Talk:Formal science

Robotics
This article describes robotics as one of the formal sciences. Is this description incorrect? Jarble (talk) 04:46, 30 November 2018 (UTC)

The etymology of the term "formal sciences"
This, in my humble opinion, would be a splendid addition to the article. Although the article does dedicate a section to the history of formal sciences, the article has no section on the history of the term and conception. If I ever find an authoritative source or a few about this, I'll be sure to cite it and summarize its content in the article, but I'd hope that someone else might have an idea as to how and what to look for. This usage of the adjective "formal" can clearly be traced as far back as Plato's doctrine on "Forms", but Plato's contemporaries did not differentiate between formal and empirical sciences. Therefore, I suspect that the phrase "formal sciences," as a unified lexical item and a term of arts, did not begin appearing in literary circulation until much later, plausibly the late 19th or 20th century, when significant paradigmatic shifts occurred in the philosophy of mathematics and philosophy of science, especially within the positivist context of early analytic philosophy. Arthur E. Stewart (talk) 15:55, 15 August 2020 (UTC)
 * By the way, there may be some merit in ascertaining and elaborating whether the term "formal sciences" was predated by related terms such as "formal systems." Arthur E. Stewart (talk) 16:02, 15 August 2020 (UTC)
 * I'm reporting back to say that, by sheer coincidence, just hours later, I came across a remark by Professor Robert Hanna that the dichotomization of formal sciences vis-a-vis empirical sciences goes even further back than the analytic tradition: to the neo-Kantian tradition. This prompted me to make a simple search on Google Books to identify a lower limit to date the coining of the term "formal sciences"; and indeed, the phrase appears in an 1838 book and also an 1839 book by Thomas Arnold. The rabbit hole goes deeper than I thought. I'll keep digging. Arthur E. Stewart (talk) 19:58, 15 August 2020 (UTC)
 * Using the Google Ngram Viewer (so as can be seen here), one could infer the following: possible 18th-century antecedent notwithstanding, it does appear that the term "formal sciences" began being mentioned regularly in literature in the early 19th century and, moreover, that so did related terms such as "formal systems" and "formal languages" (the latter two becoming much more common immediately after WWII, presumably in a turning point from the invention of digital technologies and what it entailed for the field of theoretical computer science). Of course, since the information hitherto presented in this paragraph would qualify as yet unpublished original research, it would therefore be inadmissible for mention in this Wikipedia article, but its appearance is lawful here on this talk page and, hopefully, helpful in our investigation of the origins of the term "formal sciences," potentially for the purpose of creating in the article a section on the etymological evolution of the term. Arthur E. Stewart (talk) 23:09, 15 August 2020 (UTC)
 * All this sounds very welcome. I must admit to feeling rather queasy about the term, for reasons I may add separately. It would be great to understand the recent history more fully and its prevalence when used with the meaning described here. For example, is it a term that's been gaining wider acceptance only relatively recently? Is it more prevalent in the US compared with other places such as the UK? Or maybe it's influenced by Continental thinkers? (I notice that French Wikipedia has a comparable term.) My British and now tattered Collins dictionary lists 'natural science', but not 'formal science(s)'. It refers to 'theoretical science' with much the same meaning, but not as a headword. I'd not heard of the formal sciences until yesterday when I apprehensively followed a Wikipedia link to find out what it meant. (When I typed theoretical science into Wikipedia it redirected me to Basic research which seems something else again.) NeilOnWiki (talk) 16:07, 9 November 2020 (UTC)
 * . Yes, I see how all of this may seem rather foreign or peculiar. I won't pretend to have any more knowledge on the issue than you do, but I can share the little that I do know and my thoughts on how it might all interrelate. I suspect the confusion stems from the fact that it hasn't always been clear that mathematics is not all that there could be to non-empirical science. On the one hand, mathematics is primarily (though not exclusively) the science of quantity; on the other hand, the material conditions of Modern society (such as the invention and adoption of digital technologies) have engendered an acute practical necessity for other formal languages, i.e. for other non-empirical sciences, sciences of abstractions other than quantity (i.e., of such abstractions as logical propositions, sentence structure, semantic meaning, the broader semiotic meaning, or of groups such as sets, types, categories, graph relations, and so on).
 * The distinction between mathematics and other non-empirical sciences became evident thanks to advancements in the philosophy of mathematics and linguistics between the late 19th century to the mid-20th century). In that era, analytic philosophers (and particularly the logical positivists) debated the foundations of mathematics as a science or as a language, and much of these novel understandings emerged as a side-product of those inquiries and that paradigm-building. The "holy grail," for many of those analytic philosophers, was to reduce all of mathematics to logic; nevertheless, this goal was mostly abandoned in the end because, arguably, the quest may have been proven futile by Kurt Gödel's incompleteness theorems and Alfred Tarski's undefinability theorem.
 * Now to your questions: "is it a term that's been gaining wider acceptance only relatively recently?" Well... maybe, but "jein," as the Germans say. According to Google's Books Ngram Viewer, today the term may be more popular than it has ever been, but not by much. The term has been in literary circulation for well over a century.
 * "Is it more prevalent in the US compared with other places such as the UK?" According to Google Trends, the term seems to be somewhat more common in Northern America than in the UK, but the estimations seem to be derived from small sample sizes, making them more prone to error in statistical hypothesis testing.
 * "Or maybe it's influenced by Continental thinkers?" Not impossible, but it seems unlikely. In the French corpus, the term seems to gain its beginnings no sooner than in the English corpus. Besides, you may be aware of the post-Kantian/post-Enlightenment historical rift between continental philosophy and analytic philosophy (having grown further apart with each socio-historical cataclysm: 1789, 1861/1870, 1914–1945). Both philosophical traditions have experienced a linguistic turn, but the philosophy of mathematics has featured quite more prominently in analytic philosophy than in continental philosophy. Arthur E. Stewart (talk) 18:02, 9 November 2020 (UTC)
 * Thanks, Arthur I was intending to make this a one-off visit then go elsewhere, but it would be rude not to acknowledge your informed and informative replies. I also appreciated Charles' comments on Some early uses. I do hope you've more knowledge on the issue than I do — it's so much more interesting that way.
 * I wondered how much your comments were part of limbering up to draft a section in the main article. You refer to sets, categories, etc, as groups, which has special meaning in mathematics (an abstraction in its own right), so a different word might be better. To me, all these are just abstract or mathematical structures.
 * I really appreciate your methodically answering the questions I raised. I suppose what is especially difficult to ascertain is the extent to which it formal science is used with the meaning described here. I can imagine several interpretations of the phrase — or its constituents. As an extreme example, I think Plato's forms seem very different from a hardline formalist's purely syntactic concerns. NeilOnWiki (talk) 18:01, 11 November 2020 (UTC)


