Do Propositions Exist?

Do Propositions Exist?

In this essay I shall first outline some of the reasons that have motivated philosophers to postulate the existence of propositions. Having done this, I shall outline and assess some issues with the notion of propositions raised by Quine’s critique of the notion. I shall discuss the impact of these criticisms and examine some problems with Quine’s theory, finally concluding that although I am sympathetic to those who are skeptical about the existence of propositions none of the criticisms of propositions that I look at show that their existence is impossible or that belief in them is unreasonable.

The reason that we postulate propositions is that there seems to be a significant gap in the theory of many languages that only they can fill – that is, there are some theoretical roles that seem to be part of language, but which can’t be fulfilled by either sentences or utterances. Bealer identifies some of these key theoretical roles that propositions play: 1) Propositions are the primary bearers of properties such as necessity, possibility, truth and falsity. 2) Propositions are typically public: people commonly believe one and the same proposition. 3) Propositions are what literal utterances of declarative sentences mean.

Of these, (2) needs some explanation – it looks like there are some sentences in language which are syntactically different, but which mean the same thing. If you believe that “the sky is blue” and someone in Germany believes that “der Himmel ist blau“, it looks like there is a sense in which you both believe the same thing since each sentence has the same meaning and is just spoken in a different language. Since your German counterpart does not believe that “the sky is blue“ (since he doesn’t know what that sentence means) it is generally thought that the thing that you both commonly believe is a proposition.

Bealer also outlines some key claims made by the traditional theory of propositions : 1) Propositions are mind-independent, extra-linguistic, abstract objects. 2) A belief state consists in a subject standing in the relation of believing to a proposition, and that proposition is the context of belief – likewise with other intentional states. Before I go on to look at the reasons that philosophers have given for rejecting the claim that propositions exist, I shall briefly explain (1). The relevance of (2) will become apparent when we look at the ‘single term’ argument.

The traditional view of propositions is that they are mind-independent – acceptance of this claim commits us to a form of Platonism, since we must hold that (at least some) propositions actually exist as abstract entities. The following argument is of a sort that commonly leads people to believe that this is the case:

P1: The proposition that “the Earth orbits the Sun” doesn’t entail the existence of beings which mental states.
C1: It is possible that the proposition that “the Earth orbits the Sun” is true in a world where there are no mental states.
C2: The proposition that “the Earth orbits the Sun” is mind-independent.
C3: There are mind-independent propositions.

Although some have attempted to explain away the appeal of this argument and thus render propositions mind-dependent, this will not be a focal point of my essay.

In what follows, I shall distinguish between sentence types and sentence tokens. Any two sentences which are identical in meaning (regardless of whether they are spoken, written, etc.) are instances of the same sentence type, while any given instance of a sentence is a token of some type. Thus, sentence types are abstract objects just as propositions are. If our motivation for rejecting propositions was just that they are abstract objects then sentence types are no better, and if there are some theoretical roles that sentence types struggle to fulfil then it looks likely that propositions are the objects of the formulas of logic. In any case, someone who objects to abstract objects will have to argue that the formulas of logic stand for sentence tokens.

I shall look at one preliminary argument (before I go on to look at Quine) which looks like it limits the possible candidates for being the objects that the formulas of logic stand for to sentences and propositions. I will refer back to this argument near the end of this essay. This is the ‘single term’ argument , and it considers attitude ascriptions (specifically belief ascriptions).

It looks like that-clauses in attitude ascriptions are singular terms – this would explain the validity of inferences such as the following:

P1: Graham believes that Russell was right.
C: Graham believes something.

The question is: if that-clauses refer to singular terms, what is it they refer to? They can’t refer to facts or states of affairs; beliefs can be false, and so it follows that the that-clauses in our belief reports refer to something that can be false. So the referents of that-clauses must be things that can be either true or false – that leaves us with either sentences or propositions.

Having outlined the basic motivations for postulating the existence of propositions I shall now introduce Quine’s critique of propositions, beginning with an explanation of his Nominalism.

A nominalist is someone who denies either that universals or that abstract objects exist. Quine is a nominalist in the sense that although he accepts that sets or classes exist, he denies that any universals exist . There are two general kinds of nominalist strategy: 1) to deny the existence of the alleged entities in question, or 2) to accept the existence of these entities, but to argue that they are particular or concrete.

