MEANING UNDER THE THREAT OF PARADOX ON TWO FRONTS

The paradox threatening the understanding of linguistic meaning in terms of ‘family resemblance’ refers to the open character of meaning that derives from it, or what has been called the ‘under-determination paradox’. If all that is needed to belong to the extension of a concept is some kind of resemblance or overlapping of arbitrary features with any of its already existing members (with possibly new members resembling the immediately #0#

preceding features introduced, and so forth), then ultimately anything could end up belonging to it. 1 So, if the family resemblance model was supposed to free us from a too rigid and fixed conception of meaning, now it appears to allow for the dilution of meaning altogether.
Since the beginning of the debate, there has also been an issue concerning the generality of the family resemblance claim: whether Wittgenstein considered it to apply to some specific kind of concepts only (keeping talk of common features for others), or whether it was intended as a general claim. Opinions diverge 2 regarding the textual evidence and whether it allows one thing or the other to be attributed to Wittgenstein. The way this question is settled will, of course, affect the extent of the threat upon the concept of meaning we see the paradox has.
Wittgenstein first introduced the metaphor of family resemblance in The Blue Book (1958, p. 17), expounding on it later in his Philosophical Investigations (1953, p. 65). The concept was intended to question the traditional account according to which the meaning of our words is dependent upon certain necessary and sufficient conditions, and to depict it instead as some 'crisscrossing of similarities' between the extension members of our terms. However, the reason why speaking of necessary and sufficient conditions did not fit well with Wittgenstein's understanding of meaning is best grasped, in my opinion, from the perspective of his 'Rule-Following Considerations', since the claim that no rule is given in advance for the use of a concept is tantamount to the idea that we cannot pin meaning down to a set of fixed necessary and sufficient conditions. Wittgenstein's picture of 'Rules as Rails ' (1953, §218, §219) attempted to make clear precisely that there is no possible understanding of meaning that could predict how we might have to adapt our concepts in light of an unpredictable reality, nor a pre-given reality demanding a given sort of classification in advance. Meaning is not a once-and-for-all concluded issue but a continuously reassessed one in light of new experiences. As anti-realist authors argue 3 , it requires 1 2 3 In what follows I will take as base line of my perspective the argumentation line introduced by Dummett (1978) and specially developed by Wright in several texts on the matter (1984,2001,2007). Although that doesn't mean that I would underwrite all their arguments, but rather, that I support in general terms the approach and will often be referring to it while adding some insights of my own.
continuous human evaluation to determine whether certain new cases are to count as members of a conceptual extension or not -or to put it another way, 'whether they sufficiently resemble what we have so far considered as cases of such' -and, similarly, that there are no fixed conditions to determine this. Therefore, how far or in what direction we might proceed is an open issue here too. But, can we assimilate both questions?
A paradox on two fronts Actually, I believe that the Rule-Following Paradox (RFP), elaborated by Kripke (1982), points to the same under-determination problem threatening the idea of family resemblance but from a different perspective. If anything could pertain to the extension of a concept from the one side, from the other the concept or the rule that guides its use can be made to cohere with anything. So, here we have a paradox from two sides. Now, if this is right, and if the RFP is taken to be a general one (or we should refute the paradox as a whole), why is it that many authors deny the Resemblance Paradox (RP) a parallel generality?
Consider claims 1, 2 and 3 below. Claims 1 (RFP) and 2 are obviously reversible. So, have I incurred any non-allowed assumption in asserting that therefore, since 3 (RP) is a case of 2, then the RFP and RP are two sides of the same paradox?
(1) Any course of action, or sequence of applications, can be made to cohere with the rule. (2) The rule, or concept, can be made to cohere with any course of action or sequence of applications. (3) The family of resemblances of a concept can end up including anything. The trouble appears to stem from the introduction of 'resemblances' as setting the standard of what can be included under a concept and then reading the 'coherence with any course of action' in terms of possible 'resemblances with anything' (any new potential instance considered or considerable).
