I am more than a little puzzled by Wittgenstein’s discussion of rule-following in the Philosophical Investigations. What puzzles me most is his worry that we can never know what rule we meant when we gave someone a direction.
Wittgenstein’s argument about what rule is meant starts with a scenario in which I tell someone to write “a series (say +2) beyond 1000 – and he writes 1000, 1004, 1008, 1012” (WR 105). I might object that what he wrote is not in accordance with what I meant when I told him to write a series of +2 starting at 1000, but Wittgenstein asserts that I could not have meant each addition of 2 because I was not thinking of each member of the series when I gave the order: “So when you gave the order +2 you meant that he was to write 1002 after 1000 – and did you also mean that he should write 1868 after 1866, and 100036 after 100034, and so on – an infinite number of such propositions?” (WR 106). Since I was not thinking of that infinite set of propositions, I cannot claim to have “meant” any of the steps that I wanted the person to take.
What I do not understand here is why it is not enough that each one of those propositions follows logically from the order that I gave: the order entails each of the infinite set of propositions that Wittgenstein mentioned. It is the very nature of language that it allows us to speak in terms of general concepts that entail an infinite number of specific propositions. Our memories are limited, so we cannot think of an infinite number of things at once, but we can think of one general concept that applies to an infinite number of things. For instance, I can think of or mention my childhood without thinking of my third birthday, the week that I spent in Disney World when I was eight, and the day my sister was born. But certainly when I say “my childhood” I mean each of these events and all of the others that occurred when I was young because they all fit under the concept of my childhood. Without the ability to organize particulars into concepts, Wittgenstein would not have been able even to express his worry about rule-following because he would not be able to use the concept “rule”; he would have begun by simply listing as many rules as he could think of and never gotten past that point. Of course, even stating those rules would rely on concepts as well. Without concepts, we would not be able to use language in a way at all similar to how we use it now.
A rule is just another kind of concept, except (as in the case that Wittgenstein mentioned) we are asking someone to list some of the particulars that fall under that concept. So, when I ask someone to write the series +2, I am asking her to list the particulars that fall under the “concept” of +2 after 1000. It does not matter whether I was thinking of those particulars or not because the concept of +2 entails each of them, just as mentioning my childhood entails each of the events that occurred when I was young.
I realize that this problematic position is simply one that Wittgenstein considers and ultimately rejects. However, I think that the fact that he thought it was a legitimate problem worthy of consideration is very telling. As is so often the case with philosophers who are uninterested in doing epistemology, Wittgenstein seems to be in desperate need of it, despite his assertions to the contrary.
Wittgenstein’s argument about what rule is meant starts with a scenario in which I tell someone to write “a series (say +2) beyond 1000 – and he writes 1000, 1004, 1008, 1012” (WR 105). I might object that what he wrote is not in accordance with what I meant when I told him to write a series of +2 starting at 1000, but Wittgenstein asserts that I could not have meant each addition of 2 because I was not thinking of each member of the series when I gave the order: “So when you gave the order +2 you meant that he was to write 1002 after 1000 – and did you also mean that he should write 1868 after 1866, and 100036 after 100034, and so on – an infinite number of such propositions?” (WR 106). Since I was not thinking of that infinite set of propositions, I cannot claim to have “meant” any of the steps that I wanted the person to take.
What I do not understand here is why it is not enough that each one of those propositions follows logically from the order that I gave: the order entails each of the infinite set of propositions that Wittgenstein mentioned. It is the very nature of language that it allows us to speak in terms of general concepts that entail an infinite number of specific propositions. Our memories are limited, so we cannot think of an infinite number of things at once, but we can think of one general concept that applies to an infinite number of things. For instance, I can think of or mention my childhood without thinking of my third birthday, the week that I spent in Disney World when I was eight, and the day my sister was born. But certainly when I say “my childhood” I mean each of these events and all of the others that occurred when I was young because they all fit under the concept of my childhood. Without the ability to organize particulars into concepts, Wittgenstein would not have been able even to express his worry about rule-following because he would not be able to use the concept “rule”; he would have begun by simply listing as many rules as he could think of and never gotten past that point. Of course, even stating those rules would rely on concepts as well. Without concepts, we would not be able to use language in a way at all similar to how we use it now.
A rule is just another kind of concept, except (as in the case that Wittgenstein mentioned) we are asking someone to list some of the particulars that fall under that concept. So, when I ask someone to write the series +2, I am asking her to list the particulars that fall under the “concept” of +2 after 1000. It does not matter whether I was thinking of those particulars or not because the concept of +2 entails each of them, just as mentioning my childhood entails each of the events that occurred when I was young.
I realize that this problematic position is simply one that Wittgenstein considers and ultimately rejects. However, I think that the fact that he thought it was a legitimate problem worthy of consideration is very telling. As is so often the case with philosophers who are uninterested in doing epistemology, Wittgenstein seems to be in desperate need of it, despite his assertions to the contrary.
8 comments:
Ah, but there are other concepts which you might have employed when saying "add 2" which would have made "1004, 1008, 1012" the correct way to carry on. The puzzle is how we are supposed to know that, in your mouth, "add 2" didn't mean "add 2 up to 1000, then add 4 from then on"; that you didn't mean to use the one concept rather than the other. The shift from talk of rules to talk of concepts doesn't affect the puzzle.
(I will admit that the passage you quoted may be more obscure in its purpose than its parallel in Investigations 185. I'm not actually sure what WR refers to, but it seems to be word-for-word identical with PI 185, where the discussion then continues immediately to points you made in your post.)
It is perhaps worth noting that the link between concepts and rules would not have been novel to Wittgenstein. Wittgenstein knew his Kant, and Kant had already spoken of concepts as "rules for the synthesis of intuitions".
I think you may be missing the role this confusion plays in Wittgenstein's dialectic; I'm not sure what you think is "telling" about it.
Daniel,
It is PI 185. I'm reading Anthony Kenny's Wittgenstein Reader, so that's what the WR stands for. Sorry for the confusion.
Wittgenstein's writings on Rule-Following are my least favorite of what I've read, and I feel like I do not understand these sections quite as well as the rest. So I don't really have a response to your comment as of yet, but I will definitely keep it in mind as I continue to study Wittgenstein.
You're right that it's part of the nature of language that it "allows us to speak in terms of general concepts entailing an infinite number of propositions." The rule-following discussion can be seen as asking the question of how that's possible. Ultimately, LW is trying to block the kind of debilitating scepticism you articulate here.
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