Skip to main content
Social Sci LibreTexts

15.2: When substitutivity fails

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    In Chapter 12 we used the following examples to illustrate the apparent failure of the law of substitutivity in the complement clauses of propositional attitude verbs:

    (2) a. Mary believes [that The Prince and the Pauper was written by Mark Twain].

    b. Mary does not believe [that The Prince and the Pauper was written by Samuel Clemens].

    Normally we can replace one word or phrase in a sentence by another word or phrase that has the same denotation, without affecting the truth value of the sentence as a whole. So, since the names Mark Twain and Samuel Clemens refer to the same individual, we would expect the two sentences in (2) to be contradictory. But this is not the case; it would be possible for both sentences to be true at the same time and for the same person named Mary, without any logical inconsistency. Since the denotation of the sentence is its truth value, such examples seem to challenge the Principle of Compositionality, at least as it applies to denotations.

    As you will recall, Frege’s solution to this apparent failure of compositionality was to suggest that the denotation of the complement clauses of these verbs is not their truth value when evaluated as independent clauses, but rather the propositions which they express. Essentially, Frege was pointing out that the speaker in (2) is not making a claim about the authorship of the book, but about Mary’s current beliefs. The truth value of the sentence as a whole depends not on who the actual author was, but only on what propositions Mary believes.

    The denotation of a sentence is its truth value, while the proposition which it expresses is its sense. A technical synonym for sense is the term intension. Frege showed that sentences which contain propositional attitude verbs are in fact compositional, but we can only calculate their denotation based on the intension (sense) of the complement clause. Thus these sentences are an example of an intensional context, that is, a context where the denotation of a complex expression depends on the sense (intension) of one or more of its constituents.

    Another special property of propositional attitude verbs discussed in Chapter 12 is the potential for de dicto vs. de re ambiguity, illustrated in (3). The speaker in (3a), for example, may be expressing either a desire to meet the individual who is the Prime Minister at the moment of speaking (de re), or a desire to meet the individual who will be serving in that role at the specified time (de dicto).

    (3) a. I hope to meet with the Prime Minister next year.
    b. I think that your husband is a lucky man.
    (de re: because I saw him winning at the casino last night.)
    (de dicto: any man who is married to you would be considered fortunate.)

    Under the de re reading, the noun phrase gets its normal denotation in the relevant context, referring to the specific individual who is the Prime Minister at the moment of speaking (3a), or who is married to the addressee at the moment of speaking (3b). Under the de dicto reading, the denotation of the noun phrase is the property which corresponds to its sense: the property of being Prime Minister in (3a), the property of being married to the addressee in (3b). So under the de dicto reading, the truth value of the whole proposition depends on the sense, rather than the denotation, of a particular constituent.

    In the next section we look at certain kinds of adjectives which pose a similar challenge to compositionality.

    This page titled 15.2: When substitutivity fails is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Paul Kroeger (Language Library Press) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?