Abstract
Holistic theories of meaning have, at least since Dummett’s Frege: The Philosophy of language, been assumed to be problematic from the perspective of the incremental nature of natural language learning. In this essay I argue that the general relationship between holism and language learning is in fact the opposite of that claimed by Dummett. It is only given a particular form of language learning, and a particular form of holism, that there is a problem at all; in general, for all forms of holism, and irrespective of how language learning is understood, semantic holism is conducive to language learning. The paper has three main parts. In the first, I demonstrate with the use of a simple formal system, that the form of holism that generates the problem that Dummett draws attention to is really decomposable into three distinct components, each of which is necessary for the problem to arise. In the second part, I demonstrate that even Dummett’s strong form of holism is compatible with one natural way in which to understand the incremental nature of language learning. In the third part, I outline the reasons why all forms of holism are conducive to language learning and offer two ways in which this general fact can be spelled out precisely. I end the paper by addressing some possible objections, and in doing so I draw attention to some affinities between semantic holism and the principle of compositionality, a semantic principle which has long been assumed to be conducive to language learning.
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Notes
The literature on semantic holism encompasses discussion of a variety of distinct issues. In order to keep the size of the paper manageable I will not address many of these. First of all, I will primarily be interested in the connection between language learning and what we may call pure versions of semantic holism i.e. versions that are defined directly in terms of interdependencies among meaning assignments. Claims about the interdependence of certain intentional states, e.g. requirements for knowing the meaning of an expression in terms of knowing the meaning of certain other expressions will only be of initial concern (in Section 2). It is only once we get clear about the properties of these more basic forms of holism that we should move on to more complex ones (cf. [20, pp. 6–9]). Further, forms of semantic holism that presuppose the correctness of specific semantic theories, e.g. the claim that all the inferential properties of an expression constitute its meaning (cf. [5, p 10]), will not be discussed in much detail either. By treating semantic holism separately from specific theories of meaning it will be easier to identify its essential properties and make appropriate generalizations. In addition, even though semantic holism is sometimes presented as a thesis in terms of the interdependence of meanings, this cannot (as noticed by e.g. [20]) be what is really intended. What is dependent on each other is an expression having a certain meaning (i.e. a meaning assignment) not the meanings themselves. To see this consider, for instance, a referential theory of meaning. If it is coupled with a form of holism in terms of the interdependence of meanings it entails that there are interdependencies among many distinct contingently existing worldly objects. But this is not a semantic thesis at all, but an incredible metaphysical one. Finally, even though the literature contains many arguments for and against semantic holism (e.g. it has been argued that several conceptions of meaning, such as those in terms of verification conditions [21], inferential roles [2, 5] and use properties more generally [15], lead to different forms of holism), I will restrict my attention to the arguments connected with language learning. I will thus not attempt to answer the more general question of whether or not, all things considered, meaning really is holistic.
For instance, Bilgrami [1] gives an account of Dummett’s argument that is closer to the second version of the argument but he cites Frege: Philosophy of language, the place where Dummett presents the first version.
It is doubtful that even Quine really thought this. Consider for instance the following observation due to Samir Okasha.
Some of Quine’s holistic pronouncements give the impression that he wishes to deny that individual sentences have meanings at all, rather than saying that the meaning of an individual sentence derives from the contribution it makes to the whole theory. But this cannot be Quine’s considered position, for he himself is fond of drawing the following analogy with Frege: before Frege, the word was take as the basic unit of meaning. Frege took a step in the right direction by taking the sentence as the basic unit, and Quine recommends that even this cuts the pie too finely—the basic unit is the the theory...This analogy would clearly not make sense, if Quine held that individual sentences literally have no meaning. For in saying that the sentence rather than the word is the unit of significance, Frege did not mean that individual words have no sense; on the contrary the sense of a word for Frege, derives from the contribution it makes to the sense of whole sentences.
[18, pp. 58–59]
However, it should be noted that on some occasions Quine explicitly maintains that sentences do not have meanings (see e.g. Quine [22, pp. 155–156]).
Here is for instance Davidson’s commitment to holism in Truth and Meaning.
