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Talk:History of logic

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Former featured article candidateHistory of logic is a former featured article candidate. Please view the links under Article milestones below to see why the nomination failed. For older candidates, please check the archive.
March 16, 2010Featured article candidateNot promoted

pyramids built using geometry[edit]

The pyramids are irrelevant, and the caption of the pyramid photo is silly. The geometry must have been the smallest problem the pyramid builders were facing. Could somebody remove the pyramids? — Preceding unsigned comment added by 130.233.179.227 (talk) 13:04, 31 October 2012 (UTC)

older entries[edit]

Clearly this page only follows the very attempts at logic. It should be extended to include a comprehensive look at the origins of symbolic logic, and the various logical traditions associated with it.

Reformulation[edit]

This article needs urgent reformulation. An article on the history of logic cannot pass over the polish tradition, for example. I'll try to collaborate to this reformulation myself.

What is modern logic?[edit]

I've deleted the following text:

However, the development of modern logic in its present form originates with Boole and De Morgan.

which suggests that the the kind of logic done in the British C19th algebraic school is the main kind of logic done today, which it patently is not. As to when modern logic begins, it is a matter of dispute: this isn't something for Wikipedia to be pronouncing on. --- Charles Stewart 17:41, 27 July 2005 (UTC)


However, see the article by Anellis which I linked to, which argues cogently for those origins. Perhaps something on the lines of, "the beginnings of modern logic lie in ..."?

Edward Buckner 17:41, 27 July 2005 (UTC)

Russell & 20th century logic[edit]

Nothing on Bertand Russell, curious.--62.6.139.11 13:29, 28 April 2006 (UTC)

Or Hilbert's program or Godel. I guess the 20th century section still needs to be written. CharlesGillingham 12:40, 26 June 2007 (UTC)


How about, as a start: "Highlights of twentienth century logic include the Principia Mathematica of Russell and Whitehead, which presented a system of type-theory in which most of classical mathematics could be presented; Goedel's Completeness Theorem for the first-order predicate calculus; and Tarski's analysis of the concept of truth. See also Foundations of mathematics." 131.111.164.226 11:44, 30 August 2007 (UTC)

Well until just now the section on Modern Logic ended with:

Such work has added much to logical notation since Aristotle's time. However, outside of these notational changes little else has been developed in formal logic and it has become a rather neglected subject within academic philosophy.

which I have deleted, although it was quite funny.

In fact there is more material on the history of modern logic (Post Frege) in the general article Logic than there is here, the main article. Strange. --Philogo 23:53, 24 October 2008 (UTC)

Possible concern about blocked editor continuing editing here[edit]

I have brought together a Request for Comment page, but I am not at all familiar with, nor too interested in, the rest of the process of pursuing this discussion. -- Thekohser 18:43, 24 August 2009 (UTC)

  • I'm not quite sure what your concern is. What would you like editors to comment on? - Bilby (talk) 10:39, 26 August 2009 (UTC)

Minor prose issue[edit]

I can't quite work out this sentence The period which followed the important developments in logic in the thirteenth and early fourteenth century and the beginning of the nineteenth century was largely one of decline and neglect,. Is it the period following the 13/14 C ? Or the 19th ? Or between the two? Or both? Fainites barleyscribs 20:58, 23 February 2010 (UTC)

Thanks I will correct. HistorianofLogic (talk) 21:20, 23 February 2010 (UTC)

"No citation needed for this"[edit]

[1] Really? No citations are needed for the entire paragraph? — goethean ॐ 21:28, 23 February 2010 (UTC)

Er, probably one is needed. I will look it up tomorrow. Thanks HistorianofLogic (talk) 21:32, 23 February 2010 (UTC)

Missing sources/inconsistent referencing[edit]

  • Sorry to tell you this, but your sources/referencing need more than a little sprucing up. Please check for inconsistent formatting styles.
  • Missing sources (I may have missed some; it was a bit confusing):
    • In notes but not refs: Geach, BLC, Buroker, Feferman & Feferman (but see below for "Feferman"),Ockham, Avicenna, Lenn (2003), Lenn (1992), Jevons
    • In refs but not notes: Bolzano (two instances), Boole (1854), Feferman, Gabbay, Grattan-Guinness, Haaparanta, Heath (1931).

