Pluralist conceptual engineering

ABSTRACT

Building on Wittgenstein’s ideas, I defend a brand of pluralism that associates words with conceptual families and appeals to this notion in the course of philosophical problem solving. I argue that certain problems that the received view of conceptual engineering (‘improvement by replacement’) faces can be more easily overcome if we adopt a pluralist perspective. I show that the proposed approach can circumvent the problem of topic discontinuity, whilst also avoiding the threat of trivialisation, since it can easily accommodate both coarse-grained and fine-grained topics. Finally, I argue that my variant of pluralism is compatible with de novo conceptual engineering insofar as it allows that the paradigm associated with a word may shift overtime thus creating an opportunity for new candidate members to join a conceptual family.

KEYWORDS:

• Conceptual engineering
• pluralism
• wittgenstein
• semantic underdetermination
• speaker meaning
• pragmatic enrichment

1 Introduction

In a couple of recent papers, Max Deutsch (Deutsch 2020a, 2020b) has criticised the view of conceptual engineering understood as an attempt to revise concepts by replacing them with new ones, the method he calls stipulative revision.¹ Deutsch has argued that stipulative revisions fail both on the ‘standard (i.e. semantic) picture’ of conceptual engineering and on the ‘speaker meaning picture’ advocated by Mark Pinder (Pinder 2019, 2020).² In particular, where on the speaker meaning picture stipulative revisions seem to avoid the so called ‘implementation problem’, on both approaches they fall short from being a fruitful philosophical method due to trivialising philosophical problem solving. As the direct consequence of the topic discontinuity, the ‘trivialisation problem’ lies at the heart of Strawson’s challenge (Strawson 1963).

The challenges arising from the implementation of proposed revisions and the trivialisation of problem solving put pressure on conceptual engineers to defend their trade. Whilst I agree with Deutsch’s criticisms, I nevertheless think that both challenges can be defused by adopting a different approach to word meanings and meaning change, and a different approach to engineering concepts. In what follows I propose that by endorsing pluralism as a semantics of word meaning (Wittgenstein 2009;Dobler 2019; Carston 2021) we lay the ground for a more realistic model of revisionary conceptual engineering (see also Chalmers 2020). Although the proposed semantic framework brings to light similar ideas concerning ordinary communication as the dynamic lexicon theory developed in (Ludlow 2014), I argue it does not share the same theoretical shortcomings highlighted by Cappelen (2018) and Pinder (2019). Namely, although, like Ludlow (2014), I maintain that the semantic (standing) meaning is underspecified and it undergoes different modulations and enrichments in different contexts (Carston 2002; Travis 2008; Recanati 2004), it is on the level of speaker meaning that the effect of the pragmatic enrichment of the semantic meaning is seen. By combining the idea of semantic underdetermination with pluralist semantics, it is possible to retain the notion of ‘change without discontinuity’ in the way that I aim to spell out in what follows.

The second aspect of the proposed framework draws on Wittgenstein’s meta-philosophy.³ In contrast to the received view of conceptual engineering, I argue that a Wittgensteinian approach is better equipped to deal with the problems of trivialisation and implementation. Taking Wittgenstein’s discussion of Frege’s problem with NUMBER as my main example, I demonstrate that a pluralist conceptual engineering embodies three principles, namely: pluralist semantics, the notion of family resemblances and the idea of a dominant model. The first step in the engineering intervention is to recognise that a word is associated with a conceptual family: there is not one concept that a word encodes but many. A pluralist conceptual engineer does not seek to replace a ‘faulty’ concept but she brings to view the existence or the possibility of others. The process reveals that a philosophical problem (e.g. ‘Do numbers exist independently of us?’) is often itself a symptom of a problematic view of concepts connected to essentialist thinking. A conceptual engineer treats a philosophical problem by placing it in the pluralist perspective and dissolves it by revealing its normative status as a result of accepting a certain model as dominant. We are free to champion different models for different purposes without seeking to banish individual concepts from the conceptual family.

The paper is structured as follows. In §2 I introduce the received view of conceptual engineering and its current challenges. In §3 I outline a pluralist semantics that underpins an alternative picture of the relation between standing meaning and speaker meaning. In §4, following Wittgenstein, I show how pluralism can be used as a method of philosophical problem solving. In §5, I apply the proposed framework to contemporary conceptual engineering, showing how it can respond to the two key challenges. I also position my brand of pluralism in the context of other pluralist approaches to conceptual engineering. I conclude in §6.

2 Conceptual engineering and its challenges

2.1 Standard conceptual engineering

Conceptual engineering is a recently coined term for an array of revisionary methods deployed to redefine, adjust, precisify, ameliorate, correct, replace, or eliminate ‘concepts’ (or, alternatively, representational devices, conceptions, false beliefs, linguistic or speaker meanings, uses) which are in some sense considered ‘defective’ and in need of a purposeful ‘improvement’. In contrast to the traditional idea of conceptual analysis, conceptual engineering advertises itself as a normative or prescriptive endeavour:

Conceptual engineers aim to improve or to replace rather than to analyse; to create rather than to discover. While conceptual analysts are interested in the concepts we do have, conceptual engineers are interested in the concepts we ought to have. Their project is prescriptive rather than descriptive (Nado 2019, 3)

Motivated by removing a certain perceived deficiency in a concept, the main goal of a conceptual engineer is ‘to ask what our concepts ought to be or what extensions our terms ought to have’ (Cappelen 2018, 14).

The most common illustrations of conceptual engineering in the literature are those cases where an existing concept ought to be (partially or totally) replaced by a new one. Carnap’s method of explication is considered to be a paradigm of conceptual engineering understood in this way. According to Carnap, ‘[t]he task of explication consists in transforming a given more or less inexact concept into an exact one or, rather, in replacing the first by the second’ (Carnap 1962, 3). As a simple example, Carnap takes the everyday concept FISH which ought to be replaced by a more precise concept PISCIS in order to be used in the context of zoology. One of the characteristics of the new concept PISCIS (the explicans) is that it is narrower than the former concept FISH (the explicandum) since it excludes several kinds of animals subsumed under fish such as whales and seals. Furthermore, Carnap points out that this process involves ‘a change in the rules of language’ or a ‘change in meaning’ which is ‘motivated by factual discoveries’ (Carnap 1962, 94).