A very basic reason for rejecting the existence of propositions is based on Ockham’s razor. If we should not multiply entities (or kinds of entities) unnecessarily, then we can legitimately deny that propositions exist if we can show that all the roles that propositions are supposed to play can be fulfilled by concretely existing entities (such as sentences) . Another way you might argue that it is improbable that propositions exist is to appeal to the principle that you should not postulate ad hoc entities unnecessarily . This objection is applicable in cases where to only motivation for postulating an abstract entity is that they perform a particular theoretical role. This is the case with propositions, and assuming there is no evidence for the existence of propositions independently of the roles they play, if any alternative to propositions is available, that alternative is much more appealing.

So Quine’s nominalist strategy was to try and show that all the semantic roles associated with propositions are actually played by sentences and that therefore there is no reason to think that propositions exist . Quine backs a theory of the propositional calculus which contains no inferred entities, and “no flights of abstraction beyond the realm of everyday uses of words ”. Propositions are thought of as the intensions of sentences; to eliminate them from our ontology we must show that sentences have no such intensions, and that sentences have only extensions, so an attack on propositions of this kind attempts to show that sentences simply stand for their extensions.

The extensions of sentences are individuated by their members – for example, the set of ‘creatures with hearts’ is the same as the set of ‘creatures with kidneys’. However, intensions are more fine-grained than this; the property of being a creature with a heart is different from the property of being a creature with kidneys.

The fine grained nature of intensions creates difficulties for simply inferences. Consider the following:

P1: P=Q
P2: P can X
C : Q can X

This inference is valid, but the following inference clearly is not in situations where there agent A does not know that P=Q, despite the apparently identical structure of the argument:

P1: P=Q
P2: A believes that P can X
C: A believes that Q can X

This apparent failure of substitution is due to the presence of a ‘believes that’ locution. This is an intensional operator, and it creates an intensional context.

Because of the problems that they cause, Quine denies that logic is intensional, and thinks that it contains no intensional operators or contexts . For example, logical operators may be defined solely by their extensions. It may be claimed that if two logical constants have the same set of truth conditions then they mean the same thing. For example: (~ P ⊃ Q) = (P & Q). Since it looks like logical concepts may be defined solely by their extensions, there seems to be no need to postulate intensional entities such as propositions. From this, Quine concludes that it is mistaken to interpret the propositional calculus as containing variables that range over propositions – It can be presented simply as a theory of deduction that becomes a “paradigm depicting the use of the connectives ‘or’, ‘if-then’, etc., with a view to the truthfulness of the sentences which they generate .
Quine argues that the reason philosophers wrongly think that propositions exist is routed in a confusion about the difference between using a sentence and mentioning it .

Consider the following:

i) A
ii) ‘A’ is a sentence occurring in S

In (i) the sentence is being used, and there is clearly a difference between the appearance of A in (i) and its appearance in (ii). This difference is grammatically significant; the quotation marks perform a function known as nominalization, and effectively turn A into a noun phrase.

So it looks like a believer in propositions wrongly thinks of the variables in propositional logic as being mentioned in much the same way as A is in (ii). If Quine is right then logical connectives are actually sentence connectives, which are used for making complex sentences out of simpler ones. If this is the case then the correct way to read P ⊃ Q is as a sentence in which the sentences P and Q are used to create a new sentence; they are not referring expressions in the formula.

So Quine’s positive proposal is that we may think of variables in logic as simply standing for “abbreviated sentences”, thus avoiding the presupposition that these variables stand for existing entities . On this picture, theorems are not expressions of true propositions, but are statements about sentences – namely statements which say that a given sentence has the property of being true .

Having outlined Quine’s position I shall now look at some issues with it which appear to show that sentences cannot fulfil all of the theoretical roles that propositions are supposed to and look at some suggested responses to these issues.

Proposing that the formulas of logic stand for sentences faces two main problems. Standard logic requires that whatever a formula stands for has exactly one truth-value. Since the truth-value of most sentences is context dependent, their truth-values must be derived by appeal to a principle such as this:

T1: A sentence is true iff all of its utterances are true, and false iff all of its utterances are false .

