Negotiating with the Paradox: Indeterminacy of Indeterminacy of Meaning?


In his highly influential paper Wittgenstein on Rules and Private language, Saul Kripke addresses a fundamental problem in philosophy of language, and more general language talk. This problem represents a deep rooted and abstract indeterminacy of meaning, and reduces all uses of rules into shots in the dark.

How is Kripke able to demonstrate this? He considers a sceptic who is unconvinced by meaning-talk. To avoid confusion Kripke elucidates just what the sceptic is sceptical about: how we determine truth of statements which attribute meaning to a person’s utterance. This type of statements such as “I meant to say plus”, and “She meant to say minus” are a fundamental part of everyday language, and have always held a crucial status in philosophy.When Kripke answers ‘125’, the sceptic is looking for a fact which determines that Kripke meant plus ( and was justified in saying ‘125’ as opposed to ‘5’) but this fact must also contain within it the explanatory rule which it is applying to.This account essentially refutes most standard forms of dispositional arguments. All of the dispositional arguments Kripke addresses seem to boil down to one main problem: The dispositions seem to assume the fact that the sceptic is looking for.

Any Hope for Dispositionalism?

I have discerned 3 main schools of dispositionalism as described by Kripke: Behavioral/rule following dispositions, experiential/qualia dispositions and introspective dispositions. They all have their merit, but none of them seem to have the strength to defeat the paradox.The behavioral dispositionalist account may be the most broad in how many ways there are of stating it, but it is also possibly the weakest. I count Kripke’s whole refutation of ‘privately following a rule’ along with his response to probable behavior dispositions as one large argument. He explains just what the sceptic does with these types of justification: He pulls them apart so that the definition of a rule contains an indefinite term in need of definition.This gives the sceptic another rule in need of justification, and another level of explanation to require. Besides following an endless rule for following a rule series, Kripke can also always argue that a disposition like this is not the fact of the matter he is looking for, but only gives a description of someone’s disposition which is contingent upon the fact of the matter, without finding it.

The qualia dispositionalist has a stronger claim. This theory adheres to the idea that there is a distinctive unique quality of experience which following a certain rule corresponds to. Kripke analyzes this in two ways: he assesses the possibility of qualia, and acknowledges both his own and Wittgenstein’s agreement with (or allowance of) the existence of such phenomena. He then postulates that if rule following was such a phenomenon, it would be comparable to getting a certain type of headache every time you add. He attacks this notion by putting it one level of abstraction above the paradox. This turns the headache into the previously addressed rule-following statements. In this way he is able to move the problem over and say “okay and what fact is the headache dependent on?”

Introspective dispositionalism takes the ideas of the previous two and mixes in introspective verbal reporting. These dispositions draw on not only what the person would have said if asked, but also what they later think they would have said when asked, and can also take into account self reports of any qualia-like phenomena. Kripke quotes Wittgenstein in claiming that there must be a difference between meaning addition when one says ‘plus’, and thinking you meant addition when you said plus. In this way introspection becomes reduced to behavior, because according to the sceptic, the person who says ‘57 plus 68 is 125’ cannot know that they meant addition any more than an outside observer.


Functional similarity, Temporal vagueness

The Kripkensteinian paradox has two caveats which I found intriguing: The similar and interchangeable nature of the functions which he hypothesizes about, and the soritical nature of distinguishing between past and present usage. I used these two aspects of the argument to arrive at a form of dispositionalism which seems stronger than the ones I have mentioned. It still falls short of Kripke’s demands, and does not invoke any principle that Kripke doesn’t at least partially consider.

In section 88 of the philosophical investigations, Wittgenstein entertains a point about exactness, and how there is no standard for exactness, and to say someone was exact or inexact is really just praise or condemnation. This can also be extended in this case: Someone who uses a function that is closer to addition will have an answer worth more praise. Kripke mentions this section as a precursor to the private language argument, but I think it speaks to Wittgenstein’s ( and possibly the sceptic’s) views about rules. This passage makes it clear that Wittgenstein had a theory about rules which were highly situational, In which there are two ends of a spectrum, but in these cases like exactness, we do not have a standard for an “exact” or “inexact” measurement.