Another prominent example of conceptual engineering in the literature is Sally Haslanger’s ameliorative analysis of WOMAN (Haslanger 2000). This is also often taken as an illustration of stipulative replacement.⁴ Similarly to Carnap, Haslanger seeks to fully replace some of our current gender (and race) concepts with the new ones which would better reflect the social standing of certain groups of individuals in the fight against social injustice. According to Haslanger’s proposal, instead of tracking characteristic biological features, the concept WOMAN should reflect the fact that women are systematically subordinated due to their perceived reproductive features.

Both Carnap’s and Haslanger’s methodologies see the improvement of the concept F in substituting it with the concept F *. In both cases the mode of revision is ‘one to one’ so that, as Nado puts it, ‘a target pre-engineering concept is revised into, or replaced by, a single successor’ (Nado 2021, 1). The concept expressed by the English word woman (or fish) is envisaged to be a different concept before and after the engineering intervention.

2.2 The implementation and trivialisation challenges and the semantic/speaker meaning picture

An advocate of the idea ‘improvement by replacement’ is confronted with a number of challenges of which the following two are especially pertinent:

• Implementation challenge: how can a conceptual engineer successfully implement her stipulative revisions?

• Trivialisation challenge: supposing we somehow manage to implement a revision, how can we refrain from trivialising philosophical problem solving?

The trivialisation problem is a direct consequence of Strawson’s challenge. Strawson’s objection against the use of Carnap’s methodology in philosophy turns on the idea that explications, by their very design, presuppose meaning revisions.⁵ And when the meaning of a word has changed, the subject or topic the word is about has also changed.⁶ That is, we seem to be talking about different things pre- and post-explication by using the same word. Accordingly, any philosophical questions arising in relation to the original concept remain unaddressed by applying this method. Philosophical problem solving is, therefore, trivialised because original problems are abandoned rather than tackled: ‘[t]here’s a lack of continuity of inquiry: the old questions are not being answered’ (Cappelen 2018, 101–102).

The implementation challenge for conceptual engineering has originally come up as an issue related to metasemantic externalism (see Cappelen 2018; Pinder 2019). That is, it has been argued that if externalism is a correct meta semantics for concepts – meaning that their content is determined by external, mind-independent factors – then the conceptual engineer ‘may have insufficient control over meaning to make her project a practical possibility’ (Pinder 2019, 2). And if the conceptual engineer lacks control over the determination factors of content, then, a fortiori, she cannot implement any changes relating to the content of concepts. In response to this issue, Pinder (2019) has argued that, even assuming we have no direct control over the standing, linguistic meaning of a word, speaker meaning is still fully in the speaker’s control as it supervenes on her intentions.⁷ Thus, in contrast to the ‘semantic meaning picture’ of conceptual engineering on which the standing semantics of a word is the target of an intervention, the ‘speaker meaning picture’ of conceptual engineering ‘makes conceptual engineering often easy in practice, as we have significant control over speaker-meaning’ (Pinder 2019, 2).⁸

However, although implementing a conceptual change seems more feasible if we assume the object of revision is speaker meaning, a concern has been raised that this switch renders conceptual engineering not a worthwhile philosophical methodology, and not especially new or fruitful (see Deutsch 2020a; Deutsch 2020b). The idea is that, since one can speaker-mean just about anything one pleases by the word one uses, implementing meaning changes in this way becomes a child’s play, resulting in a further trivialisation of philosophical problem solving. It, therefore, seems that overcoming the implementation problem by adopting the speaker meaning picture directly gives rise to the trivialisation problem. Moreover, Deutsch (2020b) maintains that speaker-meaning by a word something other than its semantic meaning is actually a bad policy since it may lead to confusion and hinder philosophical problem solving. In his words,

Policies of speaker-meaning not only buy no progress on philosophical problems, they can positively hinder such progress. This suggests that, in the context of philosophy, one should never adopt a policy of using a term to speaker-mean something different from its semantic meaning, regardless of whether the policy is seriously proposed. In other words, in the context of philosophy, meanings distinct from terms’ semantic meanings are bad things to speaker-mean with those terms. (Deutsch 2020b, 9)

The received view of conceptual engineering according to which this methodology primarily has to do with the replacement of faulty concepts (on either linguistic or the speaker meaning level) faces serious challenges related to the implementation of proposed revisions or trivialisation of philosophical inquiry. In the next section I want to offer a different perspective on the distinction between standing meaning and speaker meaning, and a different approach to concepts as meanings, hoping to shed a new light on conceptual engineering and propose a novel response to these two challenges.

3 Pluralism as a semantics of word meaning

3.1 Lessons from everyday communication

It is commonly assumed that concepts are word meanings (see Fodor and Lepore 2002; Fodor and Pylyshyn 2014). The English word woman is taken to express or encode the concept WOMAN. This initial picture becomes more complex when the distinction between standing meaning and speaker meaning is introduced. We have seen that a speaker is said to be at liberty to express anything she pleases by a word: by uttering woman the speaker can speaker-mean WOMAN* or ELECTRON or what have you, whilst the English word woman expresses the concept it encodes anyway (WOMAN). The idea is particularly reinforced by the phenomenon of conversational implicatures: a speaker saying one thing and meaning to convey something else. According to the approach to speaker meaning modelled by conversational implicatures, two (often distinct) concepts are expressed in a single act of utterance: one encoded and expressed by a word (standing meaning M), and another speaker-meant and expressed by the speaker when uttering the word (speaker meaning N), where M need not be the same concept as N. Whilst Deutsch (2020b) and Pinder (2020) disagree on whether it’s worthwhile that speaker meaning diverges from standing meaning, they do seem to be in a fundamental agreement about this picture of their relation.

However, if we look more closely at the phenomenon of everyday communication, an alternative picture of this relation emerges that moves away from the paradigm of conversational implicatures and ‘secondary pragmatic processes’ (cf. Recanati 2004, 50). As numerous philosophers of language and linguists have observed, what a speaker communicates on some occasion – the proposition she expresses (‘explicature’) – is, as Carston (2021) puts it, ‘seldom, if ever, fully captured by [the word’s] linguistic content and hearers must employ pragmatic inferential processes in order to determine that content’ (Carston 2021, 16). For instance, when uttering green in a given context, the speaker will often intend to express something more specific than simply being green (see Travis 1997). Thus to interpret what has been said, it won’t be sufficient to know what green in general means; a hearer will often also need to know the relevant contextual information in order to pragmatically infer what the speaker intended to say, that is, her ‘pragmatically enriched’ meaning (Recanati 2004; Pagin and Pelletier 2007).⁹

Based on these observations, the divergence of speaker meaning from standing meaning turns out to be a regular feature of communication. The speaker ‘seldom, if ever’ expresses the same content that a word lexically encodes. I maintain that this is because a word typically encodes a whole family of related concepts. In the course of communicating with each other we routinely perform ‘revisions’ of standing meaning, highlighting only those concepts from the encoded family that are contextually relevant.

