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LYRAS LECTURE ON LOGIC

 

Robert L Zook presents a translation of a lecture given by Lyras in ShiKahr shortly after the death of Surak. The contents later formed a basis for his monumental volume, _Logic and Definition_.

Lyras'at C'thia ang Kh'sparkeyralatha



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DEFINITION AND MEANING


Consider the word 'staff', and what this word means to: a farmer, a priest, and a warrior. The farmer may use that word to refer to an object used to prop oneself up when lame, or hurt. To the priest 'staff' may refer to an object used to represent his divine authority. A warrior would doubtless think a 'staff' refered to an object one uses as a weapon against one's enemies.

When we consider how this word, refers to different existential experiences for each person, to say that 'staff' or any other word has one definite or one 'true' meaning shows a certain lack of understanding about the purposes of words.

A word does not have any inherent meaning in itself, but rather finds definition in it's use. One makes clear what one means when using a word by indicating the experiences associated with it. How does one do this? By using other words, of course. Does it seem we have encountered an recursive system? Perhaps, but this one will endeavor to show a way out.

When someone asks the question, "what do you mean?", the asker of the question shows that they did not understand your use of the word and asks for a definition. We shall examine several ways of defining words, and evaluate their usefulness in relating experiences accurately.

One can define a word in a most basic way by providing a synonym. By saying, in effect,"it is like this other experience set". Our dictionaries contain many such definitions. For example, "a staff resembles a rod."

Classification of experience can provide another way of defining a word. One says that, "this word represents an instance of this category". "The word leh'matya refers to a type of animal, one with poisonous claws", for example.

One can define a word by enumerating a group of words to which it refers to collectively. For example: animal includes leh'matya, selaht, and teresh-kah.

A fourth way would involve defining by example. For instance, "One calls that animal over there a selaht."

Lastly, you may define a word by describing how one would going about experiencing for oneself that event which the word refers to. I could say, "When you combine these ingredients in these proportions and cook them in this manner, you will have cooked plomeek soup."

This one will refer to these five types of definitions as definition by synonym, definition by classification, definition by enumeration, definition by example and definition by operation, respectively.

Now let us examine the actual usefulness of these methods of defining words. Firstly, a definition by synonym has usefulness only if the synonym seems closer to our experiences than the word defined. To those who can only regard "sodium chloride" as a noise, may certainly understand what salt refers to. The reverse situation is rarely true [Translator's Note: I substatuted my own analogy here; the one Lyras used did not translate into English very well].<?P>

Definitions by classification usually have more use than definitions by synonym. I can make it more clear to someone who has never seen a leh'matya, what one seems like by saying, "A leh'matya refers to a omnivorous animal having poisonous claws, and diamond shaped markings", than by saying "a leh'matya seems like a big cat" (definition by synonym).

However, definitions by classification do not necessarily bring us closer to experience. One can define a rhikbat as an animal with "jaws that bite, and claws that slice". However that definition does not bring us closer to an experience of a rhikbat [Translator's note: rhikbat refers to a non-existant animal from ancient Vulcan legend, used by ancient Vulcan mothers to frighten their children into obeying]. One can string any words together in this manner and make it seem one has clarified one's meaning. For example, "The Good is what all things aim at." That phrase definitely does not bring us closer to any particular experience.

Definitions by ennumeration have usefulness if the members of a class will seem closer to experience than the class itself. For example, one may have familiarity with a leh'matya but not know that a biologist refers to it and others like it as felines [Translator's note: 'felines' = my best guess; the word on the original manuscript had blurred into unrecognizability].

Of course definitions by ennumeration have their drawbacks as well. Some words do not refer to classes, like 'the sun', and other may refer to classes who's members one could not practically ennumerate, like 'Vulcan'. To define 'Vulcan' by ennumeration, one would have to refer to some several billion beings now in existence. Fortunately, however, usually only a few cases would make one's meaning clear.

A great advantage to definitions by example lies in that one cannot define fictional entities in this manner. As we all know, Surak's presence no longer resides among us, so no event can we point to define the word 'Surak'. The greatest value one can gain from defining by example lies in that such definitions _do_ bridge the gap between words and experience. The only difficulty lies in words which do exist but one cannot point to them, as such. For example, electric current, or atoms.

An operational definition succeeds quite well in cases involving such abstract words. One can define an atom by describing the experiments one would have to make in order to experience or detect an atom. In a similar manner one can describe an experiment which would demonstrate the existence of the phenomena one calls 'electric current'.

Operational definitions also have the advantage that one cannot describe the steps to be taken to demonstrate some event which does not exist. They also directly bridge the gap from words to experience. Some Velarian definitions (like definition by synonym and definition by classification)[Translator's Note: by which Lyras means the work of the ancient Vulcan philosopher Velar, who coincidently has a direct earth correlary in Aristotle], seemed formed very closely to operational definition and one can translate these to the operational equivalent, without changing the meaning.

