Talk:Principia Mathematica

message: Please append new sections to the foot of the page, to retain the time order. --Ancheta Wis (talk) 02:30, 21 February 2011 (UTC)
thread_title: Untitled

message: In my edition, proposition *54·43 (from which “will follow, when arithmetical addition has been defined, that 1+1=2”) occurs on page 360, not 362 (see fac simile).  Should I correct the article, or is there some other edition in which it occurs on page 362? --Gro-Tsen 22:46, 5 February 2006 (UTC)
replies: text: I think I put that in there, and I got the 362 from The Mathematical Experience', by Davis and Hersh, page 334.  So if 360 is the correct page, go ahead and correct it.  Bubba73 (talk), 23:16, 5 February 2006 (UTC)

text: In the edition in the library at Texas A&M-Commerce, that proposition occurs on page 362.  I happened to scan the page several years ago, and in fact still have a copy: Principia page 362. According to the university's website, this is the 2nd edition, Cambridge [Eng.] University Press, 1925-1927. Agarvin 19:29, 8 February 2006 (UTC)

text: The 1910 Cambridge University Press edition has it on page 379.  Talamus 19:08, 5 May 2006 (UTC)
thread_title:  1+1=2 

message: Given that Principia Mathematica is public domain by now, I think it would be a good idea to make it available at Wikisource. Would anyone else be interested in contributing to such a thing? (The full text is available online anyway; it's just a matter of transferring and wikifying it.) --Ian Maxwell 00:24, 27 March 2006 (UTC)
replies: text: I would imagine Principia Mathematica being quite painful to wikify. :) (see some online version like http://www.hti.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAT3201.0001.001) Mathematical notation is exact, but OCR:ing it correctly would need some heavy customizationing. Quick analyzing and error-proofing program would probably be nice too -- and output in LaTeX format... Talamus 19:23, 5 May 2006 (UTC)
thread_title:  Wikisource it! 

message: I don't really know IPA well enough to use it, but I think it'd be helpful to add the pronunciation, specifically that in Principia the 'c' is hard; I always thought it was a soft c until I heard it said aloud.  When I went online to check it out, I had to search for quite a while before I found a definitive reference.
:For future reference, all cs in Latin are "hard" (i.e. sound like English ks) - "Caesar" for example, should be pronounced much more like the german word "Kaiser" than the modern English pronunciation of "Ceasar". -- Tyler 07:41, 9 May 2006 (UTC)
thread_title:  Pronunciation 

message: This article explains the Principia Mathematica 1+1=2 proof, and discusses other related matters.  Is it worth listing it in the "External links" section?  -- Dominus 11:08, 20 June 2006 (UTC)
thread_title:  1+1=2 

message: I don't know much about the subject but, from what I do, the article should refer to Peano axioms and identify Russell as the main orchestrator of the project. --Ghirla -трёп- 09:44, 10 October 2006 (UTC)
thread_title:  To do 

message: I am curious why  BetacommandBot removed "Category:Seminal works" on 25 September 2006 on line 37.  Is this not a seminal work? Malangthon 02:47, 27 January 2007 (UTC)
thread_title: Category: Seminal Works removal

message: The links below "Principia Mathematica online (University of Michigan Historical Math Collection)" do not work (as of 28 February 2009). Can anyone provide alternative links?
Ignacio González (talk) 19:35, 28 February 2009 (UTC)
thread_title:  External links 

message: I have removed the sentence about whether there will be an independent statement in the system formulated by Whitehead and Russell -- yes, there is one, the Continuum Hypothesis discovered by Cantor in 1877. —Preceding unsigned comment added by 207.6.250.155 (talk • contribs) 05:40, 7 September 2010 (UTC)
thread_title: Cantor

message: The very first paragraph is very misleading.  Type theory is not a theory of types of sets.  Russell held a no classes theory.  As a theory of sets, types are unmotivated.  The trouble is that it's intuitively easy for people familiar with set theory to think of types that way, but it is simply historically inaccurate.  Russell speaks of types of propositions and types of propositional functions.  PM is not an attempt to reduce all of mathematics to set theory (dodging paradox by types).  It rejects an ontology of sets.  If anything, it is a theory of propositional functions, however even this ontology is disputed because there is a great deal of historical evidence that Russell envisioned a nominalist semantics for propositional functions through a substitional interpretation of the higher-order quantifiers.  To be sure, you have to start somewhere and I don't think the wiki should involve all scholarly disputes, but should the very first paragraph be so misleading?~~  —Preceding unsigned comment added by 173.19.227.52 (talk) 01:42, 20 February 2011 (UTC)
replies: text: I'm not sure that what you wrote is correct. But I'm not sure it's entirely incorrect, either. Therein hidden in the tall grass is a difficulty. After his discovery of "the paradoxes" and his publishing of his Principles of Mathematics in 1903 in particular the appendix where he proposed a solution to the paradox he discovered in Frege, Russell went through 4 or 5 iterations of possible "solutions" including his "no-class theory", his "zig-zag theory", his  "theory of limitation of size" followed by his "theory of types" and then his "ramified types". (I've not read the papers -- they're obscure--but I have read the relevant letters betweeen Russel and Frege (see van Heijenoort 1967) and the appendix to Russell's 1903 which you can get from "googlebooks"). In the prefaces to the second edition of Principia Mathematica (PM) (ca 1927) he addressed the advances and criticisms between the 1st and 2nd editions of PM with his "fully extensional" notion of "matrix". For a nuanced analysis see the 1944 paper by Kurt Goedel, and an analysis of Goedel's analysis written by Charles Parsons ca 1990, re Kurt Goedel's 1944 paper "Russell's mathematical logic", a reprint of which appears in Feferman et. al. 1990 Kurt Goedel Collected Works Volume II, Oxford University Press, New York NY, ISBN-13 978-0-19-514721-6(v.2.pbk.) pages 102ff (including the paper itself from pages 119ff). Without a close examination of Goedel's analysis (even the commentator admits to difficulties) I'd be hesitant to assert that Russell didn't acknowledge the existence of "classes" that derive from descriptive functions. Bill Wvbailey (talk) 02:17, 21 February 2011 (UTC)
thread_title: No Classes