But this means that most sentences can’t be classified as either true or false, for not all utterances of a single sentence type have the same truth-value.

Firstly, take any vague or ambiguous sentence (such as “They haven’t been to the bank in a long time”) and you will see that its truth-value depends on the context in which it is uttered and that because of this, principles such as T1 will not be able to assign it a truth-value. The second difficulty with the claim that sentences are what the formulas of logic stand for is of a similar kind; for most sentence types, the truth-value of their tokens is dependent on (linguistic and factual) context. Therefore, there is no guarantee that all tokens of the same type of sentence will have the same truth-value. This is most obvious in the cases of utterances which contain indexicals (such as “you”, “tomorrow”, “there”, etc.), but also concerns most sentences containing proper names. For example, whether “Solomon is the king” is true depends on who “Solomon” refers to in this particular utterance.

So it looks like sentences are ill-equipped to play the role of primary truth-bearers and unless this criticism can be responded to it looks like we need to postulate something like propositions to play this role.

One of two proposed responses to these issues draws on the notion of eternal sentences; this amounts to a claim that formulas can’t stand for all sentences, but only as those which count as true or false according to T1 . On this proposal utterances have to be prepared before logical analysis can start – indexicals have to be tuned up with contextual information and ambiguous or vague expressions must be eliminated .
Brun outlines three problems which look damning for this proposal . Firstly, it is unclear that these problematic elements can always be eliminated. Secondly, it is not clear what conditions may be met so that a sentence counts as free from these elements which prevent utterances from clearly having only one truth-value. Finally, it has been argued that there are ‘essential indexicals’ which cannot be eliminated without dramatically altering a sentences meaning .

The problems with eternal sentences make it seem like an implausible solution to the problem of what makes sentences true. Quine realized this and put forward another possible solution: perhaps rather than attempting to eliminate context-dependency, ambiguity and vagueness, it will be enough just to eliminate equivocation within the context of an inference .

Brun summarizes this approach by replacing T1 with a new rule T2 and introducing a rule E which bans the fallacy of equivocation:

E: Within an inference, tokens of the same type must have the same semantic value.
T2: In the context of an inference i, a sentence is true iff all its utterances in i are true, and it is false iff all its utterances in i are false.

This proposal is stronger than the previous one in that it avoids the major criticisms levelled at the notion of eternal sentences. Unfortunately though, it has two problems of its own which make it an equally unappealing position to maintain. The fatal problems with this second attempt at showing that the sentences which logical formulas stand for always have only one truth value resides in the superficial appeal of E – when examined in more detail it is clearly not fit for purpose.

It can be shown that E is too strong by applying it to sentences such as: “If it is getting cold outside either I will fetch my coat or I will get you to do it.” Clearly here applying E to ‘it’ would be nonsensical, so it looks like we needn’t require that all tokens of the same type have the same semantic value, but only corresponding ones . But there is another sense in which E is too weak, since it does not address syntactic ambiguities or expressions directly relevant to logical form . It may be possible to reformulate this position to meet these criticisms, but I do not have space for a deeper discussion of that here. In any case, there are wider objections to the position that Quine argues for which even an improved defence of this kind would not be able to explain away.

The first general problem with maintaining that the formulas of logic stand for sentences is that the standard identity criteria for two tokens of a sentence being of the same type – that they contain the same words in the same order – is too fine-grained. The point is brought out most clearly in Brun, who illustrates the difficulty facing Quine’s view by observing that under it, “if we turn to a language with a systematic different word order between main clauses and subordinate clauses” it is extremely hard to find even on example of a valid inference instantiating modus ponens:

P1: Wenn Schnee weiß ist, dann Gras ist grün.
P2: Schnee ist weiß.
C: Gras ist grün.

Specifically, the issue faced by the Quinean theory is that under it logically irrelevant aspects of linguistic expression count as differences in sentence type. It looks like propositions are far better equipped for dealing with fine-grained content in logic that sentences ever could be.