• Ling.Nut 12:20, 6 March 2010 (UTC)

Formatting work still needed on citations ... and why does this article use single quotes? I haven't checked MOS ... perhaps someone else will. SandyGeorgia (Talk) 15:54, 6 March 2010 (UTC)
I've started fixing the quotations (WP:PUNC check also needed]]) ... will finish later. Dabomb87 (talk) 15:59, 6 March 2010 (UTC)

A couple of topics worth adding[edit]

First, logic, as conceived by Hegel and his followers, is something of a departure from the tradition described in the article - but it exists, was influential, and I think deserves a short section if only to explain what the difference is. (I remember being bewildered when I first opened Hegel's logic and found nothing in it resembling the logic which I'd been taught.). Second:

John Stuart Mill's A System of Logic (1843), one of the last great works in the tradition.

Not really. The tradition prospered for many years, especially in Germany, until it was extinguished by Husserl's critique in the first volume of the Logische Untersuchungen (Frege had already surpassed it, but I believe Husserl's work was the nail in the coffin). Again, worth a short section. If there is consensus that they are worth adding, I can draft something on each of these topics.KD Tries Again (talk) 17:33, 7 March 2010 (UTC)KD Tries Again

Thank you KD, civil greetings, that would be very welcome. From the other side (talk) 17:38, 7 March 2010 (UTC)
(Edit) on Mill, I think the emphasis is on the last great work. There were of course Jevons, Joseph, Joyce and a host of other writers in that tradition in England. Not to forget Bradley, Bosanquet representing the Hegelian tradition in England (Russell was forced to read them), and Lotze in Germany, plus many others I am sure. I began this to argue that Mill was the last great one, but seeing some of the names, perhaps you are right. Bradley and Bosanquet certainly worth a mention. I had something on my website about this until Geocities cruelly deleted the lot. From the other side (talk) 17:45, 7 March 2010 (UTC)

From the Logic Museum archives[edit]

"In the autumn term of 1892 Russell decided to concentrate on philosophy, and turned for advice to Joachim. He was given a reading list that included Plato, Descartes, Leibniz, Spinoza, Hume, Locke, Berkeley and Kant. Joachim was an adherent of the English Hegelian school. So, while recommending Mills System of Logic, which Russell thought good, but 'full of fallacies', he also had to read Bradley's Principles of Logic, which Russell thought 'first rate, but very hard', and Bosanquet's Logic ('good, but still harder'). "

"Bertrand Russell began work on the book we now know as The Principles of Mathematics in the beginning of 1898, when he was 27, and still under the spell of the Hegelian school of logic that dominated English philosophy at the time. Russell's purpose was to address the contradiction inherent in the nature of number. A number of things is one thing (since we talk of 'a' number or 'a' collection of things), but is also many (since it, or they, may be two or more things). He had proposed to deal with this in the Hegelian manner, by accepting the notion of quantity as inherently contradictory, then constructing a 'dialectic' around it. (A discussion of the problem survives in section 74 of the book).

"After reading Whitehead's Universal Algebra, and Dedekind's Nature and Meaning of Numbers (a title which I am unable to find in any reference to Dedekind's works, but which may be Monk's translation of Was sind und was sollen die Zahlen, Meyer 1891), he became convinced that this Hegelian approach was wrong, and began work on a book to be called An Analysis of Mathematical Reasoning. He gave up this in 1900, but used the material extensively in Principles of Mathematics, a version of which was nearly complete by mid-1900. "

From the other side (talk) 17:53, 7 March 2010 (UTC)

Where to put the Hegelians?[edit]

The question is, in which section of the article? At the tail end of Traditional Logic? The problem is that they aren't really traditional logicians. Or as part of the 'Rise of modern logic' - more accurate, because as the quotes involving Russell show, they probably had more influence on modern logic, albeit in a negative way, than traditional logic. Difficult. From the other side (talk) 17:57, 7 March 2010 (UTC)

Science of Logic[edit]

Quite unbelievably there is the article linked above. It doesn't look bad to me (but not an expert on Hegel). Perhaps I should ask the main author to help. From the other side (talk) 19:39, 7 March 2010 (UTC)

