Does Math, or analogically Language really have any impact on our "Thoughts"?

Here I see many say, language has an important impact on our thoughts.

But according to this question,

Foucault in the preface to The Order of Things wrote how he 'laughed out loud' when he discovered a Chinese Encyclopedia whose categorization of knowledge was different from his European presuppositions.

And I agreed so.

For example, kindly take a look at The Nine Chapters on the Mathematical Art, which dates back to BC179, but according to the link, Wiki says,

The full title of The Nine Chapters on the Mathematical Art appears on two bronze standard measures which are dated to 179 CE, but there is speculation that the same book existed beforehand under different titles

Consider, for example, Integral, according to Wiki, the origin of the purpose of the integral in Greece is

This method was further developed and employed by Archimedes in the 3rd century BC and used to calculate areas for parabolas and an approximation to the area of a circle.

It was used to calculate areas, ( as for now, please forget about Newton and Leibniz for further sophisticated proof. ).

Now going back to Chinese The Nine Chapters on the Mathematical Art, the contents of the books are

Contents of The Nine Chapters are as follows:

Now, according to the Wiki in my language, the 方田 ( Fangtian ), to me an Asian, explicitly understandable if you know Chinese, seems to mean to measure the size of rice field, which in my language's one says same thing. The 方田 ( Fangtian ) was used to measure the area of rice field in order for lords in feudal era to calculate the size precisely so that he or she can deduct the amount of tax.

Now more, same according to The Nine Chapters on the Mathematical Art

The method of chapter 7 was not found in Europe until the 13th century, and the method of chapter 8 uses Gaussian elimination before Carl Friedrich Gauss (1777–1855).2

So, although mostly math was developed in Western countries, I think, historically speaking, how could the Westerners not find the method 7 and 8 prior to Chinese??

And I would like to go further. I am sorry I was unable to find English source but Japanese explanation of origin of Chinese characters.

In English, "1", "2", "up", "down" expressed by linear lines-symbols respectively.

If the language has any impact on our human thoughts, since the method how to count the outside object would be different and consequently, as I said, math, particularly sophisticated in Western country, could not have been developed in China 2000-3000 years ago using their own language, I think.

There seems to me the math, and in analogy language, had no particular impact on human being's thoughts particularly especially considering integral, --- the origin of which seems to me the measurement of areas. ( By cutting curved area into rectangles and sum the size of the total sphere of each rectangles. ) Chinese could not have even tried to measure the size of the area using their own language which already existed.

And in addition, as I commented here, how come, the trading of future happened before semi-future trading was enlisted in Chicago in mid 19th century whilst there had already existed in Japan in mid or late 17th century? Did or does this have anything to do with math-in analogy-language?

If you say language had very important role on our thoughts, how come Chinese tried to measure the size of the area ( = later integral ) by their language which had already differed from the Western one at that time?

• I notice 2 votes to close, but it would be great if those that voted could comment. The question looks like a good fit, although it could use a bit more focus to draw out the question. But the precise nature of the impact on language on thought seems quite relevant. May 8, 2015 at 15:59
• What I would like say here is, simply saying, "thoughts" are more dependent on circumstances where they live, not languages. If you happen to say math is not a language, then how can human beings count outside objects?? Then naturally, math, it looks as if it is sanding alone, but when we go back to such like numbers, then what differentiates our thoughts? Chinese were unable to count? Then it would mean probably like a wild sound jazz.
– user13955
May 8, 2015 at 16:13
• Congnitive science probably has extensive inquiry and study in this question. I do not know if there is a cognitive science forum out there... May 8, 2015 at 16:16
• And to me for someone to vote to close is quite O.K. But upvoding or downvtoting together deleting my ( gone ) comment is not fair.
– user13955
May 8, 2015 at 16:17
• Anyway thank you for your comments. By the way, due to the time lag, I have to go to bed. Sorry and thank you for your comments again.
– user13955
May 8, 2015 at 16:19

I keep pushing the intuitionistic view of mathematics, in which the subject of mathematics is our accumulated, shared intuition. If mathematics arises from our notion of space, that is prior to language, and to culture. If our notion of accumulating area is inborn, and becomes mathematics when we notice it and express it in language, then whether mathematics controls our thinking depends on which side of the fence of language you are talking about.