We can make the transition from 2 to 3 plainer by reformulating 3 into 3*: (3)* The rule or concept can be made to cohere with any course of action, because resemblances can be found with any further moves that might be made. So, has some objectionable modification been introduced through this move? The perspectives are, first of all, different. The reasons why 'the rule might expand to any course of action' in 1, are left unanalysed; it is as though we were thinking in terms of possible descriptive rules, rules that can be reconstructed differently or be seen as having been understood differently by the speaker all the way through each time a new move is made, whatever that is. When we talk about resemblances, though, we are moving at the level of the members of the extension, or referential level and, further, in terms of the 'likeness' they bear of each other; as though we would have no problem in understanding the concept or rule, or would take it to be fixed and then try to see how well new candidates fulfil it through the process of comparing them 'in likeness' with previous members of the extension. That is, in 1 it is the rule that would not be clear but would need to be determined through, or at least compatible with, the ongoing sequence of moves; here, we get the impression that it would be the other way around. But the difference is only apparent, since both aspects cannot be separated from each other. We cannot consider the rule as fixed in the second case, precisely because depending on which candidates are seen as fit to be included each time will be understood one way or another (and even then, not once-and-for-all); and that is precisely what is said by 1. On the other hand, the decision on which candidates are to be included is, for its part, dependent on the various possible ways of understanding the rule. However, we might insist on the point about the legitimacy of new moves being determined specifically by resemblance, which some might argue need not be read into the RFP.
The RFP differs from this point of view insofar as the various moves that might and can be made to cohere with the rule need to have nothing to do with resemblance but rather with differently motivated decisions, as in the case of mathematics. The members of a mathematical sequence cannot be properly seen as 'resembling' each other. But is this so? If we take a look at some of Kripke's (1982, p. 58) examples to start with, such as the colour 'grue', it would appear that if, after a series of greens, the speaker is inclined also to include blues and further yellowish things (I am modifying the example for my purposes), the point might be put in terms of 'what similarities' she takes to be relevant. She may have seen a similarity in them all in the sense that they resemble 'the colours of a famous folk ceramic' or some other possibility of the sort (the different instances resembling each other or others already included), 4 since from this perspective they could be claimed to 'resemble' each other if not in a strictly perceptual sense then through them having some traceable common connection. But even when talking about mathematical sequences, it can be claimed that different moves 'resemble' each other in the sense that some likeness can be discovered in them all (so far) owing to some possible compatible function, be that what it may. We could consider the numbers in a sequence and find several possible functions that could make them alike. That much they would have in common. Remember that saying that there are no necessary and sufficient conditions goes along with the idea that there is no once-and-for-all predetermined rule; and precisely for that reason, seen from the other side the 'likeness' or connections that can be found between members of the extension and new ones is not defined either and allows for different reconstructions. Furthermore, two instances might be alike in expressing a (+2) relation while others express a (×4) etc., and out of these different 'likenesses' we could reconstruct one possible complex rule among others. If we insist that the rule is a determinate one, then the same would go for the likeness. But if we claim that we cannot commit ourselves to there being a fixed rule, then the matter of likeness remains open too.
What appears to be hindering the identification of both problems is that when we talk of 'family resemblance', even knowing that the expression is metaphorical we tend to visualise the problem on a perceptual-like level, registering some sort of undetermined likeness between already existing cases and new ones. Therefore, in expanding the rule it all appears to be a matter of finding any such similarities. But the idea that in our rule we should include similar and apparently dissimilar instances, such as from oranges to apples as could potentially be the case (the fact that up until now we have only encountered apples does not mean that the rule might not apply to oranges too), appears to put us in a different place from the problem of resemblance. But that is only because we are expecting the similarities to follow the metaphor too literally while the user might be moving at a much more abstract level in which aspects beyond form, colour or taste are considered. The resemblance might indeed be found to concern such aspects or might lie, for example, in 'playing a similar pragmatic role in our nutrition' or 'provoking the same kind of reaction' (being disgusting, for example), and so on. On the other hand, resemblances that allow the speaker to include new members in the extension of the concepts, whatever and how varied these are, will, from the reconstructive perspective of a hearer, be turned into whatever number of rules can make sense of the whole sequence so far.