3.2 Pluralist semantics

In Dobler (2019), I have outlined a two-component pluralist semantics inspired by Yablo’s work on aboutness (Yablo 2014). On this approach, the standing meaning of a word (e.g. green), consists of two components: (i) its classical denotation (i.e. the set of green things), and (ii) a ‘family’ of more specific concepts or ‘ways’ (e.g. being naturally green, being painted green, being mouldy green, being lit green etc.).¹⁰ Taken together, these ways form a cover over the broad denotation of a word.¹¹ A conceptual cover refines the original partition created by a concept, dividing the space further into more specific concepts. Take the concept WAR, for instance.¹² This concept partitions logical space into the worlds with wars and worlds with no wars. For speakers in 1688, the cell containing war worlds was covered with the division between land wars and sea wars. However, as our knowledge of warfare develops and our interests shift, the conceptual cover changes too: our ‘war’ cover is finer and richer than William III’s because nowadays we also have the concepts of NUCLEAR and CYBER WARS.

I take it that the conceptual cover associated with a concept at a time is relatively stable, and that there is a high degree of overlap between competent speakers with respect to the ways that constitute the cover. Still, this doesn’t preclude that the level of grain of certain regions of the cover may vary among different individuals: the expert in some topic will typically have a finer division of a relevant region compared to a layman. Moreover, entirely new ways may eventually be added and old ones deleted modifying not only the grain or number of cells but sometimes also the broad denotation (PLANET, WOMAN).¹³

The motivation for adding the second component to the word’s standing semantics primarily has to do with the feature of everyday communication highlighted above, namely, that what is said by using a sentence is not fully determined by its standing meaning.¹⁴ There are many different theories of this phenomenon in the literature, depending on how the space containing key concepts is carved.¹⁵ On the current approach, the divergence between sentence and speaker meaning is a result of abundance rather than scarcity: what the speaker intends to say cannot be determined by what a word means because there are many different ways in which the word can be understood.¹⁶ Like (overt) disjunctions in Yablo’s framework, simple declarative sentences can be true in different ways (and sometimes also in different ways at once), because of alternative ways we conventionally associate with certain predicates. For instance, “The leaves are green” may be true in virtue of the leaves being only naturally green, only painted green, or both. The interpreter’s task is to cancel those possible interpretations which are contextually irrelevant.

The process of pragmatic enrichment, on this approach, consists in resolving the ‘ambiguity potential’ (Poesio 1996) generated by alternative ways. Building on Yalcin (2018)’s account of subject matters, we can think of individual ways (i.e. the elements of a conceptual cover) as connecting its concept with different subject matters or topics. For instance, GREEN intersects with the subject matter BOTANY in virtue of things being naturally green. GREEN also intersects with the topic PAINTING but via a different way of being green, i.e. things being painted green. Which disambiguation is correct (intended) thus depends on the topic of discussion in a given context. In Dobler (2019) I develop this line of argument by proposing that we selectively attend (Smith 2010) to certain ways because of their relevance for fulfilling our domain goals (Roberts 2012) and getting on with our practical projects. At the same time, we temporarily ‘background’ those ways we deem irrelevant to our current topics and goals, that is, those ways that are not maximally goal-conducive.

3.3 Literal and figurative speaker meaning

By adopting a pluralist perspective, we can understand the relation between standing meaning and speaker meaning in a new light. In contrast to the picture described in §3.1, on the pluralist approach it is not the case that two distinct (unrelated) concepts are expressed in a communicative act, one by a word, another by a speaker. On the proposed approach, a word encodes a set of concepts anyway, and what a speaker means and says on an occasion by using it is only a subset (enrichment) of its standing meaning. In this way, the speaker may mean different things when she utters a word in different contexts – i.e. she may express different concepts by the word – whilst staying in agreement with the word’s standing meaning which itself remains fixed (context-independent). In order to properly understand which aspect of speaker meaning is presently under consideration, let me point out the distinction between what I call literal speaker meaning and figurative speaker meaning (Dobler 2020).¹⁷ Namely, what is described by the process of pragmatic enrichment is how literal speaker meaning fluctuates and shifts cross-contextually. The speaker meaning of F is literal whenever it agrees with the semantic meaning of F, i.e. when it’s a strengthening of it (a subset of the broad denotation associated with a word). The figurative speaker meaning expressed by uttering F, by contrast, is exemplified by the phenomena of conversational implicatures, metonymy, or metaphor, where the speaker uses F to mean something else than what F semantically means. In using language figuratively, by uttering F the speaker consciously intends to express a different set of concepts from the one encoded by F. This intention to move away from the standing meaning of F when uttering F is not a feature of the literal information exchange (in Recanati (2004) terminology, it doesn’t satisfy ‘the availability principle’).

3.4 Note on Ludlow’s dynamic lexicon theory

The feature of ordinary communication I highlighted above also plays an important role in the account of meaning change developed in Ludlow (2014). In building his theory of dynamic lexicon and micro-languages, Ludlow also appeals to what he calls ‘the extreme context-sensitivity of languages’ and, like I, maintains that a word’s standing meaning is massively underspecified. However, the theory of linguistic meaning he proposes drawing on these notions is different from the one I propose here. Namely, whilst Ludlow maintains that context- sensitivity and underdetermination militate against the notion of ‘standing’ meaning, and goes on to reject the idea that words have stable, fixed meanings, on my approach words do retain their stable albeit pluralistic meanings. That the standing meaning of a word undergoes an enrichment in context, which is manifested in a speaker meaning something more specific, does not necessarily entail that the family of concepts that a word encodes shifts between or within conversations. What the speaker means (and says) by using a word is indeed dynamic, and the word’s meaning indeed undergoes frequent modulations – still, all this is consistent with the view that the pluralistic content that the word encodes is (relatively) stable and context-independent.

