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Interpersonal Sameness of Meaning for Inferential Role Semantics

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Abstract

Inferential Role Semantics is often criticized for being incompatible with the platitude that words of different speakers can mean the same thing. While many assume that this platitude can be accommodated by understanding sameness of meaning in terms of similarity of meaning, no worked out proposal has ever been produced for Inferential Role Semantics. I rectify this important omission by giving a detailed structural account of meaning similarity in terms of graph theory. I go on to argue that this account has a number of attractive features, prominent among them that it makes sameness of meaning probabilistically determine co-reference.

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Notes

  1. Inferential Role Semantics is a particular brand of use-based theories of meaning in the tradition following [1] and [2]. See, for instance, [3–8] for worked out proposals. See, [11, 19], and [9] for examples of criticism of these theories based on interpersonal sameness of meaning.

  2. The closest philosophical theory is probably that developed for State Space Semantics by [13] which draws heavily on the work of [14]. However, this theory has drawn heavy criticism (see e.g. [15–18]) and it is unclear how to extend it to Inferential Role Semantics.

    There are also many psychological theories of meaning similarity (/semantic similarity) but none of these address Inferential Role Semantics directly and few focus on the issues of conceptual coherence central to philosophers.

  3. When I call these features, ‘mostly neo-Fregean’, I have the latter three in mind. The central notion of meaning discussed in this paper, that of an inferential role, is something quite different from Frege’s ‘sinn’. However, what I show in the latter part of the paper is that inferential roles have at least three important features that are very similar to features that Frege attributed to ‘sinn’.

  4. It is unclear if Frege himself would have agreed with the second observation since he elsewhere [21, 299–300] maintains that interpersonal comparisons of phenomenological states doesn’t make sense. On the other hand, he might have found the kind of interpersonal comparisons discussed below acceptable, since these only involve the interpersonal comparison of functional states.

  5. ‘Synonymy’ and ‘Sameness of meaning’ are used interchangeably in what follows. It should also be noted that it is assumed that they pertain to a relation between expression-types.

  6. There are many ways in which ‘use’ can be spelled out, but doing so in terms of dispositional use seems to be the most promising. For instance, the actual use of an expression is a problematic meaning-candidate since it makes all unuttered expressions synonymous, and the correct use of an expression (cf. e.g. [3, 22, 23]) lends itself less straightforwardly than dispositional use to a naturalistic account of meaning.

  7. To shorten the exposition, I use “‘cat\(_{S_{1}}\)’ means the same (/does not mean the same) as ‘dog\(_{S_{2}}\)”’ to abbreviate “‘cat’ means the same (/does not mean the same) to the speaker S 1 that ‘dog’ means to the speaker S 2”.

  8. Maintaining that the meaning of a spoken or written expression is its use in thought presupposes that a cross-medium identification of that expression can be carried out in non-semantic terms. For instance, if we say that the meaning of a written or spoken expression such as ‘wolf’ is the use of ‘wolf’ in someones thought we have to have a way to say which tokenings in the mind count as tokens of the written or spoken expression, and we cannot do this, without circularity, in terms of the meaning of ‘wolf’ . Moreover, since thought expressions and written or spoken expressions are likely to be as formally different as written and spoken expressions are, there is no easy formal way to carry out the identification. I think this deserves careful consideration but since it is not an issue which is peculiar to the account I want to develop in this paper I will not discuss it here.

  9. There are a number of other ways in which a use-theorist can try to avoid the granularity problem. For instance, she can argue that her theory is not about what meanings are, but about what determines meanings, and thus leave room for more coarse-grained meanings. Greenberg and Harman [5, 298] take this position for instance: ‘It is important to emphasize something from the start. [Conceptual Role Semantics] supposes that in some sense meaning or content is determined by (and so supervenes on) conceptual role, but that does not imply that meaning and conceptual role are the same thing.’. Another way is to argue that only certain kinds of inferences are meaning constitutive, and thus obtain more coarse-grained meanings. Peacocke [7]for instance, adopts this strategy by singling out the ‘primitively compelling’ inferences. Although there is no space do discuss these in detail neither strategy seems very promising; the first leaves meanings (what they are) unexplained, and the second makes appeal to additional semantic properties. Moreover, an explication of meaning similarity might actually be a necessary complement to both; if we go along with the first strategy, it might be the case that whatever it is that use determines, might itself not distribute in exactly they way we expect meanings to, and the same goes for the inferences that are supposed to be meaning constitutive.

  10. Armstrong [25], for instance, stresses this loose use of ‘same’ in connection with a discussion of personal identity.