 * Out of deference to my Collins dictionary I've just compared theoretical and formal science(s) on Ngram. Theoretical science is roughly twice as prevalent as formal science. Natural science dwarfs both. Of course, these numbers say nothing about how these terms are used. A quick look at 'formal sciences' seems to reveal mathematics contrasted with the formal sciences (formal logic, syntax, etc), or qualified as in the phrase formal mathematics or itself a qualifier in mathematical logic. NeilOnWiki (talk) 19:09, 12 November 2020 (UTC)


 * By all means, please feel free of any obligation to reply. Wikipedia is a collaborative platform where a project can be continued by one user where another user has left off. I feel slightly embarrassed – but also amused – for failing to notice Charles's findings sooner. I hadn't added an etymology section to the article because I was faced with a paucity of admissible sources, and such a section doesn't have to consist of more than a sentence or two, but the sources you've brought to my attention should be more than enough. Much appreciated! I agree that the connection to formalism sounds more plausible, and that I could have been more cautiously minimalistic than to assume a connection to Plato's theory of forms. The intended meaning of "formal sciences" probably has a humbler and more boring explanation, such as the juxtaposition of "form" and "content" (perhaps so as to correspond to the Kantian "abstract" and "concrete" respectively, but I'm starting to fall into wild speculation again). Arthur E. Stewart (talk) 23:16, 17 November 2020 (UTC)