My preferred form of dispositionalism uses all three other types of disposition, but also addresses functional similarity, and questions what it is to be an adder or to become an adder from the dispositional standpoint. Kripke addresses this, discussing a hypothetical ‘eureka’ moment in which it first ‘clicks’, and throwing it away because almost no one remembers this moment for themselves, and if we did and the memory of “grasping” adding was what we appealed to for every new addition, it is still subject to the indeterminacy in that we cannot know whether our own ‘eureka’ moment involved addition or quaddiition.This makes it so that someone who was in fact quadding their first time is not an adder.

I have a very different conception of the ‘community of adders’. We really may just be people who will answer as if we were adding in most circumstances. This is the idea that if we cannot determine between two functions which would give the same answer, our meaning can be assumed to be congruent for each. If we consider someone an adder, they will answer ‘125’ when asked for the sum of 67 and 58, and beyond that, we can make no other claim as to what function they ‘really’ meant. This is certainly adopts a sceptical assumption, but It helps build a more robust type of disposition.

Under this conception, there really is an addition function, but when an adder attempts to use it, they *may* just be accessing one of many very similar functions.This equivocation of functions is needed in order to frame part of the temporal sorites because when the sceptic assumes Kripke’s present use, It must be with the tolerance for functions which would yield the same answer for 68 plus 57, and with respect to what he considers the present.

On page 12, Kripke feels the need to explain how he is able to converse with the sceptic: “So I am supposing that the sceptic, provisionally, is not questioning my present use of the word ‘plus’; he agrees that, according to my present usage, ‘68 plus 57 denotes 125.”
He spends about a page qualifying how the sceptic assumes his present usage is just what the paradox says it can’t be : known to both of them. This means the sceptic would predict that Kripke would answer ‘125’, just like any other adder.
The temporal sorites addresses the sceptic’s assumption. Particularly, that he allows for somewhat determinate meaning for the sake of discourse. This assumption becomes very tricky when he attempts to claim the indeterminacy of past utterances.If the determinacy of present utterances is a ‘pile’(assumed/determined), then the extremely recent past (one millisecond) should be a ‘pile’ as well. If the present and the extremely recent past have this quality, it does not make sense to say that utterances from 10 minutes ago are also indeterminate without postulating a cutoff time in which they become indeterminate. If past utterances are indeed indeterminate, should it be on the sceptic himself to set a line? Does his argument allow for a certain cutoff point? No.  But it could be argued that the sceptic does not assume the determinacy of present meaning, but allows the types of assumptions about meaning he is attacking for the sake of the discourse. This is a crucial component of the sceptic’s reply, which follows the sorites series from the other end, and starts in the past, working towards indeterminate meaning in general.
Is either direction of induction more fruitful? When compared to other theories of induction, it seems as if reasoning from past examples forward makes more sense, but I think an elucidation of types of indeterminacy is important to distinguish why the present should be the base case which we work backwards from. If we now consider induction which makes any type of factual claim about the future, we reveal what I find to be the deciding factor in which direction to take the sorites: there may be different degrees of indeterminacy. Just like other factual claims, claims about meaning are more indeterminate when applied to the future than to the present. The sceptic allows us to continue on saying that we “know” Kripke meant addition, and is really wondering how we know Kripke meant addition. If we apply this to other factual claims(not about meaning), it is obvious: it happened and we observed it, etc. What about the future though? All predictions of future events have a type of indeterminacy which descriptions of the past and present do not. This is easily demonstrated by the fact that “ the sun will rise on the morning of May 10th, 2015” is indeterminate now as I type this, but it is assumed that it will seem to become determinate on that day.
This change which occurs in the present seems to apply quite strongly to meaning. While we can say it is present fact that I currently intend to mean addition when I say ‘plus’ ten minutes from now, the time may get there and I may precede my utterance with something along the lines of “I will consciously intend to replace ‘plus’ with ‘quus’ in my mind for the next minute” and then (within the discourse), anyone who heard me say this would undoubtedly accept this change and allow me to say “68 plus 57 is 5”, and we are left with knowing I meant ‘quus’ when I said ‘plus’ and again, not knowing what fact led us to that knowledge. But in a way, it feels as if something became unchangeable after I spoke.
Let us also say that as the speaker, my change in meaning was unknown to me until I said I would be changing my meaning, and therefore even my introspection, or prediction of future behavior is not enough. As Kripke has showed, these types of phenomena do not determine past and present meaning, but there is a change in the moment which informs us.
The sceptic would have to allow for this change, that some aspect of what I will mean/mean/meant becomes more determinate at the time of the utterance. Whatever it is which becomes ‘set’ at the time of utterance, can be soritically carried into the past. What changes in the present, is that the event (the utterance) happens. Now if the utterance is ‘68 plus 57 is 125’, what has been set is that the speaker either meant to use plus or a functionally similar connective for the specific problem( provides the same answer), or that the speaker made a mistake in my use of another function.

