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. — Ludwig Wittgenstein
An argument against using pattern sequences in IQ tests. — jgill
Are patterns exactly equal to rules? — D2OTSSUMMERBUG
200. It is, of course, imaginable that two people belonging to a
tribe unacquainted with games should sit at a chess-board and go
through the moves of a game of chess; and even with all the appropriate
mental accompaniments. And if n>e were to see it we should say they
were playing chess. But now imagine a game of chess translated
according to certain rules into a series of actions which we do not
ordinarily associate with a game—say into yells and stamping of feet.
And now suppose those two people to yell and stamp instead of playing the form of chess that we are used to; and this in such a way
that their procedure is translatable by suitable rules into a game of
chess. Should we still be inclined to say they were playing a game?
What right would one have to say so? — Ludwig Wittgenstein
201. 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. — Ludwig Wittgenstein
The answer was: if everything can be made out
to accord with the rule, then it can also be made out to conflict with it.
And so there would be neither accord nor conflict here.
It can be seen that there is a misunderstanding here from the mere fact
that in the course of our argument we give one interpretation after
another; as if each one contented us at least for a moment, until we
thought of yet another standing behind it. What this shews is that
there is a way of grasping a rule which is not an interpretation, but which
is exhibited in what we call "obeying the rule" and "going against it"
in actual cases. — Ludwig Wittgenstein
202. And hence also 'obeying a rule' is a practice. And to think one
is obeying a rule is not to obey a rule. Hence it is not possible to obey
a rule 'privately': otherwise thinking one was obeying a rule would be
the same thing as obeying it. — Ludwig Wittgenstein
The entire point of Wittgensteins argumentation was that "interpreting a rule" and "obeying a rule" are two completely different things. — Hermeticus
au contraire, Wittgenstein is saying is that all observations (word usage) are compatible with any conceivable law. — Agent Smith
the difference here amounts to the difference between a descriptive rule and a prescriptive rule. — Metaphysician Undercover
The difference between these two interpretations of "obeying a rule" is the difference between judging the cause, and judging the effect. Wittgenstein opts for the latter, making "obeying a rule" something which is observed after the fact, rather than something decided prior to the act, in the sense of interpreting a prescriptive rule, and acting accordingly. So the prescriptive rule is not relevant to Wittgenstein's position on rule following, and we must be careful when reading him not to misunderstand. — Metaphysician Undercover
It can be seen that there is a misunderstanding here from the mere fact
that in the course of our argument we give one interpretation after
another;(descriptive rule) but that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" (prescriptive rule) — Ludwig Wittgenstein
I find this confusing.Now, let's take your numerical example:
From a 2, 4, 8 sequence we could interpret all kinds of pattern (rule) that this sequence follows - but as it has been established, our interpretation of the rule has nothing to do wether we're obeying it or not.
But what exactly is our rule then? Where does it come from? How can we confirm it?
The rule, in the case of such a sequence, is determined by the author. — Hermeticus
If there genuinely is a pattern with 2,4,8,... then that pattern will describe the number chain or series to infinitum or otherwise it's a wrong pattern or the series of numbers is basically without a pattern, patternless. Here to talk about rules it would be better to talk about algorithms in the general sense. And either you have an algorithm that correctly tells you how the series 2,4,8,... goes or either you have the wrong algorithm or the series is non-algorithmic. — ssu
That what is generally depicted with 2,4,8,...yes, in the case of a potentially infinite sequence of numbers — sime
?it is meaningless to consider any particular function, let alone algorithm, as being descriptive of the sequence unless and until the sequence comes to an end. — sime
if the sequence is for example N, then the correct algorithm is "list all natural numbers". And natural numbers don't come to an end. — ssu
I'm reading this elementary textbook on math. The only way one can determine the persistence of a pattern i.e. know that a pattern you discovered will continue (is the correct one) is if you can explain it. — Agent Smith
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.
— Ludwig Wittgenstein — Agent Smith
One shows one has understood a rule not by stating it, but by following it....there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call “following the rule” and “going against it”.
Suppose I saw the ten first members of the pattern of the outcomes of your products. All smaller then e. Are we sure that only your prescription for generating the numbers (2, etc.) is unique? — Cornwell1
I actually think that's exactly what Wittgenstein himself is trying to get across. To not misunderstand one for the other.
It can be seen that there is a misunderstanding here from the mere fact
that in the course of our argument we give one interpretation after
another;(descriptive rule) but that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" (prescriptive rule)
— Ludwig Wittgenstein — Hermeticus
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