Yes, why not? The other part - basically from Mill to Frege/Husserl - I can do in a couple of paragraphs. I took a look at some materials this afternoon. The Hegel thing is a sideshow, really almost a footnote.KD Tries Again (talk) 06:49, 8 March 2010 (UTC)KD Tries Again
That article does look good. I've tried a very condensed summary of Logic in Hegel. I can support it with citations, but first of all, is it intelligible? Along the right lines? Hard to explain Hegel in a few lines, so feedback appreciated.KD Tries Again (talk) 19:58, 11 March 2010 (UTC)KD Tries Again.
Well, the claim that Hegel doesn't deal with valid inference seems wrong. The logic seems to be leading up to his very long talk on syllogisms.184.77.32.182 (talk) 07:08, 19 February 2011 (UTC)

Logic and Psychology[edit]

I dropped in a short piece on the gap between Mill and Frege, focused mainly on the Germans. I think Bosanquet and perhaps McTaggart might fit better in a similarly short - or even shorter - piece on Hegelian logic. I have interrupted the flow a little, butI didn't want to mess around with the other sections. Let's see what the User from the Other Side thinks.KD Tries Again (talk) 00:53, 10 March 2010 (UTC)KD Tries Again

User from the Other Side thinks it OK. I think it should go to FA. From the other side (talk) 13:45, 12 March 2010 (UTC)

Logic after world war II[edit]

I'm posting here to respond to a query about logic after world war II. I think the biggest difficulty in an article like this is deciding which particular topics to include, out of those possible. Also, as a mathematical logician, I am more familiar with work in this area than with work in philosophical logic or in "Logic with a capital L". So I will just talk about mathematical logic.

I don't think that the sentence "Apart from the work of Paul Cohen, logic after the 1940s was largely a period of consolidation, " is really accurate. It's true that in the period just after world war II things were consolidated as people began to really digest the results of the first part of the century. Books such as Kleene's Introduction to metamathematics gave coherent treatments of things that had previously seemed fragmented. But the major development in the second part of the 20th century was the development of the separate fields of contemporary mathematical logic as independent areas of research. Previously, someone studying mathematical logic was just "a logician". But, over times, the fields of model theory, proof theory, recursion theory, and set theory began to diverge, so that now a typical professor of logic will specialize in just one or two of those areas, and will usually self-identify in the specialty area first.

Each of the four areas had major advances in the last 50 years. In recursion theory, the priority method was discovered, leading to major advances in our understanding of computability. In set theory, the method of forcing and the study of large cardinals combined to obtain many independence results. In model theory (the area I am least familiar with), techniques such as stability and saturation became standard. User:Hans Adler can probably tell you more about model theory. In proof theory, intuitionistic logic became much better understood, with volumes like Troelstra's Metamathematical investigations showing how to understand intuitionistic arithmetic and explaining techniques such as realizability that were developed after world war II.

There are other secondary but still important developments. Examples include Robinson's work on infinitesimals; the solution of Hilbert's 10th problem; the work on randomness by Kolmogorov, Martin-Lof, Chaitin, and others; the work of Paris and Harrington on sentences independent of Peano arithmetic; Martin's work on Borel determinacy; categorical logic and topoi. Each of these leads into its own area of further contemporary research.

One source for ideas about the important developments in mathematical logic is Mathematical logic in the 20th century, a collection edited by Gerald Sacks of some of the most important papers of the century, almost exclusively from the post-world-war-II period. Also, the Handbook of mathematical logic, from 1978, gives a good overview of what happened up to the point of its publication. By that time, the fields were sufficiently differentiated that the papers in the Handbook give a good idea of the scope of mathematical logic.

