Frege–Geach Point. The main contention is that truth-functionally complex propositions do not include as their parts truth-evaluable propositions, but their simulations, which are neither forceful nor truth-evaluable. The view makes room for the idea that there is no such thing as the forceless expression of propositional contents and is attractive because it provides the resources for avoiding a fundamental problem generated by the Frege–Geach Point concerning the relation between forceless and forceful expressions of propositional contents. I further argue that the acceptance of the Frege–Geach Point mars Peter Hanks’ and François Recanati’s recent attempts to resist the widespread idea that assertoric force is extrinsic to the expression of propositional contents. Rejecting this idea, I maintain, requires a deeper break with the tradition than Hanks and Recanati have allowed for.
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Notes
Another strategy for resisting Geach’s arguments—which I am not going to pursue—is to reject their second premise. One can maintain that e.g. the antecedent of a conditional is asserted, even though in asserting the whole conditional one is not thereby asserting the antecedent.
This approach—call it the Alternative Strategy—takes assertion to compose on the model of Fregean reference rather than Fregean sense. For Frege, the sense of a part of a complex expression is part of the sense of the whole expression. The sense of “Sweden,” for instance, is part of the sense of “The capital of Sweden.” But the reference of a part of a complex expression is not necessarily part of the reference of the whole. Sweden is not part of Stockholm. “Sweden” contributes to determine the reference of “The capital of Sweden,” but doesn’t do so because its reference is part of the reference of the whole (see Frege 1997, p. 365; Johnston 2011, p. 62, connects this distinction to the problematic of assertion). Similarly, according to the Alternative Strategy, the assertion expressed by the antecedent of a conditional contributes to determine the assertion expressed by the whole conditional, but is not part of that assertion: in asserting the conditional, one is not thereby asserting, inter alia, the antecedent. As we shall see in §9, some passages in Hanks (2015, 2019) can be taken to present a version of the Alternative Strategy, and the proposal advanced in Schmitz (unpublished), as I understand it, shares its core idea.
This is not the place for evaluating the viability of the Alternative Strategy. The aim of this paper is to offer a way of resisting Geach’s arguments, not to establish that it is the only possible one. But it is worth mentioning that the Alternative Strategy faces a problem that doesn’t seem to arise in the case of reference. The view appears to entail that asserting e.g. a conditional requires a change of mind. When one utters the antecedent and the consequent, one asserts them, but in uttering the whole conditional, one does not assert them. So it seems that the assertion of the whole conditional takes back, or retracts, the assertion of the antecedent and the consequent. And this seems wrong (cf. Hanks 2007, p. 154). By contrast, it does not seem that when we use the phrase “The capital of Sweden” to refer to Stockholm we need to take back the fact that we want to use one if its parts to refer to Sweden.
Here I am concerned only with Frege’s official view, as derivable from the way he defines concepts and truth-functional connectives. Arguably, there are aspects of his system that are in tension with this official view—such as the special position given de facto to complex names of truth-values whose senses are thoughts.
Even though Frege distinguishes two models of semantic composition—a part/whole model for sense and function/argument model for reference (see above, note 1)—they both differ from the compositionality that I am ascribing to truth-functionally complex propositions. For Frege, the sense and the reference of a complex expression are both determined by the sense or reference of its parts.
This idea does not follow analytically from the Two-Model View. One may adopt the Two-Model View and still hold that propositions, qua truth-evaluable items, are not necessarily assertoric. What the Two-Model View shows is that we do not have to admit unasserted truth-evaluable propositions in order to account for the compositional structure and inferential relations of truth-functionally complex propositions.
The account I have begun to outline bears some similarities with other recent proposals. In appealing to the idea of “simulation,” I follow Recanati (2019), with the crucial difference (further discussed in §10 below) that a simulation for Recanati has the same truth-evaluable content of what it simulates. Kimhi (2018) seeks to account for truth-functional embedding through the notion of a “mere display” (as opposed to a “self-identifying display”) of an act of judgment or assertion which might be functionally equivalent to my notion of simulation, depending on whether the “mere display” of a judgment or assertion is meant to have the same truth-evaluable content of what it displays. Reiland (2019) proposes a quasi-referential account of truth-functional embedding that agrees with mine in two important respects: it holds that only what is forceful is truth-evaluable, and maintains that the items embedded in truth-functional contexts are neither forceful nor truth-evaluable. However, Reiland construes the items embedded in truth-functionally complex judgments as “objectual acts” that are directed at truth-evaluable items, where the paradigmatically objectual act is reference. Reiland is sensitive to some of the difficulties encountered by a purely referential account of truth-functional embedding (see pp. 152–154, and for additional problems, §11 below). The viability of his proposal depends crucially on the possibility of specifying a notion of “objectual act” that differs from reference in all the relevant respects while remaining objectual. Finally, Schmitz (unpublished) maintains (as Reiland and I also do) that only what is forceful is truth-evaluable, but holds that the items embedded in truth-functional contexts are both truth-evaluable and forceful (see below, note 17).
