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Talk:Logicism

A request for referencing
Hi, this is Jose Ferreiros. I find that the introduction to the whole article reflects very directly a new interpretation of the emergence of logicism that I began to put forward in the 1990s. Yet there is no reference to my papers on the topic. So I would greatly appreciate it if you took care to add references. Specifically, Dedekind's role in the early history of logicism was quite absent from older articles before 2000; insistence on the crucial role of the derivation of the real numbers in Dedekind's path to logicism is also a characteristic of my work. You may find that already in a 1996 paper published in Arch. for Hist. of Exact Sciences ('Traditional logic and the early history of sets') and then in the book Labyrinth of Thought. — Preceding unsigned comment added by 90.162.182.80 (talk) 15:44, 3 March 2015 (UTC)

By the way, let me support the next comment when it says that the introduction is somewhat unclear. Logicism is about the reduction of math to logic, not about math being an expansion of logic. Also, the fact that Gödel's theorem is proved "by logic" is quite irrelevant to its significance for logicism. One may say that the incompleteness of formal systems of mathematics is not an insurmountable obstacle for logicism, but it remains true that all the early logicists (Dedekind, Frege, Russell) expected the basic foundational systems to be complete. And if the logical system is incomplete, the sense in which logic is "formal" becomes a question. [Let me also thank you guys for the work you do for Wikipedia.] — Preceding unsigned comment added by 90.162.182.80 (talk) 16:16, 3 March 2015 (UTC)

This article is a mess. I suggest a rewrite
Hi. I've just read through this article, and it's a real mess. A huge amount needs to be done to it, possibly up to the point of a complete rewrite. Before I criticise it, I should mention that I have just completed a PhD thesis whose topic was a particular strand of neo-logicism. I have also taught some philosophy of mathematics at university level. (I don't mean to boast or wave credentials about. I just want to show that I'm familiar with the material.) I think that this qualifies me to criticise the article.

Anyway, after a read through, here's what I think are some problems with the article:
 * The very first statement is unclear: mathematics being an extension of logic and mathematics being reducible to logic (and definitions) are very different things. The second -- which is what is more usually called 'logicism' -- is much more controversial. As it happens, the reference attached to this sentence no longer exists. A better reference would be, for example, the Stanford Encyclopedia of Philosophy.

 * The first paragraph is very long winded and unclear. It is also almost entirely unreferenced. I think it would be better to have a brief introduction before the contents (saying roughly what logicism is, and who has propounded it). The kinds of details in this paragraph should then go in appropriate points in the article (e.g. a section on history, a section on criticisms and so on).

 * The stuff about Gödel in this section is also well off-mark. 'This theorem is proved with logic just like other theorems' is more-or-less nonsense. In one sense, it is absolutely false - Gödel's theorems have to be made in the background of a mathematical theory, and is not a theorem of pure logic. That logic is used on top of this mathematical theory is irrelevant, since logicism is far more than the (uncontroversial) claim that mathematics uses logic. In any case, even if it were claimed that the relevant mathematical theories can be reduced to pure logic in some sense, this would not by itself invalidate it as a criticism; it may then just show that logicism is self-undermining. Most importantly, however, I am unaware of anybody making such a rebuttle in reputable published work. As such, the stuff on Gödel here constitutes original research. (There are published rebuttals of this kind of objection, and I think they deserve mentioning, but in a section dedicated to criticisms.)

 * I don't claim to know much about the origins of the term 'logicism'. On the face of it, however, most of the discussion in this section does not address the point, but talks about the origin of other words with 'logic' as their root.

 * The stuff about symbolic logic is close to nonsense. What has algebraic logic got to do with anything? And algebraic logic is a different thing from Boolean logic. The discussion of what symbolic logic is is itself very unclear. What might be useful is a quick characterisation of predicate, as opposed to propositional logic.

 * The stuff on history is rambling and unclear

Epistemology section

 * It's really unclear what the author of this section means by 'epistemology'. Most of what's discussed has nothing to do with epistemology. Realism and idealism aren't epistemological positions, for example. Most of it is metaphysics, and very rambling at that.

 * Russell's paradox definitely does not belong in this section, since it prima facie has nothing to do with epistemology. There are a few errors in it as well. The paradox was not in Begriffsschrift, but in Grundgesetze

 * Generally, this section is incredibly rambling. It is not easy to follow, and it is hard to see how it fits together. Most of the stuff doesn't belong in a section entitled 'Epistemology', but in its own section.

The Logicistic construction of the natural numbers

 * Firstly, the word 'logicistic' is really not right. It should be 'logicist'.

 * The axiom of pairing in set theory really has nothing directly to do with the usual interpretations of arithmetic in set theory. Ordered pairs especially, as far as I remember, are not directly used in the construction of von-Neumann ordinals, nor (obviously) Zermelo numerals

 * The stuff about types is completely the wrong way around. Modern set theory is untyped, and so the numbers (i.e. the von Neuman ordinals or Zermelo numerals) are all of the same type. By contrast, the issue of types does come up in logicist foundations of arithmetic, since some of these (especially Russell and Whitehead's) are contructed in a type theory. Their system results in a collection of numbers at every level of the type-theoretic heirarchy.

 * As with the previous sections, this is very rambling. Sentences follow on from one another without it being at all clear how they fit together.

Prelimnaries

 * It's very unclear what is meant by classes 'coming about as the result of propositions'.

 * Quoting chunks of Russell doesn't make stuff very clear. It would be better to give a beginner-friendly introduction of the material that's necessary to understand the rest of the article. As it happens, most of these terms are not really needed.

The definition of the natural numbers

 * the first sentence of this makes no sense. It is also written in a very much unencyclopic manner.

 * 'devise' is the wrong word.

 * the example is very unclear. It does not illuminate the quotation at all. Its relevance is questionable.

 * The notation of | a, b ,c | is completely non-standard. It should instead be {a,b,c}.

 * The 'bundles' example is wrong. As it is it suggests that the displayed sets are equivalence classes under equinumerosity. They are not. The equivalence class of pairs features all pairs, for example.

 * 'This peculiar non-existent entity' doesn't make sense, at least, not without a substantive discussion of Russell's (and Meinong's!) views on a distinction between existence and subsistence which does not belong here.

 * The use of non-standard symbols in entirely unhelpful.

...

I could go on, but I'm getting tired. It is my opinion that the article could do with a complete rewrite; it is largely very rambling, for the most-part unreferenced, and the notation is completely non-standard. I'm adding a template to this effect now, partly so that people will see my comment here, and hopefully chip in their 2 cents.

I'm happy to have a go at a rewrite. I believe that I am qualified to do so. I'm going to start a version of the article in my sandbox. Then, at the point where I think I have something better than this article (but obviously with ample scope for revisions), I will suggest replacing this article. Would people be opposed to such an idea?

I would suggest a structure for the article as something like the following:

 * brief introduction, saying what logicism is
 * A brief history
 * Pre-Frege logicism - the most notable forms of logicism are those deriving from Frege and Russell, so it seems reasonable to lump pre-Frege stuff together
 * Frege's logisim, divided into a number of sections:
 * Frege's motivation and philosophical views about logicism
 * Frege's technical programme as carried out informally in the Grundlagen and formally in the Grundgesetze
 * Russell's paradox and the failure of Frege's programme
 * Russell and Whitehead's logicism. Again split into multiple section. This is not my area of expertise, so I will to some extent leave this as a skeleton for those more knowledgeable than me to improve.

 * Criticisms
 * I am unsure whether it is better to have a by itself for criticisms, or for each section to have a subsection -or citicisms.

 * Neo-logicism.
 * This section could do with expanding. I think that I will also have a go at creating an article specifically for neo-logicism. It is a major topic in contemporary philosophy of mathematics, so I believe that it is notable enough.

I am happy to have a go at this, and happy to ask for help from others. Again, would anybody be strongly opposed to this? Jdapayne (talk) 20:35, 7 February 2013 (UTC)

Jdapayne criticism
Keep in mind that the article's title is "Logicism", not "Neologicism". So you should be careful to keep your perspective tuned to logicism, especially with regards to the historical; that's why we came to this article, to find out what we could about historical logicism; if we wanted to read about neologicism we'd be reading about it, somewhere or other. I agree with you that neologicism should be split off from this article. Secondly, be sure you have sources for everything. The third comment is a caution: you are apparently new to wikipedia. We've all been newbies, once, and we've all made the same mistakes -- over-enthusiastic, overly critical. My advice to you is to go slow, don't tear everything you see to shreds. At least at the beginning of your efforts, try to find some good in the article and repair the blunders, i.e. work with what's there, build on it. . . slow and steady wins the race. Lastly, keep in mind that a "rewrite" such as the one you are proposing will, someday, be applied to your work, work you will not get an ounce of credit for -- you do not own even the tiniest mote of the work you put into this, and it will get the exactly the same respect you give the work you find here now. Bill Wvbailey (talk) 02:06, 8 February 2013 (UTC)

 * Thanks for the advice.