Once specific concern I saw was whether to mention reverse mathematics. This is an important program in logic, but if this section doesn't have room to mention the "big four" (model theory, set theory, proof theory, recursion theory), then it probably doesn't have room for RM. Right now the section is more focused on philosophical aspects of logic. — Carl (CBM · talk) 16:10, 14 March 2010 (UTC)

Thank you. As explained, we have no one on the contributor side who has expert knowledge of the subject. From the other side (talk) 16:31, 14 March 2010 (UTC)
No offense intended to you or CBM, but the above remark is a poor start for a 'logic post WW-II' section: IMO, the highest priority should be explaining the 'four areas' of modern mathematical logic in informal, easily understood terms. For instance, intuitionistic logic now gets a mention, but there's no explanation of what it (and structural proof theory, generally) is about. Also, there's little or nothing about interaction w/ comp sci. Classicalecon (talk) 17:04, 14 March 2010 (UTC)
My bigger concern is that all I was talking about above is the history of mathematical logic after world war II. There's also philosophical logic, but I don;t know enough to say much about it. I agree that on the mathematical logic side, starting with the big four areas is best. I just wasn't sure there is room in the article for it. I didn't really intend for my comments to become the article; I just wanted to lay out some ideas about which things might be covered. I'll work on the article for a few minutes here. — Carl (CBM · talk) 17:22, 14 March 2010 (UTC)
I can't say much about phil. logic, but various editors have vouched for the accuracy of what's currently in the article. Though I think that having one para about applications of formal philosophical logic in modern analytic philosophy would help motivate this stuff. Classicalecon (talk) 17:36, 14 March 2010 (UTC)

<--- Thanks for these suggestions. The main thing is to settle on the n main areas (say, 4) and expand a bit upon them, in a way that an intelligent non-expert finds approachable. There is no need for a detailed treatment, the links will take you there. From the other side (talk) 18:08, 14 March 2010 (UTC)


I did a little work on that just now. I indicated in comments some references I have in front of me here, so that I can go back and add more detailed references in the future. — Carl (CBM · talk) 18:25, 14 March 2010 (UTC)
It's coming on well. Some of it is unintelligible to me, however. From the other side (talk) 18:29, 14 March 2010 (UTC)
E.g. "developed an implementation of an infinitesimal-enriched continuum that resolved questions dating back to Leibniz" - this is sort of crying out for an explanatory link - what is this? From the other side (talk) 18:30, 14 March 2010 (UTC)
See non-standard analysis. Paul August ☎ 21:33, 14 March 2010 (UTC)
I reworded that, and moved the picture down so it does not crowd the text of the first paragraph. The stuff about Leibniz is explicitly mentioned in the commented reference, by the way. — Carl (CBM · talk) 18:37, 14 March 2010 (UTC)
It is looking very nice. But now I'm off to Sainsbury's. From the other side (talk) 18:40, 14 March 2010 (UTC)
I left a comment at the FAC review with some suggestions. 66.127.52.47 (talk) 10:37, 15 March 2010 (UTC)
I think non-standard analysis was a trendy topic in the 1960's that never really caught on. Mentioning it is fine but the picture of Abraham Robinson gives more emphasis to the topic than really make sense. I removed the size attribute on the picture (a peeve of mine, we should not override user preferences in picture sizes without good reason) but I wonder if there is a different picture to use instead. A photo of Paul Cohen would be great if someone could find one. 66.127.52.47 (talk) 17:18, 15 March 2010 (UTC)
You're right that it never caught on as a way to teach actual calculus (despite a couple strong proponents). But Robinson's work is very well known, and it's an important development of the work in model theory that we can, finally, give a sensible development of a field with infinitesimals. So as a historical development it's worth mentioning. The same is true, for example, for work on complete axiom systems for geometry. Plane geometry is usually still taught in a naive, Euclidean way in high schools and colleges, but the historical development of complete axiom sets for plane geometry is an important milestone. — Carl (CBM · talk) 18:14, 15 March 2010 (UTC)
Yes, Robinson's work is important and should definitely be mentioned, but if the post-ww2 section is going to have just two photos, having one of Kripke is fine but having the other one be Robinson seems to put more prominence on non-standard analysis than really makes sense. (Non-standard analysis was once the object of considerably higher hopes than merely being used to teach calculus). I agree that Tarski's work on real closed fields / plane geometry should also be mentioned. I have to leave pretty soon but might try to edit the article tonight or tomorrow. 66.127.52.47 (talk) 19:30, 15 March 2010 (UTC)

tense logic[edit]

There are several mentions of "tense logic", a phrase I had never heard before, that turns out to redirect to temporal logic, which I think is a more familiar name. It's a well-known topic with applications in computer science. Anyone object to changing the phrase? 66.127.52.47 (talk) 19:46, 15 March 2010 (UTC)