Reflects a particular perspective?
Assuming that the term formal sciences can be established as a de facto standard, the word formal seems (to me, at least) to be unavoidably loaded towards the view of mathematics put forward by Hilbert and others, known as formalism. Moreover, the text seems to echo that view, perhaps through endeavouring to be faithful to the literal elements of the title. It omits alternative views on the Philosophy of Mathematics such as the importance of intuition expressed by L. E. J. Brouwer and Henri Poincaré. The final sentence seems especially contentious within mathematics. Eg. it contradicts Kant when it claims that "theories in formal sciences contain no synthetic statements; all their statements are analytic."

Baldly stating that maths is a priori (in this case in harmony with Kant and many others) might give the reader the disempowering impression that maths is necessarily divinely ordained, rather than a human endeavour with messy origins in such unelevated concerns as taxation, gambling, eugenics and warfare (I'm ranting a bit). It also conflicts with the natural realism of the philosopher Quine who (I believe) viewed maths as part and parcel of the empirical sciences, thereby standing or falling alongside them. Stanford's article on Non-Deductive Methods is also a good source for an alternative view. NeilOnWiki (talk) 16:30, 9 November 2020 (UTC)  (PS: I realise this isn't a philosophy page! NeilOnWiki (talk) 16:33, 9 November 2020 (UTC))


 * I understand your concern and share your regret over the arguably unfortunate wording of the term, but Wikipedia is not entrusted to serve the propogation of neologisms, but only secondary-source documentation of terminology (as per WP:NEO and WP:ONEDAY), and it's not unusual for commonly accepted terms to preserve obsolete historical baggage. If it might assuage you, consider that the nomenclature at hand is secondary to a separation of sciences that is essentially methodological: whereas the methods of natural and social sciences rely on empirical (observational) evidence, mathematics and related sciences instead rely on non-empirical argumentation (by composition of proofs, which is a stricter standard of truth or verification, than is the probabilistic testing of hypotheses through empirical evidence).


 * In regards to Kant's epistemology on mathematical syntheticity, that is a yet unsolved problem in the foundations of mathematics (which, if and when it is ever solved, may or may not be ruled in favor of either Kan't position or Hume's position). I agree that the sentence quoted by you lacks academic consensus and, unless it is attributed to the opinion of a citable source, it is subject to removal as per WP:NPOV. It might be worth mentioning, however, that while Kant's position hasn't been entirely falsified, it *has* been weakened: a-priori statements that Kant deemed necessarily synthetic (e.g. elementary arithmetic equations) have been paradigmatically re-conceptualized as derivable by analytic means (e.g. as in the Peano axioms). Nevertheless, a more pro-Kantian case can be made that the truths and axioms of mathematics are more than merely tautological, but rather a mixture of both tautology and intuitive assumption. Arthur E. Stewart (talk) 16:07, 10 November 2020 (UTC)


 * Thanks again, User:Arthur_E._Stewart: Yes, I accept that commonly accepted terms often preserve unfortunate historical baggage (though I'm unsure we've established how common or accepted this term actually is). I suppose if, too, the division is methodological, one might write something like: "A defining feature of a formal science is that its preferred verification process can (at least in principle) be expressed as a formal axiomatic system."
 * The worry I've tried to express in this thread is that, in describing the disciplines that come under the umbrella of the formal sciences, and in particular mathematics, the article body might have put so much emphasis on the formal aspects that the reader is presented with a slightly skewed view of the subject. Obviously those formal aspects are an important part of modern study, but I'm not sure one would frame a description with so much emphasis on them if mathematics were being described elsewhere. The nature of a subject is wider than just how it goes about verifying things. In particular, applying a set of axioms is one thing; it would be odd if establishing them weren't also a part of the same discipline.
 * The claim in the main text that maths is analytic is sourced (and as far as I know a not uncommon position). It arguably isn't needed here, but if it is included it might need balancing with a different view to give a more rounded account. (Unfortunately, I'm a bit hampered by strong views and weak sources, so I've limited myself to comments rather than edits.) NeilOnWiki (talk) 18:08, 11 November 2020 (UTC)