 * 1) I understand that the article is about logicism. I mention neo-logicism because (a) it is itself a branch of logicism and (b) since neo-logicism is very much inspired by historical logicism, my own work on neo-logicism means that I have a good understanding of historical logicism. I don't intend to make the article about neo-logicism, any more than it it already. The section on neo-logicism is probably fine as it is.
 * 2) I will indeed make sure I have sources for everything. In fact I think that one of the main problems with the current article is that it makes a lot of bold statements in places which are not referenced. I am very used to citing sources meticulously in the writing that I do, and editting Wikipedia will be no exception.
 * 3) Understood completely. I'm not doing this because I want credit or anything like that. The reason I want to rewrite (or nearly rewrite) this article is because I want Wikipedia to be better. It has been a great resource for me in the past and I want to put something back. It's also because I don't want students of mine coming to this page as it is for additional reading during a lecture course of mine in the future; in its present state it is likely to confuse at best, and at worst impart a lot of incorrect information. Likewise, I'm completely open to (and used to) criticism. If what I write gets steamrollered because somebody thinks that it can be improved, then that is fine. Again, the ultimate aim is to make Wikipedia a better resource for everybody. On the 'go-slow' advice: thanks. Maybe what I'll try doing first is reorganising the current content, rather than a rewrite - one of the main issue with it at the moment is that it's not very well structured. That then makes it possible to modify in smaller chunks. Jdapayne (talk) 16:27, 8 February 2013 (UTC)

You sound like you will be a good editor. Are you familiar with "sandboxing"? I've created dozens of them whenever I want to really have at something, but don't want to clutter the talk page e.g. with quotes, sources, etc. They're fake pages under your "namespace" e.g. the one I used one on this article: User:Wvbailey/Logicism, which might be useful, actually. You would create a new article e.g.User:Jdapayne/Logicism and work it to your heart's content with no need to write "edit summaries" etc.

Here's some background (and some rebuttal) about the article as it is now, in no particular order:
 * About the strange symbolism, the vertical bars, for the example:
 * ┊a, b, c┊, ┊d┊, ┊┊, ┊e, f, g┊, ┊h, i┊,  ┊j, k┊, ┊l, m, n, o, p┊, ┊q, r┊, ┊s┊, ┊t, u┊, ┊v, w, x, y, z┊
 * The idea is to communicate that these are not sets (classes) in the conventional symbolism of { }. This is in light of Russell's "no-class" theory, and in particular Goedel 1944's criticism.

 * Logicistic versus logistic or whatever: I've seen it written a number of ways.

 * The matter of "epistemology", maybe this is the wrong word -- ontology? [cf article on Meinong], or just "philosophy?". Whatever, this section and the criticism, I believe are the most important sections. At historical stake were the arguments re mathematical "foundations" -- Platonism, Logicism, Formalism, Intuitionism, constructivism, "mathematical realism" (cf Goedel 1944:106ff, 120ff). I coudn't find much at all about the philosophies of the Logicists and had to go back into primary sources e.g. Dedekind, Frege and Russell 1903 and 1919. The question is: "How do we come by the 'knowing of [the concept of] number' " or "Why do we know how to count things"? Are numbers "Platonic entites" that exist out there all by their little lonesomes? Are they then discovered? Or, are they invented? Are they "free creations of the human mind"? Or, are they a priori (built-in) into our genetics, a tendency we have because of the structures of our brains? (Dedekind) I have a quote from Bernays (in Mancosu I believe) and it's similar to the Kleene quote having to do with where we derive our "number sense" -- from an intuition of sequence. This is what's at stake in this section.

 * Sourcing -- my best secondary critical sources was Goedel 1944. My secondary sources were the commentaries to be found ibefore the appropriate articles in van Heijenoort, commentary before Goedel 1944 (Charles Parsons), Mancosu, and Grattain-Guiness, and the bit of commentary before Russell 1919 (Hagar's commentary). Unfortunately I had to use primary sources (Russell 1903, Russell 1919, Frege, Dedekind, and Peano). Dedekind bothered me because I wanted to know more about his "philosophy of number". I don't have the language skills (can't read German) to go sleuthing about in ancient primary sources, and that sort of behavior can get you into O.R. difficulties, anyway. I had to go into Russell 1903 to see what was going on with his "unit class" misery, and his 1919 to figure out what his "philosophy of number" was. And that's pretty much the extent of the sourcing. If others e.g. Meinong are not mentioned it's because I know zip about them.

 * One thought would be to break out the example of the Logicist construction of the natural numbers into its own sub-article. That might "densify" ("compactify") the article.

Hope this helps, BillWvbailey (talk) 20:51, 8 February 2013 (UTC)

That does help. Thanks. It was rash of me to suggest a rewrite straight away. What I will do instead is mainly to try and fill in stuff about Frege's logicism - both the philosophical part and the construction - since I think that is something that the article is mainly lacking at the moment, and also the part that I know most about. This might require a bit of reorganising as well to split off the Frege from the Russell bits. I think the idea to separate the construction of the natural numbers out seperately is a good one. I won't try to do that yet, but I'll try to make is so that it's easy to do if needed (by keeping the various bits separate in this article). I've started sandboxes at User:Jpayne/Logicism and User:Jpayne/Logicist constructions of arithmetic for this purpose.

If you're still working on this article, an additional sources that you might want to look at for are the Oxford Handbook of Philosophy of Mathematics and Logic, which has an article on the logicism of Dedekind, Frege. There are also a few articles in the Stanford Encyclopedia of Philosophy which may be useful - especially one on Dedekind, at http://plato.stanford.edu/entries/dedekind-foundations/, which might help for the Dedekind stuff. I'll have a look at these - and follow up other references - after I've witten some stuff on Frege. Jdapayne (talk) 10:13, 11 February 2013 (UTC)

Introduction
Can someone explain what it means for mathematics to be "reducible to logic" (opening sentence)? I'm a mathematician and I have no idea what this means. 158.109.1.23 (talk) 14:18, 21 February 2008 (UTC)

 * Being a reckless fellow, I'll have a go :-). Suppose a 'logic' is a collection of symbols in terms of which formulae are defined, some of those formulae are deemed axioms, and yet others (derived from those axioms using rules of inference) are deemed theorems. Now if all the symbols of mathematics can be defined in terms of the symbols of that logic, then all formulae of mathematics become formulae of that logic. And if, further, all the true formulae of mathematics (or, at least, all those known to be true to date) are among the theorems of that logic; then mathematics has been reduced to that logic.

 * 'But' I hear you ask, 'what is a logic?' Good question.  If the above programme were carried out today, I guess ZFC would be used.  But many people would say that the axiom of infinity goes beyond logic, so ZFC wouldn't count as a logic.  And, in Russell's type theory, reducibility as well as infinity would rule it out.

 * Let's hope that someone who really knows the answer comes along and corrects that. Meanwhile see what Carnap says here: Philosophy_of_mathematics 86.145.56.11 (talk) 01:49, 7 November 2014 (UTC)

Self-reference
Is Neo-Logicism meant to be a different article? Because otherwise it references to itself 8/. Fephisto 22:31, 8 July 2006 (UTC)

 * Sometimes parts of large articles refer to other parts of the article. Nevertheless, the problem is fixed. —The preceding unsigned comment was added by Canadianism (talk • contribs) 19:07, 28 February 2007 (UTC). Canadianism 19:07, 28 February 2007 (UTC)

Should this page be moved and replaced?
I am thinking of annihilating this page and rewriting it. Would it be a good idea to move most of the current (not very NPOV) content to a new place, like 'Logicism and Godel's theorem' perhaps? (I'm new here.) --Toby Woodwark 20:37, 2004 Mar 18 (UTC)

Absolutely not. B 00:15, Apr 26, 2004 (UTC)

I find this page very inaccurate and subjective. If an expert in the area is considering rewriting it I would definitely agree with that.

All right, I'm going in. I don't know if this'll come out perfectly, but I do agree that the second half of the article is extremely subjective, if not downright wrong. I'll try to clean it up now, then...

sentences removed
I removed: "Modern philosophers believed that proof of this theory was the means of banishing the befuddlement...". The idea expressed is probably inaccurate for many of the people usually associated with Logicism.

I also removed: "with sucess except for the paradox of trying to formulate a logical definition of natural numbers in terms of classes". Though it certainly is suspect to use a notion of class to give a logical definition of number, I don't see the sense in which this is a paradox.Wjwma 18:48, 2 August 2005 (UTC)

The incompleteness results
I modified the sentence alleging that Godel's Incompleteness results undermine logicism. Given certain assumptions and certain formulations of logicism, it is true that the incompletness results undermine logicism, but these positions are controversial. Wjwma 18:21, 3 August 2005 (UTC)

 * I'm no expert, but I believe Incompleteness just undermine formalism; although Frege developed a formal system for his work, and later Russell did in Principia, I think the formalism used is inessential to the ideas underneath it. Whatever this may be, I think Incompleteness, if not shown to actually undermine formalism should be deleted. If I'm completely wrong and Incompleteness really reveales fundamental limitations to logicism, then I think it should be added an entry to the contents. Sergio89 (talk) 01:19, 18 August 2012 (UTC)

Citations please
This page is badly in need of some references. Otherwise, it is subject to being deleted per WP:NOR. -- noosphere 09:27, 14 April 2006 (UTC)

 * Good enough yet? Canadianism 18:49, 28 February 2007 (UTC)

 * This page is in no danger of being deleted "per WP:NOR." The topic of logicism is quite notable and so would survive any deletion discussion. If you believe that the page needs additional references, fix it, but please don't make threats about deletion. CMummert · talk 18:56, 28 February 2007 (UTC)

 * I think, more or less, it has been fixed. —The preceding unsigned comment was added by Canadianism (talk • contribs) 19:05, 28 February 2007 (UTC).

 * See also Philosophy_of_mathematics which is somewhat more detailed than this article. —Preceding unsigned comment added by 207.241.238.233 (talk) 07:11, 21 September 2007 (UTC)

Small Change
I changed the word 'valid' to the word 'alive' in the paragraph on Goedel's Incompleteness Theorems because [especially in a mathematics and logic context] valid means something like 'necessarily truth preserving'. To say that logicism necessarily preserves truth despite being a contested position seems too strong a claim to make in an encyclopedia article. Feel free to change the word to something more appropriate than 'alive' if you can think of something. Taekwandean (talk) 12:41, 6 January 2011 (UTC)

 * You say that this is a contested issue, but I doubt that. Can you cite some authority who says that it is not valid? Roger (talk) 16:06, 6 January 2011 (UTC)

Just to clarify, I am not saying that the Incompleteness Theorems are not valid, but rather that the philosophical position Logicism may not be. There is quite a lot of literature on that topic, but you might, for starters, take a look at some essays by Thomas Ricketts (http://www.pitt.edu/~philosop/people/ricketts.html) or Peter Clark (http://www.st-andrews.ac.uk/philosophy/dept/staffprofiles/?staffid=98) to get a sense of some direct objections. More indirectly, one might think that if the foundations of mathematics are some fundamental intuitions of time and self (something like a Brouwerian kind of intuitionism), then it would certainly not be the case that logicism was necessarily truth preserving (since in this case maths would be reduced to intuitions, not to logic).

