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  1. #31
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    Quote Originally Posted by Rincewind
    Many words have technical meanings (including "theory" which has the distinctly different technical and lay meaning) but I was not using the terms in any particularly technical way.
    I had assumed you were using it in the technical way, so our discussion really has been at cross purposes. I think it is actually a reasonable assumption that someone who speaks about the subject in a way that claims knowledge of the subject use the terms of the subject such as they are used within the subject.
    Quote Originally Posted by Rincewind
    Yes. Tho many years ago - mid-80s. As an undergraduate doing a maths major and studying logic as run by the philosophy department. It was not a text for the sujects I did (I think we used a secondary text by Baum) but I was interested and it was in the library.
    The reason I ask is because you have made a point of saying that the distribution of work was relevant. But the work Russell was responsible for in section V is in analogous form to the sections which Whitehead is responsible.

    Quote Originally Posted by Rincewind
    Like I said, a philosopher first and foremost.
    I'm not sure if this comment is in jest or not. All this is of course now irrelevant since you were never using the term "mathematical logic" as I was, but I have to say that I never claimed the guy was a mathematician.

  2. #32
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    Quote Originally Posted by Mangafranga
    I had assumed you were using it in the technical way, so our discussion really has been at cross purposes. I think it is actually a reasonable assumption that someone who speaks about the subject in a way that claims knowledge of the subject use the terms of the subject such as they are used within the subject.
    I commonly use words in ways that I believe the audience would understand them to mean.
    So einfach wie möglich, aber nicht einfacher - Albert Einstein

  3. #33
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    Does Russell's sole authorship of An Essay on the Foundations of Geometry (1897) and Introduction to Mathematical Philosophy (1919) count?
    “The destructive capacity of the individual, however vicious, is small; of the state, however well-intentioned, almost limitless. Expand the state and that destructive capacity necessarily expands, too, pari passu.”—Paul Johnson, Modern Times, 1983.

  4. #34
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    Quote Originally Posted by Jono
    Does Russell's sole authorship of An Essay on the Foundations of Geometry (1897) and Introduction to Mathematical Philosophy (1919) count?
    We have to define "mathematical logic" first. Are you using it in a technical sense, or non-technical sense?

    I use it in a technical sense and when I use it it means the same thing as symbolic logic (i.e. use of and study of logic that is formalized and mathematical). This can be contrasted with philosophical logic, e.g. discussion of the nature of truth or of the nature of logical consequence. So these would not necessarily be works of mathematical logic, and indeed not necessarily be works of logic at all.
    Last edited by Aaron Guthrie; 14-07-2007 at 11:57 PM.

  5. #35
    Reader in Slood Dynamics Rincewind's Avatar
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    Quote Originally Posted by Jono
    Does Russell's sole authorship of An Essay on the Foundations of Geometry (1897) and Introduction to Mathematical Philosophy (1919) count?
    You forgot The Principles of Mathematics (1903) a copy of which I even own.
    So einfach wie möglich, aber nicht einfacher - Albert Einstein

  6. #36
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    Quote Originally Posted by Mangafranga
    We have to define "mathematical logic" first. Are you using it in a technical sense, or non-technical sense?
    Technical.
    “The destructive capacity of the individual, however vicious, is small; of the state, however well-intentioned, almost limitless. Expand the state and that destructive capacity necessarily expands, too, pari passu.”—Paul Johnson, Modern Times, 1983.

  7. #37
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    Quote Originally Posted by Jono
    Technical.
    And does your use agree with mine?

  8. #38
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    Incidentally I have seen Russell in a map of the figures of mathematical logic, if anyone is interested I'll find the book again, scan it and post it.

  9. #39
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    Quote Originally Posted by Mangafranga
    And does your use agree with mine?
    Pretty much.
    “The destructive capacity of the individual, however vicious, is small; of the state, however well-intentioned, almost limitless. Expand the state and that destructive capacity necessarily expands, too, pari passu.”—Paul Johnson, Modern Times, 1983.

  10. #40
    Reader in Slood Dynamics Rincewind's Avatar
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    Quote Originally Posted by Mangafranga
    Incidentally I have seen Russell in a map of the figures of mathematical logic, if anyone is interested I'll find the book again, scan it and post it.
    Mangafranga, you, and now it seems Jono, are fixated on the jargon usage of "mathematical logic" which I made quite clear from the outset that I did not intend. In case you still don;t see the distinction I was trying to convey consider the following exercise:

    Collect all people associated in some way with a field that could be called "logic" and put them in order from left to right with the more mathematical to the left and the more philosophical to the right. Then whether Russell lay to the left or the right of the mid-point or some other boundary is a moot point. The point I was making is there are a number of people who are considered mathematicians lying further to the left of Russell, including Hjorth and Goedel.

