Talk:Logicism

message: 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)
thread_title: A request for referencing

message: 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)
thread_title: This article is a mess. I suggest a rewrite

message: * 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)
thread_title: The definition of the natural numbers

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

message: 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)
thread_title: sentences removed

message: 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)
replies: text: 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)
thread_title:  The incompleteness results 

message: 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)
replies: text: Good enough yet? Canadianism 18:49, 28 February 2007 (UTC)

text: 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)
replies: text: 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)

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

message: 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)
thread_title: This Assertion is Potentially Highly Misleading

message: 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)
thread_title:  On undecidability and neutrality 

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thread_title:  External links modified 

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thread_title:  External links modified 

message: ==missing in Wiktionary==
=logicalism=
Wiktionary code
==English==
===Etymology===

===Noun===

#  The doctrine that any possible real world has logical foundations.
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:: Physicalism doesn't always focus on what exactly is the physical, or it doesn't focus in one way. Logicalism is the logical axiomatic prerequisites for physical foundations. The axiomatic system of (containing) all axiomatic systems is impossible (cannot be functional due to incompatibilities and other logical problems), thus it becomes (because it cannot function as an axiomatic system) the set of all sets which doesn't exist. Still the axiomatic prerequisites for physical foundations have some criteria hypernymic to the quantum foundations. Self-causation is necessary both in the God–Universe system and in the open axiomatic multiverse trees. Not all universes are parallel, which means that not all universes are mathematically equivalent/compatible. Also not all the universe-like cosmoi/worlds meet all the criteria to be true universes.
The fact that there's no [omni]universal axiomatics = no omniaxiomatics = there isn't the axiomatic system which includes all the infinite possible (even the infinite weird experimental ones we can make) axiomatic systems, [that fact] is very important and fundamentally related both in logicism (mathematical logicism) and in logicalism (metaphysical logicism).
: Some topics are rare. Don't harm them. Ask the University of Edinburgh professors who work on these fields... but mere philosophy won't cut it. You'll need to talk to MIT professors who experiment with axioms, and quantum foundations professors at the Perimeter Institute for Theoretical Physics... But nowadays science has many gaps. Not that the axiomatic system of all axiomatic systems doesn't exist, thus no future civilization will be ever able to claim something magical and erroneous. Mistakes aren't the solution and there isn't a simple unified solution.
2A02:2149:8B63:D400:BD1F:56E8:B586:E393 (talk) 03:49, 9 November 2023 (UTC)
thread_title:  Logicalism = metaphysical logicism (an aspect of physicalism) 

message: 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)
thread_title:  Neologicism has even more aspects 

message: 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)
thread_title:  Variable logicism, non-general logicisms (in plural) and comparative logicism