Talk:Gottlob Frege

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[edit] One Pupil of Note??

What about Gershom Scholem? [1]

[edit] Logicist about arithmetic not geometry

I changed "Frege was the first major proponent of logicism- the view that mathematics is reducible to logic.". This can be misleading because Frege only held the logicist view with respect to arithmetic and analysis. He believed that geometry is synthetic a priori and hence not a part of logic.

[edit] boole?

How is the work of Gottlob Frege related to that of George Boole? --Hirzel 03:06 15 Jun 2003 (UTC)

You could say that Frege's work was later, was research rather than exposition, was deeper as an enquiry into language. In fact there is no serious intellectual connection, though obviously there might be some comparison in the use of algbra-style notations. User:Charles Matthews

As I know, Boole mostly worked on the theory of classes in logic, Frege was involved rather in the theories of first-order and second-order languages. It's a more general theory, because class theory is a logical theory, the theories of logical languages are metalogical theories (in a particular, relative meaning of metalogics). These statements are a bit inexact, but I can't explain it detail, cause English is not my original language, however it is true the relation between Boole and Frege is a quite neglected area in the Frege-research. I have no sources about it and I think even if some exists so they are unpopular (f.e. not foundable in internet or in public libraries). Gubbubu 20:37, 6 Aug 2004 (UTC)

Frege wrote two papers comparing his Begriffschrift with Boole's work. They are located in the Posthumous writings.

Jamie Tappenden has written a paper on fruitful concepts in Frege that contains a discussion of Frege's critique of Boole's logical calculus.

[edit] Comments, questions and quibbles 25-aug-2004

...such as the use of quantification...

  • Common logician's error here: in normal english phrases like "two horses", two is a quantifier: no need for variables, bound or otherwise, to have quantification. Frege's contribution was the way he expressed quantification by means of variables; he did not invent quantification itself.

Frege was the first to devise an axiomatization of propositional logic and of predicate logic.

  • Frege did not create a separate theory of propositional logic, as the above suggests, and actually it is an achievement of Frege's to combine propositional connectives and quantifiers in one calculus.
  • In fact, the formalisation of predicate logic took almost another 60 years to complete, with the publication of Hilbert and Ackermann's book in 1928.

Ludwig Wittgenstein and Edmund Husserl were among the other philosophical notables strongly influenced by Frege.

  • With Wittgenstein this is undeniable (although I think the sentence goes better elsewhere), but just how important an influence was Frege on Husserl. Husserl first agrees with Frege's objections, and then goes on to change his mind about it. That Husserl had an important correspondence is clear, but strong influence I think is going too far.

Nice article, though: I was surprised by how many things I learned reading it. ---- Charles Stewart 22:30, 25 Aug 2004 (UTC)

[edit] Failure of logicist programme

The article says:

Frege was the first major proponent of logicism -- the view that mathematics is reducible to logic. ... Russell discovered the paradox which bears his name, and that the axioms of the Grundgesetze led to this contradiction; he wrote to Frege, who acknowledged the contradiction in an appendix to volume two of the Grundgesetze, noting what he perceived to be the faulty axiom. Frege never did manage to amend his axioms to his satisfaction, however; and after Frege's death, Kurt Gödel's incompleteness theorems showed that Frege's logicist program was impossible.

This strongly suggests that logicism was a failure. But I don't think that is correct; it seems to me that Frege's program was a success. Mathematicians still view set theory and logic, as set forth by Frege, to be the proper foundations for mathematics. It's only in recent years that an alternative, in the form of category theory, has appeared.

Mathematicians do not view logicist set theory as a proper foundation for mathematics. Logicist set theory, at least as I see it, was fairly definitively refuted by the Russell paradox. We do not consider sets to be a logical notion, identified with definable properties of which they are extensions, but as a mathematical notion--collections of objects, and at the same time objects themselves. --Trovatore 06:55, 27 July 2005 (UTC)
I think I probably misunderstood what "logicist" means. Thanks for correcting me. I will do more research and try to corectly understand the situation. -- Dominus 01:32, 22 September 2005 (UTC)

The Russell paradox was satisfactorily resolved by Russell and Whitehead's theory of types and later by Zermelo's work on the axiom of foundation. It is not a serious hindrance today.