I went and changed it. 66.127.52.47 (talk) 07:36, 16 March 2010 (UTC)
It's a shame that tense and time are treated with the same sort of Kripke semantics, because they concern grammatically distinct (tense versus mode), and so even many professional logicians are blinded to the fact that sensitive treatment of natural-language inference must treat them differently. I'd prefer a short article on tense logic besides the current article on temoral logic. — Charles Stewart (talk) 10:17, 26 October 2010 (UTC)

handbook of the history of logic[edit]

The "Handbook of the History of Logic" is listed in the references section but not actually cited to anything in the article as far as I can tell. 66.127.52.47 (talk) 03:18, 16 March 2010 (UTC)

Some more sources[edit]

  • Peckhaus[2] I like this article, putatively about Leibniz but says quite a bit about historiography of logic. Seems to have a good bibliography too.
  • Jean Van Heijenoort, "From Frege to Gödel: A Source Book in Mathematical Logic". Extremely influential book.
  • Van Heijenoort, 'Logic as Calculus and Logic as Language' cited in Peckhaus above.
  • Grattan-Guinness 1988, "Living Together and Living Apart: On the Interactions between Mathematics and Logics from the French Revolution to the First World War". cited in Peckhaus, looks interesting.
  • Akihiro Kanamori has many excellent articles on his web site about the history of set theory.
  • Wolfgang Lenzen [3] about Leibniz. It is pretty interesting but Peckhaus sort of dismisses him. I'm not sure what to make of this.

Please feel free to add to this list 66.127.52.47 (talk) 09:21, 16 March 2010 (UTC)

Order of sections under Traditional Logic[edit]

The flow was worrying me here; I hope I've improved it by reversing the order of Hegel and Logic and Psychology (to reflect the correct chronology). I have also subsumed them under Traditional Logic. The stuff in Logic and Psychology is surely a continuation of the "textbook tradition" described at the beginning of the section. In its own way, the same is true of Hegel's work.KD Tries Again (talk) 14:39, 16 March 2010 (UTC)KD Tries Again

Definitely an improvement. 86.186.86.97 (talk) 17:20, 16 March 2010 (UTC)
Could you find some citations for the Hegel section? Or the citation-police will be on the case. Even the most bleeding-obvious thing has to be cited.86.186.86.97 (talk) 17:26, 16 March 2010 (UTC)
Yes, it's on my to-do list. Should be easy, just need a spare half hour.KD Tries Again (talk) 19:10, 16 March 2010 (UTC)KD Tries Again

"algorithm"[edit]

I think I'm going to un-revert this revert by Malleus Fatuorum, since I can't find any support in the article algorithm characterizations for the notion that an algorithm can produce an infinite amount of output. It's true I'd been using Knuth's definition (that requires any algorithm to halt on every input), and it turns out that some other sources allow algorithms to express partial functions (i.e. on some inputs, the algorithm doesn't halt, and never produces a result). But that is different from producing infinite output. Also, the enumeration method can't literally be a computer program since a program running on an actual computer can't produce infinite output either (due to running in finite memory, etc.)

The paragraph in question seems to have been pasted from the lede of Gödel's incompleteness theorems and then modified[4] The version that was pasted from was the result of fairly careful discussion[5] and didn't use the word "algorithm".

I've opened a separate thread about whether an "algorithm" can produce infinite output at

Talk:Algorithm characterizations#can_an_algorithm_produce_infinite_output.3F

Technical discussion about that issue should go into that talkpage rather than this one. But in this article, I like the old wording (the one from before Malleus's revert) better either way.

66.127.52.47 (talk) 21:42, 20 March 2010 (UTC)

Pyramids picture text[edit]

I would think that the pyramids were built using blocks of stone not geometry. They were perhaps designed using geometry. Myrvin (talk) 20:57, 14 December 2010 (UTC)

Needs an expert[edit]

Doing my best to say where this article is wanting. Most of all, Aristotle's section could use expansion: prose doesn't cover all the works in the list, it does little to speak of his greater emphasis on term logic and thinking in terms of predicates rather than propositions and what it means, and on the relation between the Metaphysics and prior analytics and so forth which I am unable to provide. Cake (talk) 04:33, 19 February 2017 (UTC)

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