Defining definitions–and the futility of calling it futile

1. Euclid’s definitions of line, point and plane are not formal definitions. They go back on itself – you ultimately need a conception of line to define a line etc. They serve to show what he means, but they don’t define. Check any modern geometry handbook.

 

2. Euclid defines both straight and curved line. His definitions are not very good, because he doesn’t want to formally define, but merely show what he means. Here formal definitions can be constructed.

 

3. Formal definition is something very specific. You can use the definition instead of the term defined. The defined term is merely a verbal shorthand, without any additional meaning.

 

4. We, despite appearances to the contrary, are substantially agreed. You wrote: “And where the bold philosopher does fail, and the term cannot be defined, use an analogy, quote a poem, say something so the listener knows you are talking about THIS rather than THAT.” I agree wholeheartedly.

 

5. As I wrote before, at each level of reality (physics, biology, psychology, sociology) there are primitive vel basic terms vel concepts. They cannot be defined without introducing a vicious circle. Any definition will prove to be inadequate – that is, always something which should be inside will be outside, or vice versa. We can show something, or we can explain it, or try to refer to the concept our listener already has. We must do everything possible to make our concept as precise as possible – but definition sometimes will not help.

 

This is a very important and very difficult point. Think of it in that way – each term is a way to connect a formal system of language with reality. Each important term brings some additional meaning (connotation) into the formal system. But a formal definition brings nothing new, it only serves to combine already present terms.

 

6.You gave two different definitions of “good”: “pleasure-causing” and “duty-fulfilling”. Any argument when one party uses one definition, and the other another will be pointless, that’s true. But any argument using any of those definitions will be pointless – because they are both false, as any definition of good must be.

 

7. To define good as “pleasure-causing” is to commit a deliberate fraud. The good, as commonly used, is nearly opposite to pleasure-causing. But to define good as “duty-fulfilling” is not very much better. To follow duty is good, certainly, but the obverse is not true. Here the error is much more subtle, and therefore in long term even more pernicious.

 

8. It is a favourite fraud of XIX century charlatans, like Marx, to define a thing which has commonly understood meaning as something different, and thereafter use sometimes the common meaning, and sometimes their own definition. But not many understand that to attempt to define things which are undefiniable is necessarily to commit that kind of fraud. That is the main thing which Chesterton opposes.

 

9. That is why Socrates never taught, but only asked questions (maieutic method), and why Platon, the greatest writer of antiquity, refused to wrote down his most important teachings and left them orally to his students. There are things which cannot be defined, but which most of us knows already. They must be learned by experience, and then clarified and purified by discussion. Cf neural nets – they are taught by repeatedly showing them something and correcting wrong answers, not by giving them algorithms. Brain works a bit like this.

 

9. Lack of understanding of this point is one of the reason of mushrooming of legal acts and regulations. The lawgiver wants to precisely define something in order to stop any arbitrariness of judges. But when he does that, he sees that his definition is inadequate, that he created a hole which is used to circumvent his regulation, and at the same time he affects some accidental people which shouldn’t be affected. So he makes his definition even more precise, at great length, he adds additional regulations for every case – and it works worse and worse.

First, you and I must be friends, whoever you are: anyone who called Marx a fraud and quotes Chesterton wins both my heart and my admiration.

 

Nonetheless, I respectfully disagree with most of your points. One defines unknown terms by means of known term. You and the person to whom you speak must have at least one term in common, otherwise you would not be speaking at all.

 

1. I have read both modern geometry and Euclid, thank you. The modern geometry textbook tells me on page one it cannot define its terms, and I know at that point it is humbug, written by someone who has studied geometry and has not studied philosophy. Euclid’s definitions are formal enough for his purposes. By your own argument, nothing meets the standard of pure formality you set for it: you have defined the word ‘definition’ to mean something that no one ever does and no one ever can: an empty set. If not, give me a single contrary example?

 

All that is happening is that these modern textbook writers are falling prey to the fallacy that absorbed Russell and Whitehead, who thought a definition was not a definition if it merely told you what the speaker was talking about, but did not meet a formal criterion of set theory.

 

Modern scientists make the same mistake modern geometers do, which is, they assume the metaphysical underpinnings of their particular objects of study do not exist because those underpinnings are philosophical rather than member of the set of object they study. (This nonsense was started with Hume, who adopted an a priori axiom that all knowledge was empirical, itself a statement not affirmed by any possible sense impression.)

 

No, my dear sir: you made the outrageous claim that a point is not defined, and I quoted the definition that geometers have used for two thousand years. You are the one making the claim: what is your evidence? I do not take the modern geometer as an authority over Euclid, particularly since I think I know where the moderns went wrong.