You can't get rid of a paradox by adding an axiom. What Zermelo did was to provide a formal point of reference for the notion of sets as collections of objects rather than as extensions of properties (this was made more explicit by von Neumann, I think). That's the polar opposite of logicism. --Trovatore 06:55, 27 July 2005 (UTC)
I didn't say it was resolved by the axiom; I said it was resolved by Zermelo's work. -- Dominus 18:52, 21 September 2005 (UTC)
Point taken. It addresses only the smallest part of my remarks, though. --Trovatore 18:55, 21 September 2005 (UTC)

The remark about Gödel's incompleteness theorems is a non-sequitur. The incompleteness theorems show that there can be no formal axiomatization of all of mathematics. This no more invalidates the logicist programme than it invalidates the idea of doing mathematics at all. Mathematics can be founded on logic, and frequently is; the fact that the Gödel theorems say that there will be true theorems that are not provable does not negate the usefulness or soundness of the foundation.

For these reasons, I have rewritten this paragraph of the article and removed the reference to Gödel entirely. -- Dominus 14:31, 14 Jan 2005 (UTC)

[edit] More biography needed

I think that since this is an article about Frege, it is stongly lacking in biographical information about the man.

If you speak Hungarian, see the Hungarian article. Terrible news I haven't got enough time to translate it, but maybe you can ask other hungarians. Gubbubu 10:08, 17 October 2005 (UTC)

[edit] Query

The article says he is " widely considered the greatest logician since Aristotle."I think many would say Russell or even Godel was greater. Could we not say one of the greatest to ensure NPOV? I think there would be unanimity on that assessment.Logic2go

Russell or Godel probably weren't "greater" logicians than Frege and Frege wasn't "greater" then them (imnsho). They were all great logicians, but as a matter of fact Frege was the first. Yes, he was one of the greatest logicians since Aristotle. The difference between Frege and Russel, Gödel etc. is mainly that Frege was unknown for a long time, untill Russell (re)discovered lot of his achievements. Frege was born too early. Russell done a lot to put Frege on the well-known logicians's map. So I think you're right in this question: "one of" is more candid. Gubbubu 10:54, 20 October 2005 (UTC)
I'd guess you won't find many logicians today who don't think that Frege was a greater figure than Russell. Figures from the algebraic logic tradition (Pierce, Boole, Schröder) would be better bets, Tarski has his admirers, but the claim still holds: Frege is widely considered the greatest logician since Aristotle, even if not universally. It might be a good idea to get some sources for this claim, though. --- Charles Stewart 12:29, 20 October 2005 (UTC)
There were other great logicians (like Hegel or Kant, contributors in philosophical logic). Gubbubu 16:27, 20 October 2005 (UTC)

I think I could make a cogent and even persuasive case that russell was the superior logicianN especially given recent studies of Russel's papers at Macmasters. Certainly he was more influential. But my point is that arguing this borders on original research and a POV. I think qualifiers such as " widely considered the greatest" or equivalent superlatives are inherntly problematical. I can't imagine that anyone could disagree that he was "one of the greatest." Logic2go

Part of the issue is how the word "logician" is being used. For overall accomplishment in fields called "logic", including "mathematical logic", I think Gödel has it all over Frege. But if mathematical logic is not considered part of logic proper, then Frege's claim looks a lot better. In any case I think Logic2go's point is well taken. --Trovatore 18:57, 20 October 2005 (UTC)
Mathematical logic is a field of mathematics, and wasn't there until the 1930s. Gödel was a virtuoso, while Frege was a pioneer who kick-started logic as a research area after a break of, ooo, 2000 years since the Stoics. Mathematicians are always going to think more of Gödel. Charles Matthews 15:41, 21 October 2005 (UTC)
Read this [2]. American philosophy education will never be the same.--CSTAR 05:33, 25 October 2005 (UTC)

Wow. What do you suppose is the liklihood that Cheney even knows who Frege is? Or for that matter what the Evening Star is?Logic2go