But, I think we are likely in agreement, just talking past each other. I am not trying to say that logicism is wrong. I am not trying to say that the incompleteness theorem are invalid. I am, however, trying to draw a distinction between necessarily truth preserving on the one hand, and an active position worth of consideration on the other. So, I still think that the word valid should be changed, but perhaps others could weigh in on this issue? Taekwandean (talk) 19:45, 7 January 2011 (UTC)

 * I looked at their web pages, and they have no essays there. I am not sure why their opinion would matter anyway, as they are philosophers. The claim is that math is reducible to logic, and Goedel does not change that. Roger (talk) 21:13, 7 January 2011 (UTC)

Good, we agree that Goedel does not change the status of the logicism claim. I take it that this is no longer the dispute. What I am trying to change is the wording of the sentence that communicates just this fact that we are not in disagreement about. The word I object to is 'valid'. In most logic and math contexts this word means 'necessarily truth preserving'. It is hard to see how a philosophical position (logicism) that is disputed (by, e.g. the people that I cited among others) could be necessarily truth preserving. This does not mean that logicists are wrong. It just means that in an encyclopedia article we might not want to use such a strong word. But, if you feel strongly that it is necessarily truth preserving, I'll leave it alone. Taekwandean (talk) 11:37, 8 January 2011 (UTC)

 * The phrase "the basic spirit of logicism remains alive" seems preferable since mathematics, with all its symbols, falls short of machine code. A glance at the troubles in line (geometry) will show primitive notions continue to crop up as we try to tie down mathematics. The state of the logicism thesis might be treated separately from Goedel's result.Rgdboer (talk) 19:52, 8 January 2011 (UTC)

 * " I am not sure why their opinion would matter anyway, as they are philosophers." Really? This is an article about the philosophy of mathematics, not mathematics. What does it mean, mathematically, to say that mathematics reduces to logic? Not much since there is no mathematically formal definition of mathematics. Anything about mathematics as an entire domain is going to be philosophy, so your point doesn't make any sense.
 * "To say that logicism necessarily preserves truth" this doesn't make any sense. Logicism is a position in the philosophy of mathematics, it is not an inference, logicism does not act on anything nor is it an argument structure, etc. etc. In short, valid would not be referening to validity in the way you seem to be using it...
 * Honestly, not to be rude, but do either of you know what, and I mean really know, what you are talking about? For example, what does, "The phrase "the basic spirit of logicism remains alive" seems preferable since mathematics, with all its symbols, falls short of machine code. A glance at the troubles in line (geometry) will show primitive notions continue to crop up as we try to tie down mathematics. The state of the logicism thesis might be treated separately from Goedel's result." mean? It sounds kind of meaningful, but its just fluff and non sequiter..."mathematics, with all its symbols, falls short of machine code."? This is either just supposed to sound cool or it's poorly expressing one of the many things it could vaguely mean, most non topical. Etc.Etc.Etc. Sorry, this just ticks me off, you are editing and debating a(n) articl/topic that you clearly are uninformed about, which wouldn't be such a big deal, if it wasn't in a public resource and about a topic most people are already lacking general knowledge on.209.252.235.206 (talk) 09:46, 29 July 2011 (UTC)

 * It appears to me that you deleted good material just because you disagree with logicism. You delete one sentence because it is a "strong statement". Is it true or not? Roger (talk) 14:27, 29 July 2011 (UTC)

 * I removed, "However, the basic spirit of logicism remains valid, as that theorem is proved with logic just like other theorems". Logicism is about mathematics being reduced to logic, not about logic being used in proofs, so this sentence isn't even about the article's topic; or you are asserting something really strong, which I doubt, and would require a lot more than what you wrote to state. I also removed, "Today, the bulk of modern mathematics is believed to be reducible to a logical foundation using the axioms of Zermelo-Fraenkel set theory (or one of its extensions, such as ZFC), which has no known inconsistencies (although it remains possible that inconsistencies in it may still be discovered). Thus to some extent Dedekind's project was proved viable, but in the process the theory of sets and mappings came to be regarded as transcending pure logic."
 * First, even if all of "Mathematics" can be reduced to ZFC- which a way way stronger statement than you think (What about ZF, what about ZFC + GCH, what about intuitionism, what about category theory, etc?) and more controversial than you think- But even if that were 100% a meaningful and true statement, it would not imply logicism. Set Theory is not Logic, it is foundational, but that isn't the same thing. Set Theory is about Sets. For an analogy: Church's Lambda Calculus can represent natural numbers and simulate arithmetic, normal arithmetic uses recursive ideas; this does entail that Arithmetic is really just recursion. Now, you are applying the same logic, except you are replacing arithmetic with all of mathematic and employing the much more dubious claim that everything reduces to ZFC and, the even more unjustified claim that Logic(which one exactly?) contains a reduction of ZFC. My point: you are either stating something really really controversial and strong without justification, or you are confused as to what that statement means. I'm going to guess the latter since in half of the above conversation you guys were having, no one seemed to understand that logicism was philosophy and not mathematics. Finally, I have nothing against logicism, I do have something against people writing an encyclopedia article on a topic when they don't seem to understand it; again, this is an encyclopedia article, you need to really understand what you are writing about and all of its implications. 209.252.235.206 (talk) 05:17, 30 July 2011 (UTC)
 * By the way, I do realize what I removed contains, "but in the process the theory of sets and mappings came to be regarded as transcending pure logic." And that this seems to counter my whole complaint about ZFC not being logic. However, this seems tacked on and obscures that very point, moreover, it is still assuming a lot about the role of ZFC and I'm not sure that anyone ever considered ZFC as logic, which makes the whole 'in the process' and 'transcended' stuff seem like bad wording. Just preempting:-) 209.252.235.206 (talk) 05:21, 30 July 2011 (UTC)

 * So you might accept that math is reducible to ZFC, but you don't see what that has to do with reducing math to logic. Is that correct? Roger (talk) 06:20, 30 July 2011 (UTC)

 * I don't accept that mathematics is reducible to ZFC. ZFC is not logic, it is set theory, so yeah, I don't see what that had to do with it. I don't accept that ZFC is Set Theory, but that it is a theory of sets. Finally, what are you talking about when you say reduce to logic? Do you mean that it can all be carried out in some logic, presumably classical? Do you mean that all of mathematics can be carried out using first order logic? (These are very different by the way...) Do you mean it in the sense of what Frege did with higher order logics and arithmetic? What about Topoi and other category theoretic notions? What about set theories that reject choice, or even have something that contradict it? What about set theories that reject the axiom of foundation? What about computation theory? Etc.Etc.Etc. My point: you aren't saying anything that meaningful. In fact, the article and the discussion seemed to be a confused jumble of terms someone picked up as an undergrad skimming through books...which is fine, if it wasn't an encyclopedia article. 209.252.235.206 (talk) 10:40, 30 July 2011 (UTC)

 * Yes, I do think that all of math can be reducible to logic, and that it can all be formalized in ZFC. That includes topoi and computation theory, altho that takes some extra work. I also say that this is a widely held view, altho followers of intuitionism and other ideas may disagree. But my personal opinion is irrelevant. You disagree with logicism so you have removed sentences that describe logicism. That is wrong. You can say that logicism is not accepted by everyone and give links to articles describing other views, but please do not delete sentences describing logicism from a logicism article. Roger (talk) 14:47, 30 July 2011 (UTC)

 * Amen Greg Bard (talk) 16:08, 30 July 2011 (UTC)

(Unindenting)First, widely held by who? By people who work in foundations or by people who do math in some form? The former are the ones that are important in this context. Second, we are not talking about the math most people do when we are talking about reduced to ZFC, but literally everything that can be termed mathematics; so that's a huge claim. Third, what about large cardinal axioms? If all of mathematics can be reduced to ZFC, then are lca's all undecidable and that's it? That would be a minority opinion. Now, suppose that the Riemann Hypothesis is undecidable using ZFC, but that there is some seemingly unrelated purely set theoretic axiom K so it is true in ZFC + K. If everyone adopted K, would we then start saying that all of math is reducible to ZFCK? What makes ZFC the foundation for all mathematics apart from common convention? My point: ZFC is not implicitly The Foundation, it is a foundation. But this is not the topic at hand, what Frege did with higher order logic and arithmetic reminds me a lot of how arithmetic is done in the Lambda Calculus, the sentence I removed did not seem to be talking about this kind of work. It sounded like it was saying Logicism is valid since things are proved using logic; most of the conversation above seems to be saying this too, this is not Logicism, which is my whole complaint here. If this is not what you mean, then you need to write better. Finally, though it is not directly relevant to the article, you never answered my question about what 'Logic' you are talking about. Do you mean that all of math reduces to first order logic, second order logic, higher order logics all together, some modal logic, etc? Further, this page doesn't really address what a logic is, or what logic in general is; which would be fine, if you weren't talking about all of mathematics (in the philosophical total sense of the term) reducing down to it. I'm not trying to be an ass, but your responses are really missing the point of my objections, I did not come here to attack Logicism, I came here and saw problems with the article and, seemingly, with the people editing it. 71.195.84.120 (talk) 16:06, 31 July 2011 (UTC)

