The Role of Mathematics in Human Life; What Is Math?

Great Debates
41

About the literacy sub-thread that’s appeared it is sort of missing a point about social languages - they exist in both formal and informal modes. Formal English is written English. Formal speaking sounds like it is written, or at least it does ideally. Illiterate individuals have only indirect access to formal language. They have a full grasp of the informal language and can describe the world adequately. To think otherwise is to be profoundly ignorant of linguistics. In many cultures with writing the formal language is written language. Writing allows for complicated sentences that would be nearly impossible to come up with on the fly. These are sentences that take full advantage of recursion because it is possible to look back over a written sentence or to read it slowly.

The formal language of languages without writing involves special vocabularly, structures and patterns that require specialized knowledge of the formal language. It is optimized to be done without notation and so doesn’t produce longer utterances, merely denser ones that can only be decoded by those who have a grasp of the formal language.

I’d recommend Doing Our Own Thing by John H. McWhorter for an interesting take on this issue.

I’m sure somewhere in my post there is something that applies to the main point of the thread.

42

Define ‘adequately’. Is the scope of ‘the world’ the same for both formal and informal language?

43

I mean that they can describe everything that occurs to them in their daily lives, can refer to hypothetical situations and can come up with new expressions to describe new experiences. They will be no more at a loss for words than any other speaker of the language.

As for the scope of the world I would say that in most cases there is a strong correlation with those who have a wider range of intellectual experiences and those who have learned the formal level of their language. In this regard more esoteric experiences are likely to have more representation in the formal level than the informal level. It doesn’t mean the informal language user cannot experience an equally wide intellectual world it just means they do not sound as educated when discussing them.

44

How would you go about verifying this?

45

Linguists interested in language use in a natural setting get people to agree to carry around tape recorders on their person, most of these studies seem to have been done in Britain which seems to have laxer rules about recording people who aren’t entirely aware of it. Combine this with anthropological data on cultures without writing to get a full empirical look at it.

However it seems that this isn’t all that is required to verify it. Formal language is developed by a culture, taught as a specific additional skill to the informal language and not mastered by all members. Not even literate individuals are masters of the formal language of their native language. It is rare to encounter individuals that cannot employ language for their daily needs and then some. People enjoy talking a great deal and about a great deal of issues even if they do not delight in the formal language. These facts imply that the formal language is not required for function.

My question to you is what is a concept that a literate person can express that an illiterate person cannot? What concept requires the ability to produce long sentences with numerous nested clauses in order to be expressed?

Think about having a philosophical discussion with your friends in person. If you wrote down a transcript of what was said would it look like a thread in Great Debates?

46

I wouldn’t know, I’m literate.

47

Does man select coincidental numbers to explain the Universe or do numbers dictate and reveal the absolute explanation of the mechanisms of the Universe to man?

Simple. Does one and one equal two? Of course not. First of all we must delimitate the existence of “twoness” in the Universe. And we can’t.

Oh well… :frowning:

48

I don’t use the word “know” like that. Psychic phenomena has never been a requirement for knowledge for me. Guess I’m just funny like that. :wink:

In your comments to The Tim:

I don’t think that’s quite right. The question is, what is so peculiar to written English that only written English can express it? That there is no verbal counterpart? Where there can be no verbal definition? Being literate is a requirement for answering the question, not a hindrance!

49

Well, that is certainly funny. What do you mean by ‘know’ then?

The question isn’t about having a verbal counterpart. Ultimately all written English has to be pronounced. The limitations of verbal usage, memory and interaction is what (IMO) would constrain the illiterate.

But it is. I can’t ever know whether I can, with certainty, adopt the perspective and framework of an illiterate. I can guess, but I wouldn’t know.

50

I believe I have answered the “what is it to know” question enough times already, actually.

51

Phew, well, I knew we’d get to this sooner or later so I might as well have a pop at it now.

This is perhaps the most difficult question one can ask of a physicalist like me. I believe that everything is physical or, at least that everything supervenes on the physical. And the trickiest thing to translate into a physical entity, an arrangement of spacetime, a “bunch of atoms”, is mathematics. So here goes.

The universe (at least this region of the universe having three dimensions of space and one of time) is so. It is how it is. It does not suddenly disappear occasionally, nor does gravity go repulsive at the drop of a hat, nor does the entropy of things begin to randomly decrease. This is how the universe is. We have words for “how it is”: Rule or Law or, in a scientific sense, Theory. These things exist insomuch as they are the characteristics of the universe.

Now, we humans (and even dogs to a certain extent) are able to do something called “learning”. Characteristics such as “red”, ie. electromagnetic radiation of wavelength around 630 nanometres, form chains of neural dendrites in the kilogram or so of offal residing in our skulls. These strings of atoms which encode input are called memories. After forming a “bedrock” of simple, immediate characteristics like “red”, more complex ones can be built up. For example, a toddler or a puppy who sees a ball being thrown has not yet formed a firm enough set of neural strings to be able to encode this characteristic of the universe usefully. After years of observing the same behaviour (which, could they speak English, they would associate with the sound “pa-ra-bo-la”) a string of dendrites encoding this characteristic of the universe forms. This is the reality of maths.

Now, the near-miraculous nature of the human brain is such that this is just the first step. These characteristics of the universe are cross-referenced and filed away in an impossibly byzantine structure on which “random” permutations are based, yielding new imaginary characteristics which can be compared to the real universe. With each cycle of observation, memorisation and hypothesisation the “reality” of maths-as-chains-of-atoms becomes evermore distant. Nevertheless, that reality, that physicality, is to me all that can be said to exist.

