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The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.

The article was promoted by Gog the Mild via FACBot (talk) 30 July 2023 [1].

Quine–Putnam indispensability argument

Nominator(s): Alduin2000 (talk) 17:57, 1 July 2023 (UTC)[reply]

This article is about one of the most important arguments in the philosophy of mathematics - according to some, the only good non-question-begging argument at all for platonism. The basic idea is that we should believe in numbers and other mathematical objects because they are indispensable to our best scientific theories. Behind that basic idea is a mix of complex ideas about the nature and goals of philosophy, how we come to know which things exist and which don't, and how language ties into answering these question. I believe this article should be a featured article because I think it now does justice to all of these ideas after some thorough GA and peer reviews. This is my first FAC so apologies if there are any major or obvious problems! Alduin2000 (talk) 17:57, 1 July 2023 (UTC)[reply]

First-time nomination

  • Hi Alduin2000, a little belatedly, welcome to FAC. Just noting that as a first time nominator at FAC, this article will need to pass a source to text integrity spot check and a review for over-close paraphrasing to be considered for promotion. Good luck with the nomination. Gog the Mild (talk) 17:37, 26 July 2023 (UTC)[reply]

Hi Alduin, welcome to FAC. Some comments on images:

  • File:Willard_Van_Orman_Quine_passport_cropped.jpg: the information provided under Licensing is not convincing - this may have been done to government specifications, but it's not a government work. And if it were a government work, CC-tagging it would not make sense. Nikkimaria (talk) 05:27, 2 July 2023 (UTC)[reply]
Hi Nikkimaria. Thanks for the suggestion, I'll add some alt text now. On the photo of Quine, it appears the original justification was that the uploader had gotten permission from the owner to upload with a CC license. Is it worth starting a VRT ticket? I'm not 100% sure of the process to be honest. Alduin2000 (talk) 10:16, 2 July 2023 (UTC)[reply]
It's not clear to me that the person from whom permission was received would actually be the copyright holder - it's not the subject, but perhaps a relative of theirs based on the name? And then was the photograph taken at a photo booth as the description suggests, or by an actual photographer? Unfortunately I don't have enough information to give you a good answer - if the person mentioned was the copyright holder VRT would make sense, but that's not clear. Nikkimaria (talk) 20:06, 2 July 2023 (UTC)[reply]
The relative is Quine's son Douglas Boynton Quine I believe. Not sure on photobooth vs photographer, I opened a section here: Commons:Village pump/Copyright#Copyright status of this image and both CC justifications do seem a bit iffy. It's a shame but I can remove the photo and perhaps move the Putnam photo down to another section if that's safer. Thanks. Alduin2000 (talk) 17:04, 5 July 2023 (UTC)[reply]
@Nikkimaria Update: I contacted Douglas Quine and a new photo has been uploaded to Commons and has now replaced the passport photo. Alduin2000 (talk) 08:51, 14 July 2023 (UTC)[reply]

Comments Support from Phlsph7

I'm happy to see this article finally at FAC after a lengthy preparation period. From a first look, it seems to be in good shape. One point that was already brought up at the GA review and the peer review is that the topic is difficult. There have been various improvements but going through all the explanations in detail is still not a cakewalk. However, this may be more of a problem with the abstract nature of the topic itself and less with our article. It could be simplified by leaving certain details out but that would hurt comprehensiveness.

A few observations:

  • Platonism does not face problems concerning the sematic half of the dilemma: sematic -> semantic
Done
  • Other positions that have attempted to provide a reason for the success of mathematics includes: includes -> include
Done
  • The Stanford Encyclopedia of Philosophy identifies it as one of the major arguments in the debate between mathematical realism and mathematical anti-realism alongside Benacerraf's epistemological problem for platonism, Benacerraf's identification problem, and Benacerraf's argument for platonism that there should be uniformity between mathematical and non-mathematical semantics.: could be split into 2 sentences to make it more accessible
I've simply removed all reference to other arguments here - resulting wording is still not the best but better than before I think
  • An example of this idea provided by Michael Resnik is of the hypothesis an observer will see oil and water separate out if they are added together because they do not mix.: there is something wrong with this sentence. Maybe it and the subsequent sentence could be reformulated to simplify this point. What do you think of something along the following lines: As an example, Michael Resnik considers the observation that oil and water separate out if they are added together because they do not mix. He points out that this claim in isolation cannot be confirmed through observation since it relies on additional assumptions. For example, it assumes that no chemical substances interfere with the separation and that the eyes of the observer are functioning well enough to observe the separation.
I've reworded that passage - hopefully it's ok now
  • From the text of the subsection "Mathematical explanation", it's not clear to me in what sense Melia's weaseling-argument is a mathematical explanation. It seems to be more of a criticism of mathematical explanations. Would it make more sense to put this paragraph at the end of this subsection since the other paragraphs are about mathematical explanations? An alternative would be to add an introductory sentence to clarify the relation between weaseling and mathematical explanation.
I've tried to make this a bit clearer. The idea is that Melia argues mathematics is not genuinely explanatory and so we don't need to be committed to it. Baker argues against this that mathematics is explanatory and there are genuine mathematical explanations of physical phenomena. Let me know if you still think this needs a bit more clarification.
  • WP:DUPLINK in relation to David Lewis and David Malet Armstrong in the section "Influence".
DUPLINK now allows up to one link per section if it is useful for the reader. I think in this case it is useful as Lewis and Armstrong are only really mentioned in passing previously so easy to miss for the reader.
  • WP:EARWIG shows various potential copyright violations. But they seem to be all due to quotes, book titles, or stock phrases ("indispensable to our best scientific theories", "the existence of abstract mathematical objects",...).
  • User:Headbomb/unreliable.js marks one source as unreliable. But this is only because the link to the pdf file points to a general repository and not because of the publisher.
  • there are no claims without a reference in the body of the article

Short query for the coordinators: in the course of a peer review to get the article ready for FAC, I also made a few changes to the article. Should I abstain from voting for or against because of these involvements? Phlsph7 (talk) 08:47, 3 July 2023 (UTC)[reply]

Hi Phlsph7, I'll let you know when I've addressed your comments. thanks for all the help and suggestions at peer review getting this ready btw :) Alduin2000 (talk) 11:55, 3 July 2023 (UTC)[reply]
Hi again, I've now responded to all your comments above. Alduin2000 (talk) 12:56, 3 July 2023 (UTC)[reply]
Thanks for addressing the issues. I'll get started with a short spotcheck. Phlsph7 (talk) 08:00, 4 July 2023 (UTC)[reply]
Hi Phlsph7. It's not, but thanks for pointing it out so clearly. Gog the Mild (talk) 17:39, 26 July 2023 (UTC)[reply]
@Gog the Mild: Thanks for the clarification. I changed my "Comments" to "Support". Phlsph7 (talk) 08:59, 27 July 2023 (UTC)[reply]
Spotcheck by Phlsph7 - pass
  • For example, according to this reasoning, if the sentence "Mars is a planet" implies the existence of the planet Mars, then the sentence "two is a prime number" should also imply the existence of the number two.[6] supported by the source
  • This is called Benacerraf's epistemological problem because it concerns the epistemology of mathematics, that is, how we come to know what we do about mathematics.[9] supported by Horsten 2019, §3.4
  • Platonism holds that there exist abstract mathematical objects such as numbers and sets whilst nominalism denies their existence.[10] supported by the source (it uses the term anti-realist instead of nominalist but that shouldn't be problem); I would suggest adding page 8 since it covers the previous sentence (The philosophy of mathematics is split into two main strands; platonism and nominalism) more explicitly.
  • When applied in the field of ontology—the study of what exists—they exemplify a Quinean strategy for establishing the existence of controversial entities that cannot be directly investigated. ...[14] supported by the source
  • Mark Colyvan presents the argument in the Stanford Encyclopedia of Philosophy in the following form:[2] supported by the source
  • Some philosophers infer from the argument that mathematical knowledge is a posteriori because it implies mathematical truths can only be established via the empirical confirmation of scientific theories to which they are indispensable. ...[19] supported by both sources
  • Furthermore, if an entity is dispensable to a theory, an equivalent theory can be formulated without it.[23]: supported by the source
  • According to the Stanford Encyclopedia of Philosophy, the most influential argument against the indispensability argument comes from Hartry Field.[25] : supported by Colyvan 2019, §4; I would suggest reformulating it to "one of the most influential" since it also lists other "objections that have received the most attention"
  • Field has tried to explain how it is possible for false mathematical statements to be used by science without making scientific predictions false.[32]: supported by Colyvan 2019, §4
  • This is in contrast to alternative forms of naturalism, such as a form supported by David Armstrong that holds a principle called the Eleatic principle. According to this principle there are only causal entities and no non-causal entities.[37]: supported by the source
  • Confirmational holism is the view scientific theories and hypotheses cannot be confirmed in isolation and must be confirmed together as part of a larger cluster of theories.[45]: supported by Paseau & Baker 2023, p. 9.
  • For example, Resnik has offered a pragmatic indispensability argument that "claims that the justification for doing science ... also justifies our accepting as true such mathematics as science uses".[52]: supported by Colyvan 2001, p. 14–15.
  • An example of mathematics' explanatory indispensability presented by Baker is the periodic cicada, a type of insect that has life cycles of 13 or 17 years....[69]: supported by Colyvan 2019, §5
  • Whilst developing his philosophical view of confirmational holism, Quine was influenced by Pierre Duhem.[74]: supported by the source
  • For the logical positivists, all justified beliefs were reducible to sense data, including our knowledge of ordinary objects such as trees.[81]: supported by the source
  • Putnam has said he differed with Quine in his attitude to the argument from at least 1975.[96]: supported by the source
  • Putnam has explicitly distanced himself from this version of the argument, saying; "From my point of view, Colyvan's description of my argument(s) is far from right" and has contrasted his indispensability argument with "the fictitious 'Quine–Putnam indispensability argument' ".[108] : supported by the source
  • According to his argument, quantification over possible worlds is indispensable to our best philosophical theories, so we should believe in their concrete existence.[112]: supported by Weatherson 2021, §6.1