From that point of view, we have a shared intuition of area, and we have, separately, formalized ways that try to keep that intuition free and unaffected by individual experience so that it can be shared. The former clearly controls thought, the latter helps this happen more easily, but probably contributes little control of its own.

At the same time, there are other aspects of language that I feel strongly shape our thinking. I just gave an example here https://philosophy.stackexchange.com/a/23625/9166, and plenty more examples fill Wittgenstein and other language-focussed philosophers.

There is experimental evidence that even these are a selection from among a basic range of intuitions that are promoted or suppressed selectively by exposure. This is part of the Chomsky theory of generative-transformational grammars. There is a trans-linguistic "deep structure" representation.

So to some degree, the elements of grammar that I feel deeply shape our thinking are still in the same area as mathematics. But we choose which aspects of deep structure are most accessible, and which ones will be used together differently in childhood by exposing ourselves to different languages which veil the underlying meaning in transformations and representations.

• First of all, thank you for your sincere answer, really. Now while reading, I think I was able to touch the surface what you said. Let me have some time for understanding. I sincerely would like to pay due respect to your knowledge though really. Forgive me for now.
– user13955
May 9, 2015 at 0:18
• Actually, reading other 2 people's comment is also very... stimulating as well as educative, jobermark's answer was nicest to me since he seems to know well deep enough about this issue ( I don't mean others don't ) and very positively naive. Thank you for your answer ( Actually, though, I wondered which to choose between Volumetricsteve's and this answer. ).
– user13955
May 9, 2015 at 4:31

Focusing primarily on the original statement: "language has an important impact on our thoughts." I would ask: Is language really at the root of our thoughts?

However, as the question is merely if its impact is important on our thoughts, I would say at a minimum language is a vast structure that thoughts are often concocted in and as a result of coming from that structure they are therefore shaped by it. I'd say that is an important impact.

• Thank you for your short while very suggestive answer. Only from the first line I had to think............thank you so much for anyway still.
– user13955
May 9, 2015 at 0:34

Foucault laughed out aloud when he opened a Chinese Encyclopedia whose arrangement was different from his European presuppositions.

This is Foucault positioning the Occidental against the Orient; the Occident implicitly taken as the epitome of rational ordering thought; still; I think its worth recalling that we have analytical philosophers incredulous at the the incomprehensible diction of their continental colleagues with its wayward or obscured logic; who are themselves equally puzzled by the logical orientation of the former which hardly touch the 'problems of life'.

The origin of the integral in Greece

This Archimedes description of a limiting argument to find the area of a circle; it was Descartes introduction of coordinates that allowed Archimedes method, not to be more rigourous - it was already rigourous- but to generalise it.

if language had any impact on our thoughts

Heidegger wrote that Language is the house of Being; where Human beings dwell.

Math, particularly developed in Europe cannot be developed in China using their own language, I think

I know very little about the mathematical culture of China; but in Europe it's usually taken that Euclid developed the axiomatic method for mathematics; in India, I would suggest that the axiomatic method developed not in mathematics but in grammar - Panini developed the first comprehensive grammar of Sanskrit; and this provoked a philosophy that centred on language; but it shows that the axiomatic method is not restricted to geometry or mathematics;

Further, an aspect of Paninis work might be seen as mathematics when one understands that the axiomatisation of logical languages were a feature of 20C Logic/Computer Science (to fully establish this would (or not) take careful and considered analysis).

if you say language has an important re on our thoughts how come the Chinese measured land when their language already differed?

That there might be differences doesn't exclude that there might be similarities; particularly when the pragmatic is at stake.

Still, I think when Heidegger talked about Language being the house of Being I don't think he was suggesting this; but that language is what brings people together (consider various nationalist movements in the 20C) by being in a sense between them; except that Heidegger says that is where they dwell; where they are at home and not homeless (unheimlich); this is quite noticeable in the liturgical practises of religion - Latin, Arabic and Sanskrit in their respective religous traditions; in poetry and the codification of laws; but this I think is only a trace of the reality that Heidegger is touching on.

• Thank you for your post +1. And including another people's post I think I know less. Kindly note as for now, I am limiting only to the primitive rectangle method. en.wikipedia.org/wiki/Rectangle_method Anyway, thank you sincerely.
– user13955
May 9, 2015 at 0:30