4 Pluralism as a methodology

Similarly to Ludlow’s approach, on the approach developed here ‘conceptual engineering is continuous with ordinary conversational practices’ (Pinder 2019, 18). As suggested above, in the course of everyday communication we regularly ‘engineer’ underspecified word meanings in order to convey only the information that is contextually relevant. ‘Revising’ word meanings is thus not something out of the ordinary or, pace Deutsch (2020a), incredibly hard to implement (although note that the contention is not that we thereby replace one set of concepts by another). But is conceptual engineering that presupposes pluralist semantics still a worthwhile philosophical methodology, namely, one that can help us with solving particular philosophical problems? In what follows I want to draw attention to a methodology in which pluralist semantics plays a central role in philosophical problem solving: Wittgenstein’s grammatical investigations.

4.1 Philosophical problems are conceptual confusions

4.1.1 Confusing metaphysics with grammar

Whilst natural sciences are empirical investigations dealing with how things are, philosophy as a discipline is traditionally considered to be about necessities – why things ‘must’ be or ‘cannot’ be so. Traditionally, statements of necessity are considered to be metaphysical claims ‘about’ certain metaphysical facts.

Wittgenstein famously debunks metaphysics as grammar: the alleged metaphysical statements which are supposed to describe metaphysical super-facts are nothing but expressions of how we propose to use certain words, i.e. they are ‘the rules of grammar’.

One thinks that one is tracing nature over and over again, and one is merely tracing round the frame through which we look at it (Wittgenstein 2009: §114).

Statements of rules are not descriptive but normative statements or stipulations. They express our accepted model of certain phenomena (i.e. our ‘frame’), the model which we can decide to overthrow given the right circumstances (see §5.4).

4.1.2 Language is the culprit

A philosopher misunderstands the ‘illocutionary force’ of her statements – i.e. she fails to see that they are her expression of the rules, rather than statements about the nature of X – because of certain misleading features of language itself. These misunderstandings sometimes arise because of ‘certain analogies between the forms of expression in different regions of our language’ (ibid. §90). For example, expressions of rules and factual descriptions may grammatically have the same form (e.g. ‘This is red’). Or a philosopher may take nouns as her model word and she may leap to the conclusion that all words function as nouns (ibid. §1) and that the meaning of a word must be some object that the word goes proxy for (looking for a ‘thing corresponding to a substantive’). Or she may assume that she is drawing conclusions about the nature of colour (i.e. red must be something indestructible) because ‘the sentence [Red exists] looks as if it were about the colour, while it is supposed to be saying something about the use of the word red’ (ibid. §58). Expressed in a famous slogan,‘philosophical problems arise when language goes on holiday’ (Wittgenstein 2009: §38), that is, when words are not in their ordinary circulation where different kinds of word may have very different functions, and where the same word/sentence may be used to express different things in different ‘language-games’.

4.1.3 Philosophical problems require a treatment

Underlying Wittgenstein’s position on the nature of philosophy and philosophical problems is an important distinction between empirical (factual) investigations/problems and conceptual investigations/problems, where concepts are generally understood to be linguistic meanings. Philosophy as a discipline ultimately deals with, and works on, itself; as a grammatical or conceptual investi- gation it aims to demystify or prevent ‘conceptual confusions’ – those arising in relation to the grammar of our language and its (mis)use when philosophising. In Wittgenstein’s words,

[The philosophical problems] are, of course, not empirical problems; but they are solved through an insight into the workings of our language, and that in such a way that these workings are recognized a despite an urge to misunderstand them. (PI §109)

On this view, the existence of a philosophical problem or question is itself a symptom of ‘misunderstandings concerning the use of words’ (Wittgenstein 2009: §90). Philosophical questions (such as what the meaning of five is or whether mathematical facts are objective and real) therefore require a treatment (and dissolution) rather than a solution. The philosopher’s task is to ‘treat a question; like an illness’ (PI §255). She can do that by conducting a ‘grammatical’ inquiry ‘which sheds light on our problem by clearing misunderstandings away’ (Wittgenstein 2009: §90).

4.1.4 Calling to mind

In the course of a grammatical inquiry ‘the problems are solved, not by coming up with new discoveries, but by assembling what we have long been familiar with’ (PI §109). What we thus ‘revise’ by conducting a conceptual investigation are certain misconceptions: we call to mind ‘the kinds of statement that we make about phenomena’ (PI §90) or ‘the differences between the language- games’ (PI §290); we ‘bring words back from their metaphysical to their everyday use’ (PI §116), we destroy ‘houses of cards, and we are clearing up the ground of language on which they stood’ (PI §118). The revisionary element of Wittgenstein’s grammatical method is thus importantly corrective and restorative. The concern, of course, is whether this method leaves ample room for designing and building new concepts (Chalmers 2020).¹⁸

4.2 Grammatical investigation of ‘number’

Wittgenstein has conducted many grammatical inquiries often treating questions and contentions from his own early work in the Tractatus or from other logicians, mathematicians, or philosophers of that time. An example that is particularly pertinent for the argument of this paper is Wittgenstein’s examination of Frege’s reasoning supporting the claim that numbers must exists mind-independently (Waismann 2003). Let us look at Wittgenstein’s argument in more detail and see which lessons conceptual engineers can draw from it.

4.2.1 Pluralism, family resemblance, models

As it is well known, Frege maintained that numbers are a sort of platonic entities that exist independently of thinkers in a ‘third realm’.¹⁹ Frege famously defended the so called ‘meaningful arithmetic’ where arithmetical terms have their meanings by standing proxy for numbers against the ‘formal arithmetic’ which is supposed to be ‘concerned only with the rules governing the manipulation of the arithmetical signs, not however with the reference of the signs’ (Frege (1952), GG §88). An important aspect of Frege’s philosophy of mathematics is the contention that numbers cannot be arbitrarily created:

Even the mathematician can no more arbitrarily create anything than the geographer: he can only discover what is there, and give it a name. (ibid., §96)

Note that Frege’s contention has a form of a metaphysical statement about the nature of numbers. On Wittgenstein’s approach, however, ‘what a mathematician is inclined to say about the objectivity and reality of mathematical facts is not a philosophy of mathematics, but something for philosophical treatment’ (Wittgenstein 2009: §254). His treatment of Frege’s contention begins by examining Frege’s motivation for rejecting the role of ‘creative force’ in arithmetic. The investigation uncovers that Frege’s worry boils down to this: ‘if one admitted such a ‘creative force’ then the solution of a mathematical problem would in principle be child’s play’ (Waismann 2003, 155). Namely, if we suppose that mathematicians created imaginary numbers in order to solve the equation x² + 1 = 0, then why not use this same method to solve every possible mathematical problem, including 1^x= 2? But, in the latter case, applying this method would yield a very peculiar sort of arithmetic, and the conclusion one is inclined to draw is the following:

With the task of solving the equation x² + 1 = 0, a new extension of the domain of numbers is successful, with the equation 1^x = 2 it s not. Whether it is successful or not does not depend on us but on objective laws, and it is in these that the fruitless creative force finds its limit. (Waismann 2003, 157).