  11. Ironically, one proposal that is open to this objection is Goodman’s [31] own.

  12. Although my version of Inferential Role Semantics is meant to share the standard assumptions of this kind of theory it might be worthwhile to reiterate these. Following Boghossian ([24]: 27) it will be assumed that ‘there are causal facts of the following form: the appearance in [a speaker’s] belief box of a sentence s 1, has a tendency to cause the appearance therein of a sentence s 2 but not s 3’ and that ‘we may describe this sort of fact as consisting in [the speaker’s] disposition to infer from s 1, to s 2, but not to s 3.’. Moreover, following Field, it will be assumed that Inferential Role Semantics is not meant to replace, but complement, truth-theoretic semantics. Accordingly—pace [28]—inferences are assumed to pertain to wholly internal (narrow) states, and—pace e.g. [29, 30]—deflationism about truth and reference is not assumed. This reconciliatory view of Inferential Role Semantics and truth-conditional semantics means that many of the problems discussed by e.g. Fodor and Lepore [19] for use-based theories of meaning can be avoided.

  13. This is actually also a problem for the account that sameness of meaning is meaning identity. For two sets are identical when they have identical members, and if the individuation conditions of the members of two sets are unclear so is the identity of those sets.

  14. Note that we are concerned with the actual probability of a speaker making a certain inference, not the speaker’s estimate of this probability.

  15. It will not be very consequential exactly how this derivation is performed, but for concreteness it can be assumed to be the average of the strengths of all subsumed inferences.

  16. M 1 is defined in terms of dissimilarity rather than similarity since there is a theoretical limit on how similar two inferential systems can be but not on how dissimilar they can be. One can transform a degree of dissimilarity into a degree of similarity in many ways, for instance, by prefixing it with a minus sign or prefixing it with a minus sign and adding some arbitrary number. The two measures will work the same way and either will be able to partially order pairs of words in terms of having more or less the same meaning.

  17. I here follow Goodman [31, 7]: ‘In ordinary speech when we say that two terms have the same meaning, we usually indicate only that their kind and degree of likeness of meaning is sufficient for the purposes of the immediate discourse. This is quite harmless. But we must remember that the requirements vary greatly from discourse to discourse... If we overlook this variation and seek a fixed criterion of sameness of meaning that will at once conform to these differing usages and satisfy your theoretical demands,we are doomed to perpetual confusion.’

  18. Quine [32, 22–23] writes that ‘Once a theory of meaning is sharply separated from a theory of reference it is a short step to recognizing as the business of the theory of meaning simply the synonymy of linguistic forms and the analyticity of statements; meanings themselves, as obscure intermediary entities, may well be abandoned.’

  19. See Section 3.1.

  20. By not making reference to any semantic properties M can thus be seen as a naturalistic reduction of sameness of meaning (for a subset of all terms).

  21. There are actually a number of other problems with Goldstone and Rogosky’s model. For instance, operationally speaking, they evaluate their model’s success in translating across conceptual systems without recourse to any semantic information. What they are in effect testing is to what extent an algorithm can track nodes of undirected weighted graphs through noise. This has very little to do with the translation between conceptual systems.

  22. But note that if |S 1|>|S 2| there are nodes in S 1 that are mapped to nodes in the extension of S 2 that are not in S 2. These nodes are not guaranteed synonyms in S 2 by the fact that some of the other nodes in S 1 have synonyms in S 2. Also note that even if |S 1| ⩽ |S 2| it does not follow from the Wealth of Synonyms that every node in S 1 is synonymous with every node in S 2. This would have been an extremely counter-intuitive consequence.

  23. Some kind of causal-historical theory of reference is here assumed.

  24. \(\mathcal P (P)\), like any powerset includes the empty set \(\varnothing \). For obvious reasons however, \(\text {Pr}(\varnothing )\) is always set to 0: there is a zero probability that a speaker will encounter an object with no properties.

  25. It is here presupposed that the probabilities of the clusters in a learning history are independent of each other. This is done to simplify the computer simulation described below. It is unlikely that the more generally valid equations generated via the chain-rule (i.e. calculating P r(l = < C 1,...,C n >) by P r(C n |C n−1,...,C 1) ∗P r(C n−1)|C n−2,...,C 1)∗...∗P r(C 2|C 1)∗P r(C 1) would have changed anything substantial in the results.

  26. I am simplifying away from a plausible causal theory of reference in a lot of ways here. For instance, I do not require terms to be multiple grounded, I do not make room for reference borrowing, or error, I assume that all terms have referents(/denotations) and that no two terms within an idiolect refer to the same thing (for an overview see e.g. [35]). I have no reason to think that either of these simplifications influence the general connection between sameness of meaning and co-reference, but it is likely that including them would have obscured the exposition and made it harder to understand the connection I want to draw attention to. I hope to return to this issue at a later date.

  27. This is partially due to the calculation of dsim which requires finding a large number of ‘error-correcting’ isomorphims.