Recanti holds, similarly, that the simulation of an illocutionary act employs the means that are conventionally used to perform the illocutionary act (2019, p. 1411). The crucial difference is that, for Recanati, the simulation of an assertion shares its truth-evaluable content (see below, §10).
For an account of truth-functional embedding that assigns an essential role to language, see Kimhi (2018, Chap. 1, Sect. 4).
In the second passage I quoted, Geach speaks of the “inhibition” of assertoric force, whereas in the context of a discussion of the linguistic version of the same view, he speaks of its “cancel[lation]” (1965, p. 456). I assume that the terminology here is interchangeable. In both cases, he is describing a sort of context that makes an asserted proposition or judgment lose its assertoric force.
The hopelessness of content-based accounts of assertoric force has not prevented them from being tempting. Some have thought, for example, that assertoric force can be reduced to the content supposedly conveyed by expressions such as “It is true that” or “It is a fact that.” In Begriffsschrift, for instance, Frege paraphrases his judgment stroke as “is a fact” and writes that, in his notation, the combination of the judgment stroke and the content stroke—which together he paraphrases as “The proposition that…is a fact”—is the “common predicate for all judgments” (§§2–3, in Frege 1997, pp. 53–54). Others, working in the tradition of Speech Act Theory, have thought that assertoric force can be reduced to the content supposedly conveyed by performative expressions such as “I assert that” or “I judge that” (for a classical discussion, see Levinson 1983, pp. 243–263).
An analogous point holds for different accounts of the structure of practical inference, such as views that identify the conclusion with an intention rather than an action, or views for which one of the premises must be a desire.
My claim is that the notion of judgment is necessary in order to understand the three phenomena that I have mentioned—not that it is sufficient. In the case of theoretical and practical inference, for instance, one also needs the idea that the conclusion is judged or performed on the basis of the premises (see Marcus 2012, chaps. 1 and 2).
Consider for example Scott Soames’ recent sketch of a dispositional theory of what turns a forceless act of predication into a judgment:
To judge is to predicate the property of o [i.e. an object] in an affirmative manner, which involves forming, or activating already formed, dispositions to act, both cognitively and behaviorally, toward o in ways conditioned by one’s attitudes toward things that are so-and-so. (Soames 2015, p. 220; see also pp. 18, 22)
The question is: What is it “to act…toward o in ways conditioned by one’s attitude toward things that are so-and-so”? If it is to act toward it in ways conditioned by one’s judging that it is so-and-so, than the account is plausible, but circular. If it isn’t, it is not clear that the account has any plausibility.
For Hanks, “generations” of philosophers, including Geach, followed Frege in inferring this view from the Frege Point (2015, pp. 10, 92). Hanks might be right about Frege and subsequent generations of philosophers, but the passages I discussed in §8 show that he is wrong about Geach. Hanks acknowledges that Geach employs the language of force cancellation, but reads it as a momentary slip (2015, p. 92).
Hanks puts a lot of emphasis on the fact that the difference between pure and impure acts of predication is not due to additional acts, but to the contexts in which the acts of predication are performed. But I agree with Stokke (2016) that this is a red herring.
For this reading of Hanks, see Reiland (2019, pp. 147–148) and Schmitz (unpublished, pp. 37–38), even though for Schmitz this is at most one strand in Hanks. This reading was also pressed on me by an anonymous referee: “The whole point of Hanks (2015) is to say that the extra feature over and above the [truth-evaluable] common factor [between pure and impure acts of predication] is added not to the unasserted use in order to make an asserted use but to the asserted use to cancel some of its implications. Hanks then goes on to argue that while the truth-evaluable common factor is still there the normal implications of asserting it (like that the subject believes it to be true and can be called on to justify it) have been cancelled.”