For example, "The followers of Surak, believe in non- violence", which on the surface seems like a Velarian definition. However, one can also call this an operational definition, since it implies the procedure to follow to demonstrate the experience which the definition refers to; one can go and ask a great number of those called the followers of Surak, and indeed, they will acknowledge that they follow the path of non-violence.

In modern Vulcan one calls Velarian definitions, 'intensional definitions', and definitions by ennumeration, example and operation; 'extensional definitions'. For the purposes of sharing experience, of bridging the gap between words and experience, one prefers extensional definitions. One will find that when one bridges the gap between language and experience, the bridge has formed itself of an ennumerative, example or operational definition.

Translated by
Robert L. Zook II Vulcan by choice Vulcan Science Academy, ShiKahr


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[This one presents a translation of the second of a series of lectures given by Lyras, shortly after the death of Surak. Later these lectures were gathered into the volume _Lysas'at C'thia ang Kh'sparkeyralatha_.]

Definition and Classification


I. Abstraction

Long ago proto-vulcan beings learned to form sounds and associate these sounds with specific kinds of experiences. Thus, language formed; and we came to communicate in a more complex manner. I can say the word "leh'matya" and have the reasonable assurance, that the one I speak with will understand, approximately, what I mean. With language I can provide directions to some one so they may experience what I have experienced.

A. Existants

I see a rod before me. I can measure it, and say that this rod has a length of 1m [Translator's Note: substituted metrics for the vulcan measure, to make the meaning more clear to an English reader.]. Yet the length of the rod does not lie in the rod it self, but in my act of measuring. For if I measure it again, I will get a slightly different result; I can never position my instrument in exactly the same place, nor read it exactly the same way. Surely the rod would not change with each measurement? No, this particular _abstraction_ of the rod changes, not the rod itself.

All so-called properties of events in space-time exist only as our specific abstractions of these events. Length, width, color, mass... no event 'posseses' these abstractions, they exist merely as features of language, to enable us to communicate our experiences to each other. Many people, ignorant of science, still speak of heat as a substance rather than a process. As if some thing exists that they could point to and call heat.

This sehlat here, I call Ni'rch. Those of you here for my previous lecture will note I just committed a definition by example. Yet surely, you would all agree that the word Ni'rch does not equal this beast? However, if I should talk to you later when you cannot see Ni'rch and I tell you he has died, you will react just as if you had seen Ni'rch die (doubtless not to the same degree), and offer your condolences. What did you react to? Words, as if they equaled the event they denote.

C. Ladder of Absraction

The word Ni'rch, the way I just defined it, does not even denote a space-time event but the abstraction "my pet sehlat". That concept itself consists of an abstraction of some other concept. We can 'abstract' this process of abstracting, by comparing it to a ladder.

On the bottom rung of the latter, one would have the actual space-time event, the sehlat, and all the infinite number of things one could say about this particular sehlat. The next rung up would have one's perception of that sehlat. Next rung up the ladder would hold the abstraction 'sehlat'. This would consist of all the similarities one has observed between individual sehlats, and none of the differences. Further up the ladder we have 'animal', which denotes the idea of a certain type of creature. 'Creature', of course, would have the next higher rung.

The highest rung might have the word 'exist', or 'substance'. At this level of abstraction, the words most often have lost any reference to an existant, that one could point to or give directions to experience. They may still have some use if one speaks or writes them with some meaningful context.

This represents the process of abstracting. One generalizes, groups the similarities and ignores the differences. Naturally, one would not wish to discard this process, since speaking in the abstract has allowed us to break free from the here and now of experience and think about things that could exists, or future possibilities.



II. Distrust of Absractions.



Yet in spite of the benefits, one should have awareness of the pitfalls of generalized abstraction, or classification. One should not think only at a certain level of abstraction. If one remains stuck at a low level of abstraction, one cannot draw general conclusions. To see 'the whole picture', as it were [Translator's Note: substatuted my own analogy here, Lyra's seemed a bit obscure for English speakers].

On the other hand, thinking only at a high-level of abstraction appears to never let one leave the realm of vagueness, ambiguity, and perhaps even utter meaninglessness. On one hand we have various utterance with no connections to each other, and on the other we have words cut loose from experience.

One can show how statements as well as words appear at a higher or lower level of abstraction. In this way we can see explicitly the problems of getting stuck in one of the levels.

