# What is something that math cannot be applied to and doesn't involve math?

I have been asked this question, yet I am unable to answer it.

The issue with this question is that I have given all that I know, therefore I too am at a loss.

What I do know is it has no concept of time or matter. But it has something to do with the void of existence, nothingness.

It cannot have anything to do with the mind or behaviour of someone as you can argue, when did this take place, when did you know that, etc.

It cannot have something to do with a physical object as I can argue that the shape of the object can be measured.

• You can always apply math to something, but whether it is useful or not, that depends on intent. Commented Jul 22 at 2:47
• Is it cheating to say qualia since many philsophers argue we've made almost zero/zero progress on why a toothache or taste of mint feel as they do (Maudlin, Hoffman, etc)? Commented Jul 22 at 4:25
• Could you give more details about what you mean by "applying math" or "involving math"? Let's say I toss a ball in a basket before you can take any measure or record of my action. While it is true that you can always make a mathematical model of a ball tossing, how far is it going to go depending on its speed and angle, etc, arguably you can't apply math to this specific instance of my gesture since you have gathered no data about it and it's already over. It also didn't involve math, the gesture being purely mechanical and no computation was performed and no numbers involved. Commented Jul 22 at 5:46
• as written, is too vague... does "applied" cover also counting? If so, we apply mathematics (more specifically arithmetic) also to cooking. Commented Jul 22 at 7:19
• @armand I have often wondered about the agility of squirrels. Is the squirrel's brain performing any math when a squirrel jumps between trees? The squirrel's actions can be modeled mathematically from external observations, , but internal to the squirrel, no math is involved. Commented Jul 22 at 16:19

Math has no application to the spelling of words. The fact that "dictionary" is spelled that way is a social fact, unrelated to math.

Unless you are including the mere observations and counting as "applying" math — this is how we would discover that there is a word "dictionary" spelled that way.

Or if you understand "applied to" to include modelling the historical development of English orthography in order to understand why certain spellings ended up as they did, including Old English, Norman French, Church Latin etc. as influences, then sure. But if that is what you mean by "applied to", then that is so broad then there is nothing that math cannot be applied to.

And of course math can be used to describe observations about spellings, but again, if we are understanding "applied to," to be that broad, then there is nothing that math cannot be applied to.

Comments are popping up listing examples of things that math can be applied to. This answer does not aim for a complete list of things that math can be applied to or the ways that math could be applied to spelling. As acknowledged above, depending on your understanding of "applied to," there may be nothing that math cannot be applied to.

• +1 Mathematics satifies the base criteria for a language. So the original question can be restated: "What is something that language cannot be applied to and doesn't involve language?". This changes the nature of "applied to" Commented Jul 23 at 16:51

There are two very different ideas of what mathematics really is, although they are intimately related. However, before coming to that, we have to recognise that there is something which looks like the mathematical language. The mathematical language is really just both an extension and a restriction of natural language. It is an extension because it includes expressions, symbolic expressions, which do not exist in any natural language, although it would be possible at least in principle to say the same thing as mathematicians do using the mathematical language only using a natural language. Possible in principle, but probably not interesting enough for anyone to feel motivated to do it.

The mathematical language is also a restriction because what mathematicians say using this language only involves what they themselves would call mathematical reasoning, which is really just everybody's kind of reasoning but with statements involving only mathematical expressions.

Mathematicians have come to develop and use this very specialised language because on balance it is very convenient for doing mathematics.

So, what is mathematics?

You could say that mathematics is the corpus of theories mathematicians have written using the mathematical language and which they would all agree is correct. Correct in what way? There may be other criteria, but the only well-defined one I know of is that "correct" means logical. Presumably, mathematicians are only interested in mathematics which is . . . interesting. Yet, strictly speaking, you cannot deny that for example the implication a = 4 ⊢ x = a → x > 0 although it is uninteresting is nonetheless a mathematical expression, and one which is logically true (once you understand the logic of it). Mathematicians like to restrict mathematics to interesting theorems, but I don't see any formal difference between interesting and uninteresting theorems. I guess you could say that there are therefore interesting and uninteresting mathematics.

Another way to look at mathematics is to say that it is all the theories which could potentially be written using the mathematical language, at least as long as it is logical. This is the Platonic view of it. However, most of it would be . . . uninteresting; something like mathematics, but produced by a machine.

Thus, mathematics may be something which mathematicians themselves don't really know how to define formally.

What may be missed, however, is that there is nothing which mathematicians can say using the mathematical language that couldn't at least in principle be said using any of the many natural languages used by human beings, although that would be a terribly boring thing to do and . . . uninteresting.

Still, to answer the question, the point is that as long as is it subject to human reason, and can therefore be reasoned about using a natural language, mathematicians could, potentially at least, reason about it using the mathematical language, although in most cases they would have to invent the piece of mathematical language necessary to do so.

This should leave out absurdities, because, by definition, absurdities are not logical. Yet, it does not, for mathematics does include its share of absurdities, like Bertrand Russell's paradox of the set which includes all sets which do not include themselves, and absurdities that mathematicians themselves may or may not recognise as absurdities, but even when they do, may be at a loss to exclude from mathematics.

Still, these are special cases resulting from the particular state mathematics is since the beginning of the 20th century. Absurdities are by definition illogical, and so by definition most of them are excluded from mathematics. Yet, this doesn't mean that you couldn't apply mathematics to them, only that you wouldn't expect any sensible result from doing so.

I would argue no. The reason is I believe that mathematics is a purely human construct which we use to describe our universe. I think an illustrative example is that, for much of recorded history, people regarded natural phenomenon such as the shape of plants, animals, mountains, shorelines, etc. as being non-mathematical. Then, fractal geometry was discovered. At first it was considered 'monstrous'. But then we saw that it we could model many of these previously non-mathematical features with it. The lesson, I think, is that we can (assuming we have the capability) devise new mathematics for anything we can describe.

In my ontology, there are only three things that exist outside my own mind:

1. Objects

2. Mathematics

3. Other people's opinions

Mathematics is not applicable to, for instance, my feelings when the kitty cat smiles at me. Or my motivation for eating a grilled cheese sandwich with bacon.

Unless you're talking about the mathematics of chemical reactions in the brain, the question is ridiculous.

• "Unless you're talking about the mathematics of chemical reactions in the brain" -- seems like you found a way for mathematics to apply to your feelings about the cat.
– TKoL
Commented Jul 22 at 15:17
• @TKoL Any time a quantum field is disturbed (any time a particle interacts with another), QFT mathematics describes the interaction. If you're talking at that very level, the question is boring. Yes, math describes all motions of everything. so what? Perhaps that's why it's asked in philosophy stax and not physics. Commented Jul 22 at 15:28
• Even at another layer of abstraction, it's possible our conscious experiences, including our emotions, is heavily tied in with the weighted connections between neurons - which can be represented numerically. So even at a higher level, mathematical representation is very likely pertinent
– TKoL
Commented Jul 22 at 21:07
• That's not an object and it's not mathematics. It's someone else's opinion. Commented Jul 23 at 7:12