Comments from JayBeeEll

Nice to see another math article up; a very interesting article! This is just a start, I will add more in the coming days hopefully. --JBL (talk) 18:15, 3 July 2023 (UTC)[reply]

Hi JBL, thanks for reviewing! I've responded to your comments so far below. Let me know if any still need some changes. Alduin2000 (talk) 22:01, 3 July 2023 (UTC)[reply]
  • It is presented in the Stanford Encyclopedia of Philosophy as: Some writing guides recommend that what precedes a colon in a context like this should be able to stand alone as a sentence; that happens the second time Colyvan's argument is quoted, but not here.
Fixed I think
  • The construction most-adjective appears three times; it is unusual to use a hyphen for an adverb-adjective compound.
Fixed
  • I see at least one "i.e." -- MOS advises that Most [such abbreviations] should be replaced, in regular running text, by unabbreviated expansions or essentially synonymous plain English (that is for i.e., namely for viz., and so on), when space permits or when the material would be clearer to more readers. I also think "i.e." should be followed by a comma, just as "that is" would be.
Done
  • Field tries to show this by reformulating or "nominalising" scientific theories so they do not refer to mathematical objects. what is the referent of "this"?
Fixed
  • Note [c] doesn't have a footnote; is it covered by the reference [8] to Colyvan?
    Yep, I can add the reference to the footnote too if that is clearer?
    I do not insist, but maybe it would be slightly clearer? Primarily I just wanted to be sure it was referenced. --JBL (talk) 18:15, 24 July 2023 (UTC)[reply]
    Done. Shapeyness (talk) 18:37, 24 July 2023 (UTC)[reply]
  • science and philosophy are continuous with one another is "continuous" the right word here?
    Yes, the Wikipedia article on naturalism puts it nicely: "According to this view, science and philosophy are not always distinct from one another, but instead form a continuum."
    Ok interesting; to me as a mathematician it sounds very odd, maybe because I am hung up on a particular technical meaning of the word. If no one else is bothered by it, I am fine. --JBL (talk) 18:15, 24 July 2023 (UTC)[reply]
  • I find This is in contrast to alternative forms of naturalism, such as a form supported by David Armstrong that holds a principle called the Eleatic principle according to which there are only causal entities and no non-causal entities. hard to parse -- maybe more punctuation or splitting the sentence would help?
    I've split the sentence, hopefully that's more understandable now
    Yes thanks. --JBL (talk) 18:15, 24 July 2023 (UTC)[reply]
  • Hi JayBeeEll, I was wondering if you felt in a position to either support or oppose this nomination? Obviously, neither is obligatory. Thanks. Gog the Mild (talk) 17:29, 23 July 2023 (UTC)[reply]
    Hi Gog the Mild, apologies, real life has been preventing the kind of sustained attention necessary to finish my read-through. I have blocked out an hour tomorrow afternoon to continue; I think it is likely that I will support. --JBL (talk) 19:47, 23 July 2023 (UTC)[reply]

More comments:

  • In the sentence Analogous to the law of inertia, mathematical hypotheses hold no empirical content on their own but according to Quine, they can share in the empirical confirmations of the systems of hypotheses in which they are contained, the commas are not where I personally would have placed them (but I view comma placement as largely a matter of personal style, so this need not be viewed as a call for any changes). I also wonder if it is possible to avoid having four sentences in a row that begin "[Speaker] [synonym of 'said'] ...", but again I do not view this as obligatory.
Reading over that sentence again, I do think it was a bit awkward - I've reworded it, hopefully it isn't worse now! As for "speaker said", I don't think I can fix that.
  • I always enjoy a good "whilst". I wonder if Whilst eventually becoming a platonist ... would be smoother with "he eventually became"? (Perhaps not.)
I agree
  • in which he wrote "a thoroughgoing nominalist doctrine is too much to live up to" How do we feel about inserting "that" before the quote?
I don't have any strong opinions although in this case I do slightly prefer without (assuming that's not grammatically incorrect or something)
  • I believe what one daily presupposes." should be WP:LQ.
Done
  • and presents it in the form: Per an earlier comment, I would have written "in this form:" or "in the following form:".
Done
  • Putnam has criticized Field's reformulations as only applying to classical physics and for being unlikely to be able to be extended to future fundamental physics. "as ... as" or "for ... for" perhaps?
Done
  • The capitalization of Field's Science without Numbers is odd to me, and I am confused by the OUP page for the book which also lower-cases the 'w' but which shows a picture of the cover on which the 'w' is capitalized, so who knows?
I think both are acceptable, but I agree all capitalised makes more sense to me - I previously changed the capitalisation in the primary sources section, so will change in the prose for consistency

--JBL (talk) 18:42, 24 July 2023 (UTC)[reply]

  • Having completed a thorough read-through: I am satisfied that this article is well written and researched. Stylistically it appears fine. It's a tough subject to illustrate, but the media chosen are on-point. It is an appropriate length. It deals with a very technical subject matter, in a way that is comprehensible and thorough. I support listing it as a FA. --JBL (talk) 18:47, 24 July 2023 (UTC)[reply]
Thank you for reviewing JayBeeEll! I've gone over your last few comments and made some changes, thanks for the suggestions :) Shapeyness (talk) 19:28, 24 July 2023 (UTC)[reply]
Looks good, and you're welcome! --JBL (talk) 19:32, 24 July 2023 (UTC)[reply]

Comments from voorts

I don't have much knowledge of philosophy of mathematics, so I can only opine on the quality of the writing and compliance with MOS and citation rules (criteria 1a, 1e, and 2). I copy edited the article (not much to fix), and have a few notes:

  • In the first paragraph of the background section, I think the name "Benacerraf's epistemological problem" should be introduced earlier, rather than at the end of the paragraph. Perhaps, In his 1973 paper "Mathematical Truth", Paul Benacerraf raised a problem for the philosophy of mathematics, which has since been called "Benacerraf's epistemological problem".
The issue is that the problem he raised in that paper has two parts - only the second part of the problem is Benacerraf's epistemological problem. The first part is the part about semantics and doesn't really have a name as far as I know. Both of these problems together make up Benacerraf's dilemma, so referring to the problem as a whole as "Benacerraf's epistemological problem" might give the reader the wrong idea. I can attempt to clarify a bit more in the text if you think it's needed.
  • The transition into the second paragraph of the background section feels a bit clunky.
Hmm, I'm not sure how to improve, do you have any suggestions?
  • When applied in the field of ontology—the study of what exists—they exemplify a Quinean strategy for establishing the existence of controversial entities that cannot be directly investigated. What makes the "strategy" "Quinean"?
The strategy is Quinean in that it can be traced back to Quine, I've added a link to wiktionary there now to clarify. Let me know if you think the article prose needs to explain this more.
  • The "overview of the argument" only describes the justification for the first premise, but does not summarize the second.
The second premise is generally not supported by any further justifications as it is seen as a strong premise already - it is also quite hard to explain "indispensability" without going into technical details which I've tried to separate out from this section as much as possible. I can attempt to find some sourcing to add in a sentence about how the second premise makes the argument valid to tie things together if you think that is better.
  • Since "ontological commitment" is relevant to the first premise, should it not be moved above indespensibility in the "Major concepts" section so that the order matches the order of the proof?
My approach to ordering that section was mainly in order of importance - for comparison, the Stanford Encyclopedia of Philosophy article also places its section on indispensability before naturalism/holism despite the order of premises being the other way around
  • Should the first paragraph of the indispensibility section be in wikivoice, or should it ascribe those descriptions to the particular philosophers who have expounded upon the concept?
I think wikivoice should be ok here because all sides of the debate agree that the indispensability argument needs more than eliminability to work, it needs to retain some sense of theoretical attractiveness. E.g. a key part of Field's argument which I didn't have the space to include (and isn't included in other general outlines) is an argument that his nominalistic reformulations are more theoretically attractive than platonistic versions. This idea that eliminability is not enough is also pointed out by Colyvan on the pro-indispensability argument side.
  • Therefore, dispensability requires an entity is eliminable without sacrificing the attractiveness of the theory. This sentence is unclear; what does it mean to sacrifice the attractiveness of the theory?
I've reworded the following sentence to more explicitly explain this idea
  • This explains how mathematics can be used by scientific theories without making the predictions of science false, but it does not explain why mathematics is actually useful in application. Is this sentence an objection to Field?
No, sorry, this is meant to capture the idea that Field has tried to explain both (1) how it is even possible for mathematics to be useful despite being false and (2) how it actually is useful. The first part is answered by mathematics being conservative over nominalistic science. The second part is answered by the fact that mathematics provides a useful shorthand to aid in derivations etc.
  • An example of weaseling is the statement: "Everyone who came to the seminar had a handout. But the person who came in late didn't get one." Whilst this statement can be interpreted as being self-contradictory, it is more charitable to interpret it as coherently making the claim: "Except for the person who came in late, everyone who came to the seminar had a handout." Should there be a cite for these examples?
This should be fixed now, it's all to the same citation but I've copied it to the end of each quote for explicitness
  • Frege said in 1903 that "it is applicability alone which elevates arithmetic from a game to the rank of a science".; "I will put my cards on the table now and avow my prejudices: I should like to be able to accept nominalism."; "quantification over mathematical entities is indispensable for science, both formal and physical; therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. These quotes require citations.
Same as above
  • Putnam has said he differed with Quine in his attitude to the argument from at least 1975. Does this mean he started disagreeing with Quine in 1975, or that was the first time he made clear his disagreement?
It seems from the way Putnam words it that he couldn't exactly remember when he started disagreeing but places the date to "at least" 1975 which lines up with when he first publicly disagreed - I would provide the exact quote but I seem to have lost access to the chapter on JSTOR
  • The first and second premises of the argument have been seen as uncontroversial, so discussion of this argument has been focused on the third premise. Who has accepted the premises as uncontroversial? This sentence itself could be challenged and I think needs a cite.
I've now attributed this to the Internet Encyclopedia of Philosophy, it is covered by citation 94
  • There are inconsistencies between using sentence case and title case in journal article titles in the citations.
Fixed I think, let me know if there are any I missed

