Propositional unity: what’s the problem, who has it and who solves it?

At least since Russell’s influential discussion in The Principles of Mathematics, many philosophers have held there is a problem that they call the problem of the unity of the proposition. In a recent paper, I argued that there is no single problem that alone deserves the epithet the problem of the unity of the proposition. I there distinguished three problems or questions, each of which had some right to be called a problem regarding the unity of the proposition; and I showed how the account of propositions formulated in my book The Nature and Structure of Content [2007 Oxford University Press] solves each of these problems. In the present paper, I take up two of these problems/questions yet again. For I want to consider other accounts of propositions and compare their solutions to these problems, or lack thereof, to mine. I argue that my account provides the best solutions to the unity problems.     

Russell’s Repsychologising of the Proposition

Bertrand Russell’s 1903 masterpiece The Principles of Mathematics places great emphasis on the need to separate propositions from psychological items such as thoughts. In 1919 (and until the end of his career) Russell explicitly retracts this view, however, and defines propositions as “psychological occurrences”. These psychological occurrences are held by Russell to be mental images. In this paper, I seek to explain this radical change of heart. I argue that Russell’s re-psychologising of the proposition in 1919 can only be understood against the background of his struggle with the problem of the unity of the proposition in earlier work. Once this is recognized, and the solution to the problem offered by the 1919 theory is appreciated, new light is also shed on Russell’s naturalism. I go on to compare Russell’s psychological “picture theory” with the vehemently anti-psychological picture theory of Wittgenstein’s Tractatus Logico-Philosophicus and suggest that, once the background of the dispute is brought into clearer focus, Russell’s position can be seen to have many advantages over its more celebrated rival.     

Russell and richard brinkley on the unity of the proposition

Between 1903 and 1918 Russell made a number of attempts to understand the unity of the proposition, but his attempts all foundered on his failure clearly to distinguish between different senses in which the relation R might be said to relate a and b in the proposition aRb: he failed to distinguish between the relation as truth-maker and the relation as unifier, and consequently committed himself again and again to the unacceptable consequence that only true propositions are genuinely unified. There is an anticipation of this confusion in the writings of the fourteenth-century philosopher Richard Brinkley     

The truth and nothing but the truth,yet never the whole truth: Frege,Russell and the analysis of unities

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition.     

Was Wittgenstein an Analytic Philosopher? Wittgenstein vs Russell

This article is in six main sections.In the first three sections,some indication of how and why philosophers have differed in their response to the title question is given by describing Wittgenstein's encounters with Camap,and by examining Wittgenstein's commitment to clarity and argument in philosophy,illustrating this commitment by reference to his Philosophical Investigations discussion of the will.In the remaining three sections,Russell is taken as a paradigm example of a central kind of analytic philosopher.The answer to the title question is unfolded by sketching Wittgenstein's and Russell's treatments of a few philosophical topics and problems,focusing on theories and questions surrounding propositions,judgments,and their constituents,in particular Russell's multiple relation theory of judgment and the question of the unity of the proposition.This approach displays,and does not merely assert,Russell's deployment of (sometimes repeated variants of) technical solutions to philosophical problems and how that deployment contrasts with Wittgenstein's attempts to make such problems disappear.     

Propositions as Structured Cognitive Event-Types

According to act theories, propositions are structured cognitive act-types. Act theories appear to make propositions inherently representational and truth-evaluable, and to provide solutions to familiar problems with alternative theories, including Frege’s and Russell’s problems, and the third-realm and unity problems. Act theories have critical problems of their own, though: acts as opposed to their objects are not truth evaluable, not structured in the right way, not expressed by sentences, and not the objects of propositional attitudes. I show how identifying propositions with other cognitive event-types, namely thoughts, has the perceived virtues of act theories without the defects.     

Soames’s new conception of propositions

In this paper, I argue that, when it comes to explaining what can be described as “representational” properties of propositions, Soames’s new conception of propositions—on which the proposition that Seattle is sunny is the act of predicating the property being sunny of Seattle and to entertain that proposition is to perform that act—does not have an advantage over traditional ones.     

Propositions: Individuation and Invirtuation

The pressure to individuate propositions more finely than intensionally—that is, hyper-intensionally—has two distinct sources. One source is the philosophy of mind: one can believe a proposition without believing an intensionally equivalent proposition. The second source is metaphysics: there are intensionally equivalent propositions, such that one proposition is true in virtue of the other but not vice versa. I focus on what our theory of propositions should look like when it's guided by metaphysical concerns about what is true in virtue of what. In this paper I articulate and defend a metaphysical theory of the individuation of propositions, according to which two propositions are identical just in case they occupy the same nodes in a network of invirtuation relations. Invirtuation is here taken to be a primitive relation of metaphysical explanation exemplified by propositions that, in conjunction with truth, defines the notion of true in virtue of. After formulating the theory, I compare it with a view that individuates propositions by cognitive equivalence, and then defend the theory from objections.     

Beltrami's model and the independence of the parallel postulate

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell's Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege's extant logical system, if Frege's system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege's logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therin. therein.     

How Wittgenstein Defeated Russell’s Multiple Relation Theory of Judgment

In 1913 Wittgenstein raised an objection to Russell’s multiple relation theory of judgment that eventually led Russell to abandon his theory. As he put it in the Tractatus, the objection was that “the correct explanation of the form of the proposition, ‘A makes the judgement p’, must show that it is impossible for a judgement to be a piece of nonsense. (Russell’s theory does not satisfy this requirement,” (5.5422). This objection has been widely interpreted to concern type restrictions on the constituents of judgment. I argue that this interpretation is mistaken and that Wittgenstein’s objection is in fact a form of the problem of the unity of the proposition.     