A “language of certainty”? Such a phrase does, perhaps, have some resonance with my description of what maths is. But as with many of the debates we have enjoined here, erl, I find that when I go all “first principles” on you like this, I struggle to keep up with the specific aspect of the OP you wish to explore. Apologies if I’m railroading you once again!

52

Before you get going, I think—even though I’m very far from a physicalist—that we’re quite together on this one, minues a few metaphysical points.

I tell you, though, it is hard to say that the characteristic doesn’t exist, don’t you think? I mean, what are we encoding if not a something?(—I think that kind of question goes astray, personally, but it is a good question.)

Once again? You owe me at least one for my own behavior! But no, I don’t think so. “What is math” is certainly a metaphysical question to some. Can’t go wrong there. :slight_smile:

53

I did not say that the characteristic did not exist, I merely reiterated that it exists physically; what the stuff in the universe does, its arrangement, is just as physical as what it is.

Like I said, the universe is so. It is how it is, not some other way. That statement itself holds the consequence that “characteristics”, brain patterns which correspond to how the universe is rather than how it is not, exist.

Yes, I think we are farily close on this one. One of these days I’d like to explore precisely where we’re not close, ie. why you’re not a physicalist. Perhaps you would be better framing that debate - I feel I’d just be playing dialectic Jenga with your worldview.

54

I actually feel that this is one of those topics that, mysteriously, could seperate us even while we agree because we’d get to this point from totally different places. So while tangential, it isn’t necessarily a hijack.

See, I start my worldview from the subjective and move to the objective. All things I assert or suggest must be grounded in their appearences. So right off, I’m an idealist: I have no way to suggest the independence of objects from the way they are presented to us as humans, and certainly not their physicality (as such; but I mysteriously don’t deny the ‘truth’ of “physical objects exist”). It is exactly this which causes me to focus on social phenomena rather than, say, the objective independence of physicalism. I’m a very strong believer in science, in fact I approach scientific realism (which, paradoxically, is an idealism) were it not for the fact that I view science as wholly explanatory and not descriptive, whereas I view metaphysics (and philosophy proper) as descriptive but not explanatory.

Does that make any sense?

55

Oh, certainly, but your “mysterious” non-denial of the physical prompts an obvious question: Surely, by holding that both the physical and the metaphysical exist, you are being rather savaged by Ockham’s razor?

To rephrase, why do you feel that the metaphysical is necessary?

56

Don’t you feel, by positing things you can’t experience, that you are being savaged by it? (electrons, atoms, etc)

Because description is necessary (for us to get along). But instead of beginning with assumptions that can’t be proven, we begin with the immediacy of sensation and intuition.

57

Indeed I am positing that more than my experience, sensation and intuition exists. However, I feel that this is Ockhamly necessary in order to avoid the absurdity of solipsism. I am still unsure exactly what you find absurd about considering experience, sensation, intuition and ultimately even description to supervene on the physical.

I hope you know me well enough that I am not just picking a fight; you are as thoughtful and well-rounded a Doper as any here, and I feel that exploration of your worldview can do me only good.

58

Oh, I wouldn’t say it is absurd. That’s pretty strong. After all, maybe physical reality independent of us does exist. It is only that I would know of no way to operate with that proposition. Whatever I can discuss, it must be, well, grasped by my mind. It must be apparent to my consciousness.

Actually, somewhere in these threads I took some time to explain the escape from solipsism, into subjectivity, and from subjectivity to inter-subjectivity. I’ll see if I can dig it up.

But actually, where I “begin”, metaphysically, is in either the inter-subjective or subjective/solipsistic (if that’s a real adjective!). I haven’t quite made up my mind yet, there’s some compelling (to me) arguments on both sides. I never begin with, and essentially never get to, objective reality as a realist or physicalist would understand the term. Quite frankly that kind of reality fails to obtain for me. Properties and existence are a result of my/our consciousness operating on my/our own sensations. That is the limit of description we have available to us. But we may devise explanatory theories, i.e.- scientific theories, to satisfy ourselves of the nature of reality. The danger of such explanatory devices is in their ability to make us think they are describing rather than explaining, and we come to accept them as facts as certain (if not more certain!) than our own sensations. For me, that is an anathema.

If you’d like to toss a label on it, you’d call it transcendental idealism in a phenomenological vein. But I’m still exploring the idea myself. Right now, it fits me very well in addressing a lot of the concerns I had about other metaphysical theories, such as justification, responses to skepticism, how do we assure ourselves of our own correctness (and is that circular), etc. It’s been a bumpy road. Three and a half years ago I joined the dope as an Objectivist. Since then I’ve become a left anarchist who has rejected realism completely. Of course, not all of it was due to doper interaction, but just to give you a sense of my position–it is not very absolute! It is satisfying me. For now. :slight_smile:

Definitely not picking a fight. :slight_smile:

59

Yes, I think it was a poor choice. Of course, even solipsism is not necessarily absurd, ie. logically inconsistent. It simply has very little “explaining power”, and so in order to explain this life I find myself living, I find it Ockhamly necessary to posit entities which exist independently of myself.

That “escape from solipsism” reference would indeed be appreciated.

60

Here is the post in particular, but another post that came before it also helps elucidate my position. This was written before the last upgrade, so some HTML characters won’t display anymore (damn it). Also, I describe how I escape from solipsism, but it is not a very compelling argument (there aren’t any compelling arguments, as far as I’m concerned). The entire thread here.