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Just like defining terms, the primary means of expression should be defined in debate

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Voting Style: Open Point System: 7 Point
Started: 3/11/2014 Category: Education
Updated: 7 years ago Status: Post Voting Period
Viewed: 1,035 times Debate No: 48834
Debate Rounds (5)
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I came to this forum because I wanted to see if there were people interested in the debate over the merits of mathematics and spoken language in education.

The math v. English debate is represented here.

However, this debate fails at it's start, since we do not define which means of expression has primacy over another in the context of the debate.

My thesis: We have to start by saying where the lines are drawn.

Allow me to demonstrate, by citing a New Yorker article whose author makes the exact same error. It begins:

---Here"s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

---The vast majority of people respond quickly and confidently, insisting the ball costs ten cents. This answer is both obvious and wrong. (The correct answer is five cents for the ball and a dollar and five cents for the bat.)

Actually, every single person is correct when they answer that the bat costs a dollar.

The reason for this is exasperatingly obvious.

Only people have costs. Costs are not objective properties of bats and balls, but are priced in relation to supply and demand. The cost of manufacture and marketing is then levied against balances of people's holdings by those who make and distribute bats and balls.

When someone says "The bat costs a dollar more," they are not comparing the cost of the bat to the ball. They are comparing what is given to what is owed.

So the question is "To whom does it cost a dollar more?" and not "compared to what other inanimate object that is incapable of valuing the cost of things is the cost of this other inanimate object compared?" To assume that this is the true meaning of the question as it is asked is an absurd leap into math as to be almost intrusive.

By now, I hope some of the math folks are still with me. Please don't drop out, math folks!

This is important, because very often language and math assume different rules at their outset.

The bat and ball analogy in terms of math is x +$1+x = 1.10.

That is a very precise, hard, clean expression. But unlike math, natural language starts out loose and moves toward harder, more specific expressions. It also has a bias toward active subjects, like people and animals, and not passive objects like bats and balls.

It is therefore the case that the premise of the question, that a bat and a ball "cost" is impossible. They are inanimate objects. They do not do anything until observed and acted upon by a live being.

Thus, in English, the bat and ball equation becomes:

Cost (to the person) = x +1

Now I am going to get really vague. Have you ever had a conversation that went something like this?

"How's it going?"
"I'm good."

This does not compute in a strict grammatical sense. But the semiotics, the signs, of what is intended by each speaker in the conversation allows each speaker to convey what is meant and to be understood.

This is something math cannot approach.

So when we talk about math and verbal language, let's please start by saying whether verbal language has ended and now math has begun or else risk speaking at cross purposes in aimless debates that say much and teach little.

By the way, for me - English almost never stops, and math is almost always an artificial logic imposed over normal language-centered thinking. The bat and ball question are a good example as to why.


That was a well-stated argument. I aim for my argument to be equally explicit.

Math is a language by the same principle that English is a language. In other words, both math and language contain syntax--math has subdivisions [i.e. classical physics, quantum field theory, etc.] just as language has subdivisions [i.e. Swedish, German, English, etc.]. However, although math is a product of language, we cannot deem one as more important than the other--math or language--because both are constituents of reality. And PERCEPTION is reality (my thesis for this argument).

PRO said "we have to start by saying where the lines are drawn" but we already did so when we decided that math was math and language was language. Drawing any more lines would simply be a dilution. This is the paradox: in order to objectify something, we tend to draw more lines, but doing this--increasing our perception--that something becomes more subjective.

I'll use PRO's bat and ball argument to illustrate this point.

Recall the argument: a bat and ball together cost $1.10 and the bat costs $1.00 more than the ball. How much does the ball cost? The correct answer, according to PRO, is "five cents". However, this answer is INCORRECT because it's one answer and there's more than one possible answer [there are 11 equally possible answers]. 5 cents, 10 cents, alone cannot be correct answers. They are correct POSSIBLE answers, but with the given information, the only correct answer is a list of 11 numbers--0 to 10 (including 0, obviously).

PRO also said "the question is 'To whom does it cost a dollar more?' and not 'compared to what other inanimate object that is incapable of valuing the cost of things is the cost of this other inanimate object compared?'." But these two questions are actually one in the same. 'To whom does it cost a dollar more(?)' is analogous with 'to whom are the objects inanimate(?)'. Both questions have the same answer: to whomever agrees that that's the case. For example, a book is a book only because we all agree that's what it is. It's hard to argue that 2 + 2 doesn't equal 4. In principle, if math was the ONLY language, there would be no arguments--no quibbling--among us.

I'll stop here because I'm not sure what direction the PRO was taking his argument and I don't want to waste anyone's time.
Debate Round No. 1


I think there are several instances in CON's summations and arguments that are significant. Thanks for taking the debate so seriously. However, I do think there are problems with CON's response.

My rebuttal will focus on where CON's arguments are contradictory. Then I will clarify my argument further to illustrate where we differ and why my position is more conducive to education and learning.