  28. These assumptions include i) that learning histories of all speakers have the same lengths, ii) that graphs are generated for different speakers by them sampling the same probability space, iii) that the sampling of all speakers are independent, and iv) that the probabilities are normally distributed. Some are these assumptions are obvious idealizations which have been made to simplify testing but it is unlikely that dropping them will significantly impact the results in any interesting way.

  29. There are, of course, many other aspects of the account on offer in this paper that are non-Fregean. In particular, the idea that meaning is inferential role runs counter to Frege’s anti-psychologism.

  30. For simplicity, I will confine myself in this section to beliefs of the form A ′ s are B ′ s, e.g. ‘Cats meow’, ‘Dogs bark’, ‘Birds fly’

  31. Although there are commentators (notably [36]) who deny that Frege believed in compositionality this is a minority view. Statements in Frege’s later work (e.g. [37–39]) strongly suggests that Frege, at least at this stage, believed in compositionality.

  32. ‘to understand an expression’ is here understood in terms of a speaker assigning the same meaning to an expression as that assigned to it by some relevant linguistic entity, such as a language, a group of speakers, or, in the simplest case, a particular speaker. For simplicity, the last model of understanding will be used throughout the discussion below. On this model a speaker S 1 will understand an expression t (with respect to another speaker S 2) iff \(t_{S_{1}}\) means the same as \(t_{S_{2}}\).

    See Author (b) for a detailed discussion of the reasons for believing in something like compositionality.

  33. I do not attribute any particular importance to the exact function modifying the costs in this table. What is important for the purposes of this section is just that the costs correspond to decreasing functions of remoteness-index.

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Acknowledgments

The author would like to thank James Hampton and Peter Floderus for very helpful discussions on how to best capture the ideas in this paper mathematically. He would also like to thank Jan-Erik Malmqvist for implementing the ideas in Section 4.3 in a computer program and for coming up with various ways to overcome problems related to computational complexity. The paper has been presented at the departments of philosophy at the University of Gothenburg, Ruhr-Universität Bochum and Rutgers University, and it have benefitted from the discussions that ensued on these occasions. The author would also like to thank Staffan Angere, Pernilla Asp, Ingar Brinck, Guillermo Del Pinal, Pascal Engel, Peter Gärdenfors, Bengt Hansson, Tobias Hansson-Wahlberg, Asger Kirkeby-Hinrup, Anna-Sofia Maurin, Erik Olsson, Stefan Schubert, and Markus Werning for helpful comments and discussion. The paper was supported by a grant from the Swedish Research Council.

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  1. Department of Philosophy, Lund University, Lund, Sweden

    Martin L. Jönsson

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Appendix: Avoiding the Wealth of Synonyms

Appendix: Avoiding the Wealth of Synonyms

Although the Wealth of Synonyms seems to be a welcome feature of M, in particular since it makes M practically compositional, M can easily be defined so that it does not have this feature. One way to do this is to develop a variant of d s i m(n 1, S 1, n 2, S 2) where differences in nodes and edges very close to n 1 and n 2 count for more than differences farther away.

To do this a degree of effort is calculated for every possible set E such that

  1. i)

    E contains only an extension \(N_{g1}^{E}\) of \(N_{g_{1}}\), a set of edges \(E_{g_{1}}^{E}\), a set of weights \(w_{g_{1}}^{E}\), and an isomorphism \({f_{i}^{E}}\) from \(N_{g_{1}}^{E}\) to \(N_{g_{2}}\) which is an extension of a injective function \(f_{i}:N_{g_{1}} \rightarrow N_{g_{2}}\) such that < n 1, n 2 > ∈ f i , and

  2. ii)

    the elements of E can be generated from \(N_{g_{1}}, E_{g_{1}}, w_{g_{1}}\), and f i by the three operations listed in Section 3.2.1 (repeated below).

Corresponding to each set E is a set C of nodes and edges that have been created or modified in order to turn f i into the isomorphism \({f_{i}^{E}}\). Assign every node n i or edge e i in C a remoteness-index \(i_{n_{i}}^{n}\) (/\(i_{e_{i}}^{n}\)) corresponding to the length of the shortest path in the undirected graph \(u{g_{1}^{E}}\) underlying \({g_{1}^{E}}\) that contains both n 1 and n i (/ both n 1 and e 1). The effort associated with each set E can then be calculated by using the costs in the table below, and each function f i is associated with the effort of that of the corresponding E-sets with the least effort. d s i m(g 1, n 1, g 2, n 2) is then identified with the effort e of that function f i associated with the smallest effort. By using this way of calculating costs, a variant of M is defined which does not give rise to the Wealth of Synonyms.Footnote 33

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Jönsson, M.L. Interpersonal Sameness of Meaning for Inferential Role Semantics. J Philos Logic 46, 269–297 (2017). https://doi.org/10.1007/s10992-016-9400-3

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