Having described Frege’s reasoning for rejecting a creative force, Wittgenstein sets out to show that it can be turned into an opposite argument in favour of the creative force. His strategy is to lead us towards seeing Frege’s seemingly metaphysical claim about the nature of numbers as a normative statement (i.e. the expression of a grammatical rule) about the meaning of number. According to Wittgenstein, one gets entangled by assuming ‘that it is sufficiently clear what a number is’ (157). That is, a philosopher is inclined to have a certain concept of NUMBER in mind as her model, and, thinking as an essentialist, one forms a belief that everything that we call number must have those properties the model has. A ‘grammatical’ treatment of this philosophical problem starts by accepting pluralism: ‘the first step of clarification consists in the observation that there is not one number concept but many’ (Waismann 2003, 157–9).

Once pluralism has been recognised it becomes easier to see that there are certain similarities as well as differences between these NUMBER concepts (cardinals, integers, reals etc.), that is, a certain ‘formal kinship’. In other words, specific concepts are connected by a relation of family resemblance on the basis of which we call them numbers. Furthermore, Wittgenstein maintains that among all these specific concepts one usually tends to stand out and have a special status as our accepted model or paradigm:

The concept of ‘number’ is essentially based on an analogy; i.e. it reaches as far as the analogy with the arithmetic of cardinal numbers reaches, which just happens to be our model. (Waismann 2003, 159)

Armed with the notions of pluralism, family resemblance and dominant models, it becomes easier to understand our reluctance to accept an algorithm that would solve the equation 1^x = 2. It is not as if this algorithm would as such be impossible; still,

this would be a very peculiar algorithm, entirely different from everything called ‘numerical calculation’ or ‘arithmetic’ in other contexts. Here, certain fundamental laws of our arithmetic would lose their validity; a number in this calculus would not become larger, e.g. through the addition of an ordinary number, etc. – but none of this would in the end be an obstacle to forming such a calculus. Of course, it would be something completely isolated, a foreign body in mathematics, as it were, without any connection with the other parts of arithmetic, and therefore it seems to us so unnatural to conceive of such a system as an extension, as a continuation of our realm of numbers (Waismann 2003, 159).

And because of its unlikeness to anything that we currently call number, we resist to consider such a calculus a numerical calculus; the only mistake is, Wittgenstein notes, that we ‘express this fact somewhat unclearly’ by claiming that ‘the sphere of numbers does not admit an extension in this direction; there are no such numbers’ (ibid.). Still, the main reason for not accepting such a calculus has nothing to do with the metaphysical nature of numbers but with the fact that it would be too far removed from our current paradigm of numbers because it would lack those features which we deem ‘essential’ (probably due to their utility and applicability outside pure mathematics).

4.2.2 Pluralism against essentialist thinking

Which lessons can we draw from Wittgenstein’s examination of Frege’s view of numbers? What looks like a metaphysical ‘truth’ about the nature of numbers is nothing but a projection of the model of numbers we adopt. Our model, of course, doesn’t have this special role for no reason; still, it remains one of many concepts of NUMBER that we have or could create. Conceptual pluralism comes to view when we call to mind just how diverse things that we call by the same word are. Yet, they still share a formal kinship, with certain features becoming more prominent and others fading into background – the reason why we use the same word for them all.

Philosophical thinking goes against pluralism in its quest for essences, its search for necessary and sufficient conditions, and in its ‘craving for generality’. Wittgenstein’s grammatical method debunks the idea of ‘essential features’; they are something we want a given concept to be (or better: how we want a word to be used) rather than something that we go out to discover. By stating what a number must be or what it cannot be – by making a statement about essences– a philosopher lays down a rule for how to use the word number. For example, an ‘essential feature’ of numbers is that a number cannot be larger than itself. Wittgenstein’s method shows that as a result of adopting a certain model, we are not prepared to call this thing a number because this would-be NUMBER concept would be too far removed from other accepted number concepts. However, if such a prospective concept of NUMBER would come to share more features with those things we are happy to call numbers (say with imaginary numbers which once themselves had this candidate status), then maybe its status would also change and our reasons to accept it would outweigh our reasons to reject it.

5 Pluralist conceptual engineering

In this section I argue that the approach to conceptual engineering that endorses pluralist semantics and Wittgensteinian methodology is better placed to respond to the trivialisation and implementation challenges than the received view.

5.1 Pluralism dissolves Strawson’s challenge

We have seen above that conceptual engineering in its standard form falls prey to Strawson’s challenge and thus faces the problem of topic discontinuity. One notable response to the issue of topic discontinuity is given by Cappelen (2018), who argues that the meaning change need not entail the topic change provided topics are individuated coarsely. The argument that Cappelen gives in support of individuating topics coarsely appeals to the data about samesaying: ‘if samesaying is possible despite differences in extension, then so is ‘talking about the same topic’. Sameness of topic goes hand in hand with samesaying’ (Cappelen 2018, 108). Cappelen interprets the data so that samesaying is indeed possible despite the change in a semantic value. He takes context-sensitive expressions (cold, expensive, happy) as an example, claiming that one can felicitously report that speakers A and B said the same thing (e.g. that a house is not expen- sive) even when they assign different semantic values (intension/extension) to expensive in different contexts. Although Cappelen (2018) pitches this view of samesaying as ‘the only game in town’ there are convincing arguments out there in favour of individuating samesaying and topics more finely so that they in- stead supervene on the sameness of a contextually determined semantic value of an expression (e.g. Travis 2006; Knoll 2020).