We decided a while back not to assume that parts of sentences have meanings except in the ontologically neutral sense of making a systematic contribution to the meaning of the sentences in which they occur. Since postulating meanings has netted nothing, let us return to that insight. One direction in which it points is a certain holistic view of meaning. If sentences depend for their meaning on their structure, and we understand the meaning of each item in the structure only as an abstraction from the totality of sentences in which it features, then we can give the meaning of any sentence (or word) only by giving the meaning of every sentence (and word) in the language. Frege said that only in the context of a sentence does a word have a meaning; in the same vein he might have added that only in the context of a language does a sentence (and therefore a word) have meaning.
[4, p 22]
Incidentally, this particular claim is due to [9].
Since it might be argued that in the pertinent sense of ‘understanding’, understanding a word is just assigning the correct meaning to that word, this might not be a very significant deviation from Dummett’s writing. It should be noted nonetheless.
By maintaing that this second part is empirical I do not mean to imply that it is theory neutral. On the contrary it seems quite clear that claims about the development of our semantic competence are theory relative in a way that might make them resistant to direct testing. For instance, what tendencies a child has to infer certain things from certain other things (e.g. if the child someone saying ’Toby barks’ with ’Toby is a dog’) might be fairly straightforwardly tested. If we assume an appropriate kind of inferential role semantics, we can thereby conclude things about the semantic competence of a child. However, if one is advancing a causal or referential theory of meaning where one’s tendencies to infer do not constitute meanings, one’s conclusions about the semantic competence of the child from the collected data might be very different.
See Dresner [6] for some observations pertaining to the logically posterior question.
Cf. Pagin’s [19] discussion of the ‘combinatorics of interdependence’.
If one, in spite of this, is compelled to argue that Dummet was really attacking some more superficial aspect of a particular realization of a semantic holism, the rest of this paper could still be read as a – hopefully interesting in its own right – attempt to investigate the compatibility of ’holistic cores’ with incremental language learning, something that Dummet’s argument no doubt called into question even if it was not his primary target.
If \(\mu \) but not \(\mu '\) is undefined for some term t I assume that \(\mu (t)=\mu '(t)\) is false and that \(\mu (t)\neq \mu '(t)\) is true. If both are undefined I will assume the opposite.
It should be noted that this is much stronger than the supervenience reading of the claim that the meaning of each expression is determined by the meanings of all other expressions in the language. The latter thesis corresponds to the following definition.
This restriction can be put more simply.
Note that this is only meant as an illustration and not an endorsement. See the discussion in Section 2.
Whole-hog holism is not strictly speaking stronger than restricted proliferation holism since the former does not regulate the number of expressions that must be meaningful. However, the conjunction of a whole-hog holism and a proliferation holism is strictly speaking stronger than a restricted proliferation holism.
Note that the requirement that each pair of members of \(\mathbb {L}\) be progressive1 is needed in order to avoid the conclusion that any progressive1 language acquisition process can be of arbitrary length. Note also that an unconstrained language acquisition process meeting these requirement can contain up to \( \vert \mu _T \vert \) members.
Note that all forms of semantic holism that we consider are downward monotonic in the sense that if a set of languages \(\mathbb {L}\) is holistic then any subset of this set is also holistic.
Note that establishing the amount of progression that takes place in language learning is not straightforward. See footnote 7.
My formalization differs from that of Pagin. On his definition (ibid.: 21) total pair holism is the view that for any two terms, the number of admissible meanings for one term given a meaning assignment to the other is lower than the total number of admissible meaning assignments for that term. My formalization distinguishes between different degrees of total pair holisms. It also assumes that the same restriction applies to all terms.
If \(\mu _{L_i}(t_1)\) is undefined for some i it is assumed for these purposes that some entity representing meaninglessness is added to \(M_{t_0-t_1}\).
The following should also be noted.
Cf. the quote in footnote 4.
This is not the place to grapple with the difficult exegetical questions that face a reader of Course de linguistiqe générale and I will be content with assessing this idea on its own merits. It seems clear that Saussure thought of the concept associated with a word as its meaning, (see, e.g. [23, p 67, paragraph. 4, or: p 115, paragraph 4]. And in describing the way in which language comes to be, he metaphorically likens thought to a sheet of paper and a body of water that is segmented into parts. Both of these metaphors presuppose a pre-existing whole that is divided. He also writes
So we can envisage the linguistic phenomenon in its entirety—the language that is—as a series of adjoining subdivisions simultaneously imprinted both on the plane of vague amorphous thought..., and on the equally featureless plane of sound...
(Ibid 1916: p 111)
and continues a few pages later
In a given language, all the words which express neighboring ideas help define one another’s meaning. Each of a set of synonyms like redouter (‘to dread’), craindre (‘to fear’), avoir peur (’to be afraid’) has its particular value only because they stand in contrast with one another. If redouter (‘to dread’) did not exist, its content would shared out among its competitors...So the value of any given word is determined by what other words there are in that area of the vocabulary.
(Ibid 1916: p 114, italics in original)
Saussure here seems committed at least to the idea that terms within the same area of the vocabulary compete with each over over their meaning. Additionally, my interpretation has the benefit of providing an explanation of the Sausurrean idea that items that contrast with each other (i.e. for all x and y such that ‘x’ entails ‘not y’) reciprocally determine each others meanings. For if there is only so much meaning to go around, and all meaning must be used up, then the meaning of each expression is constrained by the meanings of the others.
However, it is not clear to me whether my characterization of meaning here best fits Saussure’s conception of meaning or the related, but distinct, notion of value. Another problem with my interpretation is that it is not true to the central Saussurean idea that signifieds are purely negative. However, as critics of this idea has remarked (e.g. [14, p 129]) there might not be any good way to make sense of it. See Lyons [17] for a more worked out proposal of sausurrean semantics.
Note that this definition is insensitive to the number of synonyms in a certain language. Since there are lexical synonyms this seems to be a plausible retraction from the original stronger claim that all meaning assignments are in competition (and hence that there cannot be any synonyms).
For simplicity I will restrict myself to conjunction elimination in this example. Note that only the antecedents and the consequents of the inferences, and not the inferences themselves, are assumed to be part of the grammatical terms of the languages under consideration.
While clause ii) is just a simple variant of the claim that meaning of a term is its inferential role, clause i) is there since I want to show is that even an inferential role semantics that is strong enough to be compatible with whole-hog holism is compatible with progression.
Again, the second clause is there to prevent trivial progression.
Dresner [6] has given another account of how this can be done. However, a full scale rehearsal of his account here would take up too much space.
The ’mutual exclusivity assumption’ is actually a form of holism. See Dresner [6] for a discussion.
Note that in this and the subsequent discussion about knowledge of semantic determination relations, ’knowing a determination principle’ need not entail a certain kind of propositional knowledge. It might just involve a disposition to assign meanings in accordance with the principle.
Focusing on the maximum time rather than the minimum time it takes to learn a language might seem strange. Since an algorithm can be arbitrarily inefficient there is no upper limit to how long solving a certain problem could take. However, given that the constraints on the shape of learning acquisition processes mentioned in the main text are in place there is a worst case. We can thus view the benefits of semantic holism as protection from the worst case. If one prefers a measure of the shortest time instead, one has to introduce constraints on how much one can possible progress in one step. One such constraint would be to assign a meaning to one expression and infer whatever you are thereby committed to in virtue of known determination principles. This measure will give the same privileged place to semantic holism and the results will parallel those given concerning effort in the next section. The alternative given in the main text seemed less question begging to me since it did not require a framework where the holisms are explicitly acknowledged as inference rules.
Remember (from Section 3) that a language acquisition process is an ordered set and thus does not permit several identical members.
Note that even though we assume that all interpretation functions are total some languages only contain a few of the terms in GT T . From a combinatorial perspective this possibility is equivalent to the case where one extra meaning is added to M and the language where all terms have that meaning as meaning (i.e. the language corresponding to a language without any terms) is prohibited.
This way of modeling language learning illustrates most directly the way in which the hypothesis-limiting power of semantic holism can shorten the language learning time (= shorten the language acquisition process) since on this model each step in the process corresponds to a single hypothesis about the interpretation function. In order to have this clear analogy I used a model where evidence is provided for hypotheses about complete languages rather than for single expressions. The next section features an illustration where evidence pertains instead to individual meaning assignments.
More formally, given a language acquisition process \(\mathbb {L}\) which is successful relative a target language T, and the fact that \(\mathbb {L}\) is in accordance with a kind of holism \(\mathbb {H}\), it follows that not every language L such that \(GT_L \subset GT_T\) can be a member of \(\mathbb {L}\).
If this is not immediate, see Observation 4
It is difficult to calculate the exact number of possible hypotheses that can maximally be part of a zero-sum holism in general since this number depends on the number of synonyms in T. If we make the simplifying assumptions that for each \(l \in \mathbb {L} , GT_l=GT_T\) and \(\lnot \exists t_0,t_1\in l\) such that \(\mu _l(t_0)=\mu _l(t_1)\) things are more straightforward. Since \(T \in \mathbb {L}\), every other language l such that \(ran(\mu _l)=ran(\mu _T)\) can be in \(\mathbb {L}\). Given the previous assumptions and the assumptions in the main text, these other languages are just the permutations of meanings across the expressions of T, and there are thus \(|ran(\mu _T)|!\) many such languages. There can also be languages in \(\mathbb {L}\) with meanings from \(M-ran(\mu _T)\). Since zero-sum holism prohibits partial overlaps between ranges of interpretation functions, \(M-ran(\mu _T)\) has to be divided into m subsets, each of which corresponds to a set of languages in \(\mathbb {L}\) with interpretations functions with the same ranges. Each of these sets will contain \(n_i!\) members where \(n_i\) is the size of the pertinent subset of \(M-ran(\mu _T)\). This means that in order to calculate the maximum size of \(\mathbb {L}\) we need to calculate the maximum of \(n_1! +...+n_m!\) across different ways to divide \(M-ran(\mu _T)\) into m subsets. This equation is maximal when individual subsets of \(M-ran(\mu _T)\) are as large as possible. Since they cannot be larger than \(GT_T=|ran(\mu _T)|\) it follows (given the present assumptions) that a fair zero-sum holism can contain at most \(|M|/|ran(\mu _T)*|ran(\mu _T)!+ remainder (|M|/|ran(\mu _T))!\) members.
It does not matter which number we choose as the measure of the effort required to learn the first expression of a language since it will be the same for unconstrained learning and learning governed by a semantic holism, and only the relative difference in learning effort between these two types of learning will be part of the observations below.
Proliferation holisms also lower learning effort if \(\mu \) is not required to be total.Under certain circumstances the learner can use his knowledge of the prolific holism obtaining in order to rule out the hypotheses that certain expressions are meaningless and thereby decrease the amount of effort required.
The exact decrease in effort cannot be calculated in general since it depends on the exact nature of \(\mu _T\), in particular, on how many synonymous expressions there are.
I owe this line of criticism to one of the participants of the 2009 Lund-Rutgers conference.
I emphasize this in Section 3.
In this essay, I have limited myself to claims of the properties of semantic holism in itself. My remarks here are compatible with there existing various reasons for being a holist that might lead language learning to be harder to learn than it would otherwise be. I have only tried to isolate what is true of semantic holism.
I owe this observation to Wlodek Rabinowicz.
I owe this observation to Staffan Angere.
Given that we are concerned with pure versions of semantic holism. See footnote 1.
See Jönsson [16] for an overview of different ways in which to spell out determination in the context of compositionality.
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Acknowledgments
The author would like to thank Staffan Angere, Pernilla Asp, Sebastian Enqvist, Gabriel Greenberg, Simone Jönsson-Asp, Jan-Erik Malmquist, Erik Olsson, Peter Pagin, Wlodek Rabinowicz, Stefan Schubert, the participants of the 2009 Lund-Rutgers conference, and an anonymous reviewer for this journal for helpful comments and/or fruitful discussion. This work was made possible by a grant from the Swedish Research Council.
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Jönsson, M.L. Semantic Holism and Language Learning. J Philos Logic 43, 725–759 (2014). https://doi.org/10.1007/s10992-013-9287-1
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DOI: https://doi.org/10.1007/s10992-013-9287-1