Finally, at the beginning of this essay I introduced the ‘single term’ argument which shows that the referents of that-clauses must be either sentences or propositions. This argument is independent of Quine’s claim that intensional operators do not have a place in logic, since even if he were correct we would still be left with this question about what the referents of that-clauses are. To close this essay I shall look at some attempts to argue that sentences are the referents of that-clauses. It looks like no such proposal stands up to scrutiny, and that propositions are a much more plausible answer to the question.

There are two anti-platonist alternatives to the view that belief reports refer to propositions: Firstly, there is the mentalistic view that belief reports refer to sentences in our heads. (There are ‘Mentalese’ sentence tokens – this view is inspired by Fodor.) Secondly, there is the physicalist view that belief reports involve reference to external sentence tokens (i.e. those which are publically available, such as the written or spoken word) . Both of these views cope badly with some apparently valid inferences in a way that propositions do not.

Consider two agents, Matt and Ulgar. Both believe that the sky is blue. Ulgar speaks only Russian, while Matt speaks only English. Now consider the following argument:

P1: Ulgar believes that the sky is blue.
P2: Matt believes that the sky is blue.
C: There is at least one thing that both Matt and Ulgar believe (which is that the sky is blue).

This looks like a valid argument, and acceptance of its validity rules out the possibility that belief reports refer to sentence tokens. In order to account for the arguments validity we have to take the two that-clauses as referring to the same thing, but there is no sentence that both Matt and Ulgar could be referring to. The that-clauses cannot refer to a single external token sentence, since Ulgar cannot understand English sentences and Matt cannot understand Russian sentences. Neither though, can they refer to the same internal token sentences, since the token in Ulgar’s head is different from the one in Matt’s head. Since these are ordinary belief ascriptions that we have considered, it follows that the that-clauses in ordinary belief ascriptions do not refer to sentence tokens.

Now, as Mark Balaguer notes , the argument as I have stated it does not rule out the view that that-clauses refer to mentalese sentence types. It does however look like a parallel argument could be run to eliminate this view by replacing the two agents with creatures that have different internal languages of thought. If such an argument succeeds then it looks like the only remaining candidate for the referents of belief reports is propositions.

So to summarize: I have registered my personal feelings of unease about being forced to accept the existence of abstract objects such as propositions. Unfortunately, having looked in depth at one attempt at removing such objects from out ontology I am forced to conclude that nothing I have looked at shows that propositions do not exist. Quine’s theory struggles to account for how sentences can play the role of truth-bearers, and it looks like propositions deal with intentional attitudes such as belief reports much better than sentences can. Seeing as there is clearly a philosophical need for something that plays the role of propositions, and in the absence of a coherent alternative proposal, it looks like it is reasonable to believe in the existence of propositions.

• Balaguer, Mark (2009) “Platonism in Metaphysics” in the Stanford Encyclopedia of Philosophy
• Bealer, George (1998) “Propositions” in Mind, New Series, Vol. 107, No. 425 (Jan., 1998), pp. 1-32, Oxford University Press
• Brun Georg (2008) “Formalization and the Objects of Logic” in Erkenntnis Volume 69, Number 1, July 2008, Springer Science + Buisness Media
• Jubien, Michael (2004) “On Quine’s Rejection of Inentional Entities” in Midwest Studies in Philosophy, Vol. 28, Issue 1, July 2004, pp. 209-225, Published online:
• McGrath, Matthew (2007) “Propositions” in the Stanford Encyclopedia of Philosophy,
• Perry, John (1979) “The Problem of the Essential Indexical” in Noûs, Vol. 13, No. 1 (Mar., 1979), pp. 3-21, Blackwell Publishing
• Quine, Willard Van Orman (1934) “ Ontological Remarks on the Propositional Calculus” in Mind, New Series, Vol. 43, No. 172 (Oct., 1934), pp. 472-476, Oxford University Press
• Quine, Willard Van Orman (1951)“Mathematical Logic”, Harvard University Press
• Rodriguez-Pereyra, Gonzalo (2008) “Nominalism in Metaphysics” in the Standford Encylopedia of Philosophy,
• Teichmann, Jenny (1961) “Propositions”, in The Philosophical Review, Vol. 70, No. 4 (Oct., 1961), pp. 500-517, Duke University Press

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