Presently, I am not so much concerned with adjudicating between these positions, as I wish to point out that the brand of pluralism advocated here can easily accommodate both notions of samesaying. On this approach, the phenomenon of same-saying and thus of topics may be understood broadly or narrowly, depending on whether we associate the notion of semantic value with linguistic meaning or with (literal) speaker meaning, where speaker meaning tracks what the speaker intends to say in a given context.²⁰ Topic understood broadly (TOPIC_broad) is a general topic associated with the broad denotation of a word, what the word qua type is about. TOPIC_broad may then become refined and sharpened (‘revised’) in different ways depending on an occasion (without being replaced). We can also think of topics narrowly (TOPIC_narrow) so that a word can be (literally) used to talk about a family of related TOPICS_narrow in different contexts.

Endorsing the distinction between TOPIC_broad and TOPIC_narrow has interesting ramifications for the idea of ‘changing the subject’ that underlies Strawson’s challenge to conceptual engineering..²¹ For, as argued above, it is part and parcel of ordinary conversational practices that a TOPIC_narrow may change depending on a context whilst at the same time remaining in agreement with the TOPIC_broad (as its possible refinement). By accepting my brand of pluralism we forgo the concern that every possible divergence of TOPIC_narrow (corresponding to speaker meaning) from TOPIC_broad (corresponding to standing meaning) amounts to ‘changing the subject’ and becoming irrelevant. Pluralism further eschews the idea that the process of meaning revision characterising conceptual engineering must necessarily consist in replacing some supposedly unique broad topic associated with a word by another. All the while, speakers routinely implement standing meaning ‘revisions’ by performing contextually appropriate enrichments of it. In this way, the implementation issue in its classical form (i.e. as a matter of implementing content replacement) is dissolved without thereby triggering trivialisation.²²

5.2 Pluralism and philosophical problem solving

How does the pluralist conceptual engineer solve philosophical problems? Drawing on Wittgenstein’s methodology, the first step in dissolving a philosophical (i.e. conceptual) problem is to recognise and endorse pluralism as a correct semantics.²³ On this approach, asking a philosophical question is often a sign of forgetting that a word is associated with a family of related concepts.

Take again the concept TOPIC and the problem of topic discontinuity that arises for conceptual engineering as a methodology that promotes meaning change. The problem can be trivially resolved by stipulating that ‘sameness of topic doesn’t track sameness of extensions and intensions’ (Cappelen 2018, 108). There are several issues with Cappelen’s solution, i.e. that TOPIC amounts to (or should amount to) TOPIC_broad. First, no alternative semantic notion has been offered as a ground for the sameness of topics, giving rise to the objection that the only remaining sameness is the sameness of form (homonymy) (see Knoll 2020; Sundell 2020).²⁴ Second, by separating topic from meaning, the motivation behind the original concern is simply put aside (see Jackson on ‘belief’). Third, a more general issue is that stipulations may be difficult to implement widely.

On the pluralist approach, by recognising that topic need not exclusively express TOPIC_broad or TOPIC_narrow we accept that meanings and topics could fluctuate without creating discontinuity, but they can also remain fixed through the fluctuation. By seeing that a topic may be something that a speaker talks about in a given context, but also something that a word as such may be about, we overcome the issue of the imminent discontinuity whilst also retaining the possibility of meaning change and meaning preservation. As pluralists, we ‘call to mind’ that sometimes we use topic to talk about what a word is about, sometimes what the speaker talks about by using the word.

Depending on our purpose, we may wish highlight certain properties of topics and ignore the others (e.g. invariance matters for sciences, context-dependence for communication and action). Thus, a pluralist is free to stipulate that, for a particular purpose, a concept is best identified with one of its enrichments.²⁵ The important thing, as Wittgenstein reminds us, is not to confuse our decision to highlight certain features (e.g. invariance) that may be more dominant in a particular concept (TOPIC_broad) for the discovery of a hidden essence (maintaining, for instance, that topics are always preserved through contextual variations in meaning). Rather, by doing this, we make a decision to treat a certain member of the conceptual family (a particular enrichment) as our dominant model. And like any decision, the decision to introduce or change the dominant conceptual model may not be very easy to implement widely. Justifying this decision by restricting its application to a particular domain for a particular purpose is likely to make the implementation less of an issue. Therefore, recognising stipulative interventions for what they are, a healthy ‘division of labour’ among the members of the conceptual family, and emphasising and endorsing purpose-relativity are all effective pluralist strategies that are likely to increase the chances of a successful engineering intervention.

5.3 Other brands of conceptual pluralism

David Chalmers and Jennifer Nado have both endorsed and defended a pluralist approach to conceptual engineering in their recent publications (Chalmers 2011, 2020; Nado 2021). Just like the current proposal, they seek to connect the multiplicity of concepts (associated with a word) with the multiplicity of roles or purposes a word can be used for. Still, there are some differences between all three accounts that I wish to briefly highlight.

5.3.1 Nado’s ‘multiple successor’ pluralism

In her recent paper, Jennifer Nado points out that in many cases where we look to improve a given concept, rather than replacing it with a single successor ‘we might instead replace a suboptimal concept with multiple successors’ (Nado 2021, 1). The label ‘pluralism’ here denotes the fact that we replace a suboptimal concept F with multiple successor concept {F … F_n}. Nado’s argument for ‘multiple successors’ rests on following assumptions:

1. Multiple functionality of a pre-theoretical concept: ‘many of our ordinary pre-engineering concepts are ‘multitaskers’, playing multiple roles or serving multiple functions’ (2)

2. Multi-functionality is deficiency: the fact that F serves many pur- poses is, in fact, its weakness.

3. One concept, one role: ‘our purposes [would be] better served by a plurality of concepts, each custom-designed to best fill one of the original concept’s roles’ (3)

The conclusion is that we ought to conceptually engineer a pre-theoretical concept serving many different purposes ‘in non-optimal fashion’ so that the result is a set of custom designed, technical successors each serving one particular, designated role. Nado then argues that corresponding to a number of roles that our pre-theoretical concept of KNOWLEDGE serves – i.e. ‘to flag approved sources of testimony, to signal that one may close inquiry, to regulate permissible assertion, to regulate permissible action, and to predict and explain the behavior and mental states of our fellows’ (Nado 2021, 11) – we should aim to design custom made concepts KNOW_act, KNOW_ast, KNOW_exp, where each would display a different sort of sensitivity (subject-sensitivity, stake-sensitivity, and invariance, respectively).