I think we're more or less on the same page here. E.g. a lot of Gödel's greatness comes from his work in set theory. Is set theory part of logic? Frege thought so, which in large part explains why Frege wasn't a great set theorist. In fact, the extent to which set theory is not simply logic became much clearer as a result specifically of Gödel's work.
But whether set theory is logic or not, the fact remains that it's called logic, and therefore discussions of who is the "greatest logician" are bound to be confusing. --Trovatore 17:00, 21 October 2005 (UTC)
  • Agreed. In logic(s), I think of Frege,Russell, and Godel as the Socrates, Plato, and Aristotle of the matter in terms of greatness and importance.:)Logic2go
    • It is irrelevant now, but I don't agree. Russell wasn't greater logician then Frege, his only one important and dateless - but disputed - achievement is type theory. Frege was 100× greater then him, I think :-)). And Russell was publicated explicit silly "achievements", e.g. his description theory is totally psychotic ... Gubbubu 18:41, 21 October 2005 (UTC)

Cruising for a debate on that one(lol)! But that's the point, we have well-formed opinions on logic that a high school student looking to the encyclopedia for biographical info does not, and we shouldn't taint his understanding with our POV. We can do that in other venues. On that we can agree!Logic2go

[edit] Kudos

Nice page, the picture is nice. And what references! I wish I could find more of this qualtiy of work on wikipedia. wvbaileyWvbailey 01:37, 9 January 2006 (UTC)

[edit] Image

[edit] Frege's Metaphysics

Frege had such a horror of subjectivity in mathematics that it led him to make metaphysical statements about the ontological objectivity of mathematical concepts. He forgot or concealed the fact that concepts are mental products. In order for a concept to exist as it is, there must be a human nervous system and brain to think the concept. Frege's hatred of psychologism resulted in his conviction that there are mathematical concepts without thinking subjects.Lestrade 21:19, 21 February 2006 (UTC)Lestrade

[edit] Err emm

I guess this isn't proper to mention, but isn't Frege partly known for his later years as a far right associate to Bruno Bauch who hated liberals, Catholics, and the French?[3][4] Also as an Anti-Semite who wanted Jewish people to have their rights curtailed or even be expelled.[5]. Granted scandal maybe shouldn't be added if it's not needed, but I thought this was a well-known aspect of his history as I read it in a print encyclopedia that was over 30 years old.--T. Anthony 13:53, 28 June 2006 (UTC)

  • It is true that Frege was something of an anti-Semite in his later years, and diaries have been published in which he expounds his views on the subject. But, so far as I know, Frege never expressed these views in public forums or played any particular role in the rise of the Nazi party. That Frege was something of a xenophobe thus does not seem particularly relevant.
  • Well, relevant to what, exactly? Not to his work in logic, maybe, but this is a biography; if it's a significant aspect of Frege the man, and can be documented, then I'd include it. Bios shouldn't be limited to flattering material. On the other hand I'd be against spending lots of text on it, given that it doesn't bear much on Frege's impact on history. --Trovatore 02:11, 5 August 2006 (UTC)

[edit] Begriffsschrift notation and Peirce

Charles Saunders Peirce used a notation [6] for implication that reminds me of the two-dimensional notation used by Frege in the Begriffsschrift. Is anything known about a possible influence of Peirce on Frege's notation? Leibniz 21:54, 2 September 2006 (UTC)

[edit] "Sinn and Bedeutung"

I have to say I find the section header "Sinn and Bedeutung" to be a bit jarring, switching as it does from German to English to German in the space of three words. How about changing it to "Sense and denotation" (note capitalization), if we mean the Fregean concepts, or "Sinn und Bedeutung", if we mean the paper by that title? (By the way, I've always heard "denotation" rather than "reference"). --Trovatore 05:28, 15 September 2006 (UTC)

Denotation, reference, sense, signification, these have all been used. The real problem is that Ebglish does not have two, subtly different, words for sense. for example, in good Italian translations, this is rendered "senso e significato" (which are really synonymous just like the German sinn and bedeutung). Frege's beuteuting is neither denotation (denotazione) nor reference (riferimento) but a technical distinction which he introduced between synonynous terms to sever his purpose and not to be confused with denotation or references. Sense and signification is the best version, I think. --Francesco Franco aka Lacatosias 12:26, 12 April 2007 (UTC)

[edit] Number?

It would be nice to get a summary of Frege's definition of a number and the Julius Caesar problem. —The preceding unsigned comment was added by 75.160.146.253 (talk) 20:13, 14 April 2007 (UTC).

[edit] Version 0.7

This article has now been reviewed by the review team and will be on this DVD release. The "pass" template was added by mistake in place of the nomination template, but now it has officially passed. Walkerma 02:30, 20 June 2007 (UTC)