 

2. & 3. As above. Formality is useful only within the context of a given system; axioms are ulterior to the system to which they are axioms.

 

4. I am glad we agree.

 

5. In the context that started this thread, someone was asking me to define (by which he meant point to) the artistic qualities Homer has that comic books lack. He was not asking me for a formal definition of the type you describe here.

 

Basically, we can distinguish between honest requests for definitions, and dishonest. An honest request means a man is not sure what you mean by a word, he does not really know what you are talking about. You have to help him out, otherwise unneeded confusion grows. A dishonest request is a debate tactic, where a debater attempts to drive you back to your axioms, and then, when he discovers that the axioms are axioms, announces (illogically) that you are being arbitrary. Or, if you cannot define your axioms, he announces (illogically) that you cannot support your position. I am proof from either tactic, having been canny and fell in debate for some decades now, and not likely to caught napping.

 

Come now: let us be serious with each other. If actually do not know what a point is, I can tell you: a line can always be cut into two smaller parts, but a point cannot be, because it is not composed of smaller parts. A point has no part. It is a simple and obvious definition. I have not heard any real arguments against it, only windy statements by men like Wittgenstein, who I do not account to be a philosopher, but a poseur.

 

When you say a formal definition ‘brings nothing new’ you are falling into the modernist trap. From Euclid’s five definitions and ten common notions and axioms, I can construct a dodecahedron. A modern philosopher might say I have added nothing new to what was not logically implicitly present to begin with: this is true but trivial, because all our modern philosopher has done is define the word ‘new’ to mean something that does not exist: synthetic a priori knowledge. It is a humbug.

 

6. “But any argument using any of those definitions will be pointless…”

 

I am not sure how to apply this. Would not, by your own logic, this argument likewise be pointless, and all arguments? I wonder if you are defining the word “pointless” too broadly. It seems to encompass everything that a common men does when he thinks about good and evil.

 

When lawyers debate in a court of law to convince a jury that it is either proven or not proven that the defendant is guilty, the question of good and evil, duty and negligence, law and breech, is not pointless: a man’s life and limb depend on the outcome of the debate. Pointless?

 

When parents tell and teach their children right from wrong, the question of whether good consists of duty or of pleasure only will determine every aspect of the teaching. The child’s wellbeing depends on the outcome. Pointless?

 

This standard you erect is one no one, not even the modern philosophers who invented it, use for any purpose. Perhaps I misunderstand you here. Please clarify.

 

8. The quote you took from Chesterton does not support this point. Obviously I (and every honest man) agree with the idea that a person using a definition must not commit an ambiguity. But that was not what was being asked: to remind you of the context, I was being asked to define the difference between Homer and a comic book. Come, sir. If I cannot tell someone the difference between the greatest poet of mankind and dime-novel funnybook, I should garrote myself with my own tongue for shame.

 

9. Who has told you that Socrates never taught? The Academy would be surprised. You are confusing his means with his ends.

 

Nonetheless, I agree that some things are learned through experience, but not everything falls into this category: geometry, for example, is a priori. Law, for example, is learned by reading for the bar, not by committing crimes.

 

9. I beg to differ. The excesses of modern legislation is not caused by definitions but by the lack thereof: can any here tell me precisely what is meant by “conspiracy in restraint of trade”? I assure you I can tell you exactly what is meant by “unlawful killing of a human being without mitigation or justification.” That is why the antitrust laws are absurd and unenforceable, and the law against homicide is clear.

 

The other excess of modern legislation is caused by the intrusion of the law into private matters, where no standard of right and wrong can be defined, even by the wisdom of Solomon. I used to sit in on hearings of the Planning and Zoning board. They had no standards, no guidelines, no nothing. No definitions. This is not the fault of the act of defining one’s terms, but the fault of using the law where it (by its nature) is the wrong instrument.

 

Besides, without proper definitions, a reasonable man cannot conform his conduct to the standards of the law.

 

Having said that, your general point I agree with and with all my heart. Where modern juries and modern activist judges lack all sense of proportion and justice, frantic legislators attempt to amend such wayward and wanton abuses of the law with stricter and more exact regulation, which, as you correctly say, is no substitute.

 

And I agree with your basic point: formal definitions cannot replace wisdom! A person without a certain level of understanding cannot be reasoned with. At that point talk fails, and only emotion is left.

 

My vehement objection is that you are suggesting that I surrender before that point. There is no need–if one’s audience lacks wisdom and understanding, that point is reached all too soon.

 

There is no need to tempt one’s pride by pretending so lofty an understanding that another man cannot grasp one’s meaning. If a man asks you an honest question, answer it honestly and humbly, or otherwise do not call yourself a philosopher.