Kripke responds

I think Kripke would find the support for my claim quite shaky, but he might appreciate the attempt. I can think of several leaps I have made which his sceptic would not allow. That being said, Kripke’s sceptical solution is a bit of a cop-out itself, so maybe he of all people would understand just how hard of a problem he made, and would allow for my somewhat sketchy defense of present-backwards induction over past-forward.
The two main caveats of my argument are my clause for functional similarity which Kripke addresses at length, and my justification for my conception of the temporal sorites. The toughest thing about these two aspects of the argument are that Kripke would indeed know just how to flip either on me. For functional similarities, he could claim that a certain function only has one example problem in common with addition. If this were the case, it would be considered functionally similar for that problem (this leads back to the legitimate case of 2+2 vs 2*2). Here we have two known functions of math ( not made up quus-like functions which allow for anything) and they are functionally similar at that point.The problematic implication here would be that “two plus two equals four” would mean the same thing as “two times two equals four” .This opens up a giant can of worms especially when we cross out of mathematical rules. For math, we at least have the answer that the function gives, but with linguistic rules, comparing “closeness” of two hypothetical rules would get quite messy.Kripke never addresses some of these details, but their shortcomings are apparent in his explanation of ceteris paribus cases, and the merging of all functions which just happen to have the same answer for a given question is implicitly thrown out when he states that the sceptic is looking for the fact that determines which you meant in precisely those cases.

As far as the sorites, I think it strengthens the previous argument, but still hinges on Kripke agreeing that something about attributions of a person x’s meaning at time t are more indeterminate up until time t. He could very easily chalk this up to our general lack of knowledge of the future. He could claim we do not even know what is going to be said yet, but future determinations of meaning are the same as past ones if framed in an “If person x said ‘plus’ they would mean addition, at time t” disposition. Then these conditional statements transfer perfectly into the present and past, and become dispositional statements about the past which Kripke already addressed. If one keeps the focus on the change of determinacy that any declaration about the state of affairs at time t undergoes at time t, it appears as if for meaning-talk, that this change eliminates many possibilities from being considered true, and the indeterminacy we are left with is between nearly identical functions and mistaken slip ups, and not as open ended as it was before the time of the utterance.

These changes leave me with a slightly strengthened dispositionalism, and a sorites argument which cannot be effectively argued for without being reversed. That being said, I think like many he himself considered, this solution would fall short for Kripke. If anything he might just concede that the forwards and backwards sorites cancel eachother out. There doesn’t seem to be a reason to start with the sceptic’s assumption (Past meanings are indeterminate) instead of mine( present meanings are determinate, if only for the sake of discourse). Like so many conclusions which can be drawn from soritical arguments, It seems as if neither ‘side’ really takes precedent, but in considering both, we create a general conundrum worthy of our analytical attention.