    Where you set limits on that continuum and say mathematical logic begins here and ends there is academic and introducing such a distinction is vacuous anyway as performing the same exercise on the individual work of "logicians" will lead to considerable overlap.
    So einfach wie möglich, aber nicht einfacher - Albert Einstein

  11. #41
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    Quote Originally Posted by Rincewind
    Mangafranga, you, and now it seems Jono, are fixated on the jargon usage of "mathematical logic"
    And you seem intent on ignoring the usage that is common in the very subject you are talking about.
    Quote Originally Posted by Rincewind
    which I made quite clear from the outset that I did not intend.
    I did ask you a few times if you were aware of the technical usage. You just ignored these questions.
    Quote Originally Posted by Rincewind
    In case you still don;t see the distinction I was trying to convey consider the following exercise:

    Collect all people associated in some way with a field that could be called "logic" and put them in order from left to right with the more mathematical to the left and the more philosophical to the right. Then whether Russell lay to the left or the right of the mid-point or some other boundary is a moot point. The point I was making is there are a number of people who are considered mathematicians lying further to the left of Russell, including Hjorth and Goedel.
    Thanks for the exposition.
    Quote Originally Posted by Rincewind
    Where you set limits on that continuum
    Your continuum which has little to do with the academic usage.
    Quote Originally Posted by Rincewind
    and say mathematical logic begins here and ends there is academic and introducing such a distinction is vacuous anyway as performing the same exercise on the individual work of "logicians" will lead to considerable overlap.
    I am not sure what you are saying. Are you saying there is no way to say clearly where mathematical logic begins and ends in your system?

  12. #42
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    Quote Originally Posted by Jono
    Pretty much.
    I have Introduction to Mathematical Philosohy atm, it was recommended to me as a book that explains the (number) mathy bits of set-theory, model-theory and metalogic. I am not really sure how to classify it.

  13. #43
    Reader in Slood Dynamics Rincewind's Avatar
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    Quote Originally Posted by Mangafranga
    And you seem intent on ignoring the usage that is common in the very subject you are talking about.
    I wasn't talking about mathematical logic in the technical sense. I was contrasting different sorts of logicians and use the adjectives mathematical and philosophical in a general sense.

    Quote Originally Posted by Mangafranga
    I did ask you a few times if you were aware of the technical usage. You just ignored these questions.
    Because they were not relevant.

    Quote Originally Posted by Mangafranga
    Thanks for the exposition.Your continuum which has little to do with the academic usage.
    ...and had I used the phrase in an academic context perhaps you would have a point

    Quote Originally Posted by Mangafranga
    I am not sure what you are saying. Are you saying there is no way to say clearly where mathematical logic begins and ends in your system?
    I'm saying the labels that people apply to various fields are arbitrary and the line where what you call "mathematical logic" and what I call a logician of the mathematical tradition are blurred. Logic in the classical sense and what has become known as mathematical logic are not two distinct fields but just various regions on a continuum.

    The second point is this whole sub-thread is entirely irrelevant in the point I was trying to make about the work of Hjorth. He is of the mathematical school and classifies himself as a Set Theorist.
    So einfach wie möglich, aber nicht einfacher - Albert Einstein

  14. #44
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    Quote Originally Posted by Rincewind
    Because they were not relevant.
    But when you finally answered the question the discussion was resolved. Fairly good evidence for the question's relevance.
    Quote Originally Posted by Rincewind
    I'm saying the labels that people apply to various fields are arbitrary and the line where what you call "mathematical logic" and what I call a logician of the mathematical tradition are blurred.
    They seem fairly distinct concepts to me, actually. "mathematical logic" is a subject. "logician of the mathematical tradition" as you use it, refers to people.
    Quote Originally Posted by Rincewind
    Logic in the classical sense and what has become known as mathematical logic are not two distinct fields but just various regions on a continuum.
    Language is vague, so what? Assuming this is a case of such vagueness, this doesn't show the distinction is not valid. The distinction (between philosophical and mathematical logic) is of great use to me as it comes up a heck of a lot when I am discussing potential honours thesis topics.
    Quote Originally Posted by Rincewind
    The second point is this whole sub-thread is entirely irrelevant in the point I was trying to make about the work of Hjorth. He is of the mathematical school and classifies himself as a Set Theorist.
    Literally, since as I understand it he will be joining the mathematics department of Melbourne University.

  15. #45
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    Quote Originally Posted by Rincewind
    ...and had I used the phrase in an academic context perhaps you would have a point
    The point is that the claims that follow are just about your own system. This seems to be salient as what you say about your own system seems to be highly critical of it. Thus one may be reluctant to think that you are in fact talking about your own system of classification. Thus I wished to make clear exactly what you were doing.

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