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Applying Rules
Wittgenstein's Rule Following Paradox

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Applying Rules

Gadfly II
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Posted 10/13/09 - 06:11 PM:	#21
Cadrache, your definition of conventionalism is too broad. Conventionalism is an idea that is based on the writings of a mathematician, Poincare and others. Specifically, it concerns the meaning of a priori truths. This from the philosophy professor online: "In logic and mathematics conventionalism says that a priori truths are true only because of linguistic convention (which raises the question whether the correct application of such conventions is itself conventional: if it is we are in danger of an infinite regress of conventions)". The parenthetical above is connected to the rule following paradox and treemanshope's questions above. I"m concerned with basic, or fundamental terms that at bottom are not justified by other terms. Candidates for these basic terms are necessary and a priori terms. What determines the application of these terms to new cases? It is merely a case of applying a term to the new case or does something about the new case itself influence the application?
Dare to use your own reason. Kant

Mako
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Posted 10/13/09 - 06:46 PM:	#22
Gadfly II wrote: I'm developing an analysis of Wittgenstein's private language argument and I thought it might be useful to learn how other people here view the rule following paradox (RFP). Briefly stated any application can be made to accord with and not accord with a rule, or be made to accord with another rule. For example, the series 1,2,3,4 and be continued 5, 6, 7, 8, ... or 6, 8, 10, ... the point being that either continuation can be made to accord with an algebraic function that does not contradict the beginning series. So, the question is how do we determine the correct continuation? Are they both correct? I'm open to solutions, how this fits Wittgenstein's overall philosophy or anything else you might find relevant. Cheers Let's take Wittgenstein's quote from PI, 201a: "This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule". It would seem that to alter a rule involves bringing in yet another rule....or more seriously, to question such a fundamental logical principle as 'consistency' in the application of a rule is smply to not understand rules at all, and therefore undermines 'rule-following' itself. So my contention is that either one understands what it is to follow or rule or one doesn't. A quick, non-exhaustive analysis reveals at least four principles which ground rule-following. They are: 1) consistency (an adjunct of that principle is that rule-following is thus binary: either one is following it (consistent with) or one isn't (inconsistent with) 2), related to the first principle above, the concept of 'conservation of information' 3) predictability 4) strategy-limitation (that is, rules constrict the number of strategies one may use). So to use a rule differently is to either use another rule altogether, or secondly, it's to not understand 'rule-ness' at all, or thirdly, it's to take an extreme skeptical stance toward to rule-following altogether. Taking Kripke's 'quus' example, the applier of quus either understands 'rule-ness' and is simply creating new conditions, which in effect change the 'addition' rule...... or the 'quus-user' simply doesn't understand rules, and is thus not a rational agent. The quus rule creates an inconsistency relative to the conventional usage of addition, although there may be no inconsistency within an alternative 'quus' system. EDIT: So my larger point here is that rule-following is, like language (since rule-following grounds language use) a non-private, social-relational feature. By creating a rule, or altering an existing one, the user assumes, at least hypothetically, a possible 'community' of other users for that particular rule, in that the rule should be 'translatable' to other language users. In order to do that, the rule should (at least in my opinion) accord with the four principles listed above. So for instance, with the 'addition' rule (the + sign), an agent should normally assume a 'community of rule users' whose expectations for rules involve consistency, conservation of information, predictability and a limitation on strategies ( limited to rules of arithmetic in this case). So that, using the 'plus sign' example, one need not (as has been argued in the literature on this subject) constantly appeal to a 'higher-rule,' One is rather appealing to the fundamental principles of 'rule-ness' itself. Hence it's not an infinite regress of higher appeals to higher rules, in my opinion. It's the question of whether or not one is using the fundamental principles which ground all rule-following. Edited by Mako on 10/13/09 - 07:31 PM
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Gadfly II
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Posted 10/13/09 - 10:39 PM:	#23
Thanks, Mako. While I chew on your interesting summation, could you explain what you mean by conservation of information?
Dare to use your own reason. Kant