message: ∙⋁ ∼▪ ■∗∗ ✸ ∾  ⊃ ≡ ⊦ ⊢ ︰
RE typography -- dots: I'm using Arial unicode MS, and having problems. The sharp-eyed reader of the original will see PM 's "big square dots" being used in a different way than the commonplace period. The "big square dots" are indeed square, and they're "bigger". Here is an experiment using big square dots: 
: " ▪ ", " ■ "
Either would work, IMHO. Unfortunately there are no stacked versions of "big square dots" except maybe this one (it's not a colon)  "︰
". So three dots would be " ▪︰ "
Ergo from page 10 (1927): " ⊦︰▪ p ⊃ q ▪ ⊃ ︰ q ⊃ r ▪ ⊃ ▪ p ⊃ r. " [Note the period which is bringing this example to an end and is not part of the main formula.   
RE typography -- assertion ⊦: looks lousy on my browser. The other symbol is ⊢ (right tack). It looks lousy too (bottom vertical is shorter than the top vertical).
RE typography -- star:  *1.1 vs ✸1.1. On my browser the 2nd is more faithful to the original.
    
RE modus ponens: PM's treatment of modus ponens is wonderfully written. But I'm not comfortable with my summary of it. PM writes on page 9 (1927 edition, and more at p. 94):
:The trust in inference is the belief that if the two former assertions are not in error, the final assertion is not in error. Accordingly whenever, in symbols, where p and q have of course special determinations,
:: " ⊦p " and " ⊦(p ⊃ q)
:have occurred, the " ⊦q will occur if it is desired to put it on record. The process of the inference cannot be reduced to symbols. Its sole record is the occurrence of " ⊦q ". It is of course convenient, even at the reisk of repetition, to write " ⊦p " and " ⊦(p ⊃ q) in close justaposition before proceeding to " ⊦q " as the result of an inference. When this is to be done, for the sake of drawing attention to the inference which is being made, we shall write  instead:
:: " ⊦p ⊃ ⊦q "
:which is to be considered as a mere abbreviation of the threefold statement
:: " ⊦p " and " ⊦(p ⊃ q) and " ⊦q ".
:Thus " ⊦p " may be read "p, therefore q," being in fact the same abbreviation, essentially, as this is; for " p, therefore q " does not explicitely state, what is part of its meaning, that p implies q. An inference is the dropping of a true premiss; it is the dissolution of an implication". (p. 94).
But then on pages 98ff we see symbolism (sort of) similar to the contemporary . . . so I'm going to strike this from the article until I (or someone) can figure it out. BillWvbailey (talk) 18:02, 25 February 2011 (UTC)
thread_title:  Section on notation 

message: Whats the total page number of each edition? -194.138.39.54 (talk) 11:16, 7 October 2013 (UTC)
thread_title:  How many pages? 

message: In the section "The construction of the theory of PM", I do not understand what is meant by the sentence starting with:"Another observation is that almost immediately in the theory...". Either this sentence was butchered or the translation (from the German??) failed. My point is that observation .. in the theory will have no clear meaning to the average reader. Could someone rewrite this to make it intelligible? Its NOT a technical issue, its about using correct English. Thx.173.189.78.173 (talk) 16:02, 26 April 2015 (UTC)
replies: text: I too was disturbed by this phrasing when I read this sentence, and I also thought that the awkward formulation may have come from the deletion of part of the phrase, but after giving it some thought I think that the sentence is grammatically correct but just very awkwardly put. I believe that it is meant to say "Furthermore in the theory, it is almost immediately observable that interpretations...". Do you (or anyone who may come across this thread) think my proposition would be an adequate change? Given that this thread was started years ago, I'm not so sure the original poster will ever see this response, but given that I believe my proposition to be clearer and more legible than the current form of the sentence, I will implement my change now.Tommpouce (talk) 20:50, 30 May 2021 (UTC)
thread_title:  Edit Request 

