The Nature of Propositions

Philosophy of Language » Lecture 5

Referentialism and Sentence Meanings: Arguments for Propositions

The Meanings of Sentences

Internalist sentence meanings

An Argument for Propositions

Consider the proposition sentences:

  1. John said something.
  2. What John said was true.
  3. Though what John said was true, it would have been false had things gone differently.
  4. What John said is what Mary believed.

… the proposition sentences seem to jointly entail:

  1. There is something that John said, and which was true, and which could have been false, and which Mary believed.

… If (5) is true, then there are things which are said and believed, which are the bearers of truth values and have modal properties like being possibly true. So if (5) is true, there are propositions. (Speaks 2014: 10–11)

An Argument for Referentialism about Propositions?

Equivocation on something?

There is something they both believe is ambiguous. On [the orthodox] way of reading it, the sentence does indeed assert the existence of an object to which both [John] and [Mary] stand in the belief relation. An internalist will say that on that reading the sentence is simply false…. On another reading, the sentence … would be claiming … that [John]‘s belief and [Mary]’s belief are qualitatively identical. We can compare a sentence like There is something they both own. This could mean there is a particular concrete object of which [John] and [Mary] are joint owners; but alternatively it could mean that there is a kind of object such that [John] and [Mary] both own objects of that kind. To an assertion that [John] and [Mary]’s possessions are completely dissimilar, it would be possible to reply, ’No, there is something they both own—a house’. This would not necessarily imply that they own the same house. (Elbourne 2011: 45–46)

Does Something Really Work That Way?

  1. It is arguably nothing more than a pun or play or words to use there is something they both \(\Phi\) to mean they both \(\Phi\) the same kind of thing.
  2. It also seems the indefinite a house is significant; it is harder to get Elbourne’s reading with the definite: There is something they both own – the house; compare There is something they both accept: the thing John believes.
  3. Think about explanation. Suppose two people fall ill simultaneously, and I ask whether they ate something. If you reply, There is something they both ate, because they each ate a burger at separate restaurants across town, you are not giving the explanation sought.

The Anaphora Argument

The Relational Analysis of Attitudes

Charles believes everything Thomas says.
Thomas says that cats purr.


So, Charles believes that cats purr.

\(\forall x (\text{Thomas says that } x \to \text{Charles believes that }x)\).
Thomas says that \(p\).


So, Charles believes that \(p\).

Possible Worlds and Propositions

Referentialist sentence meanings

Ecumenical Intensions

The truth conditional hypothesis

Stalnaker’s Classification Argument

[T]he primary objects of attitudes are … alternative possible states of the world. When a person wants a proposition to be true, it is because he has a positive attitude towards certain concrete realizations of that proposition. Propositions … are simply ways of distinguishing between the elements of the relevant range of alternative possibilities – ways that are useful for characterizing and expressing an agent’s attitudes toward those possibilities. To understand a proposition – to know the content of a statement or thought – is to have the capacity to divide the relevant alternatives the right way. … To distinguish two propositions is to conceive of a possible situation in which one is true and the other false. (Stalnaker 1984: 4–5)

According to the conception of content that lies behind the possible worlds analysis of propositions and propositional attitudes, content requires contingency. To learn something, to acquire information, is to rule out possibilities. To understand the information conveyed in a communication is to know what possibilities would be excluded by its truth. (Stalnaker 1984: 85)

The Proposition Role

Possible Worlds

Possibilities and Possible Worlds

Lewis’ Argument for (Concrete) Modal Realism

I believe there are possible worlds other than the one we happen to inhabit. If an argument is wanted, it is this: It is uncontroversially true that things might have been otherwise than they are. I believe, and so do you, that things could have been different in countless ways. But what does this mean? Ordinary language permits the paraphrase: there are many ways things could have been besides the way that they actually are. On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit, ‘ways things could have been’. I believe things could have been different in countless ways. I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities which might be called ‘ways things could have been’. I prefer to call them ‘possible worlds’. (Lewis 1973: 84)

Possible Worlds without ‘Extreme’ Modal Realism

Soames on Possible World States

The fact that something in a logical model is called a ‘world’ doesn’t mean that it is a concrete entity, like our universe, existing in a ‘pluriverse of alternate realities’. It is enough that it be something relative to which sentences and other expressions are evaluated – a maximally complete and informative property that represents the universe as being a certain way – i.e., ‘a way the world might be’.