Thus, as far as it goes, I see no reason to resist the identification of both paradoxes as being the same one from two perspectives; and if generality should be attributable to one, the same, it seems to me, should go for the other.

The Paradox Again
So far, we have not made the prospects of a satisfactory conception of meaning better exactly but have simply argued that the threat that was seen to come from two sides is actually the same threat. A threat, nevertheless, though. But how bad is it, and how corrosive are the arguments in genuinely undermining our linguistic confidence?
As I see it, the main issue with the rule-following paradox is not most importantly, as Kripke (1982, pp. 96-97) puts it, that we should not be able to appeal to any fact of the matter, either in our mind or from past behaviour, that determines which rule it is that we are following. Rather, it is that there are no facts of the matter about it being a determinate rule because there cannot be any once-and-for-all rules fixed in advance, either for the individual or the community. There would be nothing like linguistic normativity in that sense. In this point I go along with Wright's (1984) interpretation, although I will not be appealing to the question of intentionality that is central to Wright's paper 5 . So, going back to our problem, we can distinguish various claims made by the RFP: (1) the impossibility of predicting decisions about the future application of a term; and (2) the idea that we cannot say what rule we are following and, therefore, that there is no specific meaning we can be said to attach to our terms. The question is whether the step that brings us from (1) to (2) is to be seen as compelling -whether we want to say a) that because it is impossible for us to predict all future applications, we cannot say what rule we are following nor attach any meaning to our words; or b) that we could not even say, for independent reasons, what rule we have been following or what we mean by the term, diluting any possible meaning contour. If we mean a), I would say that this is partially right. However, it should be given a qualified reading and surely not one that allows us to assert the second part of it, i.e. that for that reason there would be no meaning we can be said to have attached to our terms, since there is still room for an evolving and open-ended conception of meaning to which I will come in a moment. But if we mean b), that it is not just because of differing evolving possibilities that we cannot be said to know what we have been doing up to now (since we could not pin down normativity itself to any kind of fact, just as we cannot in reality -the Hume's problem of induction, causality etc. as Kripke argues -not in our mind, etc.), nor because of any specific meaning we have been implementing, then the claim is questionable, not in the sense that there should in our mental life or behaviour be the normativity that Kripke denies but in the sense that we nevertheless know what we have been doing.
The first claim above, (1), is compatible with the following situation (again modifying similar examples 6 ): I have been walking through the street lights at green and not at red in a finite set of cases, but one day I stop, puzzled and wondering when suddenly the street lights are purplish rather than red, not knowing whether to cross the street or not. Does it mean that I did not know what I was doing before? The authorities then realise that these new intelligent street lights vary their colour (as in a programme that appears to be affected by the pollution level in the street), now projecting a rather purplish light at certain times of the day in some parts of the city. Instead of changing the whole system, they might adapt the rule to make us pedestrians stop at purplish lights too. Does that mean that I had no guidelines before or that my rule could just as well have been 'red and purplish when pollution is over 50%', and that I could not tell which since I could not have said that such a progression could not be? We would rather say in the sense of 1) that my rule has evolved and adapted in light of an unforeseen reality. Insisting on the question, 'But were you then following the red/green rule or the red-purplish/green rule before (you could have)?' is in no way unsettling, unless there was some external standard already possessed by someone that could have specified in advance that it was the red-purplish one I was already supposed to be following but I had simply not gone that far in my application experience.