Unity and the Frege–Geach problem

The problem of the unity of the proposition asks what binds together the constituents of a proposition into a fully formed proposition that provides truth conditions for the assertoric sentence that expresses it, rather than merely a set of objects. Hanks’ solution is to reject the traditional distinction between content and force. If his theory is successful, then there is a plausible extension of it that readily solves the Frege–Geach problem for normative propositions. Unfortunately Hanks’ theory isn’t successful, but it does point to significant connections between expressivism, unity, and embedding.     

Propositions, Sets, and Worlds

If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics of modal logic, the ontology of logically possible worlds, and the controversy over modal realism versus actualism. Logically possible worlds as maximally consistent proposition sets exist if sets generally exist, but are equivalently expressed as maximally consistent conjunctions of the same propositions in corresponding sets. A conjunction of propositions, even if infinite in extent, is nevertheless itself a proposition. If sets and hence proposition sets exist but propositions do not exist, then whether or not modal realism is true depends on which of two apparently equivalent methods of identifying, representing, or characterizing logically possible worlds we choose to adopt. I consider a number of reactions to the problem, concluding that the best solution may be to reject the conventional model set theoretical concept of logically possible worlds as maximally consistent proposition sets, and distinguishing between the actual world alone as maximally consistent and interpreting all nonactual merely logically possible worlds as submaximal. I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy of Arts and Sciences (KNAW), for supporting this among related research projects in philosophical logic and philosophy of mathematics during my Resident Research Fellowship in 2005-2006.     

Unity through truth

Synthese - Renewed worries about the unity of the proposition have been taken as a crucial stumbling block for any traditional conception of propositions. These worries are often framed in terms of...     

The problem of empty names and Russellian Plenitude

‘Ahab is a whaler’ and ‘Holmes is a whaler’ express different propositions, even though neither ‘Ahab’ nor ‘Holmes’ has a referent. This seems to constitute a theoretical puzzle for the Russellian view of propositions. In this paper, I develop a variant of the Russellian view, Plenitudinous Russellianism. I claim that ‘Ahab is a whaler’ and ‘Holmes is a whaler’ express distinct gappy propositions. I discuss key metaphysical and semantic differences between Plenitudinous Russellianism and Traditional Russellianism and respond to objections that stem from those differences.     

The aim of Russell’s early logicism: a reinterpretation

I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from Gödel’s incompleteness theorem and from the non-logical character of some of the axioms of Principia Mathematica respectively, can be seen to be inconclusive. I then proceed to identify two challenges that Russell’s logicism, as presently construed, faces, but argue that these challenges do not appear unanswerable.     

On the structural similarities between worlds and times

In the debate about the nature and identity of possible worlds, philosophers have neglected the parallel questions about the nature and identity of moments of time. These are not questions about the structure of time in general, but rather about the internal structure of each individual time. Times and worlds share the following structural similarities: both are maximal with respect to propositions (at every world and time, either p or ～p is true, for every p); both are consistent; both are closed (every modal consequence of a proposition true at a world is also true at that world, and every tense-theoretic consequence of a proposition true at a time is also true at that time); just as there is a unique actual world, there is a unique present moment; and just as a proposition is necessarily true iff true at all worlds, a proposition is eternally true iff true at all times. In this paper, I show that a simple extension of my theory of worlds yields a theory of times in which the above structural similarities between the two are consequences.     

Imaginative resistance as imagistic resistance

When we are invited to imagine an unacceptable moral proposition to be true in fiction, we feel resistance when we try to imagine it. Despite this, it is nonetheless possible to suppose that the proposition is true. In this paper, I argue that existing accounts of imaginative resistance are unable to explain why only attempts to imagine (rather than to suppose) the truth of moral propositions cause resistance. My suggestion is that imagination, unlike supposition, involves mental imagery and imaginative resistance arises when imagery that one has formed does not match unacceptable propositions.     

语义预设的合理性辩护

弗雷格是第一个注意到命题的预设为假会影响到命题真值判定的哲学家。对这种因预设为假而形成的真值空隙,弗雷格、罗素和斯特劳森提出了不同的处理方式,由此奠定了预设的语义解释的基础。但预设的语义解释一直面临着种种质疑。这些质疑有说服力吗?应该放弃预设的语义解释吗?本文将对此进行分析,揭示这些质疑中所存在的问题,从而对预设的语义解释的合理性进行辩护。一、预设为假与真值空隙第一个把预设作为逻辑概念加以讨论的哲学家是弗雷格,其预设思想可以归纳为四点:第一,预     

Implications of an initial empirical victory for the truth of the theory and additional empirical victories

Psychologists take two propositions for granted. Specifically, empirical verification of predictions derived from a theory (a) support that the theory is more likely to be true and (b) support that additional predictions derived from the theory have an increased probability of being sustained if subjected to empirical testing. In contrast, I argue that both propositions depend strongly on whether auxiliary assumptions are taken into account. When auxiliary assumptions are not taken into account, the first proposition is valid but the second is not. When auxiliary assumptions are taken into account, the first proposition is not valid, and the second proposition encounters additional problems. I use Venn diagrams and Bayesian principles to demonstrate these conclusions.