Mako
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Posted 10/14/09 - 04:57 AM:	#24
Gadfly II wrote: Thanks, Mako. While I chew on your interesting summation, could you explain what you mean by conservation of information? I may be guilty of misapplying a physical principle here, but my sense of it is that rules for physical systems, for example, should account for (and thus descriptively preserve) the complexity of a physical or biological system, for which they serve as analytical tools. Thus, a system of rules should efficiently, yet comprehensively account for all observed/measured data (i.e. no information is lost), while still retaining the capacity to accomodate more data or generate new predictions. As for prescriptive rules (for social systems), the complexity of the rule-system should be commensurate to the complexity of the social systems for which they prescribe or legislate. In this sense, prescriptive rules should (ideally) allow for the maximal range of optimal (most desirable and hence rational) strategies. In this sense too, information is preserved (or added) by allowing for those very strategies which are most productive (practically). From a moral perspective, rules should preserve the 'good' (however one may define it), In these ways, practical and ethical strategies, which are kinds of social information, are preserved. The examples that writers such as Wittgenstein, Kripke and others have used, seem arbirtrary and contrived to the point of being counter-intuitive, relative to actual rule systems. The examples given 'add complexity' to the rules while diminishing their generative power. In othe words, they've 'flipped it over' opposite to what it should be. The examples used in the literature (such as 'quus') tend to be ones which constrict the descriptive and analytical power of rule systems, in effect doing 'generative' u-turns. From my own perspective, that's not what practical, theoretical or even prescriptive rule-systems are, or should be about. Actually, now that I think about it, perhaps I should substitute 'conservation of generative power' for 'conservation of information, for principle #2. Edited by Mako on 10/14/09 - 07:53 AM
"To alcohol. The cause of, and solution to, all of life's problems." ~ Homer Simpson

Cadrache
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Posted 10/14/09 - 02:14 PM:	#25
From my vantage - you could claim two distinct different types of priori. 1. The language itself. See Reinemann's thesis that he wrote for his degree. (I only read a partial when reading up on poincare's conjecture.) The only form of conventialism that could affect these priori are very odd and therefore do not normally constitute valid responses. (for instance - we have infinite values between each specific number 1,2,3 and so on. Yet the number of divisions and 'how far apart they are' between 1 and 2 are the exact same amount as those between 2 and 3.) 2. The ones normally relevant to the function itself.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

Gadfly II
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Posted 10/14/09 - 07:22 PM:	#26
Mako, you raise several good points. From my POV, the list you recommend could be useful if one is setting up an information system or grounding scientific research. I don't think anyone would raise an objection on practical grounds. Although, the above conditions are still vulnerable to the same philosophical objections as the arguments in the PI. For example, your first contention, "either one understands what it is to follow or rule or one doesn't." is quite amenable to consistency. One simply designates those new applications as consistent or not consistent based on the their agreement with previous use. (if things get too messy, we simply overhaul the system. Nothing, Quine tells us, is ungiveupable.) But, it is just this kind of conventionalism that W. must reject, because in order to compare a new use with previous use, a rule must be formulated in symbols and we are committed to an infinite regress. A rule, W. says, does not contain its applications. This is the same objection I raised with Banno earlier. I don't see how W. can help us determine application to new cases. The only thing we can do is announce that they are consistent or not based on past behavior. After all, we can not describe circumstances that have not come to pass and description is all W. will allow. This brings me to my main objection to the meaning is use thesis. As I understand W., at the moment, language is simply part of our behavior. In this way, we can not step outside our language to make judgments about meaning. I think this is what he meant when he said that "meaning drops out of language." Linguistic behavior determines the meaning of our terms, but we can not apply the standard to itself. It is as if we were to ask how long the standard meter is. It doesn't make sense, according to W. because that meaning describes at least in theory, a method of comparing some object to one particular object, and we can not compare a thing side by side to itself; so, the question doesn't make sense. And, if the foregoing is accurate, my concern above doesn't make sense either. Now, I would be forced to agree IF and only if language use is its only and sole source of meaning. Fortunately for me, there is reason to believe that is not. This post is long enough, however, so I'll give my reasons in another post and give people a chance to correct anything I've said here regarding W. or show how W. can help us judge the application of new cases.
Dare to use your own reason. Kant

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