Nado’s brand of pluralism rests on the assumption that before a conceptual engineer has done her job, there is a single concept KNOWLEDGE that (sub-optimally) plays a number of different roles as indicated above. She points out that epistemologists disagree whether knowledge is sensitive to an attributer or to a subject, or perhaps not sensitive to either of these. Their disagreements may be resolved by carving knowledge into several knowledge-concepts, each of which serves a different role and happens to differ in terms of sensitivity. Nado’s pluralism thus promotes the received view of conceptual engineering insofar as a conceptual engineer looks to replace an existing concept with multiple successors. By contrast, following Wittgenstein, my brand of pluralist conceptual engineering advocates revision by ‘calling to mind’ rather than revision by replacement. The first thing we call to mind is that there is no unique (pre-theoretical) KNOWLEDGE concept but many. Thus, rather than seeking to manufacture conceptual pluralism from the alleged pre-theoretical monism, we remind ourselves that pluralism’s already there, i.e. that we use the word know in different ways for different purposes. Just like not every number concept shares the same properties with cardinal numbers, so not every knowledge concept need to be subject-sensitive or attributor-sensitive.

The result Wittgenstein’s pluralism and Nado’s pluralism arrive at is similar, only, on the former approach, what we replace is merely our essentialist philosophical misconception that pulls us towards conceptual monism. To be sure, specialised technical concepts that fulfil particular purposes may still be explicitly stipulated when useful (Chomsky’s I-LANGUAGE, Haslanger’s WOMAN) but there is no general requirement to do so because multifunctionality is here not perceived as deficiency.²⁶

5.3.2 Chalmers’ pluralism and de novo CE

David Chalmers champions pluralism as a model of conceptual engineering in Chalmers (2011, 2020). The brand of pluralism I advocate seems much closer to Chalmers’ variant than to Nado’s. According to Chalmers (2011), lack of awareness of pluralism when conducting a philosophical inquiry may lead to verbal disputes.²⁷ And, so, acknowledging pluralism is also the key moment in philosophical problem solving in Chalmers’ framework as it is here.

In contrast to Nado’s approach, the general spirit of Chalmers’ pluralism is augmentation instead of replacement:

As a concept pluralist, I often want to ask, why not have both concepts? Even, say, for the case of Haslanger’s analysis of woman. Even if you think that that the old biologically-based concept of woman was an unjust concept for various social purposes, somebody might still think that nonetheless it’s a useful concept to have around, say for certain medical purposes. Just because a concept is useless for some roles, doesn’t mean it’s useless for all roles. (Chalmers 2020, 14–15)

According to Chalmers, a pluralist conceptual engineer seeks to add a new (technical) concept (WOMAN_social) fulfilling a new role (addressing social injustice) to an already existing conceptual family (including WOMAN_bio) rather than fully replace it. Chalmers calls the method of designing new concepts for new roles ‘de novo conceptual engineering’, and finds it to be more important than conceptual re-engineering whose the aim is to ‘fix or replace the old concept so the old concept is no longer around’ (Chalmers 2020, 14).²⁸

Chalmers and Clark’s analysis of BELIEF is another example of de novo conceptual engineering that presupposes conceptual pluralism. In this case, our ordinary concept of BELIEF is applied to novel cases because of them sharing ‘the most important roles’ associated with things we call beliefs. Otto who uses his notebook to memorise certain facts can be described as ‘e-believing’ those facts. Moreover, ‘these extended cases of beliefs [are] literally beliefs. So the word belief already covers them … ’ (Chalmers 2020, 8). A narrower technical concept of E-BELIEF that can be reserved for these extended cases of belief that are not ‘in the head’ is still just another member of the conceptual family associated with the word belief.²⁹

The question remains, however, whether this de novo methodology Chalmers finds so important for conceptual engineering is in the end compatible with Wittgenstein’s grammatical methods whose outlook is largely restorative? In other words, can the particular brand of pluralist conceptual engineering I’ve set myself to defend in this paper accommodate conceptual novelty and open- endedness of proposed revisions?³⁰

5.4 Addressing the open-endedness objection

To see that the answer to this question is clearly ‘yes’, I think there are two key points to bear in mind. The first point concerns the version of pluralist semantics presented in §3.2. To postulate a rich standing semantics is one way to account for the phenomenon of a word’s having the plurality of interpretations on different occasions. A relative stability and conventionality of many of those interpretations militates against the approach on which they are supposed to be entirely ad hoc and generated on the fly. Still, as I pointed out above, this doesn’t prevent lexical innovation or creativity, as new ways/senses are added to the conceptual family and old ones become obsolete.³¹

The second key thing is to understand properly what, according to the pluralist conceptual engineer, we ought to call to mind when a philosophical problem arises. First, we learn from Wittgenstein we ought to recall pluralism with respect to existing concepts for which the same word (e.g. woman) is used. Second, we ought to recall that the reason why we use the same name for these concepts rests on a ‘formal kinship’ or certain ‘family resemblances’ between these cases. Third, we ought to recall that we are ‘looking through the frame’ of our accepted paradigm. Taken together, these principles facilitate natural extensions and additions to a conceptual family, provided a new concept we aim to introduce shares enough similarity with the current ‘head’ of the family (i.e with our dominant ‘model’). Which family members are deemed to be most important (hence, whose features will matter to accepting a proposed extension) is, on this approach, not something that is set in stone; our dominant model can shift (organically or by stipulation) depending on other external things (e.g. empirical discoveries, social emancipation, change of interests, laws and so forth). In some cases, introducing a new way into the conceptual family will only refine the extant conceptual cover (NUCLEAR WAR, VIDEO GAMES) and in others it may change the original denotation of a term (WOMAN).

To better understand how the conceptual innovation is still possible in the current framework take as an example Haslanger’s ameliorative analysis of WOMAN. The way I see it, the key aim of Haslanger’s stipulative intervention is to highlight an alternative, socially based model for being a woman, instead of the one based on female sex. According to Haslanger (2000), social subordination is the pervasive feature that more accurately characterises what it means to be a woman than a person’s biological sex, effectively detaching gender from sex. As a result of hers and similar interventions, WOMAN_social may become a more dominant model (in ‘the fight against injustice’) than WOMAN_bio (although, the latter remains in the family).

