I've read a proposition somewhere: That our languange acts as a filter, allowing us to know certain things while making it impossible to know the rest(1). It seems that mathematics has some things like this, certain phenomena could only be explained when a specific kind of mathematics was developed.

I've read about a people that can't count beyond 3, I supose they couldn't handle advanced topics that would require this skill.

I also had a chat with one MSE user, it seems she's a maths/philosophy student. And the answer to my inquiry was: not really.

So, I have two questions:

  1. Is that proposition (1) true somehow?

  2. If so, who wrote about such things? I guess Wittgenstein wrote about limits of languange (which I'm not sure if has something to do with what I'm searching). At this time I'm also reading an introduction to epistemology but until now, I haven't read about such a thing.

  • 2
    You might be interested in reading about constructed languages such as John Quijada's Ithkuil: en.wikipedia.org/wiki/Ithkuil.
    – David H
    Commented Apr 14, 2013 at 3:04
  • Thanks. The concept of constructed languanges is also new to me - I knew it existed but I never tried to read about. Now I'm going to. +1
    – Red Banana
    Commented Apr 14, 2013 at 3:09
  • Great. Let me also just mention that the field of constructed languages is very broad, and Ithkuil is just one example among many. I mentioned Ithkuil because I think it's particularly relevant to the questions you're trying to address, in that it was made for the purpose of enabling greater expressive power and allowing deeper levels of cognition.
    – David H
    Commented Apr 14, 2013 at 3:20
  • Also, if you're interested I could write extensively on the isolated topic of numeracy (and related issues in mathematics and philosophy). I feel less qualified to tackle your question in full generality from a epistemological standpoint.
    – David H
    Commented Apr 14, 2013 at 3:25
  • 2
    Related: philosophy.stackexchange.com/q/3491/1582
    – DBK
    Commented Apr 14, 2013 at 4:17

4 Answers 4


As long as you can do math, the answer is theoretically no. The reason is as soon as you can formulate something equivalent to a Turing machine, you have an essentially arbitrarily capable computational engine.

So whatever filtering happens by making certain things easier or harder to express in a particular language can't filter anything out completely unless the language somehow forbids you from talking about state changes on an arbitrarily long tape. It might be inconvenient to know something if you're stuck with a language that favors the wrong structures, but it won't make it impossible.

This, I think, is the interesting part of the philosophical question: Knowability is not dependent on language. Ease of knowing may be, but quantifying that is the domain of cognitive science (or education science).


There is a complex relationship between language and the objective world. Take for example colour, and in particular red. There are a number of synonyms except of course they are not exact synonyms. For example crimson which is deeper, and scarlet which is brighter. But look at all the reds you see everyday - it is easy to see that there are an immense number of shades none of which have a specific colour name.

In that a person has a worldview and that worldview has to be articulated in words and is inherited and elaborated in words then language is the image of what can be thought and communicated.

Words are not simple. They change meaning either in combination as in compounds such as a blackboard which is not simply a board that is black; or in themselves - gay is not what gay meant a century ago.

What came first - the thought or the idea? The word atom was appropriated by the milesian materialists to formulate an idea of the physical world not directly accessible to their senses; and in fact not directly sensible till recently. Here the idea of a world appeared first and was hammered out in words.

Politicians & rhetoricians use the magic of words to hammer a consensus, a worldview that is exponentially magnified in a world of media saturation.

After reading the article about the Piraha, it seems plausible that they have no need for elaborate counting techniques; nor for elaborate arithmetic. (One could make a case that it was with the invention of cities and trade that these exigencies were forced). The case is made stronger when one reads that when the children were taught they picked it up reasonably well but then decided against it - that is they were bored and ran off. This fits in with my personal experience of how most people find actual mathematics boring as children and as adults.

Two additional and perhaps interesting points: There is a mathematical philosophy called ultrafinitist that disputes the reality of very large numbers; perhaps one could call the Pirahas view of numbers ultra-ultra-finitist. Secondly in advanced mathematics the most common numbers used are: zero, one, two and infinite - aka 0,1,2 and lots. We haven't even got to three.


Language can inhibit expression but not prevent what we know.

However, it is practical to understand that willpower / determination, and lack thereof, can allow behaviors that go against knowledge. Thus, people can withdraw from their knowledge and act within the confines of their language, 'cultural language', etc.


This is sometimes called the Sapir-Whorf Hypothesis. Wikipedia has an extensive article on the subject, which summarizes:

Currently, a balanced view of linguistic relativity is espoused by most linguists holding that language influences certain kinds of cognitive processes in non-trivial ways, but that other processes are better seen as subject to universal factors

You are right that Wittgenstein wrote on the subject, saying e.g. "The limits of my language means the limits of my world." Wikipedia has a longer list of important persons.

  • 1
    Please keep in mind that the quote from Wittgenstein is taken from the Tractatus and is opposed to any form of linguistic relativity. At the time Wittgenstein still thought of language in terms of one universal language and proposed the so called picture theory of language, according to which propositions can directly represent the world.
    – DBK
    Commented Apr 14, 2013 at 4:32
  • DBK: Thank you for the clarification, I did not remember this.
    – Xodarap
    Commented Apr 25, 2013 at 2:09

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