A. An example of language at a low-level of abstraction:

"I hold an object. The object possess a length of 1 meter, and a diameter of 0.02 meters. The object posseses a cylindrical surface area of 0.0003 meters squared. The object appears grey in color. The object has a smooth surface texture. The object has a specific gravity of approximately 7." [T.N: again substatuted the measurements English speaking people would feel familiar with].

As you can see, the writer gives very accurate reports about various measurements of said object, but never says "I hold the strut used in the shock absorbing devices of ground vehicles", to pull all those facts together into a coherent idea representative of the experience as a whole.

C. An example of language stuck at a high level of abstraction:

"In order to understand justice, one must devote oneself to the defense of truth. In the defense of truth, one follows what one knows as truth; ones morals."

Surely this seems clear? After all justice involves truth and morals, correct? Yet what does the writer mean by 'justice'/I>, and 'truth' and 'morals'? These very abstract words never get defined, and insufficient context exists for one to do anything but guess at what the speaker means. Meaning does not exist in such abstract words until the author defines them, because these words exist at the very top of that ladder of abstraction.

Thus, that passage, which doubtless has some meaning to the speaker, seems unclear to the rest of us, unless we make some assumptions about what the speaker means by those abstract words. This leads to misunderstandings, which may seem trivial, but such misunderstanding lie at the root of all the wars we Vulcans have ever had.

D. Invalid Classfications

Of course, no Vulcan gets stuck continuously, at one level, all the time, for every subject. One fluxuates between levels depending on what one wishes to communicate. One simply must have awareness of the levels and not get confused between them. I call the process of equating a concept at one level of abstraction to a concept at a total different (higher or lower) level of abstraction, an invalid classification.

If one compares all animals to one leh'matya, one would have made an invalid comparison, due to the difference in levels of abstraction. Likewise one can only compare one existant leh'matya to all animals, in a very limited way.

As a more everyday example, in your clan, during 'ankh some groups (or clans) of vulcans got classed as enemies, and others as friends, or at least as not-enemies. This situation represents a perfect example of invalid classification. A clan leader or one with great influence with the clan could say, "that group or that vulcan = enemy." Let us examine this situation to see how this exemplifies a classification error. One can determine the level of abstraction of a concept by determining what concepts it includes. In this case, 'clan' includes 'group of Vulcans' and 'group of Vulcans' includes 'a vulcan'. The concept of enemies can include any any of these objects, and thus occupies the highest level of abstraction of any of the terms in this example.

You can see these relationships in this diagram: [T.N: Lyras used a display in this lecture]



•1. enemies •2. clan = •3. group of Vulcans = •4. a Vulcan =



Looking at this table one may ask oneself, but a classification by its very nature states that set X contains thing X1...X. Where does the error lie?

The error lies in judging the existant of a word, some individual vulcan or group of vulcans, as having the same relationship to the word enemy, as the words 'clan', 'group of Vulcans', and 'Vulcan' do.

One can classify words validly, in some situations, but only in a limited way. If you classify Vulcan1 as belonging to the set of all enemies, you acknowledge the similarities between Vulcan1 and all other Vulcans you call enemies and forget the differences. You stop seeing these 'enemy' Vulcan as individuals.

D. Vulcan1 NOT = Vulcan2

Existential events do not equal one another, so any statement which tries to make some existant event equal some other existant event, constitutes a classification error. Likewise some statement in which one tries make some existant equal to an abstract word, also constitutes a classification error.

When you classify a Vulcan as an abstraction, that Vulcan no longer seems real. You have let the conceptual Vulcan in your head overlay the existant Vulcan you can experience. It seems much easier then, to kill a concept rather than an existant being like yourself. In a war, this allows one to commit any sort of atrocity to this Vulcan, on the pretext, "But this Vulcan comes from clan X and clan X = Enemy, therefore I must hate, attack or oppose him/her."

Remember a word represents a concept, an abstraction of something real. When you wish to discuss an existant event using words, beware you do not confuse the two. One cannot know c'thia if one remains stuck in the world of words, and one cannot know c'thia if one cannot assemble facts into knowledge. Just because you can speak some word, does not mean the word refers to an existant event.

Translated by
Robert L. Zook II
Vulcan by Choice
Vulcan Science Academy, ShiKahr, Vulcan

[Copyright 1996 by Robert L. Zook II, all rights reserved, but you may distribute this document freely so long as the entire document is used, along with this notice.]

[Translator's Final Note: as you all no doubt have noted, the above work has only a fictional existence. It consist of my extrapolation of what Lyras may have had to say about definitions. However, the meat of this essay has it's basis in the writings of Anatol Rapoport, and S. I. Hayakawa. So while the character of Lyras has no real basis, the information content does. Diane Carey first wrote the name of Lyras, as author of the book _Logic and Definition_ which all Vulcans supposedly study in adulthood.]

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