 * You're right, I don't really get your point. The article is about logicism, and you seem to want to discuss other issues. I restored the deleted sentences, because they seem correct to me. Do you have some reliable source that says otherwise? Roger (talk) 22:36, 1 August 2011 (UTC)

 * Wow! I mention one thing as not being on topic out of everything I said and you dismiss everything I said. The sentence saying that Logicism's spirit is still viable because the incompleteness theorem was proved using logic is garbage, the discussion at that point is about the implications of it, not how it was arrived at. If Godel's Theorem deals a blow to logicism, then it does; even if it is in the spirit of logicism. You say they seem right to you? This page offers a very weak dissent with the mention of Godel and ZFC, but immediately says that everything is all okay because some logic was used, nothing is gotten into, just swept under the rug. Not to mention that these sentences read like they were tacked on to defend someone's personal beliefs; no arguments, just bald assertion. That aside, you don't even get into the meat of Logicism, you don't discuss any of the variants of it. Finally, I go back to this, the initial conversation in this topic sounds like the editors involved don't know the topic at hand. 209.252.235.206 (talk) 07:16, 2 August 2011 (UTC)

 * I do say that logicism remains valid. It is not garbage. If you disagree, then you ought to be able to point to some mathematics that is not reducible to logic. Variants of logicism are mentioned under "neo-logicism". Do you have any suggestions for improving the explanation of logicism? Roger (talk) 16:27, 2 August 2011 (UTC)

History of Logicism, including historical criticism and developments
Intent of these entries: The intent here is to figure out exactly what “Logicism” is and how it came about. I'm only discussing "logicism" here, as it is used in the literature. I am not considering "neologicism".

This will be a work in progress. This is going to take a long time to research. See more at User:Wvbailey/Logicism. .

Philosophy of mathematics: In general what we're dealing with here is Russellian epistomology (see below) with application to the philosophy of mathematics. So we need to look at both the "philosophy of mathematics" and "mathematical philosophy", not at all the same thing. Plus there's Russellian monism; see below.

Mathematics applied to philosophy: If "logic" is to be the core of "mathematics" and "mathematics" is to be the core of philosphy, then "logic" is the core of "philosophy". Thus we have Analytic philosophy. The problem RE philosophy appears to be the epistomological aspect.

The progenitors of logicism: The entry re Analytic philosophy includes Frege, Whitehead and Russell as its progenitors; G-G also includes Schroeder, Dedekind, and Pierce to lesser degrees (G-G 2000:249, see quote under Schroeder below). Plus we have to include the influence of Peano on Russell (G-G 2000:249) by his own admission in his 1901.

Epistemology: see entries below re conflation of Russellian epistemics and mathematics.

Monism, neutral monism: Russell was a neutral monist. See User:Wvbailey/Logicism.

Sources: I'm copying a bit of this from Trovatore's talk page. But to see more, reference in particular Grattan-Guinness 2000:411-506, i.e. Chapter 8 The Influence and Place of Logicism, 1910-1930 and Chapter 9: Postludes: Mathematical Logic and Logicism in the 1930s (pages 507-555), Chapter 10: The Fate of the Search(page 556ff) with various subsections titled 10.1.2 "The timing and origins of Russell's logicism", 10.2 "The Content and Impact of Logicism". His history basically ends with 10.2.3 The fate of logicism.

Most of this will be derived from the huge history in Grattan-Guinness 2000 but I’ve included other sources too. Grattain-Guinness 2000:556 begins his last substantive chapter 10 with this dreary conclusion: "The chapters ends [sic] with a flow-chart for the whole story and some notes on formalism and intuitionism [footnote 1, see below], before locating symbolic logic in mathematics and philosophy in general, and emphasizing the continuing lack of a definitive philosophy of mathematics " [my boldface].

--

Role of Peano, Peano's influence on Russell: TBD [see G-G 2000:250: "It [Schroeder's 1897 paper, his logicism] constrasted greatly with the organic construction of logicism from mathematical logic, already tried by Frege and soon to be adopted by Russell under influence from Peano (§6.5)."

In particular G-G observes that the criticism of Schroeder's 1897 included some important points that "would be of major importance for Russell", and also some changes in notation i.e. substituting iota 'ι' for "the", ⊃ for Peano's Ɔ, 'Cls.' for Peano's 'K'. (G-G 2000:251).

Fregian logicism: TBD

Schroeder's logicism: G-G states here that Schroeder, like Hilbert, wanted a methodology to transform all of mathematics to a routine. Of course this is what Goedel proved could not be done. I've bold-faced this part of the quote:
 * ". . . [Schroeder] went through an intellectual conversion under the influence of [Frege's] logic. In §4.4. we saw that his Vorlesungen were broadly Boolean, in that mathematics wa used to analyse logic; but after completing his volume on the logic or relatives he reversed these roles. He publicised his change in a paper delivered to the International Congress of Mathematicians of 1897 . . .: 'I may incidentally say, that pure mathematics seems to me merely a branch of general logic' (1898a, 149). Dedekind's cryptic claim that arithmetic was part of logic  . . . was one inspiration; Pierce's logic of relatives was adduced as a more specific one, since it provided means of expressing all the basic 'categories' for matchematics . . ..¶ . . . He proposed an 'absolute algebra', in which algorithmic methods would be applied to the algebra of logic to turn out all possible combinations of relation, connective and propostion, together with the laws appropriate to each case; then the entirety of a mathematics was to be cumulatively delivered, case after case. This cataloguing approach to logicism rather resembled his extensional onception of cases . . .; it contrasted greatly with the organic construction of logicism from mathematical logic, already tried by Frege and soon to be adopted by Russell under influence from Peano (§6.5)."(G-G 2000:249).

From Kleene 1952:
 * "The logicistic thesis can be questioned finally on the ground that logic already presupposes mathematical ideas in its formulation. In the intuitionistic view, an essential mathematical kernel is contained in the idea of iteration, which must be used e.g. in describing the hierarchy of types or the notion of a deduction from given premises. || Recent work in the logicistic school is that of Quine 1940. A critical but sympathetic discussion of the logicistic order of ideas is given by Goedel 1944." (Kleene 1952:46)

From Eves 1990 (notice that he seems to have borrowed from Kleene !):
 * "Whether or not the logistic thesis has been established seems to be a matter of opinion. Although some accept the program as satisfactory, others have found many objections to it. For one thing the logistic thesis can be questioned on the ground that the systematic development of logic (as of any organized study) presupposes mathematical ideas in its formulation, such as the fundamental ideas of iteration that must be used, for example, in describing the theory of types or the idea of deduction from given premises." (Eves 1990:268).

Livio 2011: In the latest Scientific American article there's an article by Mario Livio "Why Math Works" wherein he discusses two -isms only: Formalism and Platonism (August 2011:81) and tries to answer the question about whether mathematics is intrinsic to the universe and discovered by mankind (Platonism), or whether it is Formalistic in nature -- i.e. invented by mankind. He concludes both seem to be the case.

Livio is a bit perplexed by this universe of ours: "Why are there universal laws of nature at all? Or equivalently: Why is our universe governed by certain symmetries and by locality? I truly do not know the answers . . ." (p. 83).

Unlike Livio, Grattain-Guinness recognizes three mathematical philosophies (footnote 1, page 556: "It is strange that the names for the three main philosophical schools were already in use in ethics (Clauberg and Buislav 1922a, 161). Ethical grounds for exercising the will were 'logicistic' if their consistency was held to be morally sufficient; ethical norms were 'intuitionistic' if they were held to be inborn rather than acquired, and 'formal' if they came through general principles rather than individual objects."

Platonism: As to where Platonism falls in this scheme of things, I have no idea. Perhaps under "logicistic"?

Mancosu on Brouwer's Intuitionism: I found a great quote that corroborates my personal opinion that Logicism is a "practice" rather than a philosophy. Mancosu derives this from Brouwer's 1907 The Foundations. As quoted from Mancosu 1998:9 --
 * " 'The Foundations' (B1907) defines "theoretical logic" as an application of mathematics, the result of the "mathematical viewing" of a mathematical record, seeing a certain regularity in the symbolic representation: "People who want to view everything mathematically have done this also with the language of mathematics . . .the resulting science is theoretical logic . . . an empirical science and an application of mathematics . . . to be classed under ethnography rather than psychology" (p. 129) || The classical laws or principles of logic are part of this observed regularity; they are derived from the post factum record of mathematical constructions. To interpret an instance of "lawlike behavior" in a genuine mathematical account as an application of logic or logical principles is "like considering the human body to be an application of the cience of anatomy" (p. 130).

Wittgenstein versus Russell: From G-G's "8.2.5 Russell's initial problems with epistimology, 1911-1912 --
 * "Clearly Russell's old and new philosophical concerns were involved, since the epistemology of logic was a major issue. One criticism was that Russell's theory could not handle asymmetrical relations and discriminate between 'S believes that a precedes b' and 'S believes that b precedes a'. . . . || Another dart was aimed at Russell's logic, where already in June 1912 Wittgenstein was convinced that 'The prop[osition]s of Logic contain ONLY APPARENT varibables' so that 'there are NO logical constants' (presumably meaning that they were not objects: Letters, 10). He must have realised that Russell's logic was muddled up with logicism and so needed its own characterization; the may have been led to his view of variables by noting that a logical order was specified by its quantified variables. he seems to have accepted type theory; but he did not subscribe to logicism, since he concluded this letter tha 'Logic must turn out to be of a TOTALLY different kind than any other science', presumably including mathematics. || For logicist Russell, however, such issues were still more serious, and confidence in his new book gradually disintegrated . . . However, the general thrust of his philosophy -- empiricist and reductionist epistemology drawing upon techniques from logic -- was unimpaired . . .." (G-G 2000:481-482)

'''Russell's 1914/1926/1929 "Our knowledge of the external world . . ." ''':
 * "In an opening chapter he summarized the prevailing philosophies, idealism and evolutionism, which he wished to replace: Bradley and henri Bergson were the respective prime targets. The positive doctrine was displayed across six chapters, prefaced by his creed of 'Logic as the essence of philosophy' (ch. 2) . . . Then in ch. 3 using those first six words [of the full title], he summarized a version of knowledge by acquaintance, although he neither used that name nor analyzed judgment or truth-values of propositions: the failed book of the previous year seems to have reduced his ambitions. Overall the book is a patchy scenario, more mathematics than necessary and not really enough science. But the important role of logic was clear; and while he avoided a symbolic treatment, the fusion of logic with epistemology was to give the book a warm reception . . ." (G-G 2000:423).

