June 4 - 7, 2006
06.04.06
When do I feel the need to ask for the meaning of... ? Because words do not have a monopoly on meaning, by which I mean (or, “in other words” or “I could also say this in the following way”) that we speak of paintings, gestures, military tactics, historical events, etc. as all ‘having meaning’.
For example: “What is the meaning of that tribal dance?” And here there seems to be a connection between the concept of meaning and the concepts of purpose and intention. But I could also say “Why are they dancing that dance?” Now, would we say that this sentence has the same meaning as the first sentence? What would the criteria be for determining this?
Perhaps we are misled by a handful of unique cases, i.e., “& means ‘and’”, “% means ‘percentage’”, etc. But in these cases we are still speaking of signs, and their meaning comes from being and being able to be translated into words. It is pointless, albeit true, to say “’And’ means ‘and’.”
06.05.06
In some situations, it may be helpful to think of mathematics as a kind of language. But this would be useful only as a kind of analogy.
Both mathematics and language, we would want to say, are governed by a system of rules, of logic or of grammar, and once we understand the rules, we “know how to proceed.” That is to say, that the rest will fall into place before our eyes.
But, upon closer inspection, we find that this is not the case, or, at least, not necessarily the case. (P.I., section X, p. 190)
P.I., p.191: “You can measure to test the ruler.”
This is one of the reasons why I want to be talking about “criteria” rather than rules. Although, on the other hand, we could be talking about rules as long as we always keep in the back of our minds the fact that the rules for the games are always changing.
Some different uses of the word ‘means’ in the English language:
1) “Red means stop.”
2) “ ‘Hund’ means ‘dog’.”
3) “When she asks, “Shouldn’t you be cleaning your room?”, she means, “Clean your room.”
4) “Professor Jones means to embarrass you in class today.”
5) “The artist means to show the horrors of war in his latest exhibition.”
To me, in (1), meaning means something akin to interpretation. (2) is an example of translation. (3) I would probably describe as explanation, while (4) and (5) both seem like examples of intention, although very different kinds of intention.
06.06.06
What is important for us to remember is that a system of signs requires interpretation - a sign points to something outside of itself, and this something is language. In other words, a system of signs is contingent upon a pre-existing language. The sign depends upon the word for its meaning. The inverse of that sentence is not true; the word is self-sufficing.
What is possible is to have a private system of signs.
06.07.06
Are Roman numerals somehow less arbitrary than Arabic numerals? Is “II” somehow closer or more representative of the idea of the number two than “2” is?
Perhaps there is no strict essential structure to language, for language is merely a social construct. But mathematics does have a central structure around which the whole system revolves, and that structure is provided by the laws of logic. “Even in Chaos World, A=A.” (But I do not begin to prove to you that I know mathematics by assuring you that “A=A.”)
Say that we create a sports league with ten teams, labeled A through J. When making the schedule, we match team (1) A against B, (2) J against C, (3) I against D, (4) H against E, and (5) G against F, and then rotate for the next set of matches, so that the schedule looks like this:
I II III IV V VI VII VIII IX
A 1 1 1 1 1 1 1 1 1
B 1 5 5 5 5 5 5 5 5
C 2 1 5 4 4 4 4 4 4
D 3 2 1 5 4 3 3 3 3
E 4 3 2 1 5 4 3 2 2
F 5 4 3 2 1 5 4 3 2
G 5 5 4 3 2 1 5 4 3
H 4 4 4 4 3 2 1 5 4
I 3 3 3 3 3 3 2 1 5
J 2 2 2 2 2 2 2 2 1
(P.I., p. 94)
When do I feel the need to ask for the meaning of... ? Because words do not have a monopoly on meaning, by which I mean (or, “in other words” or “I could also say this in the following way”) that we speak of paintings, gestures, military tactics, historical events, etc. as all ‘having meaning’.
For example: “What is the meaning of that tribal dance?” And here there seems to be a connection between the concept of meaning and the concepts of purpose and intention. But I could also say “Why are they dancing that dance?” Now, would we say that this sentence has the same meaning as the first sentence? What would the criteria be for determining this?
Perhaps we are misled by a handful of unique cases, i.e., “& means ‘and’”, “% means ‘percentage’”, etc. But in these cases we are still speaking of signs, and their meaning comes from being and being able to be translated into words. It is pointless, albeit true, to say “’And’ means ‘and’.”
06.05.06
In some situations, it may be helpful to think of mathematics as a kind of language. But this would be useful only as a kind of analogy.
Both mathematics and language, we would want to say, are governed by a system of rules, of logic or of grammar, and once we understand the rules, we “know how to proceed.” That is to say, that the rest will fall into place before our eyes.
But, upon closer inspection, we find that this is not the case, or, at least, not necessarily the case. (P.I., section X, p. 190)
P.I., p.191: “You can measure to test the ruler.”
This is one of the reasons why I want to be talking about “criteria” rather than rules. Although, on the other hand, we could be talking about rules as long as we always keep in the back of our minds the fact that the rules for the games are always changing.
Some different uses of the word ‘means’ in the English language:
1) “Red means stop.”
2) “ ‘Hund’ means ‘dog’.”
3) “When she asks, “Shouldn’t you be cleaning your room?”, she means, “Clean your room.”
4) “Professor Jones means to embarrass you in class today.”
5) “The artist means to show the horrors of war in his latest exhibition.”
To me, in (1), meaning means something akin to interpretation. (2) is an example of translation. (3) I would probably describe as explanation, while (4) and (5) both seem like examples of intention, although very different kinds of intention.
06.06.06
What is important for us to remember is that a system of signs requires interpretation - a sign points to something outside of itself, and this something is language. In other words, a system of signs is contingent upon a pre-existing language. The sign depends upon the word for its meaning. The inverse of that sentence is not true; the word is self-sufficing.
What is possible is to have a private system of signs.
06.07.06
Are Roman numerals somehow less arbitrary than Arabic numerals? Is “II” somehow closer or more representative of the idea of the number two than “2” is?
Perhaps there is no strict essential structure to language, for language is merely a social construct. But mathematics does have a central structure around which the whole system revolves, and that structure is provided by the laws of logic. “Even in Chaos World, A=A.” (But I do not begin to prove to you that I know mathematics by assuring you that “A=A.”)
Say that we create a sports league with ten teams, labeled A through J. When making the schedule, we match team (1) A against B, (2) J against C, (3) I against D, (4) H against E, and (5) G against F, and then rotate for the next set of matches, so that the schedule looks like this:
I II III IV V VI VII VIII IX
A 1 1 1 1 1 1 1 1 1
B 1 5 5 5 5 5 5 5 5
C 2 1 5 4 4 4 4 4 4
D 3 2 1 5 4 3 3 3 3
E 4 3 2 1 5 4 3 2 2
F 5 4 3 2 1 5 4 3 2
G 5 5 4 3 2 1 5 4 3
H 4 4 4 4 3 2 1 5 4
I 3 3 3 3 3 3 2 1 5
J 2 2 2 2 2 2 2 2 1
(P.I., p. 94)
posted by Joel | 4:56 PM
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