There are correct and incorrect ways to play language games.
That’s the crux. Wittgenstein himself believed otherwise and spent the most part of the book arguing against it. I think he makes good points.
At one point, he argues that there’s no single correct interpretation for “What comes next in the sequence: ‘2, 4, 6, 8, 10, 12, …?’”
Maybe this goes a bit too far. :) I think he’s right in some nitpicky sense, but for practical purposes, sane people will say “14″ every time and that works well for us.
We can see this as version of realism vs anti-realism debates: realism vs anti-realism about natural abstractions. As I argue in the linked post, anti-realism is probably the right way of looking at most or even all of these, but that doesn’t mean “anything goes.” Sometimes there’s ambiguity about our interpretations of things, but reality does have structure, and “ambiguity” isn’t the same as “you can just make random stuff up and expect it to be useful.”
That’s the crux. Wittgenstein himself believed otherwise and spent the most part of the book arguing against it.
I could be wrong, but my understanding was that Wittgenstein did think there were correct and incorrect ways of playing language games, but that this was context-dependent, and of course, someone could always choose to play another language game instead.
According to this article, the point being made with the sequences is that the correct completion is subject to interpretation and even though I could try to explain how the sequence should be interpreted, this explanation would itself be subject to interpretation, leading to an infinite regress. Wittgenstein ends up arguing in the end that we learn things through training rather than explanation.
That’s the crux. Wittgenstein himself believed otherwise and spent the most part of the book arguing against it. I think he makes good points.
At one point, he argues that there’s no single correct interpretation for “What comes next in the sequence: ‘2, 4, 6, 8, 10, 12, …?’”
Maybe this goes a bit too far. :) I think he’s right in some nitpicky sense, but for practical purposes, sane people will say “14″ every time and that works well for us.
We can see this as version of realism vs anti-realism debates: realism vs anti-realism about natural abstractions. As I argue in the linked post, anti-realism is probably the right way of looking at most or even all of these, but that doesn’t mean “anything goes.” Sometimes there’s ambiguity about our interpretations of things, but reality does have structure, and “ambiguity” isn’t the same as “you can just make random stuff up and expect it to be useful.”
I could be wrong, but my understanding was that Wittgenstein did think there were correct and incorrect ways of playing language games, but that this was context-dependent, and of course, someone could always choose to play another language game instead.
According to this article, the point being made with the sequences is that the correct completion is subject to interpretation and even though I could try to explain how the sequence should be interpreted, this explanation would itself be subject to interpretation, leading to an infinite regress. Wittgenstein ends up arguing in the end that we learn things through training rather than explanation.
Yeah, what I meant was the belief that there’s no incorrect way to set up a language game.
14 is certainly the most likely continuation but it could also be
16 if it’s a list of numbers k where k^2 + 7 is prime
18 if it’s a list of numbers of the form 3^i +/- 3^j
These continuations are unlikely in general but are the kind of thing that might show up in an academic mathematics paper.