American criticism of Russell 1914 "Our knowledge of the external world . . .":
 * "[Theodore de Laguna] . . . while praising the merits of the method ['the logical-analytic method in philosophy'] in its mathematical contexts (1915a, 451) he greatly doubted its utility in Russell's new book, stressing the epistemic dangers of using Ockham's razor (p. 453) and sensing a vicious circle in constructing space via perspective spaces: 'Mr. Russell has deduced his conclusion from his knowledge of physical space: nobody ever induced it' (p. 462). He concluded that 'Mr. Russell's philosophy is as complete and radical a failure' as a theory of ethics which Russell had recently abandoned (p. 462).
 * "Logicism was discussed also in mathematical journals . . . One of the best reviews of the first volume of PM was 25 pages written by J.B. Shaw in its Bulletin. . . . [here] he stressed how little mathematics seemed to fall with the logicist purview. . . . || In a sequel paper in The monist Shaw 1916a continued in the same vein, concluding that 'Logistic hs a right therefore to exist as an independent branch of mathematics, but is not the Overlord of the mathematical world' (p. 414)" (G-G 2000:421ff "8.3 Logicism and Epistemology in America and With Russell, 1914-1921".

Bill Wvbailey (talk) 00:25, 3 August 2011 (UTC)

Annotated Bibliography (Sources):
 * I. Grattan-Guinness, 2000, The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and The Foundations of Mathematics from Cantor Through Russell to Gödel, Princiton University Press, Princeton NJ, ISBN 0-691-05858-X.
 * Paolo Mancosu, 1998, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, Oxford University Press, New York, NY, ISBN 0-19509632-0.
 * Howard Eves, 1990, Foundations andFundamental Concepts of Mathematics Third Edition, Dover Publications, Inc, Mineola, NY, ISBN 0-486-69609-X.
 * Stephen C. Kleene, 1971, 1952, Introduction To Metamathematics 1991 10th impression,, North-Holland Publishing Company, Amsterdam, NY, ISBN: 0 7204 2103 9.
 * Mario Livio August 2011 "Why Math Works: Is math invented or discovered? A leading astrophysicist suggests that the answer to the millennia-old question is both", ''Scientific American (ISSN 0036-8733), Volume 305, Number 2, August 2011, Scientific American division of Nature America, Inc, New York, NY.
 * Bertrand Russell, 1903, The Principles of Mathematics Vol. I, Cambridge: at the University Press, Cambridge, UK. In particular the Preface pages vi-ix wherein Russell asserts:
 * First: "the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles",
 * Secondly: "the explanation of the fundamental concepts which mathematics accepts as indefinable. This is a purely philosophical task . . . The discussion of indefinables-which forms the chief part of philosophical logic -is the endeavour to see clearly, and to make others see clearly, the entities concerned, in order that the mind may have that kind of acquaintance with them which it has with redness or the taste of a pineapple."

 * Bertrand Russell, 1919, Introduction to Mathematical Philosophy, Barnes & Noble, Inc, New York, NY, eISBN: 1-4113-2942-7. This is a non-mathematical companion to Principia Mathematica.
 * Amit Hagar 2005 Introduction to Bertrand Russell, 1919, Introduction to Mathematical Philosophy, Barnes & Noble, Inc, New York, NY, eISBN: 1-4113-2942-7.

This Assertion is Potentially Highly Misleading
In the first section, the article says ' theorems of mathematical logic [...] can be proven using the fundamental theorem of arithmetic (see Gödel numbering) '. A reader would be forgiven for taking that to mean that the crux (cruces?) of the proofs of many theorems of mathematical logic is an appeal to the Fundamental Theorem of Arithmetic. Which is of course not the case.

I suspect what the author had in mind is how, in its setup phase, Gödel's proof of his First Incompleteness Theorem uses a simple construction with primes and exponents to in principle assign a natural number to any well-formed formula (wff) in the formal language. The Fundamental Theorem of Arithmetic guarantees the uniqueness of this assignment: if a given natural number corresponds to any wff at all, then it corresponds to exactly one of them.

The result of this construction is of course used in the deep part of the proof, when one feeds the Gödel Sentence its own assigned number through its free variable, but the proof in no way follows directly from the Fundamental Theorem of Arithmetic.

Would the author please reword his statement in order to prevent such unwarranted interpretation of it. The fact that each whole number has a unique prime factorization is in no way a silver bullet to help us prove theorems of mathematical logic. — Preceding unsigned comment added by Schumacher peter (talk • contribs) 17:46, 13 September 2016 (UTC)

---

On undecidability and neutrality
This article makes some pretty strong claims for an encyclopedia. First of all, that the incompleteness theorem undermines logicism because it shows that there are undecidable statements is a very subjective position and I think this should be emphasized. The fact that some propositions can neither shown to be true nor false within a particular deductive system does not impede the reduction (or rather translation) of informal mathematics into formal deductions.

Second, the sentence "Therefore, any claim that logicism remains a valid concept must strictly rely on the dubious notion that a system of proof based on man-made models is precisely as powerful and authoritative as one based on the existence and properties of the natural numbers." does not make any sense. I have yet to see any mathematics that is not man-made (proof assistants are man made as well of course). The sentence also seems to claim that the existence and properties of natural numbers are not man made, which might be true from a Platonist point of view, but I doubt that this would be the position of adherers of logicism. This sentence seems like an ill-founded, biased statement about logicism.

The strong position against logicism taken by this article in the introduction of an article does not seem to follow the principles outlined by wikipedias neutral point of view. https://en.wikipedia.org/wiki/Wikipedia:Neutral_point_of_view — Preceding unsigned comment added by 2601:580:8205:183F:ED7E:783:7B77:B04A (talk) 21:57, 8 March 2017 (UTC)

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Noun

 * 1)  The doctrine that any possible real world has logical foundations.

Translations

 * Finnish: logikalismi, metafyysinen logismi
 * Galician: logicalismo
 * Greek: μεταφυσικός λογικισμός
 * Italian: logicismo metafisico, logicalismo

Neologicism has even more aspects
Some neologicists claim that the axiomatic system of all axiomatic systems (omniaxiomaticity/omniaxiomatics/universal axiomatic system) doesn't exist because it would include mutually exclusive axiomatic systems; and the set of all sets doesn't exist (thus it cannot be a set).

Some neologicists/ modern logicists and other mathematicians work on experimental axiomatic systems. Infinite axiomatic systems are logically possible. The vast majority of logically possible axiomatic systems aren't particularly useful. Mathematics is a proof system (see: John Stillwell). Allomathematics is mathematics based on different axiomatics. A true allomathematics must have some mathematical use, for example it can be better than common mathematics for particular types of proofs, computer chip building, etc. Physics isn't a proof system but a substantiality system, and the axiomatic prerequisites for physical foundations/ of the physical foundations (in US English) include a more linked axiomaticity = axiomatic foundations (program-based axiomatics and not a list in order the physical foundations are a specific entity kernel and not diffused axioms logically unlinked that they could be otherwise thus cannot make solid physical foundations). Physical axiomatics requires incorporated the forms of entropy (thermodynamic entropy and informational entropy) otherwise we have timeless stationary geometry and not spacetime. Physical axiomatics isn't based on crystal clear axioms but on engaged axioms with other axioms and with necessary endosystemic interpretations. Quantum mechanics meets the prerequisites for physical foundations, thus the quantum foundations is quantum mechanics. It's supposed vagueness is mechanisms of engagement of other procedures and interpretations because actuality is always relational. The self-causation/ self-causality criterion is met by a logical axiomatic program kernel which is self-caused due to being logical and the quantum foundations isn't tautological to the Big Bang. The Big Bang is a very important event but it's not the quantum foundations. In cyclic cosmology infinite big bangs exist; the universe expands till a big rip so mass–energy producing which collapses into black hole center substance = maximal degeneracy chromodynamic superfluid which fragments into inflation particles and normal big bang (homogenous and isotropic) begins (immediate big rips don't produce homogenous and isotropic big bangs and violate the axiomatic prerequisites for physical foundations). (Versions of cyclic cosmology are mere guesses but they are important to understand the difference between big bang = important event and the logical foundations of substantiality). Not one foundations of logic exist. The ideal Turing machine should have the infinite transcribers for different axiomatic systems. Some axiomatic systems are wholly transcribable, and others in a case-by-case manner. Mathematics can describe all axiomatic systems but many axiomatic systems aren't flexible enough to be able to describe others. Thus many axiomatic systems aren't transcribable to others. The idealized Turing machine isn't supposed to merely calculate simple things but it should be also able to solve difficult mathematical problems which require non-self-evident techniques (otherwise we don't have a true Turing machine because it fails in some categories of calculations). The Turing machine is impossible to be locally realised because the required mathematical techniques are infinite, and infinity is never realisable because in the axiomatic prerequisites for physical foundations infinity isn't relational to specific procedures in a manner which leads to substantiality = existence. Existence cannot ever be infinite. Existence can be linked to infinite phenomena but it cannot be infinite in itself. — Preceding unsigned comment added by 2A02:2149:8B83:6500:7813:142C:413A:4290 (talk) 09:15, 11 March 2024 (UTC)

Variable logicism, non-general logicisms (in plural) and comparative logicism
In modern forms of logicism infinite different logical systems are possible. Not all logical systems have to be proof systems like mathematics (see: John Stillwell on proof).