We can agree that there is nothing like a once-and-for-all account of meaning for that reason, but that does not mean that anything goes either. It is the further idea, that anything can be made to cohere with the rule, that should be reconsidered. It is the same with the idea that there could be resemblances all the way through. That a similar issue might be raised with blue, pink, etc. street lights and that in all cases we might have decided favourably to recognise them as members (to be included as those by which pedestrians are to stop too), does not mean that our rule was in a strict sense already any of them but just that it might have evolved into any of them 'if we should have so decided'. Virtuality is far from being reality for rules too. Furthermore, the rule could never have evolved into 'going through green' since green was explicitly excluded as 'Not-Red', implying fixing a necessary and sufficient condition for exclusion. 7 That there should be vague cases that require further decisions (whether something really green, for example) does not undermine there being clear lines about standard prototype ones. Finally, should life take a perverse turn and we come to reverse the rule and allow pedestrians to proceed through red (which would require fixing green as the opposite), we would need to start talking about following a new (inverse) rule. This is because clearly if right and wrong mingle, then no talk of the same rule makes sense anymore. But it would be absurd to say that the rule I followed was, 'going through green or red' as well as 'going through green only'.
So, again, in the sense of a) neither the individual nor the community can determine which rule it is, seen from the perspective of upcoming futures that might turn what we now call 'a', into any number of 'a 1 ', 'a 2 ', 'a 3 ', …, 'a n ' (different in themselves, since allowing and forbidding different instances). But whichever rule appears to be displayed in the future and then again in the thereafter following the future, it must conform with the set of cases that have been accepted up until now and be incompatible with those that have been excluded as 'not-a' 8 ; which is actually already quite significant since it amounts to excluding from the rule to be (if you wish, or better to say 'become') a good amount of possibilities, call them 'a -1 ', 'a -2 ', 'a -3', …,'a -n '. I would expect my training situation to have made me go through not just positive cases of inclusion but also the most relevant ones to be excluded. Nor should these be arbitrary, but rather their exclusion made dependent upon specific aspects; that is, we should be given reasons for it, ultimately pinned down to some salient features that are supposed to be relevant.
Surely, as Kripke stresses, the point is supposed to be that whatever reasons we give they should be given in linguistic terms, and for each of these terms the problem again arises of what exactly is the meaning or rule to which we are supposed to be referring. Being drawn ultimately to a level where no language is available, we would simply deal just with performance. But we might also argue that at basic levels we pin terms down to basic, unidimensional, easily recognisable properties with clear opposing contraries 'hot/not hot (cold)', 'full/not full (empty)' etc. 9 For such concepts, up to a certain point, it would be easier to determine whether the corresponding property is lacked or possessed (vagueness aside). But if this is right, and if such characteristics are components of complex concepts, then excluded cases can be justified on the basis of the presence or absence of those and we can be made aware of it.
Therefore, I can consider myself safe to go on matching standardly similar cases to those in my past application history, leaving aside others banned in already experienced situations. Thereby relying on our basic capacity to distinguish cases significantly reiterating marked features in our memory of those already had, 10 from not matching ones. 11 Since, should any apparently non-significant dissimilarities among them have knowingly been relevant or confusing in advance, I would have been provided some such 8 Compare with the discussion of Williamson's position in Ramirez (2020, pp. 16-20). 9 Ibidem. 10 Such standard cases do not pose us for a decision whether to implement our pattern further, as will be the case by more diverging or novel ones, since such a decision is in a sense already made and is now a matter of course.
11 Compare with the idea of a pattern in Ramírez (2020, p. 10, and the previous discussion in pp. 8-9). reason for their exclusion (drawn down to non-linguistically cognitively apprehensible ones, if necessary). I would, namely, have been advised of it soon enough in my training. Had decisions in this regard not already been made by my community, it would be meaningless to say that because such cases might be added or refused in a future time, t 2, my rule is already a different one at t 1 .
Therefore, I can consider myself safe if I go on in matching standardly similar cases to those in my past application history, leaving aside others banned in already had situations. My rule more than a rule, since no such fact is to be found, resides rather in this more basic capacity to distinguish matching from non-matching ones. Cases, that is, which match the reiterated marked features in our memory (as in AI recognition standards) of those already had. Since, should any apparently non-significant dissimilarities among them have knowingly been relevant or confusing in advance, I would have been provided some such reasons for exclusion (drawn down to non-linguistically cognitively apprehensible ones, if necessary) and been advised of it soon enough in my training. But, of course, if decisions had not been already made in their regard by my community, it is meaningless to say that because such cases might be added or refused in a future time t2 my rule is a different one already at t1.