CON refuted my thesis by saying "PRO said "we have to start by saying where the lines are drawn" but we already did so when we decided that math was math and language was language. "

Saying that two things exist as types is not an equivalent to defining their limits. What I propose when I am used the words: 'where the lines are drawn' is to define the limits of English or math or any other means of expression in contexts where the two might be blurred.

The person using each means of expression should not assume that his or her message will be clear and unambiguous. Knowing they are melding the two, they should take a moment to discuss where there may be areas of confusion and define when they are primarily using English, or math or legalese or C++.

To say that both math and English and are both languages is overly vague and, for me, an insufficient definition. To support this I gave examples to describe certain idiosyncrasies of the English language, like a bias toward active subjects and a wider acceptance of generalities.

However, math is so different that switching from common verbal speech to employing a verbal language as a means of explaining mathematical reasoning should be announced and defined.

When speaking about math, that speech should be disclosed by the speaker, who says something like: "And now I will speak about math, using English language terms according to their common mathematical definitions."

Why do this?

Imagine I am a bilingual teacher, and I started my debate just as before. But this time, when I gave the example of the bat and ball question I began to speak in perfect Hindi (a widely spoken language of India.)

When I was done speaking, it would be up to my student to try and answer. If the student couldn't deliver the answer I might deride him or her for getting the wrong answer and, believing my own system to be just and meritocratic, I might even label the student a as a poor performer.

This, by the way, has a tendency of happening in schools where the language of a powerful population - often English - is imposed on the education of children whose first language is not that of the powerful.

So, imagine you're in school and you have to answer my little quiz, so you set about trying to learn Hindi.

What you discover is unnerving, because, not only is Hindi a language with a totally different vocabulary from English, but it's grammatical structure and therefore it's logic are totally different also.

Instead of being ordered by a subject, followed by a verb, followed by an object, Hindi moves according to a pattern of subject-object verb.

As if that were not enough, I might impose a written test where the system of script used is not based on the English or Latin or Greek alphabet, but on Sanskrit. And so you'll have to learn it, too.

The more I learn about math and about other languages and forms of expression, the more I realize that they are defined by unique rules that do not translate easily into English. Also, English does not lend itself to the adoption of many concepts, which is a very good reason to favor expressions like math or Chinese, or binary code. Often English just won't cut it.

In all of these, there are elements of expression that are "lost in translation." These are expressions that are incapable of "agreement" - to use a concept invoked by CON - from one means of expression to another.

These elements very quickly compound the more they are used, which results in a widely varying conclusions.

In our bat and ball case, there might be an verbal-only conclusion, a mathematical conclusion, a set of mathematical conclusions, a hybrid, verbal-and-mathematical set of conclusions. The permutations go on and on.

However, the point is nonetheless true, that when a person is using language to teach or to learn, they are consciously picking a means of expression to convey and share a point from one brain to the next.

When this happens, it is a like a mean, cynical trick to try and teach something via a means of expression that does not match what the student can reciprocate.

In such cases, trust in the teacher as an honest communicator breaks down, and skepticism about how far to trust a teacher weigh heavily on the student and his willingness to follow a program of education.

It is obvious by now that according to my earlier example, I would argue that casually switching from spoken language to verbal expressions of math is analogous to to suddenly switching From English to Hindi.

Really, such moves result in anti-communication - a kind of intellectual masturbation that allows someone to say "Look how smart I am compared to you." That is terribly violent, petty and wasteful behavior that can be cured by prefacing one's comments like so.

"I will now speak in Hindi. Here is a grammar book, a book on Sanskrit, and a dual language dictionary. Follow along according to your level. Study diligently. We don't expect you to pick it up at once, but we do expect you try. Now, let's begin. "

This sort of preparation is all I am arguing for. I don't think it's too much to ask.


We have evolved languages that are more universal than English, Dutch, Swedish, etc. I'm talking about the languages that describe universal truth (i.e. digital philosophy, digital physics). For example, it's hard to refute that 5 + 5 = 10. This is the case from one language to another.

I agree that trust in a teacher as an honest communicator breaks down but not at or by the point that PRO makes.
Yes, when a person uses language to teach/learn, they are consciously choosing a means of expression to convey, after all, humans possess volition. If you can't choose, you cannot perceive. In other words, cognition and perception are languages. What conclusion can therefore be educed? Reality is a language. Our choices are only drawn from the choices we're presented with. Human volition is self-contained akin to liquid water taking on the shape of its container. I agree. We humans all, well virtually all, possess volition. I like PRO's idea that switching from language to verbal expressions of math is like switching from English to Hindi. Now I understand PRO's point, when he says to determine "where the lines are drawn" is to "define the limits of English, math, [etc]." But math and language share the same limit: 0. Picture a tetrahedron, if we measure the edges around each face (twice in opposite directions), each edge cancels to 0. In other words, the limit of the limit is 0. "Vague "is not synonymous with "incorrect" however. Answers aren't always black OR white. Language and math have the same limit because perception and cognition are languages

I ran out of time. At least there's 5 rounds.
Debate Round No. 2


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Debate Round No. 3


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Debate Round No. 4


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Debate Round No. 5
1 comment has been posted on this debate.
Posted by Hematite12 7 years ago
This is a very interesting point.
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