On this reading, Hanks proposes a version of the Alternative Strategy (see note 1). Schmitz (unpublished), as I understand it, presents a similar account. For Schmitz, the clauses of a conditional express assertions, but the whole conditional expresses a “higher-level act” of “conditionalizing” performed on the lower-level acts of assertion which involves no commitment to their truth (pp. 27–35). As with Hanks, it would be uncharitable to take Schmitz to rely on a questionable notion of “non-committal assertion.” Rather, I take him to maintain that acts of assertion compose on the model of Fregean reference rather than Fregean sense: they contribute to determine higher-level acts, but someone who performs the higher-level acts is not necessarily performing, inter alia, the lower-level acts. There is however a respect in which Schmitz’s account does not fit my characterization of the Alternative Strategy. On his view, assertions can only be atomic: a conditional, for example, does not express an assertion (pp. 32–35). Thus the assertions expressed by atomic clauses cannot contribute to determine the assertions expressed by more complex constructions, for there is no such thing. They can only contribute to determine the higher-level acts expressed by more complex constructions.
I mentioned in note 1 one difficulty encountered by the view. Reiland (2019, p. 148) presents a version of the same objection that applies specifically to the case of negation.
Recanati notices the verbal similarity between Hanks’ position and Geach’s formulation of the Hybrid View (2019, p. 1406). However, he doesn’t seem to see any substance behind this verbal similarity, because he also takes for granted, with Hanks, that Geach infers from the Frege Point the Additive View (p. 1405).
See e.g. his approving rehearsal of Geach’s argument from the validity of Modus Ponens (Recanati 2019, p. 1405n4).
Some of the details may also create additional problems. For instance, it is not clear whether an illocutionary act includes for Recanati—as it does for Austin—a locutionary act. If it does, the illocutionary act would have to include a simulation of itself, which seems to involve a vicious regress.
These references to the Tractatus presuppose that the Tractarian distinction between “functions” and “truth-operations” lines up with the distinction between predicates (in the sense just defined) and truth-functional connectives. More on this below.
It is uncontroversial that the Tractatus conceives of truth-functional connectives as “operations,” but the identification of predicates (in the sense explained above) with Tractarian “functions” requires argument. I cannot provide such an argument here, but it would make use of remarks such as Wittgenstein 1922 3.318, 4.1211, 4.126, 4.24, 5.25, 5.5301. Part of what has to be appreciated in order to understand the Tractarian distinction between “functions” and “operations” is that it involves a notion of function that differs deeply from the one invoked by Frege at the level of reference (see Hylton 2005).
I borrow the notion of a non-truth-functional operation from Diamond (2012), where it is introduced in the context of a reading of the account of propositional attitude reports presented in Wittgenstein’s Tractatus. Diamond, however, does not maintain that the bases of such operations are specified by simulations.
For an operational reading of (a certain use of) the truth predicate, see Gomułka and Wawrzyniak (2013).
These suggestions resemble in one respect the account presented in Schmitz (unpublished). On both accounts, signs that would be traditionally interpreted as force indicators can be embedded. Schmitz, for instance, proposes to express the question “Did you close the door?” as “?A(aRb),” where “A(aRb)” expresses the assertion that aRb (p. 22). Similarly, he proposes to express the conditional “Fa⊃Gb” as “A(Fa)⊃A(Gb)” (p. 15). There are however at least three important differences between the two accounts. First, Schmitz is committed to a controversial notion of “representation” that is completely divorced from truth and falsity. On his account, “aRb” represents a state of affairs, but does not do so truly or falsely; only “A(aRb)” represents the states of affairs truly or falsely (pp. 7–12). Secondly, for Schmitz embedded occurrences of “A(aRb)” express assertions, which raises the change of mind problem mentioned in note 1. Thirdly, Schmitz holds that only atomic propositions (or, in his terminology, atomic theoretical postures) have truth-conditions (pp. 34–35). So, while the antecedent and the consequent of the conditional “A(Fa)⊃A(Gb)” are true or false, the whole conditional is not. The view seems to imply, surprisingly, that “p” and “¬¬p” do not have the same truth-conditions.
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Acknowledgements
I am very grateful for comments from James Conant, two anonymous referees, and the audiences of the Wittgenstein Workshop at the University of Chicago and the Humboldt Kolloquium at the University of Leipzig.
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Bronzo, S. Propositional complexity and the Frege–Geach Point. Synthese 198, 3099–3130 (2021). https://doi.org/10.1007/s11229-019-02270-1
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DOI: https://doi.org/10.1007/s11229-019-02270-1