Once these issues are addressed, I will support the nomination. voorts (talk/contributions) 23:03, 23 July 2023 (UTC)[reply]

Thanks for the review Voorts! Btw, sorry if this causes any confusion, I am Alduin2000, I requested a name change while this was an FAC. Anyway, I have responded to your comments, hopefully that covers everything! Shapeyness (talk) 15:00, 24 July 2023 (UTC)[reply]
Thank you! Support this article for FAC. voorts (talk/contributions) 00:54, 26 July 2023 (UTC)[reply]

Comments from BennyOnTheLoose

Great work. My comments will be rather footling after the comprehensive reviews above. Feel free to challenge on these minor points. Regards, BennyOnTheLoose (talk) 09:49, 27 July 2023 (UTC)[reply]

Thanks BennyOnTheLoose, and don't worry it's more than made up for by the comments from GA review! I've responded to your initial comments below :) Shapeyness (talk) 13:16, 27 July 2023 (UTC)[reply]
  • Be consistent between "David Malet Armstrong" and "David Armstrong" in the text.
Done
  • I think "used" is generally preferred to "utilized"
Done
  • "[[Scientific realist|scientific realists]] as it attempts to justify belief in mathematical entities in a manner similar to the justification for belief in theoretical entities such as [[Electron|electrons]] or [[Quark|quarks]]" should be "[[scientific realist]]s as it attempts to justify belief in mathematical entities in a manner similar to the justification for belief in theoretical entities such as [[electron]]s or [[quark]]s" (I think).
Oops, can never trust the visual editor to get that right, fixed now
  • I used the Ref check script and didn't find any changes required. The fix sources script suggested changing some "date=" parameters to "year=" but I couldn't see that this would have any worthwhile effect.
  • I ran Citation Bot - looks like the very small changes are OK, but please check.
  • Having "Quine, W. V." and "Smart, J. J. C." but fuller names for all the other authors in Primary sources seems a bit inconsistent - not sure if there is a guideline on this but even if there is, there might be a case for applying WP:IAR if those authors are best known by their initials.
A lot of philosophers from around that time seem to have gone by just their initials and surname, not sure why. I think Smart would definitely be more well known as J. J. C. Smart. Quine wrote under W. V. Quine but he is also quite well known by his full name, Willard Van Orman Quine. I don't have a strong opinion on whether to change.


The above discussion is preserved as an archive. Please do not modify it. No further edits should be made to this page.
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