But if by non-standard cases this picture relies ultimately on the decisions, as I above said, made by my community (and here I side again with antirealist readings of Wittgenstein) a worry might be raised on whether the community will have to be meeting whenever any of us has a problem of non-familiar application. But the fact is, that when such problems are relevant for whichever pragmatic reason, that is precisely what we do: ask others whether there are already laid down criteria or, otherwise, try to find together some in order to fix the line one way or the other. Meanwhile, we help each other by appeal to a history of commonly recorded application. Should same sex couples start wanting to call themselves 'marriage' and others finding it a transgression of use, the matter will be solved through a legal decision to avoid further discussion. Not because both could not have been an option from the perspective of past application and considerable resemblance, but because (among other implications of the institution that go along with the term) we must lay ourselves down to communicate, based surely too on independent reasons of social relevance. This might not solve the issue for good, 12 of course, who knows whether a triple assemble of a gender mixed character will knock someday at the door wanting to sanctify their union and reclaiming the word 'marriage' for themselves. Or whether some future genetical combinatory procedure results in beings not contemplated in today's legal systems, but with a similar desire to be bind themselves through 'marriage' for the eyes and legal recognition of all. Should their union, in this or the previous case, be included as marriage on several occasions, coherence (vagueness aside) will demand to include standard prototype cases of such to be included too from now on. Otherwise, again, we will need to find exclusion reasons for the non-admitted cases, which users should be made aware of. Was the linguistic rule of 'marriage' from the beginning on to include heterosexual couples and from a given moment on heterosexual and homosexual ones and then again triples or semi-human creatures? Well, yes and no, if you wish. It simply wasn't definitively fixed one way or the other. The normativity of the rule was no self-runner, no necessity mechanism that implements itself on its own as Wittgenstein argued. From the perspective of the future it was the same one, since it is the same rule or term that has evolved, including all past cases and from a given moment on new ones. Could the user or the community have appealed to any fact of the matter to say that the rule necessarily must have excluded homosexual ones? No, the fact that it had not done so, so far, didn't mean it could not have so evolved. Did it mean that they did not know what they have so far being doing in using the word? Of course not, either. So, if the worry is, how is it that the community can embody normativity any better, if the paradox affects it too, if it need not know any better which rule it will be. The answer is, as Wright puts it, that the point here is not one about knowing, but about deciding 13 on the face of hard cases which way to go. This amount from my perspective to giving grounds for exclusion and appealing to a precedent history to solve further queries.
Is this appeal to the community to be put together with Kripke's skeptical solution? I do not think it should. First of all, maybe, because my reading might alter the problem as Kripke sees it. Second, because the point here is not that there should be nothing constraining our behaviour. There is. Not in the sense of there being any fact of the matter, that the rules constitute; in fact, at the personal level I tend to think that what takes place is something more alike, as above said, to sorting out matching and non-matching cases, without what can be considered a constraining normativity. 14 The rule is precisely what results out of the over and over enacted decisions of the community together with the resulting divide in accepted and rejected patterns whose impression in our memories traces a path. The rule could surely become as many a 1 , a 2, a 3 …a n as you wish, but, so far it cannot be said to be any of them unless we so determine, and I might even know already that some possible paths aren't my rule at all. The reason why the community agrees is no casualty here, it is because it has set the terms and will decide them further. This seems to me a good enough solution to restore meaning confidence. But a solution, maybe, to a different problem.
To sum finally up, the proposal here made to deal with the paradox, distances itself both from Kripke's solution for the reasons just stated, and, also, to some extent, from Wright's. While it agrees on the importance of community decisions, the emphasis here given to reasons for exclusions and precedent cases makes much more explicit how such decisions are made, and the role thereby played by some necessary (negative) conditions. It also situates normativity in the meta-commitment with the virtual future decisions of the linguistic community to which one belongs. Together, these added contributions might bring the problem, if they should be right, a little bit further.