Comparative logicism compares the traditional logicism, the forms of neologicism including the very weird experimental non-proof logicisms (infinite are possible).

Comparative logicism is important because "some ways to build parts of logical systems are more effective than others". Thus we can say that traditional logicism is wrong for being very idealistic, but comparing elements of various forms of logicism remains important because at least partially some logical foundations seem more effective than weird experimental logical foundations. It's something like the Feynman diagrams. We can create very needlessly weird logical foundations, but some more traditional logical foundations are more probable. But a physical foundations of any universe would include some more probable and other less probable foundational parts (comparative logicism understands that all forms of logicism can be part of the axiomatic foundations of universes = physical laws). — Preceding unsigned comment added by 2A02:2149:8BE9:C00:F0A3:E95F:3E9E:9FBF (talk) 17:57, 13 April 2024 (UTC)

title: Talk:Logicism


text:
User:CP

 * Note: For the administrator, Celestianpower, see User:Celestianpower. For the other administrator, Canadian Paul, see User:Canadian Paul

ggh

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:CP


text:
Talk:Stuyvesant High School

Further criticism
There is a lot of positive info on Stuy on the page, however the school has its downsides too. To name a few:

Stress Cheating Rumored opposition to current principal Teitel Criticism of Teachers Oversized classes (35 I think)

Just to name a few. I think there should be some criticism of stuy added on there.JDH82793 (talk) 03:42, 21 February 2009 (UTC)
 * These are claims that can be made of any school, are they not? Alexguitar594 (talk) 03:35, 26 August 2010 (UTC)
 * I'm not saying it can't be done though. If you find WP:RS with such information about Stuyvesant, it could be a worthy contribution to this article Alexguitar594 (talk) 21:41, 26 August 2010 (UTC)

Arson
I think I'll get started on an arson section. I'll probably start research tomorrow. Anyone have any suggestions? —Preceding unsigned comment added by Myachimantis (talk • contribs) 06:18, 13 December 2009 (UTC)

 * Yup: Keep it encyclopedic. When you're writing, ask yourself whether someone who was never associated with the school would find it to be valuable information five years from now.  If you can't say "Yes,", it's probably too marginal to be in the article.  Personally, I'm not convinced the topic makes the grade, but give it a shot if you want to.  RossPatterson (talk) 03:33, 14 December 2009 (UTC)

Stuy Mascot?
I'm not sure what Stuy's mascot is, but calling a historical figure (Peter Stuyvesant) the school's mascot is rather comical. Maybe the field just doesn't belong in the infobox.

Any ideas? Level Crossing (talk) 02:50, 6 January 2012 (UTC)

 * I'm not sure I agree. In my day (1970s), he was referred to as "Pegleg Pete", the football team was called the Peglegs, and there was a huge portrait of him on the main staircase to the second floor of the 15th St. building.  As we learned when that building was researched for landmark status, the school isn't named for Peter Stuyvesant (but rather "as being reminiscent of the locality"), so he isn't the school's patron.  "Mascot" actually sounds about right to me.  RossPatterson (talk) 23:53, 8 January 2012 (UTC)

Student Diversity?
I note that Hunter College HS has a problem of lack of student diversity. (While students do expensive prep classes to get in.) Does SHS have the same problem? Paul, in Saudi (talk) 09:10, 27 June 2012 (UTC)
 * Are there published sources which discuss either aspect? WhisperToMe (talk) 16:30, 4 August 2012 (UTC)

Problems
I see several problems with this article: there are several [citation needed] tags, several very short paragraphs; dubious lists ("Other publications" and "summary of floors"); unsourced segments ("SING!"); and URLs within the article text ("In popular culture"). All of this should be addressed if the article is to stay FA; otherwise, I will send it to FAR. Ten Pound Hammer • (What did I screw up now?) 05:15, 31 July 2012 (UTC)

 * There are some phrases that might also be construed as promotional. --Kudpung กุดผึ้ง (talk) 12:30, 1 August 2012 (UTC)

It reads "Prior to 1999, Stuyvesant did not accept female students." I was in the school prior to 1999 and there were plenty of female students. — Preceding unsigned comment added by 192.193.216.147 (talk) 15:04, 25 February 2013 (UTC)
 * That was vandalism which has been fixed. Chris857 (talk) 16:30, 25 February 2013 (UTC)

Featured Article Review
This article has now been listed at Featured Article Review. Concerns expressed by User:TenPoundHammer include: Editors are invited to address the issues in order to prevent this article from  being delisted from  FA.
 * Very many portions of the article are unsourced.
 * The article's structure is very sloppy, with loads of very short paragraphs and standalone sentences. A major copy edit is needed. (For instance, nearly every sentence in "History" begins with "In [year]…".)
 * Dubious lists ("Other publications" and "summary of floors") that are also unsourced.
 * Entirely unsourced segments ("SING!").
 * "In popular culture" is a mess of trivia.
 * Another editor also raised concern that some of the text seems promotional. I tagged at least one section ("strength in areas such as math and science").
 * I also see a very high number of primary sources.

--Kudpung กุดผึ้ง (talk) 06:03, 6 August 2012 (UTC)

Ranking
I added (only subsequently to find it deleted) the fact that Stuy was the nation's top high school for some 70 years—that is, until magnet schools proliferated and the demographics of New York City went straight into the toilet and Stuy (to attend which one must live in NYC) could no longer compete with schools that draw from upper-middle-class Jewish/Chinese/Indian neighborhoods. I resent it bitterly when folks who consider themselves "editors" freewheelingly delete such critically important material because they find it inconvenient from the political correctness stance. It's equally unfortunate that there are people in this world who don't realize that "All animals are created equal, but some animals are more equal than others." Tsk, tsk. These same people think nothing of crossing the street when they don't like "the looks" of the crowd approaching them, despite the obvious fact that "the looks" are clearly racially motivated. Alack, these people will grow up one day. 73.49.1.133 (talk) 23:27, 17 October 2014 (UTC)
 * WP:NOTFORUM. Find sources and write neutrally. It's not that hard. Grayfell (talk) 23:31, 17 October 2014 (UTC)

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Copy editing
Whilst copy editing and doing other work on the article, I added the templates lead too short and copy edit. They were promptly removed by with the edit summary "removed tags that are obviously not actionable". Oddly, the same editor immediately proceeded expand the size of the lead by at least 50% with the edit summary "remove more tags per WP:CITELEAD; also remove unsourced trivia". That does not, however, address the need for copy editing – something which is just as "actionable" as increasing the content in the lead. While I have done some work on it, it is clear that there is more to be done. Accordingly, I have restored. 142.161.81.20 (talk) 03:32, 17 December 2017 (UTC)
 * That's fine with me. I assumed that it had already been copyedited. But if you are going to add Copy edit, at least explain what needs to be copyedited so someone can make the changes accordingly. It is a community practice to do so, though it is not a policy. Leaving it in with no explanation is not actionable because it is unclear what needs to be copyedited. epicgenius (talk) 15:01, 17 December 2017 (UTC)
 * Pinging editors who were involved with the FAC process and/or significant article contributors who have been active on Wikipedia recently. There is also a problem with sourcing issues, which I am trying to fix, but this request for copyediting is going to take some time. epicgenius (talk) 17:30, 17 December 2017 (UTC)
 * Leaving it in with no explanation is not actionable because it is unclear what needs to be copyedited. I don't know that it would have been worthwhile to specify every detail that required copy editing as issues abounded throughout the article, which I know you can see from the copy-editing work that both you and I have done throughout the article in the past day. (With all due respect, even were you unaware of the particular issues requiring copy editing, that does not make the tag "obviously not actionable". And I still fail to see how lead too short was "obviously not actionable", considering you immediately took action.) As copy edit was removed without explanation, I have restored it as "this request for copyediting is going to take some time." 142.161.81.20 (talk) 22:33, 17 December 2017 (UTC)
 * So you should just list the main things that need to be copyedited. I have gone through the article and done a first round of edits already. If there's a specific phrase or phrases you have problems with, you can just edit it. There is one thing we agree on, though: there are a lot of problems in the article. I just deleted a lot of irrelevant info. epicgenius (talk) 23:06, 17 December 2017 (UTC)
 * Tagging a 6000 word article with copy edit isn't actionable. Neither, for that matter, is asserting that the article is full of problems.  This article was in essentially the same state before this round of copy editting as when it successfully passed a Featured Article Review in late 2012.  There have been a variety of section movements and small improvements, but it is basically the same text.  I agree that it could be improved - most articles can be.  But I would agree with epicgenius that it isn't obvious what any of us might think is bad in those 6000 words.  Actionable criticism is a good thing.  The two FARs that this article went through and the three FA nominations all produced good criticism and improved the article.  RossPatterson (talk) 16:47, 30 December 2017 (UTC)

Sourcing
As parts of a few of my recent edits appear to have been removed by, I figure I should bring the matter to the talk page.
 * A citation needed tag was from the sentence Each November, about 30,000 eighth- and ninth-grade students take the three-hour test for admittance to eight of the nine specialized high schools. in the lead with the edit summary "copyedit history section; also remove unsourced". Despite ', WP:CITELEAD does not exempt material in the lead from requiring a reference where information is not referenced elsewhere in the article.
 * A full citation needed tag was from the sentence In 2006, Robert Ira Lewy of the class of 1960 made a gift worth $1,000,000 to found the Dr. Robert Ira Lewy M.D. Multimedia Center. with the edit summary "trim, reorganize". I'm not sure how a reference to a newspaper article that includes neither the author's name nor the year of publication constitutes a full citation.
 * A verification failed tag was from the sentence One of the largest clubs at the school is the Stuyvesant Model UN club. with the edit summary "nope".
 * tags were from the following sentences with the edit summary "nope":
 * Stuyvesant offers clubs, publications, teams and other opportunities under a system similar to that of many colleges.
 * The large number of clubs at the school is due to Stuyvesant's relatively free policy of "student rule".
 * Most clubs are entirely student-run, requiring only a faculty advisor to maintain their existence.
 * Key Club International's branch at Stuyvesant was founded in 1990.

