principles of definition

[AntonioLao]

To arrive at a good and mathematically correct definition there are four principles to serve as guides. Without these principles one can be lost in the dense forest of mathematical reasoning forever searching for certain plausible mathematical truths. The first principle requires that all terms in a definition must be predefined or stay undefined by agreement as mathematical assumptions called axioms or postulates. The second states that the term being defined should be situated in the next larger set or class to which it belongs. The third says that the defining term must be distinguished from all other members of its class. Finally, the fourth principle requires that the distinguishing characteristics of a defined term should be as few as possible.

These principles are strictly followed by the science of biology for the classification of all living things whether plants or animals. For example, as a simple test and observing the proper sequence in definition, in which order should the terms in this set of living things be defined: American, Austinian, earthling, animals, Texan, human, North American.

[labelwench]

To arrive at a good and mathematically correct definition there are four principles to serve as guides. Without these principles one can be lost in the dense forest of mathematical reasoning forever searching for certain plausible mathematical truths. The first principle requires that all terms in a definition must be predefined or stay undefined by agreement as mathematical assumptions called axioms or postulates. The second states that the term being defined should be situated in the next larger set or class to which it belongs. The third says that the defining term must be distinguished from all other members of its class. Finally, the fourth principle requires that the distinguishing characteristics of a defined term should be as few as possible.

These principles are strictly followed by the science of biology for the classification of all living things whether plants or animals. For example, as a simple test and observing the proper sequence in definition, in which order should the terms in this set of living things be defined: American, Austinian, earthling, animals, Texan, human, North American.

A game!

You are an earthling, animal, human, of the North american, specifically American, Texan, Austinian regional variety.

Okay, Antonio. You owe Caramel a horse treat for that, lol..... I'll cover it for you.

Regards,

Labelwench

[AntonioLao]

The treat can be provided once I get my horse sense back online. But in my case the sequence is changed from Austinian to Planoan since I live in the city of Plano, Texas.

[labelwench]

To arrive at a good and mathematically correct definition there are four principles to serve as guides. Without these principles one can be lost in the dense forest of mathematical reasoning forever searching for certain plausible mathematical truths. The first principle requires that all terms in a definition must be predefined or stay undefined by agreement as mathematical assumptions called axioms or postulates. The second states that the term being defined should be situated in the next larger set or class to which it belongs. The third says that the defining term must be distinguished from all other members of its class. Finally, the fourth principle requires that the distinguishing characteristics of a defined term should be as few as possible.

These principles are strictly followed by the science of biology for the classification of all living things whether plants or animals. For example, as a simple test and observing the proper sequence in definition, in which order should the terms in this set of living things be defined: American, Austinian, earthling, animals, Texan, human, North American.

Your starting post must have gotten my subconscious mind into contemplation mode, as when I awoke, the following thoughts were foremost.

The principles of definition as you describe them work quite well for the classification of observable and measureable objects, though there has been debate even there regarding how best some plants and animals should be classified, as example.

The greater difficulty arises when we define the meaning of a word, by using more words.

Language is a tool that unites the conceptual, the virtual and the measurable aspects of experience.

Objects that possess matter/mass and energy lend themselves to definition by the principles you suggest more easily than do concepts or the experiencing of the virtual.

Definition by genus and differentia is difficult to apply to the conceptual, IMO.

Which brings me to the thought of just what ratio of experiencing is internal, and what portion is external? How can we either define or measure the two until we may realize the boundary?

[austintorn@aol.com]

Texas always liked to be the firstest and the largest, etc., so,

Alaska, Yukon, Texas…

[AntonioLao]

Which brings me to the thought of just what ratio of experiencing is internal, and what portion is external?

By avoiding the question about internal and external I use the Mobius topology of one sidedness and single edgeness to describe the local infinitesimal motion of the spacetime continuum which is quantizable into spacetime charges of H-pluses and H-minuses using Hadamard algebra creating a unique algebraic topological structure of connected Hopf rings.

[AntonioLao]

Texas always liked to be

As I recall Texas joined the States of the Union by invitation and I think it can become an independent nation if it wants to.

[labelwench]

By avoiding the question about internal and external I use the Mobius topology of one sidedness and single edgeness to describe the local infinitesimal motion of the spacetime continuum which is quantizable into spacetime charges of H-pluses and H-minuses using Hadamard algebra creating a unique algebraic topological structure of connected Hopf rings.

Aha moment.

This is a "Math", thread, and I am in error in attempting to have a 'conversation'.

My apologies.

[AntonioLao]

It's not necessary to apologize but if you feel better about it then your apology is accepted. Funny thing about math is that just like any theory of knowledge we start with an undefined term which is called an axiom or postulate. However, efforts to deaxiomatize math created the problem of incompleteness and this foundational effort is proved into an incompleteness theorem by Godel.