 * Hello again, NeilOnWiki. I'm writing this message mainly only for documentation of activities (as "paper trail") so, as I've said before, there's no need for you to feel compelled to reply.
 * As one who considers one's attitude on the issue to be fortunately more agnostic than yours, I decided to take a deeper dive. Specifically, in regards to the sentence which you've identified as especially problematic, I've examined the cited sources for it. The second source apparently does not make any explicit, verbatim reference to either syntheticity or analyticity. The first source, on the other hand, is a piece written by Rudolf Carnap, who was a persistent advocate of logical positivism and therefore not exactly an unbiased secondary source. The sentence would be much less controversial if "a-posteori" was substituted for "synthetic", and "a-priori" for "analytic"; but if unsourced in this respect, the statement could constitute original research, which is prohibited by Wikipedia policy. I agree it's regrettable that we even have to open the can of worms that is the question of the synthetic a-priori, as it seems unnecessary or superfluous for the purposes of the article. What I can do, at a minimum, is to rewrite the problematic sentence in such a way as to attribute the opinion: "For this reason, in Rudolf Carnap's logical-positivist conception of the epistemology of science, theories belonging to formal sciences are understood to contain no synthetic statements, being that instead all their statements are analytic."
 * As for the rest of what you've described, it represents a broader problem, perhaps relating to the article as a whole, and is therefore more difficult to address. I'm afraid I wouldn't really know where to start, but I might get around to it some other time. Anyway, if you're hesitant to make such changes yourself, keep in mind that Wikipedia's general-purpose advice is to "Be bold" or "Go for it", so it probably wouldn't be such a terrible thing, but it's up to you. Arthur E. Stewart (talk) 23:16, 17 November 2020 (UTC)

similar article, Data Science, Re: Formalism (versus other Philosophy of Mathematics)
Does it include Data Science? I'm not Formalist but am okay with 'formal science' term (and kind of like it) though as someone criticized, there might be better future terms. Should Scientific formalism link here and vice versa?--dchmelik (t|c) 11:14, 4 March 2022 (UTC)

Scrapped most of the article
A large amount of this article was not only unreferenced but also, in my view, likely false. The history of "formal science" as a discipline, per the "philosopher's stone" paper linked in the references, likely only dates back to the 1950s, so the claims that it dates back to Ancient Sumer were too preposterous to be salvageable.

Given the number of other editors who have raised objections over the years, and the complete lack of work done to address the issues over more than a decade, I believe that none of this should be reinstated without references to independent, secondary sources. &#32;- car chasm (talk) 18:38, 13 May 2023 (UTC)

the Einstein quote
What is the purpose of this quote? How is Einstein's opinion that mathematics is "absolute" and "certain" relevant to the approach regarding it distinct from other sciences not because of this but because it is formal? 24.56.247.67 (talk) 02:08, 2 June 2023 (UTC)

"Mathematics and statistics"
and and  both redirect here. Jusr removing the hatnote notice does not change that fact. You have to change the redirects if you think this "strange" result should not redirect here. Removing the hatnote just makes readers who arrived via these redirects even more confused. The article is targetted by these redirects through a WP:RFD redirects for discussion closure on 5 October 2023. So changing this requires a new RFD or a WP:DRV discussion review -- 65.92.247.66 (talk) 22:18, 13 February 2024 (UTC)

"cryptography"
I see that cryptography was deleted as being a branch of computer science. This appears wrong; ciphers, cryptograms, cryptography and cryptology has existed since ancient times, long before electronic computers. -- 65.92.247.66 (talk) 07:10, 20 February 2024 (UTC)