message: In the past, I've seen the quote (I think it was Russell but it could have been Whitehead's) about what an enormous waste of time their 10 year effort to write this had been. It's important enough, I think, to be included here. I've not been able to find it after a brief search and besides I don't know if he maintained that POV or it was possibly just part of the "intellectual exhaustion" alluded to in the article. Either way its important, imho. Oh, while I'm at it, the fact that the first printing was published at a loss, subsidized by the authors 50 each, the Royal Society 200 and 300 (pounds) by Cambridge University Press (see Wikipedia article on Whitehead) should also be included here, certainly (in fact that whole section should be included).173.189.78.173 (talk) 16:30, 26 April 2015 (UTC)
replies: text: I should also add that http://plato.stanford.edu/entries/principia-mathematica/ (which is an external link (I think) of the article) is imho a far more clear exposition about Principia than this article. You'll profit much more from reading that than this, although this goes into the nuts and bolts (so deeply, in fact, that this looses sight of the forest through the trees).173.189.78.173 (talk) 17:18, 26 April 2015 (UTC)

text: Was Gottlob Frege's work a waste of time as well? Remember, it was invalid. The work Russell &  Whitehead did was exhausting for them, and fit for machines. Herbert A. Simon records Russell's thankful reaction to Simon's program, that there must be a better way. --Ancheta Wis    (talk  | contribs) 19:22, 26 April 2015 (UTC)
thread_title:  Missing comment? 

message: What is with the overuse of what Wiktionary calls the "heavy eight-pointed rectilinear black star"? What does it even mean? I've never come across it in an article before and can't find anything online, which worries me regarding the average user! UaMaol (talk) 20:00, 2 April 2017 (UTC)
replies: text: It's a specific character of PM. Millbug talk 22:56, 5 April 2019 (UTC)
replies: text: It would be good to mention this in the article and explain it's meaning. --Meillo (talk) 12:23, 5 December 2021 (UTC)

text: A better asterisk is ✳ (U-2733, bolded). It's 8-pointed but doesn't overkill with the black blob in the center. Milt (talk) 20:09, 6 April 2019 (UTC)

text: However, when it is inserted on an article page, it is not bolded, too light and slanted. The closest ✳ to PM is in the 2nd example at 
https://tex.stackexchange.com/questions/157416/typesetting-famous-54-43-proof-11-2-in-principia-mathematica. --Milt (talk) 11:25, 10 April 2019 (UTC)
thread_title:  ✸ 

message: Is there really a need to treat contradictions as being "some sort of catch 22"? it's strange, to say the least
are people unaware that contradiction exists outside of that popular novel?  — Preceding unsigned comment added by 188.26.59.167 (talk) 13:50, 27 August 2018 (UTC)
thread_title:  catch 22 

message: IMHO the original translation (as of 2020-04-05 10:37:51 UTC) for the formula:
    p⊃q:q⊃r.⊃.p⊃r
as
    ((p⊃q) ∧ (q⊃r))⊃(p⊃r)
was incorrect.
The rule, as stated in PM vol. I (2nd ed., 1963, https://ia800602.us.archive.org/35/items/PrincipiaMathematicaVolumeI/WhiteheadRussell-PrincipiaMathematicaVolumeI_text.pdf [viewed 2020-04-04]) reads:
"The scope of the bracket indicated by any collection of dots extends backwards
or forwards beyond any smaller number of dots, or any equal number from a
group of less force, until we reach either the end of the asserted proposition
or a greater number of dots or an equal number belonging to a group of
equal or superior force." (p. 9)
Thus, the scope of ":", even though if is in group III which has lower priority as group I single dots in the formula, still extends to the end of the formula over the smaller number of dots (single dots round the '⊃' symbol).
Also, the example on page 10 of PM is very thorough:
"“p⊃q:q⊃r.⊃.p⊃r“ will mean “if p implies q; and if q implies r then p implies r.“ (This is not true in general). Here the two dots indicate a logical product; since two dots do not occur anywhere else, _the scope of these two dots_ extends backwards to the beginning of the proposition, and _forwards to the end_." (emphasis mine)
I've fixed the formula. The text should probably also be amended, "having the same priority" -> "having higher priority".
Please double-check. Pterodaktilis (talk) 16:50, 5 April 2020 (UTC)
thread_title:  Possibly incorrect translation of a PM formula into modern notation 

message: Section 2 uses the word "comtemporary" a lot. However, it is not clear whether it is using the word in the sense of "contemporary with PM", or in the sense "present-day". I suspect the latter, in which case it is confusing, and should be replaced by "modern". Since I'm unsure, I haven't made the change. JCBradfield (talk) 09:58, 15 March 2023 (UTC)
thread_title:  "contemporary" 

message: Such as "There can be no doubt that PM is(...)" 37.60.109.133 (talk) 15:36, 28 January 2024 (UTC)
replies: text: Yes, the article is a bit of a mess and needs more eyes. I cleaned up the lede a little per your suggestion -- thanks for pointing this out. The body needs a good brush-through as well, though. SamuelRiv (talk) 19:40, 28 January 2024 (UTC)
thread_title:  Isn't the article too praiseworthy to be neutral