On this construal, what have been called ‘worlds’ are better called ‘world-states’. The actual world-state is the maximal world-representing property that is instantiated; a possible world-state is one that could have been instantiated. (Soames 2010: 52)

Propositional Attitudes

Objection: Necessary and Impossible Propositions

Some sentences, it is widely supposed, are necessarily true: they could not have failed to be true, and so, in a paraphrase widely accepted among philosophers, they are true in every possible world. Two plus three equals five, a defender of this theory will urge, is surely true in every possible world…, and the same applies to Three plus four equals seven. But if Two plus three equals five and Three plus four equals seven are both true in every possible world, the theory we have been looking at is forced to say that the meaning of each of them is the set of all possible worlds. The theory predicts, in other words, that these two sentences have the same meaning.… The same kind of objection can be launched using sentences that are necessarily false [which] too are predicted to have the same meaning, namely the empty set, the unique set that has no members. (Elbourne 2011: 51)

Belief and the Attitudes

Distribution over Conjunction

Stalnaker’s Metalinguistic Approach

The expressions ‘that \(P\)’ and ‘that \(Q\)’ are schemas for sentential complements which denote propositions. The statement ‘\(P\) is necessarily equivalent to \(Q\)’, however, is a schema for a claim about the relation between two expressions. Hence here the letters \(P\) and \(Q\) stand in for expressions that denote things that express the proposition that \(P\). Now once this is recognized, it should be clear that it is not part of the allegedly paradoxical consequence that a person must know or believe that \(P\) is equivalent to \(Q\) whenever \(P\) is equivalent to \(Q\). When a person believes that \(P\) but fails to realize that the sentence \(P\) is equivalent to the sentence \(Q\), he may fail to realize that one of the propositions he believes is expressed by that sentence. In this case, he will still believe that \(Q\), but will not himself put it that way. And it may be misleading for others to put it that way in attributing the belief to him. (Stalnaker 1984: 72)

Stalnaker’s Semantics for Belief

Alternative: Impossible Worlds

Negative Polarity Items

Evidence for the Possible Worlds Account of Propositions

Some More Detail About Set Theory

Some features of sets (see fig. 1)

A picture is worth ≈200 words

Figure 1: Sets and their relations, showing sets A, B, and C, where C \subseteq A, A\cup B is the diagonally hatched area, A\cap B in purple, B\setminus A in pink, and the complement of A\cup B in cream.

Intensions and Sets

Adjectival Modification (Morzycki 2016: §2.2)

NPIs

Characterising NPIs

Preliminaries to our answer

Downward Entailment

Example: Not

Example: No student

Downward Entailingness of no student

Example: At most three students

In Favour of Possible Worlds Semantics

References

Barwise, Jon and John Perry (1983/1999) Situations and Attitudes. CSLI Publications.
Elbourne, Paul (2011) Meaning: A Slim Guide to Semantics. Oxford University Press.
Frege, Gottlob (1892/1993) ‘On Sense and Reference’, in Adrian Moore, ed., Meaning and Reference: 23–42. Oxford University Press.
Kripke, Saul (1980) Naming and Necessity. Harvard University Press.
Ladusaw, William A (1980/2002) ‘On the Notion Affective in the Analysis of Negative-Polarity Items’, in Paul Portner and Barbara H Partee, eds., Formal Semantics: The Essential Readings: 457–70. Blackwell.
Lewis, David (1973) Counterfactuals. Blackwell.
Lewis, David (1986) On the Plurality of Worlds. Blackwell.
McGrath, Matthew and Devin Frank (2024) Propositions, in Edward N Zalta and Uri Nodelman, eds., The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/fall2024/entries/propositions/.
Morzycki, Marcin (2016) Modification, Key Topics in Semantics and Pragmatics. Cambridge University Press.
Nolan, Daniel (1997) ‘Impossible Worlds: A Modest Approach’, Notre Dame Journal of Formal Logic 38: 535–72. doi:10.1305/ndjfl/1039540769.
Schiffer, Stephen (2003) The Things We Mean. Oxford University Press.
Soames, Scott (1987) ‘Direct Reference, Propositional Attitudes, and Semantic Content’, Philosophical Topics 15: 47–87. doi:10.5840/philtopics198715112.
Soames, Scott (2010) Philosophy of Language. Princeton University Press.
Speaks, Jeff (2014) ‘What’s Wrong with Semantic Theories Which Make No Use of Propositions?’, in New Thinking about Propositions: 9–24. Oxford University Press.
Stalnaker, Robert C (1976) ‘Possible Worlds’, Noûs 10: 65–75. doi:10.2307/2214477.
Stalnaker, Robert C (1984) Inquiry, A Bradford Book. MIT Press.
Stalnaker, Robert C (1987) ‘Semantics for Belief’, Philosophical Topics 15: 177–90. doi:10.5840/philtopics198715116.