Talk:Formal science

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

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 "

By the way, there may be some merit in ascertaining and elaborating whether the term "formal sciences" was predated by related terms such as "

Arthur E. Stewart (talk) 16:02, 15 August 2020 (UTC)[reply

]

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

Arthur E. Stewart (talk) 19:58, 15 August 2020 (UTC)[reply

]

Using the

Arthur E. Stewart (talk) 23:09, 15 August 2020 (UTC)[reply

]

@

Arthur E. Stewart: 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)[reply

]

@

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,

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

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

Arthur E. Stewart (talk) 18:02, 9 November 2020 (UTC)[reply

]

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)[reply]

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)[reply]

@

Arthur E. Stewart (talk) 23:16, 17 November 2020 (UTC)[reply

]

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))[reply]

@

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

Arthur E. Stewart (talk) 16:07, 10 November 2020 (UTC)[reply

]

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)[reply]

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

Arthur E. Stewart (talk) 23:16, 17 November 2020 (UTC)[reply

]

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. - car chasm (talk) 18:38, 13 May 2023 (UTC)[reply]

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)[reply]

MathematicsAndStatistics and Mathematics and statistics and Mathematics and Statistics 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

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)[reply]