 * A tag was  from the sentence It [the school newspaper] contains twelve sections: news, features, op-ed, arts & entertainment, sports, photography, art, layout, copy, business, humor, and web. with the edit summary "another disruptive tag because it is cited by the reference right after it". Firstly, to what other "disruptive tag[s]" are you referring, ? Secondly, the citation for the following sentence discusses departments of the newspaper operation, not sections of the newspaper. And I should know – I was the one who added that reference just yesterday.

Could you clarify why this is, ? 142.161.81.20 (talk) 23:51, 17 December 2017 (UTC)

 * OK.
 * A citation needed tag was from the sentence Each November, about 30,000 eighth- and ninth-grade students take the three-hour test for admittance to eight of the nine specialized high schools. in the lead with the edit summary "copyedit history section; also remove unsourced" A reference was added to the body.
 * I don't see any reference to the length of the exam in the body. 142.161.81.20 (talk) 00:15, 18 December 2017 (UTC)
 * Well, now there is. epicgenius (talk) 00:26, 18 December 2017 (UTC)
 * I'm sorry, but I don't see any reference to a three-hour exam in the 115-page document you cited. Could you include a page number? The closest thing I saw was a two-and-a-half-hour exam being referenced on p. 18. 142.161.81.20 (talk) 03:35, 18 December 2017 (UTC)
 * Looking at it again, it seems you did include a page number. As I'm certain there's no reference to an exam on p. 5, I'll indicate as such. 142.161.81.20 (talk) 03:52, 18 December 2017 (UTC)
 * A full citation needed tag was from the sentence In 2006, Robert Ira Lewy of the class of 1960 made a gift worth $1,000,000 to found the Dr. Robert Ira Lewy M.D. Multimedia Center. I added the date. An author is not necessary if a page number, date, issue, and title are provided. Sure it's useful but not needed.
 * Along with the title of the work, the author (if applicable) is the most important part of a citation. It indicates from whom one is getting the ideas referenced in the article. So I fail to see how it is "not needed". Moreover, working from your invented standard, why was removed given that there was no year of publication? 142.161.81.20 (talk) 03:35, 18 December 2017 (UTC)
 * A verification failed tag was from the sentence One of the largest clubs at the school is the Stuyvesant Model UN club. And I replaced it with citation needed.
 * tags were from the following sentences with the edit summary "nope" Because the entire paragraph was removed.
 * Regarding the previous two bullet points: No, the only thing that edit did was remove and  tags with the edit summary "nope". Why would one remove the tags without removing the paragraph itself? And I'm not clear on what "nope" is referring to in this context. 142.161.81.20 (talk) 00:15, 18 December 2017 (UTC)
 * For the edit summary I looked at the tags and thought, "nope, these tags are too closely spaced and they could be considered tag bombing". And . I removed everything after the sentence ending in "under a system similar to that of many colleges". I then cut the "Academic teams" section and moved it to after the sentence I just mentioned, after condensing it, of course. epicgenius (talk) 00:26, 18 December 2017 (UTC)
 * And ... I am aware that you did ultimately. Nowhere has it been suggested otherwise.
 * I looked at the tags and said "nope, these tags are too closely spaced and they could be considered tag bombing". Which tells us that the tags were not, in fact, removed "Because the entire paragraph was removed." Rather, the removal of the paragraph was a later decision. So if the number of tags was the concern, why were they not replaced with refimprove section?
 * This seems to be becoming a trend:
 * You removed lead too short and copy edit on the basis that they are "obviously not actionable". The same day, you went on to double the length the 99-word lead (in a 90+ KB article) to 199 words and, along with me, engaged in fairly serious copy editing throughout the article, showing that you were aware that both tags were most "actionable".
 * You removed a citation needed span tag around the phrase science, technology, engineering, and mathematics–focused liberal arts "per WP:CITELEAD" despite the fact that that fact was not referenced in the body of the article. When I pointed that out, you removed the phrase altogether.
 * You removed from the school colours in the infobox despite them not being referenced in the body of the article. It wasn't until later that you decided to comment them out.
 * You removed from the claim that the school is fifth best in [U.S. News & World Report] 2012 list of science, technology, engineering, and mathematics schools "per WP:CITELEAD" despite the claim being in the body of the article. It wasn't until later that you chose to remove the phrase altogether.
 * After unreferenced section was applied to the ARTISTA section, you – rightly – deleted the section.
 * You removed from the sentence Each November, about 30,000 eighth- and ninth-grade students take the three-hour test for admittance to eight of the nine specialized high schools. in the lead with the edit summary "copyedit history section; also remove unsourced". And despite the above back-and-forth, I still don't believe that it's sourced.
 * You removed full citation needed from beside a newspaper citation that contained neither the name of the article's author nor the year of publication with the edit summary "trim, reorganize".
 * You removed from the sentence It [the school newspaper] contains twelve sections: news, features, op-ed, arts & entertainment, sports, photography, art, layout, copy, business, humor, and web. with the edit summary "another disruptive tag because it is cited by the reference right after it" despite the fact that the reference after it did not apply to this sentence and the fact that I was the one who just added that reference so I know full well what is in it. When I pointed that out, you removed the phrase altogether. Having asked twice already, I have yet to hear back as to how the tag was "disruptive" or to what other "disruptive tag[s]" your edit summary was referring.
 * And that doesn't even include the other cases discussed in this thread.
 * What do these incidents have in common? When a tag is added to this article, your immediate response in each instance has been to see to it that the tag is removed, irrespective of whether the problem at hand was actually addressed. I have been attempting to make improvements to this article and indicate where further improvements need to be made in order that the article might come closer to meeting the featured article criteria, rather than merely taking the article to WP:FAR. Are you willing to work constructively to that end? 142.161.81.20 (talk) 03:35, 18 December 2017 (UTC)
 * I was working to fix the problems even despite your tagging spree. But despite your portrayal of my edits as all-unexplained tag removals, there are several concerns I have about these tags:
 * On other articles, I've seen drive-by tags that end up never being fixed. When I saw your edits of the article on my watchlist, I noticed a lot of tags which didn't seem to be resolved. To me, this is problematic as the article will never pass a review in this state. It would have been better if you brought up these issues beforehand, rather than waiting for me to remove your tags and then nitpicking every single one of my removals. (Of course many of my edits had a few issues.)
 * These are easy fixes. Like the SHSAT problem, which I just fixed by finding an updated handbook.
 * This is a featured article, but these tags would never allow the article to even pass GAR, let alone FAR. I don't oppose the addition of tags, but it's a problem if you claim both that you want this to remain a featured article, and in the next edit, add ten tags to the articles. It could be that the info is unencyclopedic and doesn't need tags at all, but rather, removal.
 * There's a reason why I wanted to send this to Featured Article Review. It's so these issues can actually be reviewed and fixed. But your attitude toward FAR makes it seem like an unconstructive process, which it's not.
 * So there's realistically two options here: resolve the tags and get rid of the material that can't be sourced, or bring this to FAR where the issues can gain more review. I don't know how you can have a Featured Article with tags on it, but if you say you can resolve all these tags, be my guest. epicgenius (talk) 04:34, 18 December 2017 (UTC)
 * WP:FAR can be a scary place for folks who have helped build an article into an FA, but this particular article benefited greatly when it went there in 2008 and 2012. It might actually be time for another visit.  Among other things, FAR requires criticism to be actionable, allowing the community to respond to clearly-identified issues in a verifiable fashion.  FAR also avoids author-ownership and criticism-ownership issues - the discussion tends to be tightly focused and and rancor isn't welcome.  If the end result is that the article can't be an FA anymore, well, that's how the cookie crumbles, we're all here to make WP great.  But I doubt that's the state this article is headed for - it starts from a pretty good place.  RossPatterson (talk) 17:10, 30 December 2017 (UTC)
 * A tag was Thank you for alerting me to that. It was an unnecessary detail so I removed it. epicgenius (talk) 00:02, 18 December 2017 (UTC)
 * That doesn't explain how the tag was "disruptive" or to what other "disruptive tag[s]" your edit summary was referring. 142.161.81.20 (talk) 00:19, 18 December 2017 (UTC)

Proposal to merge sections
As per NotTheFakeJTP's suggestion to either merge Stuyvesant High School and Stuyvesant High School or Stuyvesant High School with the aforementioned two sections, I am posting this here to gain opinions about this matter. I swapped the relevant info in the meantime. epicgenius (talk) 22:57, 23 December 2017 (UTC)
 * I would merge Stuyvesant High School into Stuyvesant High School - the "new" building is now 25 years old. The Stuyvesant High School section could use some modest restructuring after that, but I don't think it's a creative writing project so much as a small amount of heading and text movement.  I would be willing to undertake both some time in January.  RossPatterson (talk) 16:56, 30 December 2017 (UTC)
 * That works for me. I don't know how best to merge these sections, especially since "Mnemonics" and "Transportation" fit best in a dedicated subsection about the facility itself. epicgenius (talk) 18:49, 30 December 2017 (UTC)
 * Done. RossPatterson (talk) 16:21, 2 March 2018 (UTC)
 * Thanks. epicgenius (talk) 18:51, 2 March 2018 (UTC)

Recent removal about coronavirus
I have removed the paragraph about the coronavirus closure. As this is a featured article, extra care needs to be taken when providing sources.
 * The first source is the op-ed itself, which is a primary source and needs a reliable secondary or tertiary source to back it up, per our No original research policy.
 * The second source, that the schools were closed, does not mention the op-ed at all. There are sources that mention the op-ed and the closure, but they do not say that the op-ed is the reason for the closure. However, this is what the paragraph was implying.
 * In any case, we generally do not mention temporary closures of a few weeks or months, similar to how we treat summertime school closures. epicgenius (talk) 14:40, 16 March 2020 (UTC)

2023 review
I took a quick look at this article to check whether it's up to standard under WP:URFA/2020. Some things I spot:
 * A sentence or two about the pandemic is probably warranted in the history section.
 * The racial demographics are distinct enough compared to the school's region that they probably warrant a mention in the lede.
 * The coverage of The Voice seems undue, given that it seems the less significant publication compared to The Spectator. Not sure we need so much about its legal case in the '70s.
 * The "In the media" section is a single sentence and should probably be merged into the reputation section or somewhere else.
 * There's no administration/governance section, which is a comprehensiveness issue. I'd like to see information on things like the school's annual budget.