This shift of a dominant model may further have a (positive) effect on accepting other prospective concept candidates which share enough features with the new model. A shift away from the biologically based paradigm to WOMAN_social as the dominant model of womanhood may open up the door to some other, not previously recognised, candidate concepts such as WOMAN_trans. By accepting WOMAN_trans as a brand new member of the conceptual family, the original extension associated primarily with WOMAN_bio as the dominant model changes, now including certain members from its complement set.³²

6 Conclusion

Following Wittgenstein and other contemporary authors, in this paper I have defended a brand of pluralism that associates words with conceptual families, and appeals to this notion in the course of philosophical problem solving. I have argued that certain problems faced by the received view of conceptual engineering can be more easily overcome if we adopt a pluralist perspective. The implementation problem doesn’t arise because implementing content revisions is part of everyday information exchange, and no requirement is made that some concepts be removed. The trivialisation problem doesn’t arise because we don’t need to assume that philosophical problem solving amounts to ‘improvement by replacement’, either of standing meaning by speaker meaning (Pinder) or of a single concept by multiple successors (Nado). Furthermore, I’ve shown that the current approach can deal with the problem of topic discontinuity, whilst avoiding the threat of trivialisation, because it can easily accommodate both coarse-grained and fine-grained topics. Finally, I’ve argued that my variant of pluralism is compatible with de novo conceptual engineering insofar as it allows that the ‘model’ we currently associate with a word may shift overtime thus creating an opportunity for new candidate members to join the conceptual family.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Deutsch (2020a) distinguishes between two variants of conceptual engineering: stipulative revision and stipulative introduction/addition. He argues that the former is impossible to implement whilst the latter is ‘deeply uninteresting’.

2 On the speaker meaning picture no requirement is made that the semantic (standing) meaning also be revised in the course of engineering concepts; it suffices that (enough) speakers adopt new meanings for old terms.

3 I find it rather peculiar that Wittgenstein’s philosophical method very seldom appears as an example in the literature on conceptual engineering despite its clear relevance for the subject. My hope is to remedy this omission.

4 Although see Deutsch (2020b) for a different take on Haslanger’s analysis.

5 Judging by his reference to ‘the rules of language’ Carnap seems to have in mind semantic (standing) meaning rather than speaker meaning.

6 Cappelen (2018) argues against the supervenience of topic change on meaning change. I discuss this view below.

7 My present argument doesn’t turn on whether intentionalism is a correct metasemantics for speaker meaning. For a non-intentionalist approach see Lewis (2020a, 2020bb).

8 According to Deutsch (2020a) it is not so much metasemantic externalism that stands in a way of implementing conceptual revisions since he finds externalism to be compatible with the semantic change. The implementation problem is rather to do with ‘how this change can be intentionally wrought’ (Deutsch 2020a, 3952).

9 Considering a multitude of examples that have been discussed in the literature, pragmatic enrichment seems to be a pervasive phenomenon (see Travis 1985, 2008 for a collection of examples with different word classes).

10 In a couple of recent papers (Carston 2019, 2021) Robyn Carston argues in favour of a similar view which she classifies as ‘radical polysemy’ (Frisson and Pickering 2001). Pragmatically derived, yet conventionalised senses form a family or the so called ‘polysemy complex’. They are stored in the ‘C-lexicon’ (or the communication lexicon) which is distinct from the narrow linguistic L-lexicon where only the word’s root is stored.

11 A cover C of the set A is the collection or family of subsets of A whose union is equal to A. For the application of covers in natural language semantics see Aloni et al. (2001)

12 This example is featured in Yalcin (2018) and Haslanger (2020).

13 As this point is also of importance for conceptual engineering, I return to it in §5.4

14 ‘[The] linguistic semantics of the utterance, that is, the meaning encoded in the linguistic expressions used, the relatively stable meanings in a linguistic system, meanings which are widely shared across a community of users of the system, underdetermines the proposition expressed (what is said)’ (Carston 2002, 19–20.).

15 For a comprehensive overview of a range of approaches and assessment of their viability see Borg (2010) and Recanati (2004).

16 Vicente (2018) and Carston (2016) discuss different ways of cashing out semantic under- specification by modelling meanings as ‘thin’ or ‘rich’. For a recent defence of the rich meaning approach see Hogeweg and Vicente (2020).

17 The distinction captures the contrast between ‘primary pragmatic processes’ and ‘secondary pragmatic processes’ (Recanati 2004)

18 I turn to this concern in §5.4.

19 Number is not anything physical, but nor is it anything subjective, an idea’ (Frege, The Foundations of Arithmetic §45).

20 The distinction corresponds to two notions of ‘saying’, i.e., in locutionary and illocutionary sense. Austin (1975)

21 I take subject matters and topics to be interchangeable

22 Another form of this issue that persists in the current framework concerns the switch of the dominant conceptual model. See next section.

23 See also Chalmers (2011) and discussion of conceptual pluralism in Cappelen (2018).

24 Sundell (2020) points out that not providing an answer to the question ‘But if identity of intension is not playing that role [explaining the continuity of inquiry], then what is?’ renders Cappelen’s account incomplete (Sundell 2020, 590). It is open for Cappelen to argue that the feature that remains invariant and underpins the sameness of topic is Kaplanian character.

25 For instance, Chomsky stipulates that, for the purposes of a naturalistic inquiry, language amounts to I-language.

26 In fact, according to some studies the opposite is true. Namely, using ‘ambiguous signalling’ and contextual information to communicate is often less costly and more effective than using disambiguated language (see Santana 2014; O’Connor 2015).

27 As Cappelen (2018) puts it: ‘because we have not been aware of conceptual pluralism and haven’t engaged in the kind of conceptual engineering that [Chalmers] advocates, very many philosophical debates have been pointless wastes of time. They have been exercises in what [Chalmers] calls ‘verbal disputes’ (Cappelen 2018, 23).

28 For a concept pluralist, de novo conceptual engineering is often better than reengineering. (Chalmers 2020, 14)

29 Those individuals who take the feature of being ‘in the head’ as a defining feature of belief will perceive this intervention as a proposal to broaden the extension of BELIEF but others (like Chalmers and Clark) won’t.

30 Thanks to an anonymous reviewer of this journal for pressing me to clarify this further.

31 See especially the discussion in Carston (2019) on lexical innovation and the interplay between pragmatics where new senses are taken to originate and their eventual semantic conventionalisation.

32 Some argue that the membership in WOMAN should be predominantly based on the so called ‘self-ID’ method. For critical discussion see Stock (2021).