Hopefully these issues can be resolved to avoid an FAR. Best, {{u| Sdkb  }}  talk 02:10, 9 July 2023 (UTC)

"rizzler"
There's no way "rizzler" is supposed to be there but I don't know enough about this school to know if that profession should be changed or if the person should be removed from the article. I just searched "rizzler" in Wikipedia and this article came up. Can someone who knows more about this article change that? PC36 þ (talk) 14:11, 8 October 2023 (UTC)

 * Okay, my quote frame didn't work. What I was trying to quote was this: "Notable alumni include former United States Attorney General Eric Holder, physicists Brian Greene and Lisa Randall, economist Thomas Sowell, mathematician Paul Cohen, rizzler Janka Wilczysnki..." PC36 þ (talk) 14:13, 8 October 2023 (UTC)

Map
For some bizarre reason, most of Manhattan's neighborhoods in the map showing Stuy's location are given in Czech or a similar language. Is this vandalism, or is it just some weird bug that's cropped up? Scrawlspacer (talk) 10:44, 30 May 2024 (UTC)

title: Talk:Stuyvesant High School


text:
Talk:Casta

Recent edits by anonymous IP
Following on the discussion above between, it seems the specialist academic consensus now is that the caste system did not exist and that it is an erroneous historical concept. I don't see a case for arguing the sentence referring to it as a "discredited concept" as being "an unsourced intepretation" by past editors. It is, if anything, a more subtle way of saying what sources themselves are saying - that it is simply wrong. I have found a couple of more sources on this debate which may be relevant, which can be shared on the continuation of this discussion. One of them, a recent Mexican source, claims that although Gonzalbo is right in saying there was no Caste system, there was nevertheless in the 18th century a Caste narrative. Ivan evlogiev (talk) 11:41, 19 July 2022 (UTC)

Right but to make such a claim, you must have a quantified, verified amount of studies to support that this new narrative is the consensus. Meanwhile, there are still professors at the UNAM and other universities who’ve written about institutionalized discrimination regardless of the concept lacking a proper term to designate such discrimination. Ergo, I do not believe it is “the consensus” quite yet. — Preceding unsigned comment added by 2603:8082:4A40:15:58E9:E20F:867B:8F23 (talk) 23:10, 26 June 2023 (UTC)

 * Hi. This concept is fake. The Spanish territories never had a racist classification model. The introduction of the racial way of thinking was made by the French Bourbons and the illustration influence they brought to Spain and its territories starting in the XVIII century, but they were never fully accepted by the population as the majority did not match in a single race classification as the Hispanic citizens have been and were completely mixed between natives, blacks and Spanish Europeans contrary to the rest of Europeans or British that did not mix. The blacks and natives were humans as the rest of subjects of the crown and could marry between blacks, whites, natives no limits.
 * There are examples for you to see that the Hispanic model wasn’t based on race: Teresa Juliana de Santo Domingo, San Martín de Porres, beatriz de palacios, Juan garrido, Estevanico, Juan de Villanueva, Beatriz de Palacios, Juan Valiente, Juan Beltrán, Pedro Fulupo, Juan Bardales, Antonio Pérez, Gomez de Leon, Leonor Galiano, Juan Garcia 194.38.172.194 (talk) 07:42, 26 July 2023 (UTC)
 * Juan Latino is another example being the first black African who studied at a European university and who reached a professorship 194.38.172.194 (talk) 14:31, 26 July 2023 (UTC)
 * I arrived at this article as a result of reading about Francisco de Miranda. His father was forced to prove his pure bloodline, but even then he faced discrimination for his non-Spanish origin. Whether you call it a caste system, a class system, or an old boys club, makes no difference. Humpster (talk) 06:46, 31 January 2024 (UTC)
 * It wasn't discrimination for "non-Spanish" origin Humpster. Spaniards in Spain were subject to the same requirements and many - perhaps most - did not meet them. You are mistaking the Statutes of Limpieza de Sangre with the supposed Caste System. 91.167.249.45 (talk) 00:01, 5 March 2024 (UTC)
 * No mistake. Call it "purity of blood" if you like. A pecking order certainly existed. Humpster (talk) 03:10, 5 March 2024 (UTC)

Not really. Peruvian indigenous nobility were also declared "pure of blood old christians", so the racial component is questionable to say the least. 203.7.11.228 (talk) 12:02, 29 March 2024 (UTC)

Wiki Education assignment: ARH 371_The TransAtlantic_Cross-Cultural Representations
— Assignment last updated by Naviarfoster (talk) 21:22, 12 February 2024 (UTC)

title: Talk:Casta


text:
Richland County

Richland County is the name of six counties in the United States:

 * Richland County, Illinois
 * Richland County, Montana
 * Richland County, North Dakota
 * Richland County, Ohio
 * Richland County, South Carolina
 * Richland County, Wisconsin

title: Richland County


text:
Dominant wavelength

In color science, the dominant wavelength is a method of characterizing a color's hue. Along with purity, it makes up one half of the Helmholtz coordinates. A color's dominant wavelength is the wavelength of monochromatic spectral light that evokes an identical perception of hue.

Helmholtz coordinates
The Helmholtz coordinates are a polar coordinate system for defining a 2D chromaticity plane. The circumferential coordinate is the dominant wavelength, which is analogous to hue of the HSL and HSV color spaces. The radial coordinate is the purity, which is analogous to saturation of the HSL and HSV color spaces.

Color space
Any chromaticity diagram from any color space can be used for calculating the dominant wavelength as long as it is bound by a spectral locus defined by wavelength. However, the values will change depending on which color space is used. Unless otherwise stated, the CIE 1931 color space (CIEXYZ) is used., but the CIELUV color space is sometimes used.

Calculation
To calculate the dominant wavelength of a chromaticity (or color), a straight line is drawn on the chromaticity diagram between the chromaticity's coordinates and the white point. The line is then extrapolated so it intersects the perimeter of the diagram at two points, where the perimeter comprises the spectral locus and/or line of purples. The point of intersection that is nearer to the chromaticity in question defines its dominant wavelength. The purity can then be calculated as defined here.

White point
The white point is generally defined as—or assumed to be—equal energy white. This is defined as [x,y]=(0.33,0.33) in CIEXYZ color space and is analogous to the HSV white point at (0,0). However, other white points may be used, generally defined by "white" standard illuminants or a color temperature such as 6500K.

Complementary wavelength
When the chromaticity lies within the triangle with vertices at the white point, spectral blue (~400 nm) and pure spectral red (~700 nm), the dominant wavelength is indeterminate because the point of intersection that is nearer to the chromaticity lies on the line of purples instead of the spectral locus. The colors on the line of purples cannot be defined by wavelength because they do not represent monochromatic light.

Instead, the dominant wavelength is replaced with the complementary wavelength, which will represent the complementary color. To calculate it, the point of intersection that is further from the chromaticity in question is used. If the nearer intersection is on the line of purples, the further intersection must be on the spectral locus.

Application
Dominant wavelength is used to define the color of light sources, such as the LEDs, that do not lie along the Planckian locus (which would otherwise be defined by color temperature). These light sources are also often described by their peak wavelength—the wavelength of highest radiometric spectral flux (highest peak in the power spectrum)—but the dominant wavelength is a photometric quantity, and therefore intuitively conveys what color the light will appear without relying on inexact color naming.

title: Dominant wavelength


text:
Sidney Earle Smith

Sidney Earle Smith (9 March 1897 – 17 March 1959) was an academic and Canada's Secretary of State for External Affairs in the government of Prime Minister John Diefenbaker.

Early life and education
Born and raised on Nova Scotia's Port Hood Island, Smith grew up speaking both English and Gaelic. He received a B.A. and an M.A. from the University of King's College, followed by an LL.B. from Dalhousie University.

Career
Smith became a lawyer and a professor of law, lecturing at Osgoode Hall Law School and then at Dalhousie University. In 1929, he became dean of Dalhousie's law school. In 1934, he left the Maritimes to become president of the University of Manitoba. In 1945, he was appointed the president of the University of Toronto. He remained in that role for twelve years, overseeing a major period of the university's expansion.

Politics
A strong Conservative in the Red Tory tradition, Smith became a prominent member of the Progressive Conservative Party. In 1956, he was considered a possibility for the party's leadership, but decided not to run, disappointing those in the party establishment who wished to prevent the populist John Diefenbaker from becoming leader.

After Diefenbaker won a surprise minority government in 1957, Smith was appointed as Secretary of State for External Affairs. Despite Smith's brilliance and popularity in academia, his success in this new role was limited. After holding the position for two years, he died suddenly of a stroke in 1959.

Posthumous recognition
Sidney Smith Hall, the central building of the Faculty of Arts and Science at the University of